Modelling how responsiveness to interferon improves interferon-free treatment of hepatitis C virus infection

Analytical refractory period distribution for a class of time-variant biochemical systems with second-order reactions

Refractory period (RP), the waiting time between signals, can induce complex signaling dynamics, such as acceleration, adaptation, and oscillation, within many cellular biochemical networks. However, its underlying molecular mechanisms are still unclear. Rigorously estimating the RP distribution may be essential to identify its causal regulatory mechanisms. Traditional methods of estimating the RP distribution depend on solving the underlying Chemical Master Equations (CMEs), the dominant modeling formalism of biochemical systems. However, exact solutions of the CME are only known for simple reaction systems with zero- and first-order reactions or specific systems with second-order reactions. General solutions still need to be derived for systems with bimolecular reactions. It is even more challenging if large state-space and nonconstant reaction rates are involved. Here, we developed a direct method to gain the analytical RP distribution for a class of second-order reaction systems with nonconstant reaction rates and large state space. Instead of using the CME, we used an equivalent path-wise representation, which is the solution to a transformed martingale problem of the CME. This allowed us to bypass solving a CME. We then applied the method to derive the analytical RP distribution of a real complex biochemical network with second-order reactions, the Drosophila phototransduction cascade. Our approach provides an alternative to the CMEs in deriving the analytical RP distributions of a class of second-order reaction systems. Since the bimolecular reactions are common in biological systems, our approach could enhance understanding real-world biochemical processes.

Modelling how increased Cathepsin B/L and decreased TMPRSS2 usage for cell entry by the SARS-CoV-2 Omicron variant may affect the efficacy and synergy of TMPRSS2 and Cathepsin B/L inhibitors

The SARS-CoV-2 Omicron variant harbours many mutations in its spike protein compared to the original SARS-CoV-2 strain, which may alter its ability to enter cells, cell tropism, and response to interventions blocking virus entry. To elucidate these effects, we developed a mathematical model of SARS-CoV-2 entry into target cells and applied it to analyse recent in vitro data. SARS-CoV-2 can enter cells via two pathways, one using the host proteases Cathepsin B/L and the other using the host protease TMPRSS2. We found enhanced entry efficiency of the Omicron variant in cells where the original strain preferentially used Cathepsin B/L and reduced efficiency where it used TMPRSS2. The Omicron variant thus appears to have evolved to use the Cathepsin B/L pathway better but at the expense of its ability to use the TMPRSS2 pathway compared to the original strain. We estimated >4-fold enhanced efficiency of the Omicron variant in entry via the Cathepsin B/L pathway and >3-fold reduced efficiency via the TMPRSS2 pathway compared to the original or other strains in a cell type-dependent manner. Our model predicted that Cathepsin B/L inhibitors would be more efficacious and TMPRSS2 inhibitors less efficacious in blocking Omicron variant entry into cells than the original strain. Furthermore, model predictions suggested that drugs simultaneously targeting the two pathways would exhibit synergy. The maximum synergy and drug concentrations yielding it would differ for the Omicron variant compared to the original strain. Our findings provide insights into the cell entry mechanisms of the Omicron variant and have implications for intervention targeting these mechanisms.

The role of Type I interferons in the pathogenesis of foot-and-mouth disease virus in cattle: A mathematical modelling analysis

Type I interferons (IFN) are the first line of immune response against infection. In this study, we explore the interaction between Type I IFN and foot-and-mouth disease virus (FMDV), focusing on the effect of this interaction on epithelial cell death. While several mathematical models have explored the interaction between interferon and viruses at a systemic level, with most of the work undertaken on influenza and hepatitis C, these cannot investigate why a virus such as FMDV causes extensive cell death in some epithelial tissues leading to the development of lesions, while other infected epithelial tissues exhibit negligible cell death. Our study shows how a model that includes epithelial tissue structure can explain the development of lesions in some tissues and their absence in others. Furthermore, we show how the site of viral entry in an epithelial tissue, the viral replication rate, IFN production, suppression of viral replication by IFN and IFN release by live cells, all have a major impact on results.

Modulating Immune Response in Viral Infection for Quantitative Forecasts of Drug Efficacy

The antiretroviral drug, the total level of viral production, and the effectiveness of immune responses are the main topics of this review because they are all dynamically interrelated. Immunological and viral processes interact in extremely complex and non-linear ways. For reliable analysis and quantitative forecasts that may be used to follow the immune system and create a disease profile for each patient, mathematical models are helpful in characterizing these non-linear interactions. To increase our ability to treat patients and identify individual differences in disease development, immune response profiling might be useful. Identifying which patients are moving from mild to severe disease would be more beneficial using immune system parameters. Prioritize treatments based on their inability to control the immune response and prevent T cell exhaustion. To increase treatment efficacy and spur additional research in this field, this review intends to provide examples of the effects of modelling immune response in viral infections, as well as the impact of pharmaceuticals on immune response.

Modeling recapitulates the heterogeneous outcomes of SARS-CoV-2 infection and quantifies the differences in the innate immune and CD8 T-cell responses between patients experiencing mild and severe symptoms

SARS-CoV-2 infection results in highly heterogeneous outcomes, from cure without symptoms to acute respiratory distress and death. Empirical evidence points to the prominent roles of innate immune and CD8 T-cell responses in determining the outcomes. However, how these immune arms act in concert to elicit the outcomes remains unclear. Here, we developed a mathematical model of within-host SARS-CoV-2 infection that incorporates the essential features of the innate immune and CD8 T-cell responses. Remarkably, by varying the strengths and timings of the two immune arms, the model recapitulated the entire spectrum of outcomes realized. Furthermore, model predictions offered plausible explanations of several confounding clinical observations, including the occurrence of multiple peaks in viral load, viral recrudescence after symptom loss, and prolonged viral positivity. We applied the model to analyze published datasets of longitudinal viral load measurements from patients exhibiting diverse outcomes. The model provided excellent fits to the data. The best-fit parameter estimates indicated a nearly 80-fold stronger innate immune response and an over 200-fold more sensitive CD8 T-cell response in patients with mild compared to severe infection. These estimates provide quantitative insights into the likely origins of the dramatic inter-patient variability in the outcomes of SARS-CoV-2 infection. The insights have implications for interventions aimed at preventing severe disease and for understanding the differences between viral variants.

Physical 'strength' of the multi-protein chain connecting immune cells: Does the weakest link limit antibody affinity maturation?: The weakest link in the multi-protein chain facilitating antigen acquisition by B cells in germinal centres limits antibody affinity maturation

The affinities of antibodies (Abs) for their target antigens (Ags) gradually increase in vivo following an infection or vaccination, but reach saturation at values well below those realisable in vitro. This 'affinity ceiling' could in many cases restrict our ability to fight infections and compromise vaccines. What determines the affinity ceiling has been an unresolved question for decades. Here, we argue that it arises from the strength of the chain of protein complexes that is pulled by B cells during the process of Ag acquisition. The affinity ceiling is determined by the strength of the weakest link in the chain. We identify the weakest link and show that the resulting affinity ceiling can explain the Ab affinities realized in vivo, providing a conceptual understanding of Ab affinity maturation. We explore plausible evolutionary underpinnings of the affinity ceiling, examine supporting evidence and alternative hypotheses and discuss implications for vaccination strategies.

Targeting TMPRSS2 and Cathepsin B/L together may be synergistic against SARS-CoV-2 infection

The entry of SARS-CoV-2 into target cells requires the activation of its surface spike protein, S, by host proteases. The host serine protease TMPRSS2 and cysteine proteases Cathepsin B/L can activate S, making two independent entry pathways accessible to SARS-CoV-2. Blocking the proteases prevents SARS-CoV-2 entry in vitro. This blockade may be achieved in vivo through 'repurposing' drugs, a potential treatment option for COVID-19 that is now in clinical trials. Here, we found, surprisingly, that drugs targeting the two pathways, although independent, could display strong synergy in blocking virus entry. We predicted this synergy first using a mathematical model of SARS-CoV-2 entry and dynamics in vitro. The model considered the two pathways explicitly, let the entry efficiency through a pathway depend on the corresponding protease expression level, which varied across cells, and let inhibitors compromise the efficiency in a dose-dependent manner. The synergy predicted was novel and arose from effects of the drugs at both the single cell and the cell population levels. Validating our predictions, available in vitro data on SARS-CoV-2 and SARS-CoV entry displayed this synergy. Further, analysing the data using our model, we estimated the relative usage of the two pathways and found it to vary widely across cell lines, suggesting that targeting both pathways in vivo may be important and synergistic given the broad tissue tropism of SARS-CoV-2. Our findings provide insights into SARS-CoV-2 entry into target cells and may help improve the deployability of drug combinations targeting host proteases required for the entry.

A dynamical motif comprising the interactions between antigens and CD8 T cells may underlie the outcomes of viral infections

Some viral infections culminate in very different outcomes in different individuals. They can be rapidly cleared in some, cause persistent infection in others, and cause mortality from immunopathology in yet others. The conventional view is that the different outcomes arise as a consequence of the complex interactions between a large number of different factors (virus, different immune cells, and cytokines). Here, we identify a simple dynamical motif comprising the essential interactions between antigens and CD8 T cells and posit it as predominantly determining the outcomes. Viral antigen can activate CD8 T cells, which in turn, can kill infected cells. Sustained antigen stimulation, however, can cause CD8 T-cell exhaustion, compromising effector function. Using mathematical modeling, we show that the motif comprising these interactions recapitulates all of the outcomes observed. The motif presents a conceptual framework to understand the variable outcomes of infection. It also explains a number of confounding experimental observations, including the variation in outcomes with the viral inoculum size, the evolutionary advantage of exhaustion in preventing lethal pathology, the ability of natural killer (NK) cells to act as rheostats tuning outcomes, and the role of the innate immune response in the spontaneous clearance of hepatitis C. Interventions that modulate the interactions in the motif may present routes to clear persistent infections or limit immunopathology.

Interferon at the cellular, individual, and population level in hepatitis C virus infection: Its role in the interferon-free treatment era

The advent of powerful direct-acting antiviral agents (DAAs) has revolutionized the treatment of hepatitis C. DAAs cure nearly all patients with short duration, oral treatments. Significant efforts are now underway to optimize DAA-based treatments. We discuss the potential role of interferon in this optimization. Clinical studies present compelling evidence that DAAs perform better in treatment-naive individuals than in individuals who previously failed treatment with interferon, a surprising correlation because interferon and DAAs are thought to act independently. Recent mathematical models explore a mechanistic hypothesis underlying this correlation. The hypothesis invokes the action of interferon at the cellular, individual, and population levels. Strong interferon responses prevent the productive infection of cells, reduce viral replication, and impede the development of resistance to DAAs in infected individuals and improve cure rates elicited by DAAs in treated populations. The models develop descriptions of these processes, integrate them into a comprehensive framework, and capture clinical data quantitatively, providing a successful test of the hypothesis. Individuals with strong endogenous interferon responses thus present a promising subpopulation for reducing DAA treatment durations. This review discusses the conceptual advances made by the models, highlights the new insights they unravel, and examines their applicability to optimize DAA-based treatments.

Mutational pathway maps and founder effects define the within-host spectrum of hepatitis C virus mutants resistant to drugs

Knowledge of the within-host frequencies of resistance-associated amino acid variants (RAVs) is important to the identification of optimal drug combinations for the treatment of hepatitis C virus (HCV) infection. Multiple RAVs may exist in infected individuals, often below detection limits, at any resistance locus, defining the diversity of accessible resistance pathways. We developed a multiscale mathematical model to estimate the pre-treatment frequencies of the entire spectrum of mutants at chosen loci. Using a codon-level description of amino acids, we performed stochastic simulations of intracellular dynamics with every possible nucleotide variant as the infecting strain and estimated the relative infectivity of each variant and the resulting distribution of variants produced. We employed these quantities in a deterministic multi-strain model of extracellular dynamics and estimated mutant frequencies. Our predictions captured database frequencies of the RAV R155K, resistant to NS3/4A protease inhibitors, presenting a successful test of our formalism. We found that mutational pathway maps, interconnecting all viable mutants, and strong founder effects determined the mutant spectrum. The spectra were vastly different for HCV genotypes 1a and 1b, underlying their differential responses to drugs. Using a fitness landscape determined recently, we estimated that 13 amino acid variants, encoded by 44 codons, exist at the residue 93 of the NS5A protein, illustrating the massive diversity of accessible resistance pathways at specific loci. Accounting for this diversity, which our model enables, would help optimize drug combinations. Our model may be applied to describe the within-host evolution of other flaviviruses and inform vaccine design strategies.