key: cord-343303-by0b3gy0
authors: Nishinari, Katsuyoshi; Fang, Yapeng
title: Molar mass effect in food and health
date: 2020-09-03
journal: Food Hydrocoll
DOI: 10.1016/j.foodhyd.2020.106110
sha: 
doc_id: 343303
cord_uid: by0b3gy0

It is demanded to supply foods with good quality for all the humans. With the advent of aging society, palatable and healthy foods are required to improve the quality of life and reduce the burden of finance for medical expenditure. Food hydrocolloids can contribute to this demand by versatile functions such as thickening, gelling, stabilising, and emulsifying, controlling texture and flavour release in food processing. Molar mass effects on viscosity and diffusion in liquid foods, and on mechanical and other physical properties of solid and semi-solid foods and films are overviewed. In these functions, the molar mass is one of the key factors, and therefore, the effects of molar mass on various health problems related to noncommunicable diseases or symptoms such as cancer, hyperlipidemia, hyperglycemia, constipation, high blood pressure, knee pain, osteoporosis, cystic fibrosis and dysphagia are described. Understanding these problems only from the viewpoint of molar mass is limited since other structural characteristics, conformation, branching, blockiness in copolymers such as pectin and alginate, degree of substitution as well as the position of the substituents are sometimes the determining factor rather than the molar mass. Nevertheless, comparison of different behaviours and functions in different polymers from the viewpoint of molar mass is expected to be useful to find a common characteristics, which may be helpful to understand the mechanism in other problems.

2.2 Molar mass effect on the diffusion 12 38 3. Molar mass effect on mechanical properties of gels and solids 16 39

3.1 Minimum chain length for helix formation 16 

To contribute to the universal demand for secure and sustainable food supply, food colloids 21 science and technology can do many things. It can create palatable foods from underutilized 22 resources, and can reduce the food loss. It is reported that there are many people who die from the 23 insufficient supply of foods and malnutrition while food was wasted by improper distribution in 24 some regions as pointed out by the World Health Organization (WHO). International Union of 25 Food Science and Technology (IUFoST) aims to supply sufficient foods helping secure the 26 world's food supply and eliminate world hunger. While the life expectancy in Japan is the longest 27 in the world, it is demanded to extend the healthy life expectancy, which is defined as the period in 28 which the person can enjoy life without any limitation in day-to-day activities resulting from 29 health problems, because the increase of the life-style related diseases make some people ill, 30 which lowers quality of life and causes a significant financial burden. 31

Palatable, healthy, and sustainable foods are demanded. From the nutritional standpoint it is 32 possible to have a completely adequate diet in the form of fluid foods that require no mastication. 33

However, few people are content to live on such a diet. Modern food and pharmaceutical 34 companies sell manna-like foods, which proclaim to be palatable and healthy. But, people don't 35 eat them every day. Bourne (2002) raises the great number of dentists in the developed countries 36 which supports his argument. Even if ready-made convenient foods are palatable and good for 37 health, most people like to eat something different every time when the situation allows except in 38 a serious calamity such as the earthquake and typhoon/hurricane. Palatable and healthy foods are 39 even more demanded in such a situation as in the age of covid-19 because disadvantaged persons, 40

such as refugees and patients, are under the harsh stresses. 41 unchangeable products are required in the other industry, food should be fragile in a sense that it 23 should be chewable and digested by enzymes to be processed in oral and gastrointestinal organs. 24

It is well known that not only the molar mass but also the structural characteristics such as 25 linkage mode of glucose in polysaccharides make the performance diversity even for similar molar 26 mass compounds. Functional proteins have their specific molar mass because their role in the life 27 phenomenon is designed naturally. Therefore, it seems to be absurd to dare to write an overview 28 on the effects of molar mass in food quality and health related properties. The authors tried to find 29 some common characteristics or rules governing the mechanism which could be applied to other 30 materials or phenomena within food and health problems. 31 steak consisting of minced meat with granular protein. Size and shape of this granular soy protein 1 can be controlled by changing the extruder outlet, composition of raw materials, running condition 2 of extrusion (Isobe & Noguchi, 1988) . Not only the fibrous texture but also juiciness is an 3 important texture characteristics to produce an authentic meat mouthfeel (Puolanne, 2017; Warner, 4 2017 ). 5

Low molar mass and high molar mass emulsifiers act differently on the surface of oil droplets. 6

While low molar mass emulsifiers may adsorb faster on the surface of oil droplets because their 7 diffusion coefficient is larger than that of high molar mass ones, high molar mass emulsifiers may 8

show a steric stabilisation effect (Dickinson, 2009 ). The steric repulsion is dependent not only on 9 molar mass of the polymer forming layers surrounding droplets but also on the conformation and 10 branching (Dickinson, 2018). 11 12

All the hydrocolloid scientists know the importance of molar mass, for example, to control the 14 viscosity of fluid foods, high molar mass polysaccharides can increase the viscosity at a very low 15 dose (concentration) if the conformation is not completely random coil. Random coil 16 polysaccharides such as pullulan and dextran are not effective to increase the viscosity. The 17 solution viscosity of low molar mass saccharide is much lower than that of higher molar mass 18 saccharide, i.e. polysaccharide. Though there have been many papers studying food processing or 19 health related problems by changing the dose (concentration) of different polysaccharides without 20 controlling the molar mass, it is evident that it is not possible to compare the concentration 21 dependence or the different effects of these polysaccharides when the molar mass of each 22

polysaccharide is different. In the industrial application of these thickening and gelling 23 polysaccharides, the solubility and the hydration rate and extent are important, which are related to 24 the molar mass and other structural characteristics. In electrolytic copolymers such as pectins and 25 alginates or chitosans, the degree of blockiness, type of cations/anions, the position of 26 cations/anions, degree of substitution (methoxylation/acetylation) are also determining factors of 27 the function. In cellulose derivatives, the degree of substitution and its position and length are 28 determining factor of the function. Although the conformation or the stiffness of polysaccharide 29 chain plays important roles in their performance, it is worthwhile to pay attention to the molar 30 mass effect. In the present paper, the terms molar mass, molecular mass, and molecular weight 31 represented in Da (Dalton) or g/mol are used interchangeably. Since it is generally time/energy 32 consuming to obtain food polymers with narrow molar mass distribution, most published papers 33 used polydisperse polymers. Nevertheless, high molar mass and low molar mass have been shown 34 to affect the function /property differently as will be discussed in the present review. The molar 35 mass of some polysaccharides have not been determined with high precision because their 36

structures are heterogeneous and difficult to purify to be subjected to molar mass determination. 37

Since fibrils of globular protein appeared, the concept of globular protein that forms a gel only 38 at high concentrations changed drastically. It was reported that fibrils of β-lactoglobulin can form for the smooth movement of joints of knee or any other part conferring the lubrication as well as 36 shock absorption. Hyaluronan (also called hyaluronic acid, HA) is a main ingredient, also 37 occurring in connective, epithelial, and neural tissues e.g., in eyes, umbilical cord, skin, blood 38 vessels, heart valves (Laurent, & Fraser, 1992) . Many elderly persons suffer from knee joint pain 39 from osteoarthritis (OA), and the traditional therapy was an injection of hyaluronic acid (Balazs & 40 Denlinger, 1985) . Since hyaluronan is hydrolyzed by endogenous hyaluronidase and cannot 41 function for a long time, cross-linked hyaluronan was introduced, which can keep longer (Balazs 42 et al., 1985) . HA a copolymer consisting of glucuronic acid and N-acetyl-glucosamine, and 43 occurring naturally, but is also produced by microbial fermentation. Its molar mass is reported to 44 J o u r n a l P r e -p r o o f specific problem, the degradation and reconstruction of molecules are governed by specific 23 enzymes and thus different problems cannot be compared directly each other, but methods of 24 study are sometimes similar thus a study on one problem can learn from another study, and finally 25 the total aspects should be overviewed to solve each specific problem. It is the authors' hope that 26 each specialists share their own area with other areas to collaborate to find a better solution. 27

The viscosity of the liquid foods is in most cases determined by food macromolecules and the 28 molar mass is the determining factor together with the structural characteristics, conformation, 29 molecular shape, stiffness, and degree of branching. Some problems of the mixture of high molar 30 mass and low molar mass polymers, which have an important practical significance in medical 31 problems such as hyaluronate related with knee pain, and alginate related with cystic fibrosis, and 32 also the interaction between polysaccharides and proteins in food industry are also discussed. 33 There have not been many studies on the effect of molar mass distribution by mixing 34 monodisperse polymers because it is time/energy consuming to get well fractionated polymers 35 with wide molar mass range. The elasticity of solid or semi-solid, gel-like foods is also dependent 36 on molar mass and also the structure of junction zones, the network density and the elastically 37 active network chains, which are also dependent on molar mass. Electric charges, ionic strength 38 and pH are also important factors, and therefore the effect of molar mass is not isolated from these 39 factors. Nevertheless, it is expected that extraction of common features in various phenomena 40 which are strongly influenced by the molar mass of polymers which play an important role is 41 useful. From this overview, unresolved problem may find a clue from the other problems.

in food and health are overviewed in the present paper. 1 2

There are many methods to obtain or analyse polysaccharides and proteins with different molar 4 masses (Table 1) . Each methods have advantages and disadvantages. For example, oligomers of 5 sulphated polysaccharides have been attracted much attention because of their biological activities, 6 and depolymerized by ultrasonication, gamma-irradiation, acid or enzymatic hydrolysis. Sulphate 7 groups tend to be removed by acid hydrolysis, while the structure of the repeating units was 8 retained by gamma-irradiation in fucoidan (Choi & Kim, 2013) . In another report, the sulphate 9 content of fucoidan slightly increased by ultrasonic degradation (Guo, Ye, Sun, Wu, Wu, Hu, et al., 10 2014). In ultrasonic degradation of xanthan, removal of pyruvate groups from native xanthan 11 increased the thermal stability keeping the helical conformation, and lowered the sensitivity of 12 molecular conformation to the salt concentration, and thus led to lower degradation efficiency (Li 13 & Feke, 2015) . 14 Some methods of molar mass change, decrease or increase, applied to polysaccharides and 15 proteins in food and health industries are shown in Table1. 16 6 The intrinsic viscosity (also called limiting viscosity number) is often determined by an 7

Ubbelohde type capillary viscometer. The relative viscosity is defined as the ratio of the viscosity 8 of the solution to that of the solvent η rel = η/η s , and the specific viscosity (relative viscosity 9 increment) η sp = (η -η s )/η s = η rel -1 per unit concentration is extrapolated to zero concentration to 10 obtain the intrinsic viscosity [η]= Lim (C→0) η sp /C. The intrinsic viscosity has a unit of the inverse 11 of the concentration, and represents the volume the polymer occupies in the solution. Therefore where K and a depend on solvent quality, a < 1/2 for poor solvent, a = 1/2 for θ solvent, a > 1/2 for 3 good solvent (Doi, 2013; Tanaka, 2011) . The MHS exponent a is reported as 0.5 for amylose (in 4 0.33 molar KCl), dextran (water), and 0.8 for stiff chains such as locust bean gum, 0.8~1.1 for 5 anionic polysaccharides such as carboxymethyl cellulose, alginate, κ-carrageenan, xanthan, pectin 6 (Walstra, 2003). Solution properties of pullulan was extensively studied (Kawahara, Ohta, to zero shear rate is used to understand the concentration dependence systematically. 19 20 Fig.2 21 22 The critical coil overlap concentration C* is approximately given by 4/[η], and at this 23 concentration the zero shear viscosity was found η sp ~ 10. The slope above the critical 24 concentration was found about 3.3 for most random coil polymers including the data for 25 polystyrene in toluene, but this slope was approximately 4.4 for guar gum and locust bean gum for 26 which the critical concentration was found a little bit lower than for the other random coil 27 polymers. The deviation of the behavior for galactomannans (guar gum and locust bean gum) may 28 be due to specific attractive interactions between side groups on the polymer chains or the stiffness 29 of polymer chains. It should be reminded that a typical behaviour shown in Fig.2 is limited to the 30 viscosity at very low shear rates. 31

As typical shear rate dependence of the viscosity for the solutions of water soluble polymers, 32 data for cellulose derivatives and cereal β-glucans are shown in Fig.3A and B. While all the 33 glucose residues are linked byβ-(1→4) in cellulose which is insoluble in water, in cereal β 34 -glucans about one third of the linkages between the glucose residues are β-(1→3) linkages in 35 addition to β-(1→4) linkages, and more soluble in water. Cellulose derivatives are soluble and 36

have been studied extensively. For cellulose derivative compounds with different molar masses 37 but approximately the same degree of substitution, the steady shear viscosity of 2% solutions as a 38 function of shear rate is shown in Fig. 3A . A similar shear rate dependence of the steady shear 39 viscosity for beta glucans from oat, barley, wheat flour and wheat bran is shown in Fig.3B . The following features are noted: 1) the viscosity at lower shear rates increases with increasing 45 molar mass; 2) the viscosity decreases with increasing shear rate, which is called shear thinning; 1

3) The viscosity of the solution of the lowest molar mass does not depend so much on the shear 2 rate, and shows approximately a constant value at lower shear rates. This is called a Newtonian 3 plateau. Because of the limited sensitivity of the rheometer, the viscosity at very low shear rates 4 cannot often be measured. In this case, the viscosity of the solution of the lowest molar mass was 5 not measured below the shear rate of 3 s -1 (Fig. 3A) or 0.1 s -1 (Fig. 3B ) or 2 s -1 (Fig. 3C ). It should 6 be noted that some published papers erroneously showed a steep rise of the viscosity at lower 7 shear rate with decreasing shear rate, which were probably caused by neglecting the low 8 sensitivity limit of the sensor. 9 10

Diffusion is a ubiquitous phenomenon of motion of molecules or particles in any phase (gas, 12 liquid, or solid) caused by the concentration gradient. This is caused not by an external force but where k is the Boltzmann constant (1.38 × 10 −23 J K −1 ), T is the temperature (K), R H is the 26 hydrodynamic radius of a spherical particle (m), η the viscosity of the surrounding medium

(Pa.s). This equation is valid only for an infinitely dilute solution, and for a particle which is larger 28 than the solvent molecule. 29

The hydrodynamic radius R H is related with the radius of gyration R g = KM ν (Flory Equation, 30

ν is called Flory exponent) by ρ = R g / R H.. For linear, flexible chains in the theta solvent ρ = 31 1.505, while in the limit of large excluded-volume effects (v = 0.587) a value of ρ = 1.78 is 32 obtained. Polydispersity increases this value by 14% (i.e. ρ = 2.05) for a most probable 33 (Schulz-Flory) distribution with a polydispersity index PI, the ratio of weight average molecular 34 weight M w and the number average molecular weight M n, PI = M w /M n = 2 (Burchard, 1994). denaturing solutions increased tended to approach 0.6, similar to the exponent expected for a 8 random coil polymer in a good solvent as mentioned above. This difference in the ν value can be 9

used to distinguish between folded, disordered and denatured proteins (Evans, 2020). Dudás & 10

Bodor (2019) acquired diffusion coefficients of 12 globular proteins and 10 intrinsically 11 disordered proteins (IDPs). They reported ν = 0.382 for native folded globular proteins, and ν= 12 0.492 for intrinsically disordered proteins (Fig.4) . The value close to 0.5 indicated that the 13 . 17 18

Fig4 19 20 Pullulan has been studied extensively as a water soluble, model random coil polysaccharide. 21

The diffusion coefficient of pullulan as a function of molar mass is shown in Fig.5A where ξ H is hydrodynamic correlation length, should be used (de Gennes, 1979) . Diffusion 1 coefficient of pullulan was found to decrease with increasing concentration for lower MW 2 (5.5kDa -23.8 kDa) observed by ultracentrifuge and for higher Mw (53.9 kDa-478 kDa) observed 3 by PCS (Nishinari et al., 1991) . Diffusion coefficient of α S -casein as a function of concentration 4 is shown in Fig.6A (Kusova, Sitnitsky, Idiyatullin, Bakirova, & Zuev, 2018). This dependence can 5 be generalised by scaling as shown in Fig.6B (Nesmelova, Melnikova, Ranjan, & Skirda, 2019). and increased with further cooling, as shown in Fig. 7(b) . The decrease of solute gellan 21 concentration at T I(0) might cause a decrease in the local viscosity because solubilized random coil 22 gellan molecules were incorporated into helices and their aggregates. The increase of D gel at T I(0) 23 was more pronounced than expected from the decrease of local viscosity. Therefore, it is 24 considered that the MW distribution of the gellan remaining as a random coil as a solute among 25 the network of aggregates was shifted to lower MW values because higher molar mass gellan 26 chains were preferentially incorporated to junction zones than lower MW chains. This is 27 consistent with the observation that shorter chains preferentially eluded out from gellan gels when 28 gels were immersed in solvents (Hossain & Nishinari, 2009 The diffusion coefficient of pullulan decreased with decreasing temperature, and it was concluded 39 that pullulan chains were not involved directly in the aggregation of gellan, and remained 40 dissolved during the gelling process, probably due to the high solubility of pullulan in water. The 41 diffusion of pullulan is thought to be restricted by the hydrodynamic interaction with the solute 42 gellan as well as the network of aggregates. The restriction became smaller with decreasing solute 43 gellan concentration and increasing network pore size, both of which result from the thickening of 44 the aggregates. 45

Since probe molecules (pullulan) in the solution have no intermolecular interaction with the 46 host polymer (gellan) except the hydrodynamic interaction, the diffusion is expressed as follows 1 (Cukier, 1984; de Gennes, 1979; Matsukawa & Ando, 1996) : 2

where D inHost and D inPure are D of the probe molecule in the host polymer solution and that in pure 4 dilute solution, respectively, and ξ is the hydrodynamic mesh size which represents the 5 hydrodynamic mesh size made of the solute gellan and the network of aggregates. Values of ξ are 6 shown in the right vertical axis in Fig.7d . The change in the microscopic surroundings of pullulan 7 during the cooling process is shown schematically in Fig.8 .

When a physical polymer gel is immersed in a solvent, molecular chains which are not 12 connected to the junction zones were found to release out from the gel to the solvent (Djabourov et 13 al., 2013). It has been observed that the immersion of potassium type deacylated gellan gels in 14 water or electrolyte solution induces chain release, and this release is more noticeable for shorter 15 chains. Ultimately the gel becomes eroded and then disintegrates, and the rate of collapse depends 16 on polymer concentration, original molecular mass and the initial salt content of the gels and the 17 solvent. Salt diffusion from the gels into the solution is faster than chain release; chains which lose 18 condensed or bound ions cannot retain a helical conformation, and so they diffuse out into the immersion in pure water. They estimated the diffusion coefficient (1.6 ~ 2.8) × 10 -11 m 2 s -1 , which 25 was slightly larger than diffusion coefficient ranging from 0.6 × 10 -11 m 2 s -1 to 1.0 × 10 -11 m 2 s -1 26 at 25 ℃ in 25mM NaCl for molar mass range from 2.2 × 10 5 to 1.3 × 10 5 reported by Takahashi 27 et al. (2004) . This is reasonable since molecular chains released out from the gel network were 28 shorter than un-released chains 29

De Silva, Poole-Warren, Martens, & in het Panhuis (2013) studied the chain release of also 30 deacylated but Ca 2+ cross-linked gellan gels at 37 ℃ in a phosphate buffer saline (PBS). These 31 authors also found the chain release as mass loss up to 168 days. Since the CD ellipticity was 32

proportional to the gellan concentration, they estimated the diffusion coefficient of gellan from 33 the CD data D = 1.1 × 10 -13 m 2 s -1 , which was two orders of magnitude smaller than the reported 34 value of deacylated gellan at 40 ℃ (Takahashi et al., 2004). They ascribed this difference to the 35 retardation of the mobility of gellan molecules in gel network. 36 37

Molar mass is a key for the gel formation. When the material changes from sol state to gel 39 state, the molecules are connected each other spanning the whole space in the vessel, and this is 40 called the percolation at which the molar mass is thought to diverge to infinity (de Gennes, 1979; 41 Nishinari, 2009; Tanaka, 2011; Tokita, 1989) . Gelling polysaccharides and proteins have been 42 used widely for controlling the food texture. Mechanical strength of gels can be indexed by the 43 elastic modulus and/or fracture stress/strain. Although the oral processing is a dynamic process, 44 that is time dependent, only the fracture stress has been used to characterize the mechanical 45 J o u r n a l P r e -p r o o f properties quite often neglecting the intermediate stress/ strain of the compression/shearing in the 1 mastication. For example, in fishery industry in Japan a so-called "gel rigidity", which was 2 defined as the ratio of the force to deformation at break using a spherical probe of 5mm diameter, 3 has been used widely. Though it may have some merit, it does not distinguish two concave and 4 convex curves connecting the origin and the break point in the force-deformation plot. We hope 5 that these distinction will be taken into account in the near future. 6 7

Since the average number of residues per helical turn to form α-helix has been established as 9 3.6, and 13 atoms are involved in the ring formation by hydrogen bond, α-helix is also called 10 3.6 13 -helix. The average number of residues per helical turn for other protein helices is also 11 determined as 3.0 for 3 10 

Amylose gelation is known to be a triggering in the early stage of retrogradation of starch, but 3 only a few studies have been published on the gelation kinetics using amylose samples with 4 different chain lengths (Clark, Gidley, Richardson, & Ross-Murphy, 1989 ). Fig.10A shows the 5 gelation process of 2% solutions of amylose with different chain lengths. Storage shear modulus 6 G' increased fast and then reached a plateau value earlier in lower molar mass samples. The 7

plateau value increased with increasing molar mass within the DP range from 250 to 1100 8 however the highest molar mass DP 2550 still continued to increase even after 10000 min (Clark 9 et al., 1989) . The concentration dependence of plateau modulus of amylose gels and β-glucan gels is shown 27 in Fig.11 . While the plateau storage modulus of amylose gels in the concentration range from 1 to 28 3%, the modulus is higher for higher molar mass than for lower molar mass (Fig.11A) , the 29 modulus of β-glucan gels in the concentration range from 4 to 12 %, the modulus is higher for 30 lower molar mass than for lower molar mass (Fig.11B ), 31 32 In amylose gelation, the plateau value increased with increasing molar mass as shown in 35 Fig.10A , while in β-glucan gelation, the plateau value seemed to decrease with increasing molar 36 mass as shown in Fig.10B , though for slow gelling samples with higher molar mass did not reach 37 the plateau within 100 h. The apparent inconsistency between Fig.11A and Fig.11B , that the 38 apparent plateau modulus increases with increasing MW in the former (amylose) while it is 39 smaller for higher MW in the latter (β-glucan), originates from the non-equilibrium nature of these 40 apparent plateau moduli. As shown in Fig.11B , the gelation proceeds much slower in β-glucan 41 than in amylose, it is impossible to compare directly with Fig.11A and Fig.11B . This reminds us 42 the slow gelation rate of gelatin solutions. The storage modulus of 1.95% (w/w) gelatin/water 43 increased faster at lower temperatures but it has not reached an equilibrium plateau but continued 44 to increase even after100h (te Nijenhuis, 1981) . It is also necessary to take into account the molar 45 mass range and in addition molecular conformation, flexible or stiff, when the modulus of 1 different gelling polymers are compared as a function of molar mass. The effect of minor 2 component of intermediate DP higher than 4 and a small amount of protein in β-glucan seems to 3 be difficult to be quantified accurately, and is a future problem. 4

It should be noted that there is a critical molar mass and a critical concentration below which 5 no gelation occurs. For amylose this critical molar mass was in between DP=110 and DP=250, 6 and below DP= 110 only precipitates were observed. The critical concentration for gelation of 7 amylose was found to depend on the molar mass (Gidley & Bulpin, 1989 ). 8 9

Since it is difficult to prepare samples with different molecular weight and with a narrow 11 molecular weight distribution, there have not been so many studies on the molecular weight 12 dependence of elastic modulus of gels. Saunders &Ward (1955) studied rheological properties of 13 gelatin gels with different molecular weights indexed by intrinsic viscosity, and showed that the 14 elastic modulus increased with increasing molecular weight up to a certain value and then levelled 15 off whilst the breaking stress continued to increase with increasing molecular weight (Saunders & 16 Ward, 1955 Shear modulus of alginate gels as a function of weight average degree of polymerization 23 was reported to show two regions; the initial steep ascending region and then levelled off and 24

show a long horizontal region. Smidsrød (1974) showed this tendency for both alginate gels and 25 κ-carrageenan gels. He suggested that the difference of the plateau values, independent of the DP, 26 is due to the difference in the number or the strength of the junctions in alginate and κ-carrageenan. 27

Twenty years later, the same group Draget, Skjåk Braaek & Smidsrød (1994) reported the molar 28 mass dependence of apparent Young's modulus E app and storage shear modulus G' of gels of 29 alginate. In the range of molar mass from 300 kDa to 700 kDa, they observed that both E app and G' 30 increased with increasing molar mass and did not show the molar mass independency as shown in 31 Fig.12 . It should be mentioned that they noticed that elastic modulus increased with increasing 32 guluronic acid residues as reported previously from the same group (Smidsrød & Haug, 1972) . 33

This comparison is difficult because it is difficult to obtain the series of samples with the same 34 molar mass and only different in the guluronic acid residue content. Quite a similar behavior was 35 reported for κ-carrageenan gels with different molecular weights (Rochas, Rinaudo, & Landry, 36 1990 ). These tendencies can be summarised as shown in Fig. 12 . The elastic modulus increases 37 steeply with increasing molar mass, and then it levels off above a certain molar mass. 38

The temperature dependence of the elastic modulus has been attracting much attention. 39

Whether the elasticity of agarose is entropic or energetic has been debated for a decade just after 40 the 2 nd world war in Japan (Nishinari, 2000a). Nishinari, Watase, & Ogino (1984) tried to separate 41 the entropic term and energetic term from the observed temperature dependence of Young's 42 modulus E′ for gels of agarose with different molar masses (indexed by the intrinsic viscosity) and 43

with the same sulphate content and the 3,6 anhydro-L-galactose content, both of which are 44 important factors influencing the helix and gel formation (Nishinari & Fang, 2017). The Young's 45 modulus E′ increased with increasing molar mass and temperature for higher molar mass fractions 1 (Fig.13A) . The tendency observed for the increase of E′ with increasing molar mass is consistent 2 with the above Fig.12 for gels of gelatin, κ-carrageenan, and alginate. The elastic modulus was 3 determined as dynamic Young's modulus E′ by observing longitudinal vibrations of a cylindrically 4 moulded gel, which is free from slippage. While E′ decreased monotonically for a gel of agarose 5 with a low molar mass (F1), E′ of other gels with higher molar masses (F2, F3, F4, F5) increased 6

gradually from 5° C up to a certain temperature T max , and then decreased (Nishinari et al, 1984) . 7

This temperature T max shifted to higher temperatures with increasing molar mass and concentration 8 (Fig.13A) . It was found that the entropic part decreased while the energetic part increased with 9 increasing temperature. The increase of E′ with increasing temperature was explained by a 10 reel-chain model (Nishinari, Koide, & Ogino, 1985) . 11

Stress relaxation of agarose gels with different molar masses were observed, and the relaxation 12 spectra were obtained using time℃ temperature superposition (Watase & Nishinari, 1983) . It was 13

shown that box type spectra extended to longer relaxation times with increasing molar mass at a 14 constant concentration, and that both breaking stress and breaking strain increased with increasing 15 molar mass (Fig.13B) . More recently, Moritaka. Yamanaka, Kobayashi, Ishihara, & Nishinari (2019) examined the 20 size distribution of the masticated fragments of agarose gels, and found that the size distribution 21 depended on molar mass as well as a mouthful size. As expected, the size of masticated fragments 22 decreased with decreasing molar mass of agarose, which forms more brittle gels broken at lower 23 fracture strains. high-sensitivity isothermal titration calorimetry (ITC), Ca 2+ -selective potentiometry, and relative 35 viscometry. The results revealed three distinct and successive steps in the binding of calcium to 36 alginate with increased concentration of Ca ions. They were assigned to (i) interaction of Ca 2+ 37 with a single guluronate unit forming monocomplexes; (ii) propagation and formation of egg-box 38 dimers via pairing of these monocomplexes; and (iii) lateral association of the egg-box dimers, 39 generating multimers. The boundaries between these steps were found critical, and they were 40 closely correlated with the Ca/guluronate stoichiometry expected for egg-box dimers and 41 multimers with 2/1 helical chains. In this multi-step binding of Ca to alginate, the dimerization 42 process was found to be highly critical, only occurring when the stoichiometry of egg-box dimers 43 is met, that is, Ca/ G = 0.25, one calcium ion per four guluronate residues. The formation of 44 egg-box dimers and their subsequent association are thermodynamically equivalent processes and 45 J o u r n a l P r e -p r o o f can be fitted by a model of independent binding sites. In addition, the step (iii) showed different 1 association modes depending on the molar mass of alginate. While the relative viscosity η r 2 continues to increase in (iii) indicating that lateral association of egg-box dimers for lower molar 3 mass alginate occurs between different dimers, η r decreases in (iii) for higher molar mass 4 alginate indicating the association makes the volume of aggregates smaller. 5 Fig. 14A shows the gelation profiles of 5 mg/mL ALG with and without addition of 5 mg/mL 6 oligoguluronate, guluronate block (GB) at various concentrations of Ca-EDTA. It is well known 7 that alginate forms an inhomogeneous gel by a rapid ionic reaction, and the slow release of 8 calcium from calcium carbonate or Ca-EDTA in the presence of slow acidifier like 9 glucono-delta-lactone is used to make a homogeneous alginate gel (Draget, Ǿstgaard, & Smidsrød, 10 1991; Thu, Smidsrød, & Skjåk Braaek, 1996) . Gelation kinetics and equilibrium gel properties of 11 alginate aqueous solutions induced by in-situ release of Ca ions from Ca-EDTA during 12 D-glucono-delta-lactone (GDL) hydrolysis were observed and the modulatory effects of GB were 13 analysed quantitatively. It is apparent that when Ca-EDTA < 51.20 mM the systems without 5 14 mg/mL GB gelled faster than those with the addition of 5 mg/mL GB and also attained a higher 15 value of saturated equilibrium storage modulus. It manifests an inhibitory effect exerted by the 16 addition of GB. On the contrary, when Ca-EDTA > 51.20 mM, the systems with 5 mg/mL GB 17 tended to end up with a higher saturated equilibrium storage modulus than those without 5 mg/mL 18 GB. Moreover, the gelation kinetics seems not to be altered significantly by the addition of GB. The effect of guluronate block GB depends on the ratio of calcium ions to guluronate unit, R = 23

Ca/G. The addition of GB shows an inhibitory effect in the range of 0.25 < R (Ca/G) < 0.60, and 24 promotive effect in the range of R > 0.60 based on static and dynamic viscoelastic measurements. 25

Mixed egg-box dimers between ALG and GB were ruled out because of cooperativity requirement 26 of dimerisation. The promotive effect in the higher Ca concentration regime was assigned to the 27 role of GB dimers participating in and enhancing the lateral aggregation of ALG dimers. In 28 conclusion, short chain guluronate block is found to inhibit the gelation of alginate at low 29 concentration of Ca 2+ ions while it enhances the gelation at higher Ca 2+ concentration. Inhibitory 30 effect is attributed to the binding of calcium ions to shorter guluronate chains. Those findings may 31 be useful in food processing and also have some therapeutical significance in the rheology of 32 sputum as discussed in the following section. significantly different from the case of alginate where no gelation could be induced at all. In the 38 range of 0.25 < R < 0.60, the addition of GB was found to inhibit the gelation of LMP, whereas it 39 had a negligible effect on the gelation of alginate as long as a fixed R was considered. In the range 40 of R > 0.60, GB was found to promote the gelation of LMP again, which is similar to the case of 41 alginate as described above (Fig.14B) . 42

Polysaccharides are frequently used to reduce the fat content, and to improve the texture and 43 water holding capacity (WHC) of protein gels. Yao, Zhou, Chen, Ma, Li, & Chen (2018) recently 44 examined the effect of the addition of sodium alginate (SA) with three different molar masses on 45 the WHC of chicken breast myosin gels. They found that WHC increased simultaneously with 1 turbidity and thermal stability, accompanied with the decrease in surface hydrophobicity with 2 increasing molar mass of added SA. They noticed that the addition of sodium alginate shifted the 3 thermal transition temperature to higher temperatures detected by DSC with the higher 4 contribution by a higher molar mass SA, which is consistent with the same stabilisation by the 5 addition of flaxseed gum to salt-soluble meat protein, but is contradictory with the reported 6 thermal destabilisation of myofibrillar, sarcoplasmic and connective tissue protein by the addition 7 of SA. They observed that inhomogeneity of cavities formed in SA-protein gel network was 8 enhanced by the higher molar mass SA, which resulted in the increase in WHC because they 9 thought that large cavities could store more water. 10 11

Some polysaccharides such as locust bean gum and cereal β-glucan as well as poly(vinyl 13 alcohol) (PVA) form cryogels after freezing and thawing cycles while most polysaccharides such 14 as agarose, carrageenans donot but only framework structure remains after freezing because water force-extension curves for cryogels of PVA with different DPs 500 (curve (1)), 1 000 (curve (2)), 23 1700 (curve (3)), and 2400 (curve (4)). However, the storage shear modulus G′ of oat β -glucan 24 cryogels showed opposite tendency as illustrated in Fig.15C . The finding that G′ increased with 25 increasing concentration of βglucan is a common phenomenon. However, the G′ values of cryogels decreased with increasing molecular size. Lazaridou & 30 Biliaderis (2004) had found a similar trend in their earlier study for cereal β-glucan gels formed at 31 room temperature and it had been attributed to the higher mobility of shorter chains (Lazaridou et 32 al., 2003 (Lazaridou et 32 al., , 2004 . Their interpretation was as follows: the molecular size has a significant impact on 33 the viscosity of polymer solutions, thus influencing the diffusion rates of the interacting 34 polysaccharide chains. However, it is difficult to understand this explanation because the 35 stress-strain curves shown in Fig.15A , the Young's modulus estimated from the initial slope of the 36 curve is the largest for the gel from the higher molar mass oat glucan 200 kDa and the smallest for 37 the gel from the lowest molar mass oat glucan 110 kDa. Unfortunately, gels from 65 kDa were so 38 weak to keep the shape to do the compression measurements. The inconsistency between the 39 Young's modulus from the slope of stress-strain curves in Fig.15A and the storage shear modulus 40

shown in Fig.15C should be studied further. 41

Heat set gel formation also depends on molar mass. The gelation process of solutions of 42 methyl cellulose (MC) with different molar masses and with approximately the same methoxy 43 content (29 wt%) was observed by measuring G' and G" at a constant temperature 55℃. The 44 gelation time at which G' began to increase above the base line was shorter in a higher molar mass 45 MC solution. This rheological tendency is in accordance with DSC observation in which an 1 endothermic peak appeared on heating accompanying the gelation. The longer chains have a 2 greater tendency to form junction zones which are induced mainly by hydrophobic interaction 3 (Nishinari, Hofmann, Moritaka, Kohyama, & Nishinari, 1997) . Whether the gel formation of MC 4 is caused by spinodal decomposition or by the nucleation and growth is still a matter of hot debate 5 (McAllister, Schmidt, Dorfman, Lodge, & Bates, 2015). More detailed studies on the gelation of 6 MC changing molar masses at a constant degree of substitution, preferably using regioselective 7 substitution, are expected in the future. 8

The gelation of KGM occurs through the alkali-induced removal of acetyl groups which 9

confer the solubility for this polysaccharide (Nishinari, 2000b). KGM forms a thermally stable gel 10 by deacetylation upon addition of alkaline coagulant and the gelation of KGM is promoted by 11

heating, in contrast to many other cold-set thermo-reversible gels. The increase in the 12 concentration or molecular weight of KGM shortened the gelation time and increased the rate 13 constant of gelation, and the resulted gels show higher modulus (Yoshimura & Nishinari, 1999; 14 Zhang, Yoshimura, Nishinari, Williams, Foster, & Norton, 2001) . This is consistent with the 15 general tendency observed in gelatin, carrageenan, alginate and agarose gels as described above. 16

The effect of the degree of acetylation (DA) on the gelation of KGM was studied (Huang et al., 17

2002; Gao et al., 2004) . To understand the effect of molar mass on the gelation, it is necessary to 18 obtain KGM sample with a constant degree of acetylation (DA) with different molar masses, but 19 this has not yet been done because of the difficulty of sample preparation. The same difficulty is 20 encountered in the study of the interaction of KGM with other polysaccharides such as 21 κ-carrageenan, agarose, starch or proteins such as gelatin and myofibrillar proteins although these 22

mixtures have been used in food products without understanding the detailed mechanism. The 23 more detailed knowledge will improve further the products. 24 25

Crystallinity of solid fat is generally much higher than high molar mass polysaccharides and 27 proteins, and the linear elastic range is much narrower than in semi-solid foods mainly composed 28 of polysaccharides and proteins. Spreadability of semi-crystalline solid fat such as butter and 29 margarine is an important functionality during consumption, and this characteristics is different 30 from high molar mass polysaccharide and protein food gels. As is shown in Fig.16 , the gel strength was found to increase with mass fraction of EC in a 43 power law fashion, and also to increase with increasing molar mass of EC. From the cryo-SEM 44 observation of partially de-oiled gels, it was found that the internal structure consisted of oil 45 droplets entrapped within a network of interconnected strands or bundles of EC, which formed a 1 scaffolding to support the gel (Zetzl, Gravelle, Kurylowicz, Dutcher, Barbut, & Marangoni, 2014). 

Rennet-induced gelation of casein micelles has been studied extensively because it is the 22 basis of cheese production. Niki, Kohyama, Sano, & Nishinari (1994) prepared the casein micelles 23 with different sizes by differential centrifugation. Since the κ-casein, the substrate of rennet 24 enzyme chymosin, exists mainly on the surface of casein micelles, the smaller micelles are richer 25 in κ-casein content. Therefore, glycomacropeptide is liberated faster in smaller casein micelles as 26 shown in Fig.17A . 27 28 The saturated value of the storage shear modulus was largest in the gel formed by the 31 smallest casein micelles (Fig.17B) . Then, the smallest casein micelles can form a gel faster 32 and can form a stronger gel. In this case, the gelation is dominated not only the size of the 33 casein micelles but the difference of the distribution of κ-casein in the casein micelles should 34 also be taken into consideration. 35

Gluten network determines the dough rheology, and thus governs the quality of bread. It has 36 been generally accepted that glutenin contributes to the elasticity and gliadin is for the viscosity, 37 and this is mainly ascribed to the high molar mass of the glutenin and the lower molar mass of of mixing (arrival time) LMW and HMWglutenins were found to form aggregates, which were 44 then distorted to form a uniform network with gliadin when mixed until the dough reached peak 1 time. The development of this gluten network formed by the assembly of the three gluten subunits 2 was thought to be related to the significant increase of dough strength. Further mixing after peak 3 led to departure showing less dense structure characterized by the increase in mean lacunarity. 4 Recent trend to exploit the possibility to use biowaste or to add more values to plant 5 proteins is becoming more and more active (Petrusan, Rawel, & Huschek, 2016) . Felix, 6

Perez-Puyana, Romero, & Guerrero (2017) examined enzymatic hydrolysates of pea protein 7 isolate expecting the improvement of functional properties. They found that although the 8 solubility increased by hydrolysis, the gelling ability was reduced. It should be noticed that 9 the lipid content and the surface hydrophobicity decreased by enzymatic hydrolysis, and 10 therefore, the decrease in gelling ability was the result of all these interactions. Gelling ability 11 of plant proteins was reported to decrease by enzymatic hydrolysis, but a limited enzymatic 12 hydrolysis makes the buried peptide groups exposed on the surface, and the ionizable groups 13 liberated thus increasing the protein-protein interaction and leading to strengthen the gelling 14 ability (Wouters, Rombouts, Fierens, Brijs, & Delcour,. 2016). Since transglutaminase (TGase) 15 can make new covalent bonds, ε-(γ-Glu)-Lys crosslinks, it has been used widely to increase 16 the gelling ability of many proteins such as soy proteins, sunflower protein, canola proteins 17 (Wouters et al, 2016). Here, the molar mass decrease by hydrolysis and then its increase by 18 TGase are the main governing principle of the decrease and increase in the gelling ability. 19 20

To control the mechanical properties of solid foods, it may be useful to remind the 22 fundamentals of glass transition (Bhandari & Roos, 2017). Glass means the amorphous solid not 23 only the glass used for windows or cups. On lowering the temperature, the solid behaviour 24 changes from rubber-like to solid-like at the glass transition temperature T g . This transition is 25 different from a simple liquid to a simple solid (crystal) transition, and was studied extensively for 26 amorphous polymers. The solid-like amorphous glass is in a non-equilibrium super cooled liquid 27 state, and different from an equilibrium crystalline state. Large scale main chain motion is allowed 28 and the amorphous solid is ductile/plastic above T g , while the large scale motion is frozen and the 29 solid becomes brittle below T g . This can be detected as a drastic decrease of elastic modulus from 30 ca 10 9 Pa to 10 6 Pa on raising the temperature. In the first-order transitions such as melting and 31 boiling, there is a discontinuity in the volume-temperature (V-T) or enthalpy-temperature (H-T) plot, 32 while in the glass transition, these changes are gradual. Therefore, the first order temperature derivative Above the glass transition temperature T g , the amorphous polymer behaves rubber-like and 39

shows a larger strain at break, but below T g , the polymer showed a brittle fracture. The glass 40 transition temperature of synthetic polymers has been studied extensively, and a Fox-Flory 41 equation T g = T g0 -K/M, where T g0 is the T g of the polymer when the molar mass M approaches 42 infinity, and K is a constant (Nunes et al., 1982) . Unfortunately, this equation was not found to fit 43 well to experiments for polysaccharides and proteins, though not so many papers have been 44 published. Since fractural behaviour of solid state is crucial in the application of plastics, effects of 1 molar mass was studied using polystyrene with different molar masses from 24.5 kDa to 1500 kDa 2 in the early days (Onogi, Matsumoto, & Kamei, 1972) as shown in Fig.18 . The elongation test of 3 film (3cm length and 1 cm width) was performed at the elongation rate from 0.028 to 0.56 cm/s 4 and at a temperature range from 115 to 180 ℃. They found that stress σ f and strain γ f at fracture 5 as a function of elongation rate dγ f /dt could be superposed by shifting horizontally as had been 6 done for linear viscoelastic studies (Ferry, 1980) . The shift factor was found to be similar to that 7 used in WLF equation. The resulted master curves of σ f or strain γ f as a function of dγ f /dt was 8 divided into four regions, I. Brittle to ductile transition, II. Ductile, IV. Viscous fluid, and III. 9

Between II and III. The molar mass dependence was more clearly observed at regions III and IV. 10

In other words, mechanical properties are less sensitive to molar mass in the region I and II. At 11 regions III and IV in master curves log σ f or γ f vs log s T dγ f /dt were obtained by superposition 12 with a suitable shift factor s T (Fig.18 ). Higher MW film showed a higher fracture stress or fracture 13 strain at the same elongation rate where the elongation rate is slow. 14 15 In food science/technology, it should be reminded that water plays an important role of 31 plasticiser (Bhandari & Roos, 2017). Amorphous solid polymers can be made more pliable by 32 lowering its T g , and this can be achieved by incorporating quantities of high-boiling, 33 low-molar-mass compounds in the material. These are called plasticisers and must be compatible which is similar to non-degraded starch. However, the reported values donot agree exactly with ca 1 188 ℃ (Roos & Karel, 1991). The effectiveness of the concept of the glass transition in low 2 temperature preservation of food was shown in many foods, e.g. in frozen starch products. Below 3 the glass transition temperature amylose and amylopectin chains mobility is reduced, preventing 4 the molecular association leading to the restructuring (retrogradation) (Zaritzky, 2010) . 5

Maltodextrins are used widely as drying aids in spray drying of, for example, skim milk. It is 6 desirable to prevent powders sticking and it is effective to raise the T g so that the surface of 7 powders might become less sticky; above the glass transition temperature the powders are in 8 glassy state and less sticky. Bakery products formulations taking into account the glass transition 9

were recently reviewed (Wang & Zhou, 2017) . Since polysaccharides and proteins have hydrophilic residues such as hydroxyl groups or 16 amide groups, the glass transition is influenced by these intermolecular interactions. Main-chain 17 motion is restricted owing to these intermolecular interactions and the glass transition temperature 18 is higher than that of the hydrophilic polymer in the completely dry state (Hatakeyama & 19 Quinn,1999) . In most dried proteins and polysaccharides no glass transition or melting is observed 20 until decomposition of the main chain occurs because intramolecular and intermolecular hydrogen 21 bonds stabilise the high order structure of these polymers. Glycerol, sorbitol, or 22 dimethylsulphoxide were used to plasticise the amylose/starch films to study the glass transition at 33 Since gelatin has been widely used in food industry although its usage in photographic film 34 has been reduced, understanding the interaction of water and gelatin remains important. DSC 35 heating curves for gelatin gels of different concentrations from 23.2 to 57.7 wt%, quenched from 36 room temperature to -150 ℃ using liquid nitrogen, are shown in Fig l9A. A step-like change in 37 baseline observed at around -100 ℃ was attributed to glass transition. The glass transition 38 temperature T g is shown by an arrow in Fig 19A. T g shifted to higher temperatures with decreasing 39 gelatin concentration beyond 55%. It is reported that various kinds of hydrogels form glassy state 40 by quenching from a sol state to -150 ℃, and a part of water molecules associated closely with 41 matrix polymers solidify into an amorphous state (Hatakeyama & Hatakeyama, 1998). By heating, 42 amorphous ice associated with matrix become mobile. The free molecular motion commences in 43 gelatin gels with amorphous ice, which is detected as T g in heating DSC curves. A broad 44 exothermic deviation is observed in samples containing a small amount of water (Fig. 18A, curves  1 a-c), which was attributed to the cold crystallization. Water molecules solidified in an amorphous 2 state are mobilized at T g on heating, and molecular motion is enhanced by successive heating and 3 reorganised as unstable ice just before melting. This is confirmed by the fact that the exotherm 4 disappeared if the sample is annealed at a temperature lower than melting. This suggests that cold 5 crystallization can be observed for thermally unstable samples prepared by quenching 6 (Hatakeyama & Hatakeyama, 1998). 7

The phase transition temperatures of gel are shown as a function of water content W c in Fig.  8 19B. The water content W c is defined as W c (g/g) = W w /W s (g/g), where W w is the weight of water 9

in the system, and W s is that of completely dried sample. At water content range higher than W c = 10 0.78 (a water content between curves a and b in Fig. 19A ), movement of gelatin molecules is 11 restricted by the presence of ice, and on this account, T g shifted to higher temperatures with 12 increasing water content. It was difficult to obtain a complete dissolution for gelatin solutions 13 above 60% (Molar mass of gelatin was 11000 Da and the isoelectric point was 6.7). However, T g 14 water, they also might have found the shift of T g to higher temperatures with increasing water 28 content above a certain W c . It is well known that T g of a polymer shifts to lower temperatures by 29 the addition of a plasticiser (Cowie & Arrighi, 2007). T g shifted to lower temperatures with 30 decreasing gelatin concentration, i.e. with increasing water content below W c =0.78, since water 31 molecules play a role of plasticiser. It is also well known that T g shifts to higher temperatures in 32 the presence of a large amount of water, because in such a case the whole system cannot be 33 converted to glassy state, but some ice crystals are formed, and they inhibit the molecular motion 34 of polymer chains (Hatakeyama & Hatakeyama, 1998). The glass-transition temperature T g of 35 gelatin gels as a function of gelatin concentration, therefore, showed a minimum around gelatin 36 concentration 56% (W c = 0.78) (Fig. 19B) . 37

This phenomenon which shows the minimum of T g as a function of water content is widely 38 observed in many polysaccharides-water systems. The relation between W c and the temperature 39 T g,min at which T g becomes minimum is shown in Fig.19C for gellan (closed circle),xanthan gum, 40 cellulose sulphate, alginic acid, carboxymethylcellulose, hyaluronic acid (Hatakeyama, Nakamura, 41

Takahashi & Hatakeyama, 1999). The glass-transition temperature T g and the melting temperature T m of 40% gelatin gels containing 2 sugars (deoxyribose, ribose, glucose, sucrose, raffinose, maltotriose, maltotetraose, α-cyclodextrin, 3 maltohexaose) or polyols (ethylene glycol, propylene glycol, glycerin) with different 4 concentrations as a function of molecular weight of sugars or polyols is shown in Fig. 19D . T g 5

shifted to higher temperatures with increasing molecular weight of sugars or polyols added, and it 6 ranged from 165 to 190 K. T m also shifted to higher temperatures with increasing molecular 7 weight of sugars or polyols added, but it ranged from 268 to 273 K, and the shift was not so 8 pronounced in comparison to that for T g . It is reasonable to see that T g was lowered by adding 9

higher sugar or polyol. However, the efficiency as a plasticizer of each sugar or polyol to lower 10 the glass transition temperature is reduced with increasing molar mass of sugar because their 11 glass transition temperature is higher than that of water (-135℃ = 138K), and their unfrozen water 12 content per unit mass is also increasing with molar mass (Levine & Slade, 1987) . In addition, the 

Edible films made from polysaccharides, proteins, lipids, or the combination, are used to 23 protect foods from contamination of harmful microorganism and oxidation, and also used as are water vapor permeability (WVP) and oxygen permeability (OP). These parameters are known 28 to be influenced by molar mass, plasticizer, film production methods including casting, extruding, 29 temperature control, and drying rate. There have been not so many papers reporting the effect of 30 molar mass. In contrast, many papers report the effects of plasticisers, methods of production of 31 films without controlling the molar mass. 32

Chitosan films are widely used in food and pharmaceutical industry. Chitosan (CH) is a cationic 33 polysaccharide composed of randomly distributed (1,4)-linked 2-amino-2-deoxy-β-D-glucose 34 units, and is obtained by deacetylation of chitin (Rinaudo, 2006) . As expected, TS of chitosan 35 films prepared from chitosan solutions with different solvents, acetic acid, citric acid, lactic acid, 36 and malic acid, all increased with increasing molar mass, while EB also showed the same 37 tendency except the film prepared using citric acid. The EB of films prepared from citric acid was found that WVP was not influenced significantly by the molar mass of chitosan. They also found 40 that OP of films prepared with malic acid was the lowest, followed by acetic, lactic, and citric 41

More recently, films of CH with three different molar masses (110 kDa, 50 kDa and 7 kDa) 43

and with approximately the same degree of deacetylation 85.5%) were prepared with and without 44 glycerol as a plasticiser to see the effect of molar mass (Liu, Yuan, Duan, Li, Hu, Liu et al., 2020). 45

As expected TS and EB increased with increasing MW in all the films with different glycerol 1 contents. WVP and OP decreased with increasing MW. They further applied these CH films for 2 packaging fresh strawberries. They found the weight loss was reduced and the colour was 3 maintained by CH films, and in addition by virtue of antibacterial properties of CH, thus it was 4 useful to extend the shelf life. They found that the film with high MW (110kDa), high CH content 5 and 50% glycerol/chitosan (w/w) showed the best performance among 27 types of films with 6 different CH and glycerol contents 7

The effect of molar mass of chitosan on the film properties of chitosan (CH) -corn starch (CS) 8 composite (50:50 mixing ratio) was studied using low, medium and high molecular weight (LMW, with HMM CH is approximately the same to that of HMW CS alone (Fig 19A) , values of WVP 15

for the CS/CH blend film with LMW CH and MMW CH were significantly lower than those for 16 LMW CH and MMW CH alone. This was interpreted as follows: The developed interactions 17 between CH and CS, mainly hydrogen bonding type, reduced the hydrophilic groups availability 18 of chitosan matrices, leading to a reduction in water vapor transmission rate. More recently, effects of molar mass on blend films of galactomannan and κ-carrageenan were 23 studied using partially hydrolysed galactomannans (Rodriguez-Canto, Cerqueira, Chel-Guerrero, 24

Pastrana, & Aguilar-Vega, 2020). From a widely accepted view that the film strength may 25 decrease with decreasing molar mass, it seems to be of no use to lower the molar mass, however, 26 the molar mass reduction leads to lower the viscosity of the solution, which is advantageous for 27 fluid transportation by pumping to lower the energy cost and also for spray drying coating (Garcia, (60:40 weight % mixing ratio). While TS was increased by mixing DRGM hydrolysate with 38 κ-carrageenan and the composite with LWWH shows the lowest TS, this composite showed the 39 lowest WVP (Fig.20B) , which was attributed to a more compact molecular arrangement with 40 physical bonding interactions, such as higher hydrogen bonding, in the structure of the films as a 41

consequence of galactomannan shorter chain length (Rodriguez-Canto et al, 2020). This is the 42 opposite tendency as described above for CC/CH film where the longer chain CH was believed to 43 make the structure more compact. The finding that TS of the composite of κ-carrageenan with 44 HMWH was lower than that of κ-carrageenan with MMWH was interpreted that the molar mass 45 above MWWH was higher than the limiting value of the molar mass above which no increase of 1 mechanical strength was observed. As was widely known, the mechanical strength of solid 2 polymers is not increased with increasing molar mass above a certain limiting value of molar mass 3 while EB decreased with increasing molar mass of PEG. It was also found that the higher MW 22 PEG (>800) showed higher WVP, and the authors concluded that lower MW PEG were more 23 effective to decrease the moisture transfer between the food and the surrounding atmosphere. 24

As described above, some contradictions among previous papers about the molar mass effects 25 on the film properties, TS, EB, and WVP, have been found, and these should be clarified to 26 develop further application of films. More systematic study should be done for polysaccharides 27 and proteins to get more basic knowledge to develop further the utilization of polysaccharide and 28 protein films. Film thickness, plasticizers, deformation rate, production method, all these affect the 29 film characteristics. Not only trial and error approach but also more systematic study to make 30 films are expected in future. 31 32

Interaction of polysaccharide and protein has been studied by many research groups because of 35 DSC curves of κ-car during cooling at different mixing ratio r= β-lg/κ-car were not influenced by 42 the addition of β-lg at higher pH than the isoelectric point (IEP) of β-lg (pH =5.2) where no 43 electrostatic complexation occurs. On the other hand, at lower pH=4.7, the DSC exothermic peak 44 on cooling accompanying the conformational and gelling transition of κ-car was suppressed with 1 increasing mixing ratio r= β-lg/κ-car. It was suggested that β-lg/κ-car forms soluble complexes on 2 cooling at low r, but insoluble complexes are formed at high r. Relative extent of conformational 3 transition of κcar φ (r) was defined as a ratio of DSC enthalpy change ∆H (r) for the mixture 4 with mixing ratio r to that of κ-car without addition of β-lg ∆H(0) : φ (r)=∆H(r) /∆H(0). The 5 extent φ (r) as a function of β-lg/κ-car mixing ratio r at different pHs decreased more steeply at 6 lower pH below φ = 0.93 (Fig.21B ). This decrease of φ (r) as a function of r was analyzed more 7

quantitatively by using McGhee-von Hippel (1974) theory which was used to understand the 8 binding of protein to DNA. The number of binding sites consecutively occupied by one protein 9 molecule to κcar and the binding constant were found to increase with decreasing pH. In addition 10

to DSC results, the number of binding sites consecutively occupied by one protein molecule to κ-11 car and the binding constant determined from ITC measurement also showed a good agreement 12 with the results from DSC. This inhibitive effects of β-lg on the helix formation and gelation of 13 κ-car were further studied by using β-lg hydrolysates with different molar masses. It was found and gelation temperature shifted to higher temperatures on cooling by the addition of glucose or 29 mannose. On heating the gellan gum gels containing glucose or mannose after cooling, the storage 30 modulus began to decrease accompanying the gel to sol transition at a certain temperature, and 31 this temperature shifted to higher temperatures with increasing concentration of added glucose or 32 mannose. As shown in the previous section 4.1. Effect of molar mass of β-lactoglobulin hydrolysates on the 37 gelation of κ-carrageenan, lysine and S3 (lower molar mass (<1000 Da) hydrolysate of β-lg) 38 enhanced the gelation of κ-carrageenan but β-lg and its higher molar mass (>2000 Da) hydrolysate 39 inhibited the gelation of κ-carrageenan. Since these two gel-promotion or gel-inhibition 40 phenomena show a common effect, there may be a boundary molar mass for KGM and its 41 hydrolysate above which the inhibition by adding KGM and below which the promotion by 42 adding KGM hydrolysate occurs. Although the promotion of gelation and the increase in the 43 elastic modulus of resulted gels by the addition of a monosaccharide and disaccharide for agarose, 44 κ-carrageenan, or gellan is well documented (Nishinari and Fang, 2016), the mechanism whether 45 it is due to the increase in the effective concentration of polymers by the hydration of a 1 monosaccharide and disaccharide or it is due to the direct binding of residue in the polymer with 2 the hydroxyl group in a monosaccharide and disaccharide is still a matter of debate (see Stenner, 3

Matubayasi, & Shimizu, 2016). 4 5

Since starch is an important ingredient of many cereals, tubers, pulses and other crops and an 8 important energy source, and used to control texture of many processed foods, its gelatinization amylose. These NSPs increased the effective concentration of starch and RVA peak viscosity, but 38 never led to gel formation judging from small deformation oscillatory measurements, G' < G" and 39 tan δ was increased. These NSPs accelerated the short term retrogradation but retarded the long 40 term retrogradation. 41

Since the interaction between NSP and starch depends on the molar mass of NSP, 42 amylose/amylopectin ratio and the concentration of starch, it is necessary to compare the effects of 43 NSP with different molar masses using different starches with different amylose/amylopectin 44 ratios to understand better the mechanism. Funami, Kataoka, Omoto, Goto, Asai, & Nishinari 1 (2005b), using guar gums with eight different molar masses (g/mol) (G1 = 34.6 ×10 5 , G2 = 34.5 2 ×10 5 , G3 = 20.1 ×10 5 , G4 = 16.5 ×10 5 , G5 = 12.2 ×10 5 , G6 = 10.1 ×10 5 , G7 = 4.7 ×10 5 , 3 G8 = 0.02 ×10 5 ), and three maize starch samples with different amylose contents 50 %, 26 % 4 and 14 % prepared by mixing high amylose maize (61.9% amylose), normal maize (26.2% 5 amylose) and waxy maize (1.4% amylose), studied the effect of molar mass employing the same 6 methods as mentioned above. For the 5% and 15 normal maize, the addition of 0.5% guar gum 7 increased the RVA peak viscosity and setback values (with some exceptions), and this increase 8 was found more pronounced with increasing molar mass of guar gum. The onset of the viscosity 9

increase on heating was shifted to lower temperatures with increasing molar mass of guar gum 10 which was thought to interact with amylose, and the increasing of the RVA peak viscosity was 11 attributed to the interaction between guar and amylopectin. 12

It was shown that the short term retrogradation was retarded by the addition of 0.5% guar gum 13 to 5% maize starch, which was suggested by the increase of the loss tangent as a function of molar 14 mass, and this retarding effect was shown to be correlated with the decreasing leached amylose. 15

This leached amylose in starch-guar system was found to decrease with RVA peak viscosity 16 values (Funami, Kataoka, Omoto, Goto, Asai, & Nishinari (2005c). For the longer term 17 retrogradation, higher molar mass guar G3 and G6 were effective to retard the retrogradation in 18 higher amylose 5% starch (50% amylose) than in low amylose starch (26% amylose), which 19

indicated that high molar mass guar suppress effectively the gelation of amylose until 5 days. For 20 a higher starch concentration (15% maize starch), the rate constant k of retrogradation kinetic 21

the rate constant) was found to decrease with increasing molar mass of the added guar gum (0.5%) 23

for higher molar mass than 10.1 ×10 5 (G6), however, the lower molar mass guar gum, G7 and 24

G8 were found to promote the retrogradation ( Fig 23A) . Syneresis for 5% normal starch was quantified with and without guar (0.5%) (Fig. 23B ). For 31 the control, syneresis was estimated to be 13.4 ± 1.5 and 30.6 ± 0.5% after storage at 4 ℃ for 7 and 32 after freeze-thawing, and reported that syneresis was increased with increasing cycle of 2 freeze-thawing and that pectin reduced the syneresis. However, in this experiment the lower MW 3 pectin was more effective to reduce the syneresis, which is opposite in the result for maize-guar 4 system shown in Fig.23B . Whether this contradiction is due to the difference in the syneresis 5 observed in the starch stored at 4 ℃ and that subjected to freeze-thawing is not clear, and should 6 be studied further. 7

Corn fibre gum (CFG) has been attracting much attention because of its adhesive, thickening, properties of rice flour mixed with native β-glucan and with partially hydrolysed β-glucan, and 29

found that the RVA peak viscosity decreased by adding β-glucan, and the extent of the decrease 30 was more pronounced by the addition of hydrolysed β-glucan. Dangi, Yadav, & Yadav (2019b) 31

reported that the RVA peak viscosity for barley starch decreased by adding lower MW pectin 32 (pectin hydrolysate) but the peak viscosity was higher when native pectin (high MW) was added. 33

Dangi, Yadav, & Yadav (2019a) reported that the RVA peak viscosity for pearl millet starch 34 increased by adding even lower MW guar (guar hydrolysate), and the peak viscosity was higher 35 when high MW guar was added. This was also reported for wheat starch-arabinoxylan system 36 (Hou, Zhao, Tian, Zhou, Yang, Gu, et al., 2020). The RVA peak viscosity in the gelatinization of 37 wheat starch during heating was found to be suppressed by the presence of arabinoxylan (AX), 38

and this effect was more pronounced for lower molar mass AX. It was interpreted by the insertion 39 of lower molar mass AX in the molecular chain of amylose which limit the formation of double 40

helices. This interpretation was based on the lowering of the enthalpy of amylose -lipid complex 41 formation and melting on cooling and heating DSC, and this decrease was more pronounced in the 42 presence of lower molar mass AX. Although the amylose -lipid complex formation has been 43 studied extensively by X-ray diffraction, NMR, and other methods, the insertion of short 44 polysaccharide chains have not been studied, and should be studied further. As for the RVA peak 1 viscosity, non-starch polysaccharides inhibit the gelatinization and decreased the value, but 2 opposite tendency was also found. Whether the increase in the peak viscosity by the addition of 3 non-starch polysaccharide is due to its own high viscosity or not should be clarified 4

The so-called setback values of RVA were not consistent among literatures probably because 6 of its structure break down nature in the measurement as pointed out in Chantaro, Pongsawatmanit 7 & Nishinari (2013). In addition to molar mas effect, the structural complexity of starch, the chain length 24 distribution of amylose and amylopectin, degree of branching, and the mixing ratio and 25 concentration effect also influence the gelatinisation and retrogradation. It is not easy to 26 examine all these aspects in one laboratory, and the collaborative research is required. 27 28

Gluten network determines the dough rheology, and thus governs the quality of bread. It has 30 been generally accepted that glutenin contributes to the elasticity and gliadin is for the viscosity, 491kDa) and F60 (MW= 454 kDa). They found that the added WEAX reduced the heat-induced 8 polymerisation of gluten, and this reduction rate was more pronounced for the lower molar mass 9 fraction F60. Since the loaf volume was found to decrease with increasing heat-induced 10 polymerisation of gluten, it was suggested that the lower molar mass fraction F60 was more 11

suitable for the production of steamed bread. However, they also stated that excessive inhibition of 12 gluten polymerisation resulted in the weakened gas retention capacity and thus the loaf volume 13

could not be increased. In addition, the two fractions are different not only in molar mass but also 14 in ferulic acid content, and monosaccharide (especially arabinose and mannose), more detailed 15 study is required to understand the mechanism. 16 17

When two polymer solutions are mixed, phase separations due to thermodynamic 19 incompatibility or synergistic interaction due to weak secondary molecular forces occur. Phase fractionation for higher molar mass GA (EM10) with MW of 4.07× 10 6 g/mol and a polydispersity 30 index (M w /M n ) of 8.0 than for lower molar mass STD (standard gum arabic) with 0.55 × 10 6 g/mol 31 and 2.5. In the phase separation induced fractionation of gum arabic /hyaluronan mixed systems at 32 a fixed HA concentration of 0.25%, the AGP content was found to increase from 34% to 55% 33 when the EM10 concentration was decreased from 5% to 2.5%. The AGP content of standard gum 34 arabic also increased from 11% to 18% when the concentration of STD was decreased from 10% 35 to 5%. The extent of increase in AGP content was much more significant for EM10/HA system 36 than STD/HA system. This is in line with the previous findings that the fraction of higher 37 molecular weight tends to segregate while the lower molecular weight fraction has relatively 38 Biopolymer are also used for stabilising dispersed particles or emulsion droplets by forming a 9 steric stabilising layer, and higher molar mass biopolymers are more effective to make a thicker Selenium is an essential micronutrient although it is toxic in large doses. Its deficiency is 20 believed to cause some diseases such as Kashin-Beck disease, and thus selenium nanoparticles 21 (SeNPs) were prepared by the stabilisation of gum arabic (Kong, Yang, Zhang, Fang, Nishinari, & 22

Phillips, 2014). SeNPs are not stable without any dispersant and show aggregation. Chitosan was 23 found effective to stabilise the SeNPs (Son, Chen, Zhao, Sun, Che & Leng, 2020), which will be 24 discussed later. GA was found effective to stabilise SeNPs, and SeNPs (particle size of 34.9 nm) 25 were found to be stabilised in gum arabic aqueous solutions for ca. 30 days (Fig.27B) . The 26 alkali-hydrolysed GA (AHGA) was also prepared and its efficiency in stabilising SeNPs was 27 found to be less effective than GA. It was concluded that the branched structure of GA as well as 28 molar mass were important for the stabilisation. It was also found that hydroxyl radical scavenging 29 ability and 2, 2-diphenyl-1-picrylhydrazyl (DPPH) scavenging ability of GA-SeNPs were found 30 higher than those of AHGA-SeNPs. 31 32 AGP thus the emulsification ability of ASY was enhanced. ASY modified in this way contained a 40 two-fold AGP content and 3.5 times higher average molar mass, and ASY-stabilised emulsions 41

were found resistant against severe conditions, such as high saline or low pH conditions (Fig.27C) . 42

More recently, in the study of the stability of emulsions stabilised by conjugates prepared by 43

Maillard reaction between whey protein hydrolysates and linear dextrin with three DPs (24, 48, 44 65), the highest stability was found for the emulsion prepared with the linear dextrin with the 1 highest DP, which conferred the highest steric hindrance ( chain to the hydrophilic sodium alginate chain, and prepared Ugi-Alg with three different molar 7 masses (685 kDa, 307 kDa and 48 kDa). It was found that this amphiphilic Ugi-Alg formed 8 self-assembled micelles, and the critical aggregation concentration was lowest for the highest 9 molar mass Ugi-Alg, and this micelle with higher molar mass Ugi-Alg formed a more compact 10 and stable micelle. It was also found that emulsions of soybean oil/water and styrene/water were 11 stabilised better by higher molar mass than lower molar mass Ugi-Alg, which were proposed to be 12 used as a drug delivery based on a model experiment of curcumin release. It is expected that the 13 study on the safety of this kind of hydrophobically modified polysaccharides in food use will be 14 clarified in the near future 15

Maltodextrin is often used with a small molecule emulsifier to stabilise the emulsion. Anti-tumour activity of β-(1→3)glucans such as schizophyllan, lentinan, grifolan, and others 11 have been studied extensively. It is well known that schizophyllan (SPG) takes a triple helix 12 conformation in water, and random coil in DMSO or alkaline solvent (Norisuye, 1985) , and it has 13 been used as anti-tumour agent. Tumour inhibition ratio was evaluated by the inhibiting effect of and below that molar mass SPG was found random coil, and examined the molecular weight 26 dependence of the tumour inhibition ratio using Sarcoma 180 ascites for the random-coil and the triple 27 helix species of SPG. They concluded that schizophyllan has anti-tumour activity against Sarcoma 28 180 only when it has a molecular weight higher than 5 x 10 4 and a triple helical structure in 29 aqueous solution (Fig.29) . Zhang, Li, Xu, & Zeng (2005) also reported that the triple helix 30 conformation is necessary for lentinan, also a β-(1→3) glucan having β-(1→6) branching structure 31 as SPG, to show anti-tumour activity, and thus lower molar mass lentinan is not effective. They found that the highest anti-tumour activity for USPG60 which has a lower MW than 41 non-degraded SPG and USPG40 (Fig.30) , which seems to be contradictory to the results shown in 42 decreased below the molar mass of ca 10 6 , and the lower anti-tumour activity found for USPG80 44 than for USPG60 (Fig.30 ) is in accordance with the previous finding shown in Fig. 29 . degraded SPG inhibited the production of NO, but the lower mass SPG was more effective. 9

However, the criteria used to estimate the anti-tumour activity are different in research groups 10 unfortunately, and thus the direct comparison is not possible. This should be further clarified. Saccharomyces cerevisiae had anti-tumour effects in S180 tumour cells, and the effect was found 13 dose dependent but the molar mass of β -glucan was not changed in their experiments. to inhibit the hemolysis was found more pronounced for high MW β -glucan (dotted line) than for 31 low MW one (broken line). 32

All these evidences suggest that the immune response is in part non-specific, determined by and low MW oat β-glucans were found beneficial, but high MW oat β -glucan was proved to be 3 more effective in decreasing stress oxidation in animals with LPS induced enteritis. Low MW oat 4 β -glucan was found more effective in alleviating parameters in animals without administered 5

A similar difference between high and low MW barley β -glucans in the antioxidant activity The molar mass was found in the order of oat (172 kDa), wheat (635 kDa) and barley (743 kDa). 13

The reduction of total cholesterol, triglyceride and malondialdehyde as well as the increase of 14 SOD in the liver by the administration of β -glucans were found more conspicuous with 15 increasing MW. Although the polydispersity in the MW distribution was different in three cereals, 16 the difference in the effectiveness was believed due to mainly the difference in MW. 17 Since it has been demonstrated that molar mass, conformation, chemical modification, and 18 solubility of β -glucans significantly affect their anti -cancer, immune -modulating, and anti -19

inflammatory properties, further studies are necessary to understand the mechanism using better 20 Balazs (1968) reported mechanical spectra for synovial fluids taken for a healthy young adult, 35 and a healthy elderly person and an osteoarthritis (OA) patient. A cross-over frequency at which 36 the storage modulus and loss modulus coincide was found to shift to higher frequencies with 37

increasing age, and no such crossover was found for a synovial fluid from an old person. Similar 38 but more complete data were collected from normal 61 samples and OA 72samples by Kawata, 39

Okamoto, Endo, & Tsukamoto (2000). Kawata et al (2000) showed that the mechanical spectra of 40 an OA patient becomes closer to that of a normal healthy person by adding high molar mass HA 41 (Fig.32C) . 42

Since it was reported that molar mass of HA decreases or the concentration of HA decreases 43 with aging, it is an important therapeutic problem how the rheology changes when short chains 44 (sHA) coexist with long chains HA. If G′ and G of HA are decreased by adding sHA, is it better to 1 remove sHA? Welsh, Rees, Morris, & Madden (1980) reported that the addition of 60 2 disaccharide units drastically changed the mechanical spectra of HA from an entanglement 3 solution behavior in which G′ and G〞show a crossover at ca 3-6 rad/s to a dilute solution 4 behavior in which G′ was smaller than G〞at all the angular frequency range from 0.1 rad/s to 30 5 rad /s and both moduli are strongly frequency dependent ( Fig.32A(a) ). However, Fujii, Kawata, 6

Kobayashi, Okamoto, & Nishinari (1996) found a slight increase of both moduli on adding 50 7 disaccharide units (Fig.32A(b) ). They prepared HA short chains with various chain lengths not includes a chain-length effect, a sugar effect, and a salt effect. Therefore, effects of the addition of 17 sHA were explained in terms of the superposition of these three distinct effects. A shift factor "A" 18 which depends on these three effects was developed to explain these additive effects quantitatively. Bursitis is known to be a common knee pain symptom which is induced by excessive synovial 38 fluids. Effects of injection of high or low molar mass HA to the joint synovial fluid of OA patients 39 were studied, and it was found that higher MW HA decreased some specific protein such as mammary gland branching and 10 kDa HA fragments strongly stimulate branching, but the 15 activity of HA decreases with increasing molecular weight and 500 kDa HA strongly inhibited this 16 morphogenetic process. HA was used as wound healing therapy. Here again, the physiological 17 function is found to depend strongly on molar mass, and high molar mass HA and low molar mass 18

HA were reported to function in opposite directions: while high molar mass HA has already been 19 used in would healing based on its anti-inflammatory and immunosuppressive properties, low 20 molar mass HA was reported to be a potent proinflammatory molecule. 21

Oligo HA, 2-10 disaccharide units, were shown to stimulate endothelial proliferation at a 22 lower concentration than native higher molar mass HA. In addition, the lesion area was found 23 completely recovered when the endothelial layer was exposed to oligo HA for 40 h after injury, 24

while the wound remained half recovered pretreated with native HA at the same condition (Gao, Pseudomonas aeruginosa produces extracellular alginate which interacts with 2 tracheobronchial mucin. Thick and sticky mucus is accumulated. Lung disease results from 3 clogging of the airways due to mucus build-up, decreased mucociliary clearance, and resulting 4

inflammation. This is one of main signs and symptoms of cystic fibrosis. In the pulmonary 5 clearance mechanism, tracheobronchial mucus traps inhaled particles and bacteria, which should 6 be carried away by mucociliary transport. However, Pseudomonas aeruginosa, an opportunistic 7 human pathogen cannot be easily removed by this mechanism. 8

Mucin is known to consist of heavily glycosylated regions and sparingly glycosylated region, 9

and these units are linked by intra-and inter-molecular disulfide bonds (Fuongfuchat, Jamieson, sputum sample from a cystic fibrosis patient after pre-shear (60 s at 20 s -1 ) decreased by the 12 addition of sodium chloride, but much more decreased by guluronate block, GB (degree of 13 polymerisation, Dp20) and by the addition of GB (Dp10) decreased to 1/6 of the control sputum 14 without addition of NaCl or GB (Fig.33 ). 15 16 Fig 33 17 18

Immunogenic response was also reported for high molar mass alginate, which was lost by JAAS8 grew on all GOs up to DP15, K25 grew only on GOs up to DP5, and S52 grew only on 8 GO1. Since they found the different growth rates for each strains, they expect that further study on 9 the molar mass effect will be interesting. 10 11

Ulvan is a sulphated polysaccharide, extracted from green algae Ulva and Entermorpha, 13 mainly composed of rhamnose, xylose, glucose, glucuronic acid, iduronic acid, and sulphate, with increased, which is more beneficial, in comparison with diet for control rats. However, the TC and 27 LDL were rather increased in comparison with control and non-degraded ulvan although the 28 difference was not significant. Since the main difference between non-degraded ulvan and 29 degraded fractions U1, and U2 was the molar mass because the sulphate and uronic content were 30 not so different, the above mentioned physiological difference found in rats fed with the 31 non-degraded ulvan and degraded U1 and U2 samples might be attributed to the molar mass 32 difference. However, it is difficult to find a conclusive mechanism from these data because lower 33 molar mass U2 increased HDL but increased also TC, TG and LDL than in U1 and non-degraded 34 ulvan fed rats. 35 36

Antioxidant activity of carrageenans was found to increase by gamma-irradiated degradation 38 into oligosaccharides (Abad, Relleve, Racadio, Aranilla, & de la Rosa, 2013). Among κ-, ι-, 39 λ-carrageenan samples, κ-carrageenan showed the highest DPPH radical scavenging activity, and 40 this activity was increased with increasing concentration of carrageenan, and with decreasing 41 molar mass. DPPH scavenging activity of carrageenans was found lower than that of ascorbic acid. oligosaccharides prepared by four methods, using free radical depolymerisation, mild acid 4 hydrolysis, κ-carrageenase digestion and partial reductive hydrolysis. As in a previous report 5 (Abad et al, 2013) , they also recognized the importance of the reducing sugar content which 6 increased simultaneously with decreasing molar mass in addition to the sulphate content. 7

Low molecular weight carrageenans were reported to exert anti-tumour effects by promoting the 8 immune system in mice inoculated with S180 tumour cell suspension (Fedorov, Ermakova, 9

Zvyagintseva, & Stonik, 2013). However, as will be discussed below, some negative function such 10 as inducing colitis has been also reported. the induction of colitis in C57BL/6J mice. They found some differences in these three 38 carrageenans, for example, κ-carrageenan seemed to be a promoter for the growth of 39

Helicobacteraceae, while ιand λ-carrageenan appeared to be inhibitors for the growth of this 40 bacterium. They also found that non-fermentable κand ι-carrageenans inhibited the growth of 41 this bacterium Desulfovibrio, probably due to the antibacterial activity of κand ι-carrageenans, 42

while λ-carrageenan promoted the growth of this bacterium. Most importantly, the authors found 43 all κ-, ι-, λ-carrageenans significantly decreased the populations of Akkermansia muciniphila 44 J o u r n a l P r e -p r o o f which is a potent anti-inflammatory commensal bacterium in the gut. Thus, they concluded that 1 this decrease of anti-inflammatory bacterium caused by the intake of carrageenans led to induce 2 the colitis. This is surely an interesting point as the authors stated. Although the pathological 3 analyses were done in detail, unfortunately the detailed information on the molar mass and the 4 sulphate content, which might have some influences on the pathology, were not described. Pretreatments of most of polymeric carrageenans at 250-500 µg/mL were found significantly to 29 increase the TNF-α level, implying the co-inflammatory effects with LPS. The co-inflammatory 30 effectiveness of pure carrageenans at 125 µg/mL was notable for λ-carrageenan, followed by 31 ι-carrageenan, and insignificantly for κcarrageenan. Sulphate content is κcar < ιcar < λcar. 32

This suggested a non-negligible role of sulphate content. Oligo ι-carrageenan and κ-carrageenan 33

were found to decrease TNF-α significantly, and were expected to be anti-inflammatory agents. 34

The authors found that anti-inflammatory effects of carrageenan oligosaccharides in their study 35

were comparable to those found for chitin oligosaccharides at 100-500 µg/mL Ai et al. found the highest activity in F 5-30k , and the reason for the lower activity of the lowest MW F <5k 28 was attributed to the removal of sulphate groups during hydrolysis because they also believed that 29

sulphate played an important role as in previous reports. They also examined the conformation of 30 fucoidan hydrolysates based on the relation between the radius of gyration and the weight average 31 molecular weight obtained from the HPSEC-MALLS measurement. They reported that the highest 32 MW fraction F >30k was compact spherical conformation and the anionic sulphate groups available 33 to bind proteins on the cell surface may be hidden inside the chains while F 5-30k fraction took more 34 loose and entangled conformation allowing sulphate groups in the chain are available to bind the 35 proteins. It was unfortunate that the sulphate content of F 5-30k fraction was higher (ca 35.5%) than 36 the other two fractions F >30k and F <5k , which makes the speculation difficult; which of the two, 37 sulphate content or the conformation, was more influential to the activity. In addition, the 38 monosaccharide composition was reported to be slightly different. It is indeed not so easy to 39 obtain clear-cut sample fractions. They also pointed out that the affinity of heparin to anti-thrombin is so high that in vivo, i.e. in the 32 presence of anti-thrombin, all other activities are considerably weakened due to its binding to 33 anti-thrombin. Then they concluded that their in vitro data were in line with animal experiments 34

showing that the anti-inflammatory activity of fucoidan is superior to that of heparin (Pomin, 35 2015) . 36 37

Bioactive characteristics of a polysaccharide ascophyllan extracted from a brown seaweed 39

Ascophyllum nodosum have been studied extensively. It has similar but distinct structure of experimental concentration (0-200 µg/mL) were found, and rather both these saccharides were 5

shown to promote significantly HSF cell proliferation. Moreover, the promotion of LMWAs-L 6 was more significant than that of native ascophyllan. POA was found to decrease with the lapse of 7 time after 12, 24 and 36 h after treatment by ascophyllan and LMWAs-L, and the decrease was 8 more pronounced when treated by LMWAs-L than by native ascophyllan (Fig. 34) . Although the 9 detailed mechanism for the difference of effectiveness between a high and low MW 10 polysaccharides was not elucidated, the authors interpreted as follows: Since the molecular size of 11

LMWAs-L is much lower than that of native ascophyllan, the molar concentration of LMWAs-L 12

should be much higher than those of native ascophyllan under the same mass concentration 13

conditions. Therefore, the higher molar concentration of LMWAs-L than ascophyllan can 14 effectively and sufficiently bind with some receptors on the cell-surface of HSF cells, which 15 promotes the migration of HSF cells. 16 17 Fig. 34 18 19 The authors further examined the antibacterial activity using a gram-positive bacteria 20

LMWAs-L were found to inhibit the growth of these bacteria, and the effect was found more concentration up to 50 µg/mL but HP with highest sulphate content decreased the activity above 5 that concentrations, which was attributed to negative impact of HP on cell viability at higher 6 concentrations (Song et al, 2018) . This negative effect of HP was in good agreement with a 7 previous study (Peschel et al., 2012) . It was believed that higher sulphate contents as well as 16 Konjac glucomannan has been traditionally used in Asian countries, and many papers on its 17 texture modifying function, physiologically beneficial function such as prebiotics, lowering assay and superoxide radical assay showed that the scavenging activity of these mucilages were 6 increased with increasing concentration and with decreasing molar mass. Anti-mutagenic activities 7

showed the same order as in antioxidant activities although authors were not sure for the 8 mechanism of these beneficial functions. Although body weights of mice did not decrease significantly by the administration of NPs, the 4 tumour volume and weight were reduced significantly (Fig.35) . Therefore, the authors concluded 5 that CS-Se 0 NPs have promising anti-tumour activity with less side effects, and the higher molar 6 mass CS (600 kDa) was more effective. 7 8

Since it was clarified that the highest MW chitosan among several MW chitosans (< 3kDa, 3 kDa, 11 65 kDa, 200 kDa, and 600 kDa) showed the highest performance, it is expected in the future to be 12 clarified whether higher molar mass chitosan (> 600kDa) or a chitosan with MW in between 200 13 kDa and 600 kDa shows a stronger bioactivity or not. 14 15

Sporotrichosis is a zoonotic mycosis, caused by species belonging to the S. schenckii complex, 

Digestion is the breakdown process of food substances to small molecules which can be 31 absorbed. Digestion begins from the oral processing, and then digestive organs which secrete 32 digestive enzymes. Carbohydrates are decomposed into monosaccharides, proteins are into amino 33 acids and fats are into fatty acids and glycerol, monoacylglycerol. Food digestion process consists 34 of physical process and chemical process. Physical process is the breakdown foods from the larger 35 size food to smaller size, increasing the surface area thus more susceptible to digestive enzymes. 36

Chemical process is the catalytic reaction which breakdowns food fragments into molecular length 37 scales and further into structural elements, monosaccharides, amino acids and fatty acids and 38 glycerol, which are ready to be absorbed at intestines. Food processing and cooking improve the 39 palatability and facilitate the enzymatic reaction. Gelatinized starch, denatured proteins, and 40 emulsified lipids are more susceptible for enzymatic reaction. 41

While in vivo test is required finally to understand the digestion and absorption of foods, in 42 vitro test has many advantages, rapid, less expensive, reproducible, easy sampling, free from the 43 individual differences, and therefore is suitable for screening better candidates from many samples, 44 and in addition it is possible to compare the results obtained in different laboratories. Thus, the 1 international protocol for the digestion study was proposed (Minekus, Alminger, Alvito, Ballance, Dietary fibre has been studied more than 50 years for its beneficial effects on health, but its 44 definition has been a matter of debate. After Codex Alimentarius issued the definition of dietary 1 fibre in 2009: Dietary fibre is carbohydrate polymers that are not digested in the small intestine of 2 humans and categorised into the following three materials 1) edible carbohydrate polymers 3 naturally occurring in the food; 2) carbohydrate polymers, which have been obtained from food 4 raw material by physical, enzymatic, or chemical means; and 3) synthetic carbohydrate polymers 5 (Jones, 2013). In the early stage of the discussion, oligosaccharides with degree of polymerisation 6 DP <10 were excluded, but now these are also included if these are not hydrolysed in the small 7 intestine and fermented in the large intestine (Jones, 2013). 8

The importance of glycemic index (GI ) as a valid and reproducible method of classifying 9 carbohydrate foods was confirmed and there was consensus that diets low in GI and glycemic load 10 In contrast, the rate of amylolytic hydrolysis of maize starch were not so much influenced by 1 granular sizes of maize starch; larger granules (> 20 µm) compared with smaller granules (< 10 2 µm) were hydrolysed almost at the same rate. This similarity in hydrolysis extent was explained 3 by the structural difference in large and small granules: there are surface pores and channels in 4 maize starch granules that can dramatically increase the available surface area for amylase 5 catalysed hydrolysis while there are no such pores, channels and cavity in potato starch (Dhital et  6 al., 2017). The same research group compared the starch hydrolysis of barley and sorghum, and 7

found that the hydrolysis of barley was faster than sorghum for the similar grain fragment sizes. It 8 was interpreted that more coexisting protein bodies/matrices in sorghum hinder the amylase 9

accessibility toward the starch granules. The hydrolysis extent was found negatively correlated 10 with particle size, as milling to smaller fragments can break down the cell wall and protein 11 matrices increasing the accessibility of amylases towards the starch granules (Dhital et al., 2017).

As was described for the rennet gelation of casein micelles with different micelle sizes (3.7 Molar 13 mass effect in protein gelation), the gelation was governed by not simply the micelles sizes but 14

was influenced by the microstructural difference.

It is now widely recognised that postprandial increase of GI is lower in the slowly digestible concluded that starch samples with higher amounts of amylose short-medium chains and relatively 30

shorter amylose medium chains showed slower digestion, which they attributed to the denser 31 small cells forming the gel matrix, limiting its susceptibility to digestion enzymes (Fig.38 ). Since 32 amylopectin is digested faster, and was not found to decrease in the digestion rate. 33 pectin. This increase was found more pronounced in the presence of pectin and its effect was more 13 conspicuous for higher molar mass pectin, which was consistent with the relative crystallinity 14 estimated by X-ray diffraction; starch in the presence of higher MW pectin showed a higher 15 relative crystallinity. However, the relative crystallinity was found lower in the starch with pectins 16 than in starch alone. Although it is believed that the higher crystalline starch was believed to be 17 slowly or hardly digested than less crystalline starch, this was found not to be the case in this study, 18

and should be studied further. β-glucan viscoelastic gels containing low MW β-glucan 4LG (▲) was not found effective to 27 reduce the blood glucose rise. It is clear that the higher MW is effective to lower the blood glucose, 28 and it is lost when it is in a gel state. To see what is the key factor of the dietary fibre which lowers glycemic index, two solutions 33 of xyloglucan with high and low molar masses but with approximately the same steady shear 34 viscosity at a lower shear rate 0.5 s -1 were ingested by nine healthy male subjects. The blood was 35 taken every 30 min up to 120 min after the ingestion of the mixed solution of glucose and 36 xyloglucan. The rise of blood glucose was blunted by ingesting both solutions of xyloglucan with 37 high and low molar masses, and the effect of the solution of higher molar mass xyloglucan was 38 slightly higher (Fig.39B) , which was in line with the previous report that the lowering effect was 39 mainly governed by the product of the peak value of molar mass and the concentration of the 1978) asserting that the high viscosity is the determining factor because the polymer solution 45 viscosity is higher when the molar mass is high at the fixed concentration as shown in Fig.3 in 1

Although more detailed studies are required to get a clearer insight on the mechanism of the 3 blood-glucose-lowering-effect of xyloglucan, the results exclude an explanation that attributes this 4 lowering effect to the binding of glucose with dietary fibre xyloglucan which are expelled out 5 from the body without being absorbed. If this explanation is valid, the Xyloglucan B sample 6 would have shown a greater effect, which was not the case. 7

In the intervention study on health benefit of dietary fibres, baseline diet, mode of feeding (e.g., 8

whether fed alone or with meals, as a single bolus in a liquid or added to foods), the total dose, 9

characteristics of the subjects, and other important study conditions should be taken into account 10 (Jones, 2013). Although an intervention study such as glucose intake is useful to assess the acute 11 glycemic effects, long-term (multimonth) data from well-controlled intervention clinical studies 12 are necessary to establish a clinically meaningful health benefit for improved glycemic control Although the molar mass seems to be the key factor to determine the activities, slight 38 difference in monosaccharide composition or linkage patterns may inhibit the comparison or 39 not is expected to be clarified. The authors submitted another paper before these two reports BBP-24 ( MW=177 KDa), and noticed that primary structure was retained. A slight increase of 7 reducing sugar with decreasing MW may have some effect, which also was noticed in the 8 degradation performed to improve the bioactivity in other polysaccharides. Fig.40 shows the IC 50 9

(the concentration of the polysaccharide required to inhibit 50% of the α-glucosidase activity) of 10 BBP, BBP-8, BBP-16, BBP-24, together with acarbose, an α-glucosidase inhibitor, widely used 11 for diabetes treatment. 

Digestion of lipids dispersed as oil droplets in foods has been studied actively and as 25 Wood believed that the high viscosity of β-glucan in the gut is the governing factor to lower 42 the cholesterol (Tosh, 2013). His group obtained β-glucan from various cereals, oat, barley, wheat 43 flour and wheat bran. LDL cholesterol was significantly lowered in the subjects who were given 44 high molar mass β-glucan cereals, and low molar massβ-glucan was not effective. They 1 concluded that intake of 3 g of oat β-glucan/d with a high molar mass (2.21 ×10 6 g/mol) or a 2 medium molar mass (0.53 ×10 6 g/mol) lowered LDL cholesterol, but a lower molar mass (0.21 3 ×10 6 g/mol) β-glucan was less effective (Wolever, Tosh, Gibbs, & Brand-Miller, 2010). They 4 recognized that the viscosity is a very important criterion for lowering the LDL cholesterol as was 5 asserted (P = 0.001), and concluded that log(MW × C) was a significant determinant of LDL 6 cholesterol (P = 0.003) by analysis of covariance (Fig.41A) . They also noticed that treatment 7 effects were not significantly influenced by age, sex, study centre, or baseline LDL cholesterol. 8

The ineffectiveness of low molar mass β-glucan to lower LDL cholesterol was confirmed later 9

(Hu, Sheng, Li, Liu, Zheng & Chen, 2015) 10 11 Effects of molar mass of β-glucan added to canola oil emulsion on the lipolysis were recently 28 studied (Zhai, Gunness & Gidley, 2020). As has been reported, the lipolysis of emulsion foods is 29 influenced by mixing methods and emulsifier types. Non-food emulsifier Triton X-100 was used 30 because the initial droplet shape using this emulsifier was more uniform than that using WPI or 10wt% rapeseed oil, four of which were heated at 80 ℃ to gel. They found that the proteolysis in 42 gastric phase (pH 3) was faster in a liquid food at the initial stage but at later (120min), more 43 proteins were digested, and in addition, they found the similar tendency also in the intestinal phase. This was explained by the higher susceptibility of heat-denatured whey protein than native whey 1 protein. They found it was consistent with in vivo study in which a higher protein content was 2 found in the caecum for the liquid-food-fed-rats than for the solid-food-fed-rats. The degree of 3 lipid hydrolysis in the intestinal phase (pH7) is shown for four different food models, Liquid Fine 4

Coarse Emulsion with a modified o/w interface (GCEi) in Fig.43 . 2.0 wt% guar gum solution stirred at room temperature for 10 h, then heated at 75°C for 1 h. 6

Sample 2 (G2), 2.6 wt% guar gum solution stirred at room temperature for 10 h, then heated at 7 75°C for 1 h and sterilized at 121°C for 20 min. Sample 3 (X2), 4.1 wt% xanthan solution stirred 8 at room temperature for 10 h, then heated at 75°C for 1 h and sterilized at 121°C for 20 min. All 9

these solutions contain X-ray contrast medium which was affirmed to be non-toxic for lung. The 10 order of the magnitude of the viscosity at higher shear rates and that at lower shear rates is 11 opposite: η (X2) > η (G1) > η (G2) at lower shear rate but η (X2) < η (G1) < η (G2) at higher shear 12 rates. Thirty-two observations were analyzed, and it was found that the incidence of aspiration was 13 4 for X2, 5 for G1 and 7 for G2. The experimental observation that a higher molar mass guar G1 14 showed more shear thinning than a lower molar mass G2 is consistent with widely observed 15 behaviour for water-soluble polymer solutions (See Fig.3 ). 16 17 Thus, there is a general tendency that the viscosity at lower shear rate seems to be more 26 important rather than that at 50 s -1 or higher shear rate. The probability of the aspiration seems to 27 decrease with increasing the viscosity at lower shear rate (Table 2 ). Since the number of 28 observation is not sufficiently high, this supposition should be confirmed with larger number of 29 data in the future. It should be mentioned here that when the concentration of guar gum was higher 30 to increase the viscosity at lower shear rates, panellists found the difficulty to swallow. Therefore, 31

solutions of the guar gum with lower molar mass which is less shear thinning than xanthan 32 solutions seem to be not suitable as a thickening agent to lower the risk of aspiration. On the other 33 hand, shear thinning solutions were generally evaluated easy to swallow. 34

Extensional rheology has been studied in dysphagia because the bolus is believed to be 35 subjected to extensional flow when bolus is squeezed between the tongue and the palate and also 36 in the subsequent pharyngeal phase in swallowing process. In addition, both bolus elasticity and 37 its cohesiveness of bolus were found to be important for dysphagia treatment, and the extensional 38 The rate of aspiration 4 /32 (▲X2) < 5 /32 (■G1) < 7 /32 (•G2) Table 2 The relation between the viscosity at lower shear rates and the rate of aspiration (Nishinari et al., 2011) palatability and the subsequent reduction of liquid intake, leading to dehydration and malnutrition, 1 the optimum thickening level should be identified. At the same time, apart from its viscosity, the 2 bolus cohesiveness is another key factor which influences the aspiration. The cohesiveness is 3 shown to be highly correlated with the extensibility which can be characterized by the break-up It is generally known that oligosaccharides with higher degree of polymerization (DP) and 21

polysaccharides donot give sweet taste, but it is also empirically known that when starch is 22

masticated for a long time in the mouth, it gives some sweetness sensation as mentioned earlier.

To understand this problem more quantitatively, it is necessary to notice that carbohydrates have test in which subjects are asked to discriminate 3 samples including blank stimuli containing 29 tasteless methylcellulose to balance the viscosity, they found that subjects discriminated S1 and S2 30 but not S3. They noticed that the detectability of the average DP 7 was higher than that of the 31 average DP 14 at both 6% and 8% concentrations. They concluded that humans can perceive the 32 taste of α-glucan with DP up to 14 but below 44, and the upper limit is still not known (Lapis, 33

Penner & Lim, 2014; 2016). They further examined the discriminability of 3 34 maltooligosaccharides, DP 3-4, DP 5-6, DP 6-7 together with glucose (DP1), maltose (DP2) and 35 maltotriose (DP3) in the presence and absence of sweetness inhibitor lactisole (Fig.46) . All six stimuli were perceived, and the discriminability (d′) among all six stimuli was not 40

significantly different in the absence of lactisole, but in the presence of lactisole it was found that 41 glucose (DP 1), maltose (DP 2) and maltotriose (DP3) were not discriminated because their 42 sweetness was suppressed, while 3 maltooligosaccharides, DP 3-4, DP 5-6, DP 6-7 were detected 43

indicating that these maltooligosaccharides were discriminated. These results led these authors to 44

think that there are unidentified receptor which is different from those already discovered recently 45 by Zuker's group. 1 WHO (2015) recommends to reduce intake of monosaccharides and disaccharides added to 2 foods and beverages, and sugars naturally present in honey, syrups and fruit juices (Di Monaco, 3

Miele, Cabisidan & Cavella, 2018). . Since oligosaccharides have been attracting much attention 4 by virtue of their prebiotic function, their sweetness intensity has been studied (Ruiz-Acceituno, 5

Hernandez-Hernandez, Kolida, Moreno & Methven, 2018) using ten commercial and four novel 6

prebiotics ( 4-galacosyl-kojibiose, lacturosucrose, lactosyl-oligofructosides and 7

raffinosyl-oligofructosides). Based on the sensory evaluation and principal component analysis, 8

Ruiz-Aceitunoo et al. (2018) concluded that chain length was the most important determining 9

factor for sweetness intensity of these carbohydrates rather than the types of linkage or the 10 presence of ketose groups. Disaccharides (lactose, lactulose, kojibiose, leucrose, maltulose, 11 turanose and others) showed higher sweetness (relative sweetness 49.8 -68.3 to sucrose sweetness 12 100), than trisaccharides (4-galactosyl-kojibiose and lacturosucrose) (41.4 -46.5), which in turn 13 exhibited higher sweetness than mixtures of oligosaccharides having DP above 3 (11.2 -37.1). 14 15

It is generally believed that the perceived sweetness intensity is decreased with increasing 17 concentration of coexisting thickening agents (Morris, 1993) . Experimental results of Morris 18 showed that this decrease of sweetness intensity did not depend on the kind of thickening agent 19 such as guar gum, alginate, carboxymethyl cellulose but only on the viscosity (Fig.47) . 20

Nottingham group using guar and dextran with different molar masses examined the saltiness 21 intensity as a function of the zero shear viscosity and polymer concentration (Fig.48) They found that saltiness intensity decreased with increasing viscosity at lower shear rate, which 27

was consistent with results on sweetness intensity by Morris (1993) shown in Fig.47 . The 28 difference in saltiness intensity was recognized only when the zero shear viscosities are very 29 different. They also found that the saltiness intensity increased with increasing polymer 30 concentration at a constant zero shear viscosity. This observation became possible because they 31 used dextran which is not commonly used as a thickener in food industry because dextran is not so 32 effective as a thickener in comparison with guar, locustbean gum, and xyloglucan. The reason why 33 dextran is not effective as a thickener may be attributed to its chain flexibility caused by alpha 1,6 34 linkage than other polysaccharides. Therefore, it was necessary to add a large amount of dextran 35

with lower molar mass to make a solution with the same zero shear viscosity of solutions of guar 36 or high molar mass dextran. The saltiness increasing effect of the addition of a low molar mass 37 dextran may be attributed to one of the following reasons: the effective concentration of salt 38

increases because water is hydrated with dextran, or the direct interaction of salt with some part of 39 glucose residues of dextran. It is difficult to conclude which one or the other mechanism is 40 responsible for this effect at present. 41

As for solid foods, Morris (1993) found a good correlation between the intensity of the flavour 42 release and the fracture strain; he found that the sweetness intensity and strawberry flavour 43 intensity decreased with increasing fracture strain. It was understood as the decrease in the surface 44 area of the fragments from which taste and aroma compounds were released. Clark (2002) showed 45 that the overall flavour intensity decreased linearly with increasing hardness for dessert gels. 1

However, a deformable/cohesive gel consisting of 0 4% low acyl gellan, xanthan, and locust bean 2 gum did not show a good flavour release than other gels having the same hardness because the 3 flavour remained trapped in the gel. Although gelatin gel is deformable/cohesive, it showed a 4 better flavour release in the mouth than other gels having the same hardness because it melted at 5 body temperature. Therefore, both interpretations of Morris (1993) and Clark (2002) are not 6 contradictory but complementary. As described in Section 3.3 Elastic modulus and fracture stress 7 of gels as a function of molar mass, lower molar mass gelling agents form less deformable and 8 brittle gels, these will form gels with higher flavour release. In addition to the fracture strain, the 9 flavour release is known to be enhanced by syneresis (Nishinari & Fang, 2016) . The relation 10 between water and aroma holding capacity and the molar mass of the food matrix should be 11 further studied. To develop further a better method for aroma retention or release, it is necessary to understand 28 the flavour characteristics and carrier (polysaccharides, proteins and lipids) characteristics, sample 29 preparation before encapsulation (e.g. initial emulsion formation before spray drying), method of 30 encapsulation (e.g spray drying emulsification, extrusion), and operating condition of 31 encapsulation (operating conditions of spray drying) (Saifullah, Shishir, Ferdowsi, Rahman, & 32

Vuong, 2019). 33

Since molar mass plays an important role in flavour characteristic and carrier, these two 34 factors are discussed in this section. The general tendency of the retention has been found is in the order of acids < aldehydes < 42 esters ≤ ketones ≤ alcohols, indicating that acids tend to most easily to release. Therefore, it can be 43 To understand systematically the aroma retention or release, it is logical to examine the 1 influence of molar mass, chemical groups, polarity and volatility of aroma compounds retained in 2 various carriers, glucose, maltose, maltodextrin, starch, thickening or gelling polysaccharides, 3

proteins, and lipids. A general tendency that higher molar mass aroma compounds are better However, the retention of ethyl butyrate was higher than that of isoamyl butyrate in maltose and 9

maltodextrin (DE 28.5), which was an exception to the above mentioned general rule. Zhao, Su, & Sun, 2014). It seems that more release (less retention) was found in the following 4 order; alcohols (1-pentanol, 1-hexanol, 1-octen-3-ol, 1-octenol) > aldehydes (pentanal, hexanal, 5 heptanal, octanal) > ketones (2-pentnon, 2-hexanone, 2-heptanon, 2-octanone), and longer chain 6 (higher molar mass ) compounds seem to be more retained probably because of stronger 7 hydrophobic interactions. The hydrophobicity is represented by partition coefficient. The water-air 8 partition coefficient (logPwa) representing the volatility (from water) of aroma compounds and an decreases with decreasing molar mass and moisture content. The mobility of aroma compounds 28 encapsulated by these polymers is higher in rubbery state than in glassy state. Therefore, to 29 prevent the loss of aroma compounds during storage, wall/carrier materials should be kept in 30 glassy state. It is generally found that the concentration of oxidation products of encapsulated 31 flavours during storage is lower for low molecular weight matrices, in particular when produced 32 by spray drying. This is related to the matrix free volume, which decreases with the decreasing with DP=10) to CD12 (CD with DP=12) were believed to be different from CD6 (α-CD) to CD8 6 (γ-CD) while still providing sufficient rigidity to form stable complexes. Thus, CD10 to CD12 7 were thought to act as chiral selectors (Sonnendecker et al., 2019) . Therefore, the flexibility is 

Other factors such as binding of aroma compounds with carriers, taste-odour interaction 24

should also be taken into account to understand whole aspects of aroma release (Gupta et al., 25

As has been widely reported, texture, taste and aroma interact with each other before and 27 during eating. For example, when isoamylacetate (IAA) which is a key compound of banana and 28 sucrose solution are injected to the mouth, most subjects perceived banana flavour, but when the 29 sucrose solution is replaced by water, most subjects donot perceive the banana flavour. This is 30 understood by the fact that most humans have never eaten banana from which sugars are removed, 31

and they always perceive a banana flavour key compound in the presence of sugars (Hort & 32

Hollowood, 2004). 33 34

It is well known that gel formation of food biopolymers is strongly influenced by the molar 36 mass, ionic strength, pH, temperature and other environmental conditions. Some typical examples 37 were discussed. However, needless to say, it is important to study the effect of detailed chemical 38 structure, the degree of substitution and the position of the substituent in cellulose derivatives, 39 KGM, pectin, alginate, galactomannans, native gellans, and other gelling polysaccharides and 40 proteins. Although it is possible to prepare the rigorously controlled cellulose derivatives by 41 regio-selective substitution, it is difficult to get a large amount of sample at present, which makes 42 the collaborative works very difficult. As for the polyelectrolytes such as ionic polysaccharides, 43 gellans, carrageenans, pectins, alginates, chitins, and others, effects of the type of cations or anions 44 present are sometimes more important than a small difference in molar mass. The large scale 1 preparation methods to study polysaccharides with narrow molar mass distribution are not well 2 established in addition to the above-mentioned requirement of chemical purity. 3

Collaborative research using a common sample is expected to be useful. Molecular level study 4 such as rearrangements of biopolymers during structure formation has been reported and this may 5 be distinguished from syneresis (this is also a kind of rearrangement) causing slippage in 6 rheological measurements. Although Pickering emulsion is widely studied, the mechanism is not 7 yet clarified. It is necessary to study the emulsion activity and stability using the solid particles 8 with different lengths and flexibilities and lipophilicities. Again, a common sample distributed in 9

the collaborative work will be useful. It is necessary to combine the fundamentals and applications 10 in different disciplines. Collaborative research work done in IFOGEST using a common protocol 11 of in vitro digestion study and in the Japanese research group using a common gellan sample 12 proved to be fruitful, and such collaborative research is expected to flourish in many food 13 hydrocolloids related areas. 14 15

The research was supported by the grants from the National Natural Science while it decreases when it is degrade or digested 5 6 Fig.2 renneting. Casein micelle solution (3%) in artificial milk serum. The enzymatic reaction was 10 performed at 30°C (Niki et al., 1994) . 11 for the control (without guar); 12.6 ×10 -2 (Funami et al., 2005c). 6 Fig. 23B Syneresis for 5% normal maize starch/0.5% guar system after storage at 4 ℃ for either 7 7 or 14 days as a function of molecular weight of guar gum. Dotted line in the figure represents the 8 syneresis for the control (5% normal maize starch without added guar) after storage for 7 days; 9

13.4%, whereas solid line stands for the syneresis for the control after storage for 14 days; 30.6%. presence (dark bars) of the sweetness inhibitor lactisole. Subjects performed discrimination tests.

The proportion of correct responses (right y-axis) was used to obtain the discriminability (d′). The 110mm) with 3mm thick was clamped between metal plates having 18 mm diameter hole in the center, and 168

were subjected to compression using 5mm diameter spherical metal probe at 50mm/min (Watase & 169

Nishinari, 1985). 

and Investigative Medicine

Effect of degree of acetylation on gelation of konjac glucomannan

Butyrate improves 4 insulin sensitivity and increases energy expenditure in mice

Antifungal activity of different molecular weight chitosans 7 against planktonic cells and biofilm of Sporothrix brasiliensis

Edible Films and Coatings. Fundamentals and Applications

Nitric Oxide Releasing Polyamide Dendrimer with Anti-inflammatory Activity

Aggregation of amylose in aqueous systems: The effect of 15 chain length on phase behavior and aggregation kinetics

Physico-chemistry of (1,3)-β-Glucans

Chemistry, Biochemistry, and Biology of 1-3 Beta Glucans and

Functional categorisation of dietary fibre in foods: Beyond 20 'soluble' vs 'insoluble'

Distribution of short to medium amylose

A study of self-diffusion of molecules in polymer gel by 7 pulsed-gradient spin-echo 1 H NMR

Hyaluronan: More than just a wrinkle filler

Thermodynamics of aqueous methylcellulose solutions

Theoretical aspects of DNA-protein interactions : 12 Cooperative and non-cooperative binding of large ligands to a one-dimensional homogeneous 13 lattice

Clarifying the 15 confusion between poligeenan, degraded carrageenan, and carrageenan: A review of the 16 chemistry, nomenclature, and in vivo toxicology by the oral route

Evidence-based approach to fiber supplements and clinically meaningful 19 health benefits, part 1: What to look for and how to recommend an effective fiber therapy

Evidence-based approach to resolving enduring

Effects of the 11 gel size before ingestion and agarose molecular weight on the textural properties of a gel bolus

Rheological and organoleptic properties of food hydrocolloids

Food Hydrocolloids Structures, Properties and Functions

Gelation of gellan -A review

Transglutaminase and its use for food processing

Insight into the 2 stabilization mechanism of emulsions stabilized by Maillard conjugates: Protein 3 hydrolysates-dextrin with different degree of polymerization

Characteristics of different molecular weight 5 chitosan films affected by the type of organic solvents

Antihyperlipidemic effects of different molecular weight sulfated polysaccharides from Ulva 9 pertusa (Chlorophyta)

Modulation of osteogenic activity of

BMP-2 by cellulose and chitosan derivatives

Protein-rich vegetal sources and trends in human 13 nutrition: a review

Improvement of canola protein gelation properties through 15 enzymatic modification with transglutaminase. LWT -Food Science and Technology

Sulfated glycans in inflammation

Conformations and interactions of 20 pectins. II. Influences of residue sequence on chain association in calcium pectate gels

Effects of γ-irradiation on molar mass and 23 properties of Konjac mannan

Developments in our understanding of water-holding capacity in meat

κ-Carrageenan from marine red algae, Kappaphycus alvarezii-a 30 functional food to prevent colon carcinogenesis

Compound formation and glassy solidification in the 32 system gelatin-water

Chitin and chitosan: Properties and applications

Effects of sucrose, guar gum, 36 and carboxymethylcellulose on the release of volatile flavor compounds under dynamic 37 conditions

Role of the molecular weight on the mechanical 39 properties of kappa carrageenan gels

Spectroscopic characterisation and 41 conformation of oligo kappa carrageenans

Delonix regia galactomannan-based edible films: Effect of molecular weight and 45 k-carrageenan on physicochemical properties

Delonix 47 regia galactomannan hydrolysates: Rheological behavior and physicochemical characterization

Chemoenzymatic synthesis of ultralow and 11 low-molecular weight heparins. BBA -Proteins and Proteomics

Non-equilibrium states and glass transitions in bakery products

Non-Equilibrium States and Glass Transitions in Foods

Processing Effects and Product-Specific Implications

The eating quality of meat -IV Water-holding capacity and juiciness

Medicinal mushrooms as a source of antitumor and immunomodulating 19 polysaccharides

Role of Extractive Components 21 of Scallop in its Characteristic Taste Development (Taste-active Components of Scallop Part II

Effect of sodium alginate with three 2 molecular weight forms on the water holding capacity of chicken breast myosin gel

The influence of non-ionic

surfactant on lipid digestion of gum Arabic stabilized oil-in-water emulsion

Dynamic viscoelastic study on the gelation of konjac 8 glucomannan with different molecular weights

Molecular characteristics of partially 10 hydrolyzed fucoidans from sporophyll of Undaria pinnatifida and their in vitro anticancer activity

A low-molecular-weight 13 ascophyllan prepared from Ascophyllum nodosum: Optimization, analysis and biological 14 activities

The adsorption of 16 alpha-amylase on barley proteins affects the in vitro digestion of starch in barley flour

Chemical and physical deterioration of frozen foods

Chemical Deterioration and Physical Instability of Food

Multicomponent biopolymer gels, Fig.16 Back Extrusion force for oleogels (soybean oil) as a function of mass fraction of EC (Φ EC ) with 182 different molar masses, 28.6 ± 6.2 kDa (•)

Casein micelle solution (3%) in artificial milk serum. The enzymatic reaction was performed at 30°C (Niki 189

G" sat (closed circles) and 191 loss tan δ (open squares). The experiments were carried out at 30°C. Casein micelle solution: 3% (Niki et 192 al

L51 (388 kDa), and L52 (131 kDa) at 130°C, where s T represents a shift factor

19A DSC heating curves for gelatin gels of different concentrations: (a) 57.7%; (b) 55.0%; (c) 51.2%; 220 (d) 46.9%; (e) 35.2% (f) 23.2%; Gels were quenched from the room temperature to -150 ℃ by liquid 221 nitrogen, and then heated at 5 ℃/min

Relationship between phase-transition temperatures and water content W c (g/g) for gelatin water 223 system. T g : glass-transition temperature, T pm : pre-melt crystallization, T cc : cold crystallization 224 temperature, T m : melting temperature

19C Relation between the lowest T g value (T g,min ) and the W c where the lowest T g was observed for 226 various kinds of water-polysaccharide systems

From light to dark gray from left to right: control (evaporation without 608 starch), maize, potato, and pea. 1, acetaldehyde (MW= 44 Da); 2, dimethyl sulfide (MW= 64 Da); 3, 609 diacetyl (MW= 86 Da); 4, allyl isocyanate (MW= 99 Da)

Error bars indicate ±SD. Different 611 letters denote significant difference (p<0.05) between starches

Competitive inhibition in Fig.32A (a) and Fig.32B (a) and Enhancement of entanglement or 428 association in Fig.32A (b) and Fig.32B(b) . Solid curves in Fig.32A represent G′ and G〞of HA 429while broken lines stand for G′ and G〞of HA to which 60 disaccharide ( Fig.32A(a) ) or 50 430 disaccharide ( Fig.32A(b) ) units were added (Fujii et al., 1996) . HA short chains inhibit the 431 entanglement or association of longer HA molecular chain in Fig.32B (a) (competitive inhibition) 432while they can rather contribute to the entanglement or association in Fig.32B (b) . 

There is no conflict of interest.