key: cord-0886186-m8entot9
authors: Varfolomeev, Sergey D.; Panin, Alexander A.; Bykov, Valeriy I.; Tsybenova, Svetlana B.; Chuchalin, Alexander G.
title: Chemical kinetics of the development of coronaviral infection in the human body: Critical conditions, toxicity mechanisms, “thermoheliox”, and “thermovaccination”
date: 2020-08-01
journal: Chem Biol Interact
DOI: 10.1016/j.cbi.2020.109209
sha: be648eff54cf56889ca4f0da8649190cc8a281a4
doc_id: 886186
cord_uid: m8entot9

Kinetic modeling of the behavior of complex chemical and biochemical systems is an effective approach to study of the mechanisms of the process. A kinetic model of coronaviral infection development with a description of the dynamic behavior of the main variables, including the concentration of viral particles, affected cells, and pathogenic microflora, is proposed. Changes in the concentration of hydrogen ions in the lungs and the pH -dependence of carbonic anhydrase activity (a key breathing enzyme) are critical. A significant result is the demonstration of an acute bifurcation transition that determines life or system collapse. This transition is connected with exponential growth of concentrations of the process participants and with functioning of the key enzyme carbonic anhydrase in development of toxic effects. Physical and chemical interpretations of the therapeutic effects of the body temperature rise and the potential therapeutic effect of “thermoheliox” (respiration with a thermolized mixture of helium and oxygen) are given. The phenomenon of “thermovaccination” is predicted, which involves stimulation of the immune response by “thermoheliox”.

In the most recent decade, many studies have appeared on the topic of modeling viral growth dynamics in the organism with consideration of the production of pathogenic microflora and the response of the human immune system [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] . A review of the mathematical models of influenza development dynamics inside the organism with and without consideration of the immune response is presented in 8 . For example, the authors modified the simplest model of influenza virus infection with the addition of equations for the delay of virus production (6-8 hours) , the induction of interferon to inhibit virus replication in an infected cell, and the treatment process [9] . Most mathematical models describe the incubation period, the period of viral growth, the inclusion of the body's immune system and the treatment of infection, but do not consider the causes of system collapse, i.e., the molecular causes of death associated with the development of the disease. Mathematical models do not include disorders of the acid-alkaline balance (pH), which plays an important role in the functioning of the respiratory tract and metabolism. The increase in carbon dioxide and the accumulation of acidic metabolites lead to a decrease in pH in the lesion zone and a decrease in the catalytic activity of carbonic anhydrase, which corresponds to respiratory acidosis.

Infection of a living organism by viral particles with the development of clinical symptoms that potentially lead to collapse (death) of the body is a complex, dynamic process. The most important parameters determining the process dynamics are the concentration of the infecting agent or virus, the concentration of pathogenic microflora symbiotrophically developing on the affected cells of the body, and the physical conditions of the process development, such as the temperature and pH of the medium.

Currently, the etiology of acute coronavirus infection is becoming clearer. The disease development process involves several stages: -The initial stage includes infection and growth of viral concentration. This incubation period can occur without visible clinical changes. Therefore, in the case of a powerful immune system in the body, the virus does not continue to develop. In the second case, the immune system cannot cope with the virus, and viral penetration into the host cells initiates an exponential increase in the concentration of viral particles and the transition from the mild to the severe form of the disease.

-The next stage is destruction of the host cells by the virus and accumulation of dead cells.

-Under intensive aerobic conditions, necrotic biochemical processes of oxidation take place in dead cells, including lipid peroxidation, release of organic acids of the tricarboxylic acid cycle, ATP (adenosine triphosphate) hydrolysis with formation of phosphoric acid and other acidogenic processes.

-Local acidification of the lesion zone occurs.

-All enzymes with the imidazole group of histidine (pK a ∼7.0) in the active center, particularly the key enzymes of carbonic anhydrase and plasmin in the plasminogenic fibrinolytic complex, stop working in the lesion zone. The protonation of them blocks catalytic activity by reducing the pH (increasing the concentration of hydrogen ions). The lesion zone stops releasing CO 2 into the gas phase and accumulates bicarbonate.

-Microvessels are clogged in the lesion zone. Thrombus formation means that the plasmin-plasminogenic system that continuously dissolves fibrin clots and blood clots in the body is locally "turned off". Disabling the plasmin-plasminogenic system has the same effect as the "shutdown" of carbonic anhydrase. The active center of the plasmin contains an imidazole group of histidine, the protonation of which reversibly blocks the activity of plasmin in the lesion zone.

Plasmine stops hydrolyzing fibrin clots, and thus a blood clot occurs.

To create conditions for the suppression of viral infection and management of the treatment process, it is necessary to build and analyze kinetic models that describe the dynamics of the pathological process.

The obtained solution qualitatively describes the phenomenon of infection and disease development:

1. Incubation period during which practically no signs of the disease are observed. From 2. At the end of the incubation period (induction period), rapid symbiotrophic growth of the virus concentration and pathogenic microflora concentration with significant accumulation of virus and microorganisms is observed.

3. In primary periods of pathology development (the incubation period and initial period of active growth of the virus and pathogenic microflora concentrations), the pH value in the lesion zone is in the range 7.4-7.2. In the absence of treatment and a purposeful effect on the system behavior, bifurcation growth and pH blocking of carbonic anhydrase activity are observed. As a consequence, complete respiratory failure occurs. With the given parameters (listed above), the model predicts that respiratory arrest should be observed on the 15th-16th day after infection.

The collapse has a bifurcated character, and the transition point is clearly identified graphically (see Figure 1 ). The bifurcation point is a fundamentally important characteristic of the process and is the point of "no return", i.e., the time of death of the body. When passing through this point, the release of CO 2 from the liquid phase to the gas phase is stopped. Uncontrolled growth occurs in the bicarbonate concentration in the blood, i.e., complete blocking of breathing occurs. It is of interest to study the influence of parameter variations on the system behavior to identify the most sensitive elements and methods of process control. Let us consider several important cases.

Virus destruction (immune response). The most sensitive parameter defining the system behavior is the characteristic of the rate of viral destruction (α parameter). Under natural conditions, the destruction process is based on activation of the immune system to produce antibodies against viral proteins. Within the studied model, a highly convenient parameter characterizing the main feature of the process is τ cr , which is the time at which the system can exist before collapse (life-time after infection). The integration of the equation system and computational procedures allow visualization of this time. The lifetime is the time before the bifurcation transition of hydrogen ion concentration (break point and experimentally rapid growth of H + (see Figure 1 ).

The dependence of τ cr on α parameter is observed using methods of mathematical experiments. The critical point is the point α = k 1 , at which the growth rate of the viral concentration in the body becomes equal to zero. This is the condition of complete recovery.

Antibiotics (suppression of pathogenic microflora growth). The growth rate of pathogenic flora (equation (4)) has a significant impact on the development of the infectious process.

In therapy, this process is regulated by the introduction of antibiotics that suppress the growth of microorganisms to varying degrees. The results of a mathematical experiment on the influence of the µ m and K p parameters on the system lifetime are presented in Figure 3 . A decrease in the rate of growth of microorganisms (decrease in µ m and increase in K p ) has a favorable effect on the lifetime (time before bifurcation transition, i.e., before the pH jump).

Key role of carbonic anhydrase. The carbonic anhydrase enzyme plays a crucial role in the respiratory mechanism. The enzyme "discharges" the biochemically formed bicarbonate ion in the form of gaseous CO 2 and a hydroxyl ion. Under normal physiological conditions (pH∼7.4), this reaction is practically irreversible (a system is open by CO 2 ). The catalytic activity of carbonic anhydrase is controlled by an ionogenic group with pK a ∼7 (see equation (6)).

The shift in pH (even a notably small shift) in an acidic medium (decrease in pH) reduces the catalytic activity of the enzyme while decreasing the rate of production of OHions. The process is self-accelerating, leading to bifurcation of the pH jump. observed that the lifetime (τ cr ) can be significantly increased by increasing the catalytic activity of the enzyme. Carbonic anhydrase contains a Zn 2+ ion in the active center [11] , which means that the patient's metabolism must be saturated with Zn 2+ ions for the effective treatment of viral 8 damage. Ion Zn 2+ of carbonic anhydrase plays the role of electrophilic agent, which is a key element of the active center of the enzyme. 

Under conditions of deep aeration, e.g., when using artificial lung ventilation devices, the oxidation processes with the formation of acids develop in the affected cells with broken membranes. One of the main processes of this type is lipid peroxidation. Within the discussed model, this process is presented by the term ωP in equation (5).

We analyzed the influence of the ω parameter on the system behavior, and the dependence of bifurcation point (τ cr ) on ω was also studied. A decrease in the acid production rate by dead cells influences τ cr significantly, and this dependence is nearly linear. It can be expected that the use of antioxidants is a positive factor in the treatment of coronavirus infection. Therapeutic effect of high temperature. The natural process of disease development is associated with an increase in body temperature. The inflammatory response is initiated by a large complex of biochemical reactions, including the synthesis of inflammation mediators of the prostaglandin type [12, 13] , synthesis of heat shock proteins, and activation of the immune system.

The increase in temperature first affects the increase in the rate of thermal death of microorganisms and viruses. It is known that as the temperature increases the concentration of microorganisms and viruses decreases exponentially as a result of thermal death: [14] .

A more detailed analysis of the data presented in these figures shows that the dependence of the kinetic parameters of thermal death k N (t) and k M (t) is subordinate to the classical Arrhenius equation: 

Within the discussed model, it appears possible to consider the effects of direct inactivation of viruses and pathogenic microorganisms at the transition from the "normal" temperature of 36°C to the temperature of the inflammatory process, 41°С. It is well known that an increase in temperature to 40-42°C is an important factor in the development of inflammatory process [13] .

If the activation energy of thermal destruction of viruses is conditionally taken to be equal to 40 kcal/mol, then the transition from normal temperature to inflammation temperature increases the Therapeutic effect of "thermoheliox". The use of "thermoheliox", which is a thermolized mixture of helium and oxygen, appears to be the most promising therapeutic means of suppressing viral growth. The essence of the approach is to influence the patient's respiratory system with a "thermoheliox" at relatively high temperatures. The therapeutic procedure consists of supple-menting the patient's breathing with a helium-oxygen mixture (80-60% helium, 20-40% oxygen) at gas-mixture temperatures of 50-90°C.

The methodology of using a thermolized mixture of helium and oxygen has a detailed scientific justification and has found highly effective application in the treatment of pathologies of the respiratory system, ischemic stroke [15] [16] [17] . "Thermoheliox" is also used for treatment of saunas. This is also confirmed by clinical experience [15] [16] [17] .

A thermolized mixture of helium and oxygen behaves in a similar way. Helium, with its high diffusion capacity, drains well, bypasses all body tissues, and significantly improves microcirculation in all organs and tissues. "Thermoheliox" significantly improves oxygen delivery, reduces airway resistance, improves the ventilation-perfusion ratio through the alveolar-capillary membrane of the lungs and normalizes the acid-alkaline state. "Thermoheliox" is much more effective than a mixture of oxygen and helium at room temperature. Mammalian and human cells use specialized protection mechanisms against temporary overheating (heat-shock proteins). At the same time, the virus is effectively destroyed by denaturation of proteins and nucleic acids.

For example, the flu virus at 50-60°C "lives" for a few minutes, the HIV virus is inactivated by a factor of 100 at 56°C for 30 minutes, the hepatitis virus loses its activity at 100°C for 2 minutes, and foot-and-mouth disease virus is destroyed at 50-60°C in 5-10 minutes [14, 19] .

The principle of instability of viruses to increased temperatures is the basis for the seasonal nature of viral infections transmitted by airborne means. It is of interest to analyze the influence of "thermoheliox" within the discussed model of the development of the virus-microbial lesion.

If we take the activation energy of viral thermodestruction as 50 kcal/mol, a thirty-minute exposure of the lesion at 60°C of the medium can reduce its concentration by several times (Figure 6 ).

Subsequent exposures lead to a dramatic reduction. It is possible to estimate the dependence of the destruction degree of the pathogenic virus on temperature (N/N 0 ) at a 30-minute respiratory exposure.

In this work, T w is the "working" temperature of the affected medium. When "thermoheliox" is used, the gas mixture enters the respiratory system with the nominal temperature T n and usually has a gas-mixture temperature that is 10-20 degrees lower at the outlet. In this equation, α(T 36 ) is the kinetic parameter at normal body temperature (in this case, 5⋅10 -3 h -1 ), and ∆t exp is the 14 breathing time of an exposure (usually 0.5 hours). From the equation, it follows that at a "working" temperature of 50°C, N/N 0 = 0.91; at 60°C, N/N 0 = 0.41; at 65°C, N/N 0 = 0.056, i.e., at 50°C, "thermoheliox" destroys only approximately 10%.

"Thermovaccination" as the stimulation of the immune response by "thermoheliox".

One of the expected effects of using "thermoheliox" at increased temperature (70-90°C) is thermoinactivation (thermal destruction) of viral particles, which means the appearance of destroyed viral particles that are unable to multiply protein-nucleic associates in the patient's blood. In this case, the higher the temperature of heliox is during the exposure, the more effective the destruction of viruses, and consequently, the higher the concentration of particles. Inactivated viral and protein components of the virus in the blood are natural vaccines. The body must synthesize antibodies according to a standard immune response procedure. A natural "thermovaccination" The results of the calculations with variation of parameter σ (the characteristic rate, the activation time of the immune system and antibody synthesis) are presented in Figure 9 , which shows that the higher the activation rate of the immune system is, the faster the virus is destroyed.

More significant effects are to be expected when using "thermoheliox", which is a breathing mixture of oxygen and helium with increased temperature (55-90°C). Figure 10 shows the results of calculations when the system of exposure with increasing the temperature from 50-90°C is included in the mechanism of pathology development. Estimations show that with the transition from 36°C to 60°C, α(T) increases by 10 to 15 times. Considering the relative multiplicity of lung treatment with "thermoheliox" (30 minutes, at an external temperature range of 70-90°C), this process is presented in Figure 10 by a jump in antigen concentration. It is observed that this result leads to a dramatic increase in the rate of accumulation of J antibodies and a significant increase in the rate of elimination of the virus. This work describes the general regularities of stimulation of the immune system by "thermoheliox". Application of this method to each individual patient has personal features. It is important to control the general state of the body and blood oxygenation because it is necessary to achieve 97-99% the oxygenation of the patient's blood. To achieve these values at patient inhalation, it is necessary to individually set more or less oxygen content in heliox during a single procedure. The oxygen level in the helium-oxygen respiratory mixture should not be overly high.

It is methodologically advisable to apply this method of vaccination for patients in the initial stage of infection and for patients with medium disease severity at repeated exposure with use of (1) where N is the concentration of viral infection; k 1 is a specific rate of virus replication in the body; α(Т) is a parameter characterizing the rate of virus destruction due to temperature inactivation, immune response, etc.; N 0 is the initial infecting viral concentration.

As the virus penetrates into the body's cells, especially lung cells, it multiplies and destroys the infected cells. The destruction product (P) is metabolically destroyed cells, which are a favorable medium for the growth of pathogenic microorganisms (M). The products (P) are in fact dead cells, which act as a substrate for the growth of pathogenic microflora. , 0 , 0 ,

The specific rate of the growth of microorganisms µ(P) depends on the concentration of the "destroyed" cells P and can be presented by Mono's equation:

where µ m is a maximum specific growth rate. K p is the pathogen affinity for substrate P and β(T) is a parameter characterizing the thermal death of microorganisms.

Under conditions of limited aeration and in zones of weak air exchange, pathogenic microflora, e.g., pneumococci, are optional anaerobes that use an anaerobic mechanism of ATP synthesis producing organic acids. This is the path to local mild acidosis and to collapse (death) of the body.

It is known that a pH value of 7.15 in the blood system is critical. The body's metabolism cannot function sustainably if the pH value is below 7.15 in the blood system because many enzymes contain the imidazole group of histidine as a component of the active center with pK a 7.0-7.2, depending on the protein structure [22] . Protonation of the imidazole group leads to complete loss of the catalytic activity of the enzyme.

The key enzyme for the functioning of the respiratory system is carbonic anhydrase, which performs the reaction 

where it is assumed that the proton production rate is proportional to the concentration of pathogenic microflora. The coefficient δ characterizes the productivity of microorganisms in the proton emission and the buffer properties of the blood system. 

Under conditions of a constant bicarbonate concentration (a relatively small region of process development), the constant multiplier in equation (6) is combined by constant A.

The solution of the system of equations (1)-(6) allows to obtain a kinetic description of the observed phenomenon of pathology development due to infection of the organism by coronavirus. One of the process scenarios is presented in Figure 1 . The integration of equations (1)- (6) was performed with the following parameter values: k 1 = 2⋅10 -2 h -1 , k 2 = 10 -2 h -1 , α = ω = 5⋅10 -3 h -1 , β = 10 -3 h -1 , γ = 0. 

The σ parameter corresponds to approximately three days of "maturation" of the immune response (σ ∼ 0.015 h -1 ). It is assumed that antigen a is formed by inactivation and destruction of the viral particles. The process of "maturation" of the immune system with the formation of antibodies and the rate of "killing" of the virus and its removal from the system are linearly dependent on the concentration of antibodies J and the virus concentration (-ξN⋅J term). It is qualitatively observed that at certain values of parameters α(T), σ and ξ in equation dN/dt, the negative terms exceed k 1 and the virus is killed. tration grows exponentially, reaches a maximum and falls to zero. Computing calculations were performed at ξ = 0.03 h -1 , σ = 0.015 h -1 , a(0) = J(0) = 0, and the values of the parameters given above.

The kinetic model is based on the kinetic equations describing the growth and evolution of microbial and viral populations [20, 21] . The ODE (ordinary differential • Acidification and pH dependence of key enzymes is discussed as a basis of viral toxicity.

• An acute bifurcation transition of the system to collapse is demonstrated.

• The theory and experimental facts of "thermoheliox" therapy are discussed. • "Thermovaccination" by "thermoheliox" is predicted.

Influenza virus infection model with density dependence supports biphasic viral decay

Influenza. A virus infection kinetics: quantitative data and models

Modeling the viral dynamics of influenza A virus infection

Mathematical analysis of viral replication dynamics and antiviral treatment strategies: from basic models to age-based multi-scale modeling

Modeling influenza virus infection: a roadmap for influenza research, Viruses

Influenza virus population dynamics in the respiratory tract of experimentally infected mice

Mathematical model of antiviral immune response III. Influenza A virus infection

A review of mathematical models of influenza A infections within a host or cell culture: lessons learned and challenges ahead

Kinetics of influenza A virus infection in humans

Determinants of blood pH in health and disease

Effects of pH and inhibitors on some properties related to metal binding in bovine carbonic anhydrase

Prostaglandins -molecular bioregulators

Arachidonic acid cascade

Efficacy and safety of thermic helium-oxygen (t-HeO2) mixture in reducing hypoxemia in acute ischemic stroke patients

T-HeO 2 effect on central hemodynamics and oxygen transport in patients with acute COPD, Moscow medicine

Effect of t-HeO2 on central hemodynamics and oxygen transport in patients with COPD exacerbation and acute respiratory failure

Registration certificate for a medical device RNZ 2016\3988. Medical device "Heliox Extreme

Inactivation of foot-andmouth disease virus by pH and temperature changes and by formaldehyde

Biotechnology: Kinetic bases of microbiological processes, Vysshaja shkola

Chemical enzymology

declare the following financial interests/personal relationships which may be considered as potential competing interests: The authors