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

Advances in the mathematical modeling of posttreatment control of HIV-1

PURPOSE OF REVIEW

Several new intervention strategies have shown significant improvements over antiretroviral therapy (ART) in eliciting lasting posttreatment control (PTC) of HIV-1. Advances in mathematical modelling have offered mechanistic insights into PTC and the workings of these interventions. We review these advances.

RECENT FINDINGS

Broadly neutralizing antibody (bNAb)-based therapies have shown large increases over ART in the frequency and the duration of PTC elicited. Early viral dynamics models of PTC with ART have been advanced to elucidate the underlying mechanisms, including the role of CD8+ T cells. These models characterize PTC as an alternative set-point, with low viral load, and predict routes to achieving it. Large-scale omic datasets have offered new insights into viral and host factors associated with PTC. Correspondingly, new classes of models, including those using learning techniques, have helped exploit these datasets and deduce causal links underlying the associations. Models have also offered insights into therapies that either target the proviral reservoir, modulate immune responses, or both, assessing their translatability.

SUMMARY

Advances in mathematical modeling have helped better characterize PTC, elucidated and quantified mechanisms with which interventions elicit it, and informed translational efforts.

Trade-off between the antiviral and vaccinal effects of antibody therapy in the humoral response to HIV

Antibody therapy for HIV-1 infection exerts two broad effects: a drug-like, antiviral effect, which rapidly lowers the viral load, and a vaccinal effect, which may control the viral load long-term by improving the immune response. Here, we elucidate a trade-off between these two effects as they pertain to the humoral response, which may compromise antibody therapy aimed at eliciting long-term HIV-1 remission. We developed a multi-scale computational model that combined within-host viral dynamics and stochastic simulations of the germinal centre (GC) reaction, enabling simultaneous quantification of the antiviral and vaccinal effects of antibody therapy. The model predicted that increasing antibody dosage or antibody-antigen affinity increased immune complex formation and enhanced GC output. Beyond a point, however, a strong antiviral effect reduced antigen levels substantially, extinguishing GCs and limiting the humoral response. We found signatures of this trade-off in clinical studies. Accounting for the trade-off could be important in optimizing antibody therapy for HIV-1 remission.

Antiviral capacity of the early CD8 T-cell response is predictive of natural control of SIV infection: Learning in vivo dynamics using ex vivo data

While most individuals suffer progressive disease following HIV infection, a small fraction spontaneously controls the infection. Although CD8 T-cells have been implicated in this natural control, their mechanistic roles are yet to be established. Here, we combined mathematical modeling and analysis of previously published data from 16 SIV-infected macaques, of which 12 were natural controllers, to elucidate the role of CD8 T-cells in natural control. For each macaque, we considered, in addition to the canonical in vivo plasma viral load and SIV DNA data, longitudinal ex vivo measurements of the virus suppressive capacity of CD8 T-cells. Available mathematical models do not allow analysis of such combined in vivo-ex vivo datasets. We explicitly modeled the ex vivo assay, derived analytical approximations that link the ex vivo measurements with the in vivo effector function of CD8-T cells, and integrated them with an in vivo model of virus dynamics, thus developing a new learning framework that enabled the analysis. Our model fit the data well and estimated the recruitment rate and/or maximal killing rate of CD8 T-cells to be up to 2-fold higher in controllers than non-controllers (p = 0.013). Importantly, the cumulative suppressive capacity of CD8 T-cells over the first 4-6 weeks of infection was associated with virus control (Spearman's ρ = -0.51; p = 0.05). Thus, our analysis identified the early cumulative suppressive capacity of CD8 T-cells as a predictor of natural control. Furthermore, simulating a large virtual population, our model quantified the minimum capacity of this early CD8 T-cell response necessary for long-term control. Our study presents new, quantitative insights into the role of CD8 T-cells in the natural control of HIV infection and has implications for remission strategies.

Modelling HIV-1 control and remission

Remarkable advances are being made in developing interventions for eliciting long-term remission of HIV-1 infection. The success of these interventions will obviate the need for lifelong antiretroviral therapy, the current standard-of-care, and benefit the millions living today with HIV-1. Mathematical modelling has made significant contributions to these efforts. It has helped elucidate the possible mechanistic origins of natural and post-treatment control, deduced potential pathways of the loss of such control, quantified the effects of interventions, and developed frameworks for their rational optimization. Yet, several important questions remain, posing challenges to the translation of these promising interventions. Here, we survey the recent advances in the mathematical modelling of HIV-1 control and remission, highlight their contributions, and discuss potential avenues for future developments.

Understanding early HIV-1 rebound dynamics following antiretroviral therapy interruption: The importance of effector cell expansion

Most people living with HIV-1 experience rapid viral rebound once antiretroviral therapy is interrupted; however, a small fraction remain in viral remission for an extended duration. Understanding the factors that determine whether viral rebound is likely after treatment interruption can enable the development of optimal treatment regimens and therapeutic interventions to potentially achieve a functional cure for HIV-1. We built upon the theoretical framework proposed by Conway and Perelson to construct dynamic models of virus-immune interactions to study factors that influence viral rebound dynamics. We evaluated these models using viral load data from 24 individuals following antiretroviral therapy interruption. The best-performing model accurately captures the heterogeneity of viral dynamics and highlights the importance of the effector cell expansion rate. Our results show that post-treatment controllers and non-controllers can be distinguished based on the effector cell expansion rate in our models. Furthermore, these results demonstrate the potential of using dynamic models incorporating an effector cell response to understand early viral rebound dynamics post-antiretroviral therapy interruption.

Understanding early HIV-1 rebound dynamics following antiretroviral therapy interruption: The importance of effector cell expansion

Most people living with HIV-1 experience rapid viral rebound once antiretroviral therapy is interrupted; however, a small fraction remain in viral remission for an extended duration. Understanding the factors that determine whether viral rebound is likely after treatment interruption can enable the development of optimal treatment regimens and therapeutic interventions to potentially achieve a functional cure for HIV-1. We built upon the theoretical framework proposed by Conway and Perelson to construct dynamic models of virus-immune interactions to study factors that influence viral rebound dynamics. We evaluated these models using viral load data from 24 individuals following antiretroviral therapy interruption. The best-performing model accurately captures the heterogeneity of viral dynamics and highlights the importance of the effector cell expansion rate. Our results show that post-treatment controllers and non-controllers can be distinguished based on the effector cell expansion rate in our models. Furthermore, these results demonstrate the potential of using dynamic models incorporating an effector cell response to understand early viral rebound dynamics post-antiretroviral therapy interruption.

Dynamical Modeling and Qualitative Analysis of a Delayed Model for CD8 T Cells in Response to Viral Antigens

Although the immune effector CD8 T cells play a crucial role in clearance of viruses, the mechanisms underlying the dynamics of how CD8 T cells respond to viral infection remain largely unexplored. Here, we develop a delayed model that incorporates CD8 T cells and infected cells to investigate the functional role of CD8 T cells in persistent virus infection. Bifurcation analysis reveals that the model has four steady states that can finely divide the progressions of viral infection into four states, and endows the model with bistability that has ability to achieve the switch from one state to another. Furthermore, analytical and numerical methods find that the time delay resulting from incubation period of virus can induce a stable low-infection steady state to be oscillatory, coexisting with a stable high-infection steady state in phase space. In particular, a novel mechanism to achieve the switch between two stable steady states, time-delay-based switch, is proposed, where the initial conditions and other parameters of the model remain unchanged. Moreover, our model predicts that, for a certain range of initial antigen load: 1) under a longer incubation period, the lower the initial antigen load, the easier the virus infection will evolve into severe state; while the higher the initial antigen load, the easier it is for the virus infection to be effectively controlled and 2) only when the incubation period is small, the lower the initial antigen load, the easier it is to effectively control the infection progression. Our results are consistent with multiple experimental observations, which may facilitate the understanding of the dynamical and physiological mechanisms of CD8 T cells in response to viral infections.

The Eradication of Carcinogenic Viruses in Established Solid Cancers

Carcinogenic viruses (oncoviruses) can initiate cancer, but their impact on established cancer varies. Some of these viruses prolong survival while others shorten it. This study classifies oncoviruses into two categories: viruses which induce a strong CD8+T cell reaction in non-cancerous tissues, and viruses which induce a weak CD8+ T cell reaction in non-cancerous tissues. The classification proves useful in predicting the effect of oncoviruses on the prognosis of solid cancers. Therefore, while eliminating carcinogenic viruses in healthy individuals (for example by immunization) may be important for cancer prevention, this study suggests that only viruses which induce a weak CD8+ T cell reaction should be eradicated in established solid tumors. The model correctly predicts the effect of oncoviruses on survival for six out of seven known oncoviruses, indicating that immune modulation by oncoviruses has a prominent effect on prognosis. It seems that CD8+ T cell response to oncoviruses observed in infected benign tissues is retained in infected tumors. Clinical significance: the effect of oncoviruses on solid cancer prognosis can be predicted with confidence based on immunological responses when clinical data are unavailable.

Mathematical model on HIV and nutrition

HIV continues to be a major global health issue, having claimed millions of lives in the last few decades. While several empirical studies support the fact that proper nutrition is useful in the fight against HIV, very few studies have focused on developing and using mathematical modelling approaches to assess the association between HIV, human immune response to the disease, and nutrition. We develop a within-host model for HIV that captures the dynamic interactions between HIV, the immune system and nutrition. We find that increased viral activity leads to increased serum protein levels. We also show that the viral production rate is positively correlated with HIV viral loads, as is the enhancement rate of protein by virus. Although our numerical simulations indicate a direct correlation between dietary protein intake and serum protein levels in HIV-infected individuals, further modelling and clinical studies are necessary to gain comprehensive understanding of the relationship.

Modeling the interplay between albumin-globulin metabolism and HIV infection

Human immunodeficiency virus (HIV) infection is a major public health concern with 1.2 million people living with HIV in the United States. The role of nutrition in general, and albumin/globulin in particular in HIV progression has long been recognized. However, no mathematical models exist to describe the interplay between HIV and albumin/globulin. In this paper, we present a family of models of HIV and the two protein components albumin and globulin. We use albumin, globulin, viral load and target cell data from simian immunodeficiency virus (SIV)-infected monkeys to perform model selection on the family of models. We discover that the simplest model accurately and uniquely describes the data. The selection of the simplest model leads to the observation that albumin and globulin do not impact the infection rate of target cells by the virus and the clearance of the infected target cells by the immune system. Moreover, the recruitment of target cells and immune cells are modeled independently of globulin in the selected model. Mathematical analysis of the selected model reveals that the model has an infection-free equilibrium and a unique infected equilibrium when the immunological reproduction number is above one. The infection-free equilibrium is locally stable when the immunological reproduction number is below one, and unstable when the immunological reproduction number is greater than one. The infection equilibrium is locally stable whenever it exists. To determine the parameters of the best fitted model we perform structural and practical identifiability analysis. The structural identifiability analysis reveals that the model is identifiable when the immune cell infection rate is fixed at a value obtained from the literature. Practical identifiability reveals that only seven of the sixteen parameters are practically identifiable with the given data. Practical identifiability of parameters performed with synthetic data sampled a lot more frequently reveals that only two parameters are practically unidentifiable. We conclude that experiments that will improve the quality of the data can help improve the parameter estimates and lead to better understanding of the interplay of HIV and albumin-globulin metabolism.

Dynamical modelling of viral infection and cooperative immune protection in COVID-19 patients

Once challenged by the SARS-CoV-2 virus, the human host immune system triggers a dynamic process against infection. We constructed a mathematical model to describe host innate and adaptive immune response to viral challenge. Based on the dynamic properties of viral load and immune response, we classified the resulting dynamics into four modes, reflecting increasing severity of COVID-19 disease. We found the numerical product of immune system's ability to clear the virus and to kill the infected cells, namely immune efficacy, to be predictive of disease severity. We also investigated vaccine-induced protection against SARS-CoV-2 infection. Results suggested that immune efficacy based on memory T cells and neutralizing antibody titers could be used to predict population vaccine protection rates. Finally, we analyzed infection dynamics of SARS-CoV-2 variants within the construct of our mathematical model. Overall, our results provide a systematic framework for understanding the dynamics of host response upon challenge by SARS-CoV-2 infection, and this framework can be used to predict vaccine protection and perform clinical diagnosis.

Relationship between the inclusion/exclusion criteria and sample size in randomized controlled trials for SARS-CoV-2 entry inhibitors

The coronavirus disease 2019 (COVID-19) pandemic that has been ongoing since 2019 is still ongoing and how to control it is one of the international issues to be addressed. Antiviral drugs that reduce the viral load in terms of reducing the risk of secondary infection are important. For the general control of emerging infectious diseases, establishing an efficient method to evaluate candidate therapeutic agents will lead to a rapid response. We evaluated clinical trial designs for viral entry inhibitors that have the potential to be effective pre-exposure prophylactic drugs in addition to reducing viral load after infection. We used a previously developed simulation of clinical trials based on a mathematical model of within-host viral infection dynamics to evaluate sample sizes in clinical trials of viral entry inhibitors against COVID-19. We assumed four measures as outcomes, namely change in log10-transformed viral load from symptom onset, PCR positive ratio, log10-transformed viral load, and cumulative viral load, and then sample sizes were calculated for drugs with 99 % and 95 % antiviral efficacy. Consistent with previous results, we found that sample sizes could be dramatically reduced for all outcomes used in an analysis by adopting inclusion/exclusion criteria such that only patients in the early post-infection period would be included in a clinical trial. A comparison of sample sizes across outcomes demonstrated an optimal measurement schedule associated with the nature of the outcome measured for the evaluation of drug efficacy. In particular, the sample sizes calculated from the change in viral load and from viral load tended to be small when measurements were taken at earlier time points after treatment initiation. For the cumulative viral load, the sample size was lower than that from the other outcomes when the stricter inclusion/exclusion criteria to include patients whose time since onset is earlier than 2 days was used. We concluded that the design of efficient clinical trials should consider the inclusion/exclusion criteria and measurement schedules, as well as outcome selection based on sample size, personnel and budget needed to conduct the trial, and the importance of the outcome regarding the medical and societal requirements. This study provides insights into clinical trial design for a variety of situations, especially addressing infectious disease prevalence and feasible trial sizes. This manuscript was submitted as part of a theme issue on "Modelling COVID-19 and Preparedness for Future Pandemics".

Epigenetic perspectives of COVID-19: Virus infection to disease progression and therapeutic control

COVID-19 has caused numerous deaths as well as imposed social isolation and upheaval world-wide. Although, the genome and the composition of the virus, the entry process and replication mechanisms are well investigated from by several laboratories across the world, there are many unknown remaining questions. For example, what are the functions of membrane lipids during entry, packaging and exit of virus particles? Also, the metabolic aspects of the infected tissue cells are poorly understood. In the course of virus replication and formation of virus particles within the host cell, the enhanced metabolic activities of the host is directly proportional to viral loads. The epigenetic landscape of the host cells is also altered, particularly the expression/repression of genes associated with cellular metabolism as well as cellular processes that are antagonistic to the virus. Metabolic pathways are enzyme driven processes and the expression profile and mechanism of regulations of the respective genes encoding those enzymes during the course of pathogen invasion might be highly informative on the course of the disease. Recently, the metabolic profile of the patients' sera have been analysed from few patients. In view of this, and to gain further insights into the roles that epigenetic mechanisms might play in this scenario in regulation of metabolic pathways during the progression of COVID-19 are discussed and summarised in this contribution for ensuring best therapy.

Age-Related Changes to the Immune System Exacerbate the Inflammatory Response to Pandemic H1N1 Infection

Age-induced dysregulation of the immune response is a major contributor to the morbidity and mortality related to influenza a virus infections. Experimental data have shown substantial changes to the activation and maintenance of the immune response will occur with age, but it remains unclear which of these many interrelated changes are most critical to controlling the survival of the host during infection. To ascertain which mechanisms are predominantly responsible for the increased morbidity in elderly hosts, we developed an ordinary differential equation model to simulate the immune response to pandemic H1N1 infection. We fit this model to experimental data measured in young and old macaques. We determined that the severity of the infection in the elderly hosts is caused by a dysregulation in the innate immune response. We also simulated CD8+ T cell exhaustion, a common consequence of chronic and extensive infections. Our simulations indicate that while T cell exhaustion is possible in both age groups, its effects are more severe in the elderly population, as their dysregulated immune response cannot easily compensate for the exhausted T cells. Finally, we explore a therapeutic approach to reversing T cell exhaustion through an inflammatory stimulus. A controlled increase in inflammatory signals can lead to a higher chance of surviving the infection, but excess inflammation will likely lead to septic death. These results indicate that our model captures distinctions in the predominant mechanisms controlling the immune response in younger and older hosts and allows for simulations of clinically relevant therapeutic strategies post-infection.

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.

CD8+ T Cells in SARS-CoV-2 Induced Disease and Cancer-Clinical Perspectives

Dysregulated innate and adaptive immunity is a sign of SARS-CoV-2-induced disease and cancer. CD8+ T cells are important cells of the immune system. The cells belong to the adaptive immunity and take a front-line defense against viral infections and cancer. Extreme CD8+ T-cell activities in the lung of patients with a SARS-CoV-2-induced disease and within the tumor microenvironment (TME) will change their functionality into exhausted state and undergo apoptosis. Such diminished immunity will put cancer cases at a high-risk group for SARS-CoV-2-induced disease, rendering viral sepsis and a more severe condition which will finally cause a higher rate of mortality. Recovering responses from CD8+ T cells is a purpose of vaccination against SARS-CoV-2. The aim of this review is to discuss the CD8+ T cellular state in SARS-CoV-2-induced disease and in cancer and to present some strategies for recovering the functionality of these critical cells.

Effect of innate and adaptive immune mechanisms on treatment regimens in an AIDS-related Kaposi's Sarcoma model

Kaposi Sarcoma (KS) is the most common AIDS-defining cancer, even as HIV-positive people live longer. Like other herpesviruses, human herpesvirus-8 (HHV-8) establishes a lifelong infection of the host that in association with HIV infection may develop at any time during the illness. With the increasing global incidence of KS, there is an urgent need of designing optimal therapeutic strategies for HHV-8-related infections. Here we formulate two models with innate and adaptive immune mechanisms, relevant for non-AIDS KS (NAKS) and AIDS-KS, where the initial condition of the second model is given by the equilibrium state of the first one. For the model with innate mechanism (MIM), we define an infectivity resistance threshold that will determine whether the primary HHV-8 infection of B-cells will progress to secondary infection of progenitor cells, a concept relevant for viral carriers in the asymptomatic phase. The optimal control strategy has been employed to obtain treatment efficacy in case of a combined antiretroviral therapy (cART). For the MIM we have shown that KS therapy alone is capable of reducing the HHV-8 load. In the model with adaptive mechanism (MAM), we show that if cART is administered at optimal levels, that is, 0.48 for protease inhibitors, 0.79 for reverse transcriptase inhibitors and 0.25 for KS therapy, both HIV-1 and HHV-8 can be reduced. The predictions of these mathematical models have the potential to offer more effective therapeutic interventions in the treatment of NAKS and AIDS-KS.

Dynamically linking influenza virus infection kinetics, lung injury, inflammation, and disease severity

Influenza viruses cause a significant amount of morbidity and mortality. Understanding host immune control efficacy and how different factors influence lung injury and disease severity are critical. We established and validated dynamical connections between viral loads, infected cells, CD8⁺ T cells, lung injury, inflammation, and disease severity using an integrative mathematical model-experiment exchange. Our results showed that the dynamics of inflammation and virus-inflicted lung injury are distinct and nonlinearly related to disease severity, and that these two pathologic measurements can be independently predicted using the model-derived infected cell dynamics. Our findings further indicated that the relative CD8⁺ T cell dynamics paralleled the percent of the lung that had resolved with the rate of CD8⁺ T cell-mediated clearance rapidly accelerating by over 48,000 times in 2 days. This complimented our analyses showing a negative correlation between the efficacy of innate and adaptive immune-mediated infected cell clearance, and that infection duration was driven by CD8⁺ T cell magnitude rather than efficacy and could be significantly prolonged if the ratio of CD8⁺ T cells to infected cells was sufficiently low. These links between important pathogen kinetics and host pathology enhance our ability to forecast disease progression, potential complications, and therapeutic efficacy.

COVID-19 virtual patient cohort suggests immune mechanisms driving disease outcomes

To understand the diversity of immune responses to SARS-CoV-2 and distinguish features that predispose individuals to severe COVID-19, we developed a mechanistic, within-host mathematical model and virtual patient cohort. Our results suggest that virtual patients with low production rates of infected cell derived IFN subsequently experienced highly inflammatory disease phenotypes, compared to those with early and robust IFN responses. In these in silico patients, the maximum concentration of IL-6 was also a major predictor of CD8+ T cell depletion. Our analyses predicted that individuals with severe COVID-19 also have accelerated monocyte-to-macrophage differentiation mediated by increased IL-6 and reduced type I IFN signalling. Together, these findings suggest biomarkers driving the development of severe COVID-19 and support early interventions aimed at reducing inflammation.

Mechanistic Modeling of SARS-CoV-2 and Other Infectious Diseases and the Effects of Therapeutics

Modern viral kinetic modeling and its application to therapeutics is a field that attracted the attention of the medical, pharmaceutical, and modeling communities during the early days of the AIDS epidemic. Its successes led to applications of modeling methods not only to HIV but a plethora of other viruses, such as hepatitis C virus (HCV), hepatitis B virus and cytomegalovirus, which along with HIV cause chronic diseases, and viruses such as influenza, respiratory syncytial virus, West Nile virus, Zika virus, and severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), which generally cause acute infections. Here we first review the historical development of mathematical models to understand HIV and HCV infections and the effects of treatment by fitting the models to clinical data. We then focus on recent efforts and contributions of applying these models towards understanding SARS-CoV-2 infection and highlight outstanding questions where modeling can provide crucial insights and help to optimize nonpharmaceutical and pharmaceutical interventions of the coronavirus disease 2019 (COVID-19) pandemic. The review is written from our personal perspective emphasizing the power of simple target cell limited models that provided important insights and then their evolution into more complex models that captured more of the virology and immunology. To quote Albert Einstein, "Everything should be made as simple as possible, but not simpler," and this idea underlies the modeling we describe below.

A quantitative model used to compare within-host SARS-CoV-2, MERS-CoV, and SARS-CoV dynamics provides insights into the pathogenesis and treatment of SARS-CoV-2

The scientific community is focused on developing antiviral therapies to mitigate the impacts of the ongoing novel coronavirus disease 2019 (COVID-19) outbreak. This will be facilitated by improved understanding of viral dynamics within infected hosts. Here, using a mathematical model in combination with published viral load data, we compare within-host viral dynamics of SARS-CoV-2 with analogous dynamics of MERS-CoV and SARS-CoV. Our quantitative analyses using a mathematical model revealed that the within-host reproduction number at symptom onset of SARS-CoV-2 was statistically significantly larger than that of MERS-CoV and similar to that of SARS-CoV. In addition, the time from symptom onset to the viral load peak for SARS-CoV-2 infection was shorter than those of MERS-CoV and SARS-CoV. These findings suggest the difficulty of controlling SARS-CoV-2 infection by antivirals. We further used the viral dynamics model to predict the efficacy of potential antiviral drugs that have different modes of action. The efficacy was measured by the reduction in the viral load area under the curve (AUC). Our results indicate that therapies that block de novo infection or virus production are likely to be effective if and only if initiated before the viral load peak (which appears 2-3 days after symptom onset), but therapies that promote cytotoxicity of infected cells are likely to have effects with less sensitivity to the timing of treatment initiation. Furthermore, combining a therapy that promotes cytotoxicity and one that blocks de novo infection or virus production synergistically reduces the AUC with early treatment. Our unique modeling approach provides insights into the pathogenesis of SARS-CoV-2 and may be useful for development of antiviral therapies.

Early events in hepatitis B infection: the role of inoculum dose

The relationship between the inoculum dose and the ability of the pathogen to invade the host is poorly understood. Experimental studies in non-human primates infected with different inoculum doses of hepatitis B virus have shown a non-monotonic relationship between dose magnitude and infection outcome, with high and low doses leading to 100% liver infection and intermediate doses leading to less than 0.1% liver infection, corresponding to CD4 T-cell priming. Since hepatitis B clearance is CD8 T-cell mediated, the question of whether the inoculum dose influences CD8 T-cell dynamics arises. To help answer this question, we developed a mathematical model of virus-host interaction following hepatitis B virus infection. Our model explains the experimental data well, and predicts that the inoculum dose affects both the timing of the CD8 T-cell expansion and the quality of its response, especially the non-cytotoxic function. We find that a low-dose challenge leads to slow CD8 T-cell expansion, weak non-cytotoxic functions, and virus persistence; high- and medium-dose challenges lead to fast CD8 T-cell expansion, strong cytotoxic and non-cytotoxic function, and virus clearance; while a super-low-dose challenge leads to delayed CD8 T-cell expansion, strong cytotoxic and non-cytotoxic function, and virus clearance. These results are useful for designing immune cell-based interventions.

In silico dynamics of COVID-19 phenotypes for optimizing clinical management

Understanding the underlying mechanisms of COVID-19 progression and the impact of various pharmaceutical interventions is crucial for the clinical management of the disease. We developed a comprehensive mathematical framework based on the known mechanisms of the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) infection, incorporating the renin-angiotensin system and ACE2, which the virus exploits for cellular entry, key elements of the innate and adaptive immune responses, the role of inflammatory cytokines, and the coagulation cascade for thrombus formation. The model predicts the evolution of viral load, immune cells, cytokines, thrombosis, and oxygen saturation based on patient baseline condition and the presence of comorbidities. Model predictions were validated with clinical data from healthy people and COVID-19 patients, and the results were used to gain insight into identified risk factors of disease progression including older age; comorbidities such as obesity, diabetes, and hypertension; and dysregulated immune response. We then simulated treatment with various drug classes to identify optimal therapeutic protocols. We found that the outcome of any treatment depends on the sustained response rate of activated CD8+ T cells and sufficient control of the innate immune response. Furthermore, the best treatment-or combination of treatments-depends on the preinfection health status of the patient. Our mathematical framework provides important insight into SARS-CoV-2 pathogenesis and could be used as the basis for personalized, optimal management of COVID-19.

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.

Pre-existing resistance in the latent reservoir can compromise VRC01 therapy during chronic HIV-1 infection

Passive immunization with broadly neutralizing antibodies (bNAbs) of HIV-1 appears a promising strategy for eliciting long-term HIV-1 remission. When administered concomitantly with the cessation of antiretroviral therapy (ART) to patients with established viremic control, bNAb therapy is expected to prolong remission. Surprisingly, in clinical trials on chronic HIV-1 patients, the bNAb VRC01 failed to prolong remission substantially. Identifying the cause of this failure is important for improving VRC01-based therapies and unraveling potential vulnerabilities of other bNAbs. In the trials, viremia resurged rapidly in most patients despite suppressive VRC01 concentrations in circulation, suggesting that VRC01 resistance was the likely cause of failure. ART swiftly halts viral replication, precluding the development of resistance during ART. If resistance were to emerge post ART, virological breakthrough would have taken longer than without VRC01 therapy. We hypothesized therefore that VRC01-resistant strains must have been formed before ART initiation, survived ART in latently infected cells, and been activated during VRC01 therapy, causing treatment failure. Current assays preclude testing this hypothesis experimentally. We developed a mathematical model based on the hypothesis and challenged it with available clinical data. The model integrated within-host HIV-1 evolution, stochastic latency reactivation, and viral dynamics with multiple-dose VRC01 pharmacokinetics. The model predicted that single but not higher VRC01-resistant mutants would pre-exist in the latent reservoir. We constructed a virtual patient population that parsimoniously recapitulated inter-patient variations. Model predictions with this population quantitatively captured data of VRC01 failure from clinical trials, presenting strong evidence supporting the hypothesis. We attributed VRC01 failure to single-mutant VRC01-resistant proviruses in the latent reservoir triggering viral recrudescence, particularly when VRC01 was at trough levels. Pre-existing resistant proviruses in the latent reservoir may similarly compromise other bNAbs. Our study provides a framework for designing bNAb-based therapeutic protocols that would avert such failure and maximize HIV-1 remission.

Antiretroviral therapy (ART) can control but not eradicate HIV-1. Stopping ART leads to rapid viral resurgence and progressive disease. ART is therefore administered lifelong. Tremendous efforts are ongoing to devise strategies that will enable stopping ART and yet prevent viral resurgence. One such strategy involves the administration of broadly neutralizing antibodies (bNAbs) of HIV-1 at the time of stopping ART. This strategy is expected to delay if not prevent viral resurgence. Surprisingly, treatment with VRC01, a potent bNAb, resulted in hardly any improvement in viral remission. In this study, we elucidate the cause of this failure. We hypothesized that VRC01-resistant strains may pre-exist in latently infected cells, which are unaffected by ART. They can thus outlast ART and get reactivated, triggering VRC01 failure. We built a detailed mathematical model based on this hypothesis and showed that it quantitatively captured observations of VRC01 failure in clinical trials on chronic HIV-1 patients. Our study thus identifies a potential vulnerability of bNAbs, namely, bNAb-resistant strains pre-existing in latently infected cells. Our model offers a framework for predicting bNAb-based treatment protocols that would preclude failure due to pre-existing resistance and maximally prolong remission.

The Good, The Bad and The Ugly: A Mathematical Model Investigates the Differing Outcomes Among CoVID-19 Patients

The disease caused by SARS-CoV-2—CoVID-19—is a global pandemic that has brought severe changes worldwide. Approximately 80% of the infected patients are largely asymptomatic or have mild symptoms such as fever or cough, while rest of the patients display varying degrees of severity of symptoms, with an average mortality rate of 3–4%. Severe symptoms such as pneumonia and acute respiratory distress syndrome may be caused by tissue damage, which is mostly due to aggravated and unresolved innate and adaptive immune response, often resulting from a cytokine storm.

Cytokine storm: A sudden acute increase in circulating levels of different inflammation causing cytokines including IL-6, IL-1, etc.

Here, we discuss how an intricate interplay among infected cells and cells of innate and adaptive immune system can lead to such diverse clinicopathological outcomes. Particularly, we discuss how the emergent nonlinear dynamics of interaction among the components of adaptive and immune system components and virally infected cells can drive different disease severity. Such minimalistic yet rigorous mathematical modeling approaches are helpful in explaining how various co-morbidity risk factors, such as age and obesity, can aggravate the severity of CoVID-19 in patients. Furthermore, such approaches can elucidate how a fine-tuned balance of infected cell killing and resolution of inflammation can lead to infection clearance, while disruptions can drive different severe phenotypes. These results can help further in a rational selection of drug combinations that can effectively balance viral clearance and minimize tissue damage.

Early exposure to broadly neutralizing antibodies may trigger a dynamical switch from progressive disease to lasting control of SHIV infection

Antiretroviral therapy (ART) for HIV-1 infection is life-long. Stopping therapy typically leads to the reignition of infection and progressive disease. In a major breakthrough, recent studies have shown that early initiation of ART can lead to sustained post-treatment control of viremia, raising hopes of long-term HIV-1 remission. ART, however, elicits post-treatment control in a small fraction of individuals treated. Strikingly, passive immunization with broadly neutralizing antibodies (bNAbs) of HIV-1 early in infection was found recently to elicit long-term control in a majority of SHIV-infected macaques, suggesting that HIV-1 remission may be more widely achievable. The mechanisms underlying the control elicited by bNAb therapy, however, remain unclear. Untreated infection typically leads to progressive disease. We hypothesized that viremic control represents an alternative but rarely realized outcome of the infection and that early bNAb therapy triggers a dynamical switch to this outcome. To test this hypothesis, we constructed a model of viral dynamics with bNAb therapy and applied it to analyse clinical data. The model fit quantitatively the complex longitudinal viral load data from macaques that achieved lasting control. The model predicted, consistently with our hypothesis, that the underlying system exhibited bistability, indicating two potential outcomes of infection. The first had high viremia, weak cytotoxic effector responses, and high effector exhaustion, marking progressive disease. The second had low viremia, strong effector responses, and low effector exhaustion, indicating lasting viremic control. Further, model predictions suggest that early bNAb therapy elicited lasting control via pleiotropic effects. bNAb therapy lowers viremia, which would also limit immune exhaustion. Simultaneously, it can improve effector stimulation via cross-presentation. Consequently, viremia may resurge post-therapy, but would encounter a primed effector population and eventually get controlled. ART suppresses viremia but does not enhance effector stimulation, explaining its limited ability to elicit post-treatment control relative to bNAb therapy.

In a remarkable advance in HIV cure research, a recent study showed that 3 weekly doses of HIV-1 broadly neutralizing antibodies (bNAbs) soon after infection kept viral levels controlled for years in most macaques treated. If translated to humans, this bNAb therapy may elicit a functional cure, or long-term remission, of HIV-1 infection, eliminating the need for life-long antiretroviral therapy (ART). How early bNAb therapy works remains unknown. Here, we elucidate the mechanism using mathematical modeling and analysis of in vivo data. We predict that early bNAb therapy suppresses viremia, which reduces exhaustion of cytotoxic effector cells, and enhances antigen uptake and effector stimulation. Collectively, these effects drive infection to lasting control. Model predictions based on these effects fit in vivo data quantitatively. ART controls viremia but does not improve effector stimulation, explaining its weaker ability to induce lasting control post-treatment. Our findings may help improve strategies for achieving functional cure of HIV-1 infection.