key: cord-102383-m5ahicqb
authors: Romano, Alessandra; Casazza, Marco; Gonella, Francesco
title: Energy dynamics for systemic configurations of virus-host co-evolution
date: 2020-05-15
journal: bioRxiv
DOI: 10.1101/2020.05.13.092866
sha: 
doc_id: 102383
cord_uid: m5ahicqb

Virus cause multiple outbreaks, for which comprehensive tailored therapeutic strategies are still missing. Virus and host cell dynamics are strictly connected, and convey in virion assembly to ensure virus spread in the body. Study of the systemic behavior of virus-host interaction at the single-cell level is a scientific challenge, considering the difficulties of using experimental approaches and the limited knowledge of the behavior of emerging novel virus as a collectivity. This work focuses on positive-sense, single-stranded RNA viruses, like human coronaviruses, in their virus-individual host interaction, studying the changes induced in the host cell bioenergetics. A systems-thinking representation, based on stock-flow diagramming of virus-host interaction at the cellular level, is used here for the first time to simulate the system energy dynamics. We found that reducing the energy flow which fuels virion assembly is the most affordable strategy to limit the virus spread, but its efficacy is mitigated by the contemporary inhibition of other flows relevant for the system. Summary Positive-single-strand ribonucleic acid ((+)ssRNA) viruses can cause multiple outbreaks, for which comprehensive tailored therapeutic strategies are still missing. Virus and host cell dynamics are strictly connected, generating a complex dynamics that conveys in virion assembly to ensure virus spread in the body. This work focuses on (+)ssRNA viruses in their virus-individual host interaction, studying the changes induced in the host cell bioenergetics. A systems-thinking representation, based on stock-flow diagramming of virus-host interaction at the cellular level, is used here for the first time to simulate the energy dynamics of the system. By means of a computational simulator based on the systemic diagramming, we identifid host protein recycling and folded-protein synthesis as possible new leverage points. These also address different strategies depending on time setting of the therapeutic procedures. Reducing the energy flow which fuels virion assembly is addressed as the most affordable strategy to limit the virus spread, but its efficacy is mitigated by the contemporary inhibition of other flows relevant for the system. Counterintuitively, targeting RNA replication or virion budding does not give rise to relevant systemic effects, and can possibly contribute to further virus spread. The tested combinations of multiple systemic targets are less efficient in minimizing the stock of virions than targeting only the virion assembly process, due to the systemic configuration and its evolution overtime. Viral load and early addressing (in the first two days from infection) of leverage points are the most effective strategies on stock dynamics to minimize virion assembly and preserve host-cell bioenergetics. As a whole, our work points out the need for a systemic approach to design effective therapeutic strategies that should take in account the dynamic evolution of the system.

Virus cause multiple outbreaks, for which comprehensive tailored therapeutic strategies are still missing. Virus and host cell dynamics are strictly connected, and convey in virion assembly to ensure virus spread in the body. Study of the systemic behavior of virus-host interaction at the single-cell level is a scientific challenge, considering the difficulties of using experimental approaches and the limited knowledge of the behavior of emerging novel virus as a collectivity. This work focuses on positive-sense, single-stranded RNA viruses, like human coronaviruses, in their virus-individual host interaction, studying the changes induced in the host cell bioenergetics. A systems-thinking representation, based on stock-flow diagramming of virus-host interaction at the cellular level, is used here for the first time to simulate the system energy dynamics. We found that reducing the energy flow which fuels virion assembly is the most affordable strategy to limit the virus spread, but its efficacy is mitigated by the contemporary inhibition of other flows relevant for the system.

Positive-single-strand ribonucleic acid ((+)ssRNA) viruses can cause multiple outbreaks, for which comprehensive tailored therapeutic strategies are still missing. Virus and host cell dynamics are strictly connected, generating a complex dynamics that conveys in virion assembly to ensure virus spread in the body.

This work focuses on (+)ssRNA viruses in their virus-individual host interaction, studying the changes induced in the host cell bioenergetics. A systems-thinking representation, based on stockflow diagramming of virus-host interaction at the cellular level, is used here for the first time to simulate the energy dynamics of the system. By means of a computational simulator based on the systemic diagramming, we identifid host protein recycling and folded-protein synthesis as possible new leverage points. These also address different strategies depending on time setting of the therapeutic procedures. Reducing the energy flow which fuels virion assembly is addressed as the most affordable strategy to limit the virus spread, but its efficacy is mitigated by the contemporary inhibition of other flows relevant for the system.

Counterintuitively, targeting RNA replication or virion budding does not give rise to relevant systemic effects, and can possibly contribute to further virus spread. The tested combinations of multiple systemic targets are less efficient in minimizing the stock of virions than targeting only the virion assembly process, due to the systemic configuration and its evolution overtime. Viral load and early addressing (in the first two days from infection) of leverage points are the most effective strategies on stock dynamics to minimize virion assembly and preserve host-cell bioenergetics.

As a whole, our work points out the need for a systemic approach to design effective therapeutic strategies that should take in account the dynamic evolution of the system. interaction between a (+)ssRNA virus and the host cell and therefore addressing effective intervention strategies.

Starting from the knowledge of relevant processes in (+ss)RNA virus replication, transcription, translation, virions budding and shedding and their energy costs (reported in Supplementary Methods Table 1) , we built up a systems-thinking (ST) based energy diagram of the virus-host interaction. Figure 1 shows the stock-flow diagram for the system at issue, where each stock was quantified in terms of embedded energy of the corresponding variable. Symbols are borrowed from the energy language 51, 52 : shields indicate the stocks, big solid arrows the processes and line arrows the flows, whereas dashed lines indicate the controls exerted by the stocks on the processes. All stocks, flows and processes are expressed in terms of the energy embedded, transmitted and used during the infection. We used ATP-equivalents (ATP-eq) as energy unit 53 referred to cellular costs, by using the number of ATP (or GTP and other ATP-equivalents) hydrolysis events as a proxy for energetic cost 53, 54 . The dynamic determination of flows was based on the knowledge of characteristic time-scales of well-established biological processes (for more details see Supplementary Methods). The output flows J4 and J5 were set to be effective only if the value of the respective stocks Q3 and Q5 is higher than a threshold, as represented by the two switch symbols in the diagram.

The stock Q1 represents the embedded energy of resources addressed to protein synthesis in the host cell. The dynamics of allocation for protein synthesis depends on the cell bioenergetics, e.g., the number of mitochondria, OX-PHOS activity levels, and the cell cycle phase [55] [56] [57] (for more details, see Supplementary Methods). In the absence of virus, energy flows from Q1 (flows J1, J2A and J2B) to produce short-half-life proteins (stock Q2A) and long-half-life proteins (stock Q2B), whose synthesis, degradation and secretion follow dynamic stationary conditions. In particular, typical of the specialized cells such as those of the pulmonary epithelium, there is a flow of proteins destined for degradation and recycling through the recruitment of autophagic receptors or organelles or proteasomes (identified in the diagram by the flows J21A and J21B, Supplementary Methods Table   1 ). The outflow of folded, fully functional proteins addressed to secretion or surface exposure is First, we investigated the system dynamics under different initial conditions, exploring the possible role of different initial viral loads (Figure 2 ). In the configuration of initial null viral load (Q3 stock value=0) the value of stocks Q1, Q2A and Q2B were constant and the system behavior was stationary (Figure 2A) . Assuming a different viral loads (time zero) in the 10-10,000 virions range, we found that there is a threshold in the initial viral load for triggering the progressive reduction of Q1, whose amount could in turn trigger the cell death in different ways. Apoptosis is a cellular process requiring energy, and a deflection in Q1, as shown in Figure 

When a (+)ssRNA virus enters the single host cell, the Q3 stock is fed, and its proteins can interact with the host proteome to sustain RNA replication. Based on previous works in the field 59-63 , we identified a time delay of 2 to 6 hours required to record changes in the Q5 stock. Moreover, the value of Q5 varies over the time due to changes occurred at a different timepoints in the stocks Q2B, Q3 and Q4. To be effective, a therapeutic strategy should limit the outflows of virions, J7 and/or J50.

However, minimization of J7 seems to be counter-effective in our simulation, due to the increase of Q5 as consequence of the feedback action in the virus replication (VR) process. The minimization of J50 prevents the outflow (viral shedding) from Q5 without stopping its growth. At the same time, this leads to increased resources diverting from Q1 and Q2B that could promote the cell death, with consequent spread of the virions in the environment. arising from targeting J5 was mitigated by the combination with reduction of J50 or J21 (Figure 3) . The partial reduction of J21, alone or in combination, did not change significantly the dynamic growth of Q5, induced increase of Q3 at Day 5, though it could prevent a reduction of Q1, to preserve the cell bioenergetics and preventing the cell death by ATP lack.

We also simulated the effect of applying the same external inputs at different times: after 1 (Extended Data Figure 4 ), 3 (Extended Data Figure 5 ) or 5 days (Extended Data Figure 6 ) from the initial infection, alone or in combination (Figure 4) . Application of external forcing factors at Day 1, Day 3 or Day 5 could affect in a non-linear way the system response, with the largest efficacy targeting J5 (Figures 4-5) . The combination of external driving forces acting on J5 and J21 did not result to be significantly synergic, while targeting J50 and J21 increased the Q5 stock value instead of the expected reduction. It is worth stressing that this kind of behavior is a typical systemic feature, where an intervention on a specific local process may lead to counterintuitive rearrangements in the system dynamics as a whole. Late suppression of J5 and J50 at Day 5 could reduce only the stock values of Q4. Only early full reduction of J5 (by Day 1) could significantly limit the growth of Q5, while the combination of contemporary suppression of J5 and J50 could not prevent Q5 growth (Figure 5) .

Thus, application of external driving forces at different timepoints is expected to model additional resilience configurations.

In this work, we approached the host-virus interaction dynamics as a systemic problem and, for the first time in the field, we used combined Systems Thinking tools as a conceptual framework to build up a systemic description of the viral action and host response, critically depending on the existing metabolic environment. The complex dynamic behavior was described in terms of underlying accessible patterns, hierarchical feedback loops, self-organization, and sensitive dependence on external parameters, that were analytically computed by a simulator. The following novelties were addressed: i) the use of energy language as a common quantitative unit for different biological cells and used mass spectrometry to measure protein-protein interactions 6 . With this experimental approach, they identified 332 interactions between viral and host proteins, and noted 69 existing drugs, known to target host proteins or associated pathways, which interact with SARS-CoV-2, addressing the importance to target the host-virus interaction at the level of RNA translation.

There are known advantages of in silico modelling the action of therapeutic agents on known diseases through agent-based modelling 74 . However, the literature evidenced some intrinsic limitations on the choice of parameters, like the size of investigated populations 75 , while major problems are related to model validation 75, 76 , also requiring to supplement the models with adequate formal ontologies 77 . Thanks to its abstract nature, stock-flow description can be used in a wide range of different fields, realizing the conceptual bridge that connects the language of biological systems to that of ecology.

Our approach unveils the potential of systems thinking for the study of other diseases or classes of disease, since it appears more and more clear how some incurable pathologies can be described only by adopting a more comprehensive systemic approach, in which the network of relationships between biological elements are treated in quantitative way similar to that applied in this paper.

The method used to study the dynamics of the virus-host interaction system is structured in 3 basic steps, namely, the development of a flow-stock diagram, that describes the virus-host interactions, the development of a virus-host systemic simulator, and, finally, its calibration and validation (Extended Data, Figure 1) .

A typical Systems Thinking diagram is formed of stocks, flows and processes. Stocks are countable extensive variables Qi, i=1,2,...,n, relevant to the study at issue, that constitute an n-ple of numbers that at any time represents a state of the system. A stock may change its value only upon its inflows and/or its outflows, represented by arrows entering or exiting the stock. Processes are any occurrence capable to alter -either quantitatively or qualitatively -a flow, by the action of one or more of the system elements. In a stationary state of the system, stocks values are either constant or regularly oscillating. In the dynamics of a system, stocks act as shock absorbers, buffers, and time-delayers. Processes are all what happens inside a system that allows the stationarity of its state, or that may perturb the state itself. To occur, a process must be activated by another driver, acting on the flow where the process is located. These interaction flows may be regarded as flows of information, that control the occurring processes and so the value and nature of the matter flows.

The pattern of the feedbacks acting in the system configurations is the feature that utlimately defines the systems dynamics.

We adopted an energyy approach, where stocks, flows and processes are expressed in terms of the energy embedded, transmitted and used, respectively, during the system operation. The equations, that characterize the flows relevant to the diagram, are typical of dynamic ST analysis 51, 78 , and their setting up is linked in many respects to the energy network language 79 . In this approach, each flow depends on the state variables Qi by relationships of the kind dQi/dt=kf(Qj), i,j=1,...,n, where n is the number of stocks in the system. Given a set of proper initial conditions for the stocks (i.e., the initial system state) and a properly chosen set of phenomenological coefficients k, the set of interconnected equations will be treated by standard finite-different method, taking care of choosing a time-step short enough to evidence the possible dynamics of any of the studied processes. The coefficients ki are calculated using data on the dynamics of any single stock, in particular, by estimating the flows and the stocks during the time interval set for the simulation steps (as described in Supplementary Methods). When different flows co-participate in a process, a single coefficient will gather all the actions that concur to the intensity of the outcoming flow(s). These phenomenological coefficients are not, therefore, related to specific biophysical phenomena or processes, but are set to describe how and how fast any part of the system react to a change in any of the other ones. In general, our model may be then regarded as based on a population-level model (PLM) as defined by 80 , which can be run at different scales from organism to sub-cellular ones (see for example 58, 81, 82 ), that already increased the existing knowledge on the life cycle of different infections, like for example the ones generated by HIV and Hepatitis C virus 83 . To obtain the simulations, we used the open-source computation software SCILAB (https://www.scilab.org).

The model simulations are developed based on the choice of the initial stock conditions, as well as of the parameters ki (see Supplementary Information for further details) . A model is valid as far as its output reproduces the reality, and systems modelling must be tested under two aspects, concerned with the capability to correctly describe the system and its dynamics, respectively 84 

Extended Data Figure 1 Workflow and study design Extended Data Figure 3 Effects of targeting leverage points upon the applcation of generic external driving forces D at Day 0

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Competing interests. Authors declare no competing financial interests.

The author to whom correspondence and material requests should be addressed is:Dr. Marco Casazza