A modular framework for multiscale, multicellular, spatiotemporal modeling of acute primary viral infection and immune response in epithelial tissues and its application to drug therapy timing and effectiveness

An adaptive numerical method for multi-cellular simulations of tissue development and maintenance

In recent years, multi-cellular models, where cells are represented as individual interacting entities, are becoming ever popular. This has led to a proliferation of novel methods and simulation tools. The first aim of this paper is to review the numerical methods utilised by multi-cellular modelling tools and to demonstrate which numerical methods are appropriate for simulations of tissue and organ development, maintenance, and disease. The second aim is to introduce an adaptive time-stepping algorithm and to demonstrate it's efficiency and accuracy. We focus on off-lattice, mechanics based, models where cell movement is defined by a series of first order ordinary differential equations, derived by assuming over-damped motion and balancing forces. We see that many numerical methods have been used, ranging from simple Forward Euler approaches through to higher order single-step methods like Runge-Kutta 4 and multi-step methods like Adams-Bashforth 2. Through a series of exemplar multi-cellular simulations, we see that if: care is taken to have events (births deaths and re-meshing/re-arrangements) occur on common time-steps; and boundaries are imposed on all sub-steps of numerical methods or implemented using forces, then all numerical methods can converge with the correct order. We introduce an adaptive time-stepping method and demonstrate that the best compromise between L∞ error and run-time is to use Runge-Kutta 4 with an increased time-step and moderate adaptivity. We see that a judicious choice of numerical method can speed the simulation up by a factor of 10-60 from the Forward Euler methods seen in Osborne et al. (2017), and a further speed up by a factor of 4 can be achieved by using an adaptive time-step.

Influenza A virus during pregnancy disrupts maternal intestinal immunity and fetal cortical development in a dose- and time-dependent manner

Epidemiological studies link exposure to viral infection during pregnancy, including influenza A virus (IAV) infection, with increased incidence of neurodevelopmental disorders (NDDs) in offspring. Models of maternal immune activation (MIA) using viral mimetics demonstrate that activation of maternal intestinal T helper 17 (TH17) cells, which produce effector cytokine interleukin (IL)-17, leads to aberrant fetal brain development, such as neocortical malformations. Fetal microglia and border-associated macrophages (BAMs) also serve as potential cellular mediators of MIA-induced cortical abnormalities. However, neither the inflammation-induced TH17 cell pathway nor fetal brain-resident macrophages have been thoroughly examined in models of live viral infection during pregnancy. Here, we inoculated pregnant mice with two infectious doses of IAV and evaluated peak innate and adaptive immune responses in the dam and fetus. While respiratory IAV infection led to dose-dependent maternal colonic shortening and microbial dysregulation, there was no elevation in intestinal TH17 cells nor IL-17. Systemically, IAV resulted in consistent dose- and time-dependent increases in IL-6 and IFN-γ. Fetal cortical abnormalities and global changes in fetal brain transcripts were observable in the high-but not the moderate-dose IAV group. Profiling of fetal microglia and BAMs revealed dose- and time-dependent differences in the numbers of meningeal but not choroid plexus BAMs, while microglial numbers and proliferative capacity of Iba1+ cells remained constant. Fetal brain-resident macrophages increased phagocytic CD68 expression, also in a dose- and time-dependent fashion. Taken together, our findings indicate that certain features of MIA are conserved between mimetic and live virus models, while others are not. Overall, we provide consistent evidence of an infection severity threshold for downstream maternal inflammation and fetal cortical abnormalities, which recapitulates a key feature of the epidemiological data and further underscores the importance of using live pathogens in NDD modeling to better evaluate the complete immune response and to improve translation to the clinic.

Spatial information allows inference of the prevalence of direct cell-to-cell viral infection

The role of direct cell-to-cell spread in viral infections-where virions spread between host and susceptible cells without needing to be secreted into the extracellular environment-has come to be understood as essential to the dynamics of medically significant viruses like hepatitis C and influenza. Recent work in both the experimental and mathematical modelling literature has attempted to quantify the prevalence of cell-to-cell infection compared to the conventional free virus route using a variety of methods and experimental data. However, estimates are subject to significant uncertainty and moreover rely on data collected by inhibiting one mode of infection by either chemical or physical factors, which may influence the other mode of infection to an extent which is difficult to quantify. In this work, we conduct a simulation-estimation study to probe the practical identifiability of the proportion of cell-to-cell infection, using two standard mathematical models and synthetic data that would likely be realistic to obtain in the laboratory. We show that this quantity cannot be estimated using non-spatial data alone, and that the collection of data which describes the spatial structure of the infection is necessary to infer the proportion of cell-to-cell infection. Our results provide guidance for the design of relevant experiments and mathematical tools for accurately inferring the prevalence of cell-to-cell infection in in vitro and in vivo contexts.

Characterization and expression profiling of buffalo IFN-lambda family

Interferon lambda (IFN-λ) is an important type III interferon triggered mainly by viral infection. IFN-λ binds to their heterodimeric receptors and signals through JAK-STAT pathways similar to type I IFN. In this study, we deduced the buffalo IFN-λ sequences through the polymerase chain reaction, and then studied IFN-λ's expression patterns in different tissues, and post induction with poly I:C and live MRSA using RT-qPCR. The full-length sequences of buffalo IFN-λ3, IFN-λ receptors, and a transcript variant of IFN-λ4 were determined. IFN-λ1 is identified as a pseudogene. Virus response elements and a recombination hotspot factor was observed in the regulatory region of IFN-λ. The IFN-λ3 expressed highest in lungs and monocytes but IFN-λ4 did not. The expression of Interferon Lambda Receptor 1 was tissue specific, while Interleukin 10 Receptor subunit beta was ubiquitous. Following poly I:C induction, IFN-λ3 expression was primarily observed in epithelial cells as opposed to fibroblasts, displaying cell type-dependent expression. The cytosolic RNA sensors were expressed highest in endometrial epithelial cells, whereas the endosomal receptor was higher in fibroblasts. 2',5'-oligoadenylate synthetase expressed higher in fibroblasts, myxoma resistance protein 1 and IFN-stimulated gene 56 in epithelial cells, displaying cell-specific antiviral response of the interferon stimulated genes (ISGs). The endometrial epithelial cells expressed IFN-λ3 after live S. aureus infection indicating its importance in bacterial infection. The induction of IFN-λ3 was S. aureus isolate specific at the same multiplicity of infection (MOI). This study elucidates the IFN-λ sequences, diverse expression patterns revealing tissue specificity, and specificity in response to poly I:C and bacterial stimuli, emphasising its crucial role in innate immune response modulation.

SimService: a lightweight library for building simulation services in Python

SUMMARY

Integrative biological modeling requires software infrastructure to launch, interconnect, and execute simulation software components without loss of functionality. SimService is a software library that enables deploying simulations in integrated applications as memory-isolated services with interactive proxy objects in the Python programming language. SimService supports customizing the interface of proxies so that simulation developers and users alike can tailor generated simulation instances according to model, method, and integrated application.

AVAILABILITY AND IMPLEMENTATION

SimService is written in Python, is freely available on GitHub under the MIT license at https://github.com/tjsego/simservice, and is available for download via the Python Package Index (package name "simservice") and conda (package name "simservice" on the conda-forge channel).

Choice of spatial discretisation influences the progression of viral infection within multicellular tissues

There has been an increasing recognition of the utility of models of the spatial dynamics of viral spread within tissues. Multicellular models, where cells are represented as discrete regions of space coupled to a virus density surface, are a popular approach to capture these dynamics. Conventionally, such models are simulated by discretising the viral surface and depending on the rate of viral diffusion and other considerations, a finer or coarser discretisation may be used. The impact that this choice may have on the behaviour of the system has not been studied. Here we demonstrate that under realistic parameter regimes - where viral diffusion is small enough to support the formation of familiar ring-shaped infection plaques - the choice of spatial discretisation of the viral surface can qualitatively change key model outcomes including the time scale of infection. Importantly, we show that the choice between implementing viral spread as a cell-scale process, or as a high-resolution converged PDE can generate distinct model outcomes, which raises important conceptual questions about the strength of assumptions underpinning the spatial structure of the model. We investigate the mechanisms driving these discretisation artefacts, the impacts they may have on model predictions, and provide guidance on the design and implementation of spatial and especially multicellular models of viral dynamics. We obtain our results using the simplest TIV construct for the viral dynamics, and therefore anticipate that the important effects we describe will also influence model predictions in more complex models of virus-cell-immune system interactions. This analysis will aid in the construction of models for robust and biologically realistic modelling and inference.

Modeling and Remodeling the Cell: How Digital Twins and HCMV Can Elucidate the Complex Interactions of Viral Latency, Epigenetic Regulation, and Immune Responses

Purpose of Review

Human cytomegalovirus (HCMV), while asymptomatic in most, causes significant complications during fetal development, following transplant or in immunosuppressed individuals. The host-virus interactions regulating viral latency and reactivation and viral control of the cellular environment (immune regulation, differentiation, epigenetics) are highly complex. Understanding these processes is essential to controlling infection and can be leveraged as a novel approach for understanding basic cell biology.

Recent Findings

Immune digital twins (IDTs) are digital simulations integrating knowledge of human immunology, physiology, and patient-specific clinical data to predict individualized immune responses and targeted treatments. Recent studies used IDTs to elucidate mechanisms of T cells, dendritic cells, and epigenetic control-all key to HCMV biology.

Summary

Here, we discuss how leveraging the unique biology of HCMV and IDTs will clarify immune response dynamics, host-virus interactions, and viral latency and reactivation and serve as a powerful IDT-validation platform for individualized and holistic health management.

Influence of cell type specific infectivity and tissue composition on SARS-CoV-2 infection dynamics within human airway epithelium

Human airway epithelium (HAE) represents the primary site of viral infection for SARS-CoV-2. Comprising different cell populations, a lot of research has been aimed at deciphering the major cell types and infection dynamics that determine disease progression and severity. However, the cell type-specific replication kinetics, as well as the contribution of cellular composition of the respiratory epithelium to infection and pathology are still not fully understood. Although experimental advances, including Air-liquid interface (ALI) cultures of reconstituted pseudostratified HAE, as well as lung organoid systems, allow the observation of infection dynamics under physiological conditions in unprecedented level of detail, disentangling and quantifying the contribution of individual processes and cells to these dynamics remains challenging. Here, we present how a combination of experimental data and mathematical modelling can be used to infer and address the influence of cell type specific infectivity and tissue composition on SARS-CoV-2 infection dynamics. Using a stepwise approach that integrates various experimental data on HAE culture systems with regard to tissue differentiation and infection dynamics, we develop an individual cell-based model that enables investigation of infection and regeneration dynamics within pseudostratified HAE. In addition, we present a novel method to quantify tissue integrity based on image data related to the standard measures of transepithelial electrical resistance measurements. Our analysis provides a first aim of quantitatively assessing cell type specific infection kinetics and shows how tissue composition and changes in regeneration capacity, as e.g. in smokers, can influence disease progression and pathology. Furthermore, we identified key measurements that still need to be assessed in order to improve inference of cell type specific infection kinetics and disease progression. Our approach provides a method that, in combination with additional experimental data, can be used to disentangle the complex dynamics of viral infection and immunity within human airway epithelial culture systems.

Involvement of CD27 in innate and adaptive immunities of Nile tilapia (Oreochromis niloticus)

CD27 is a member of the TNF-receptor superfamily and plays various roles in immunities. However, the detailed information and mechanism of CD27 in bony fish immunity remain unclear. Therefore, in this research, certain interesting roles of CD27 in Nile tilapia (On-CD27) were determined. On-CD27 was largely expressed in the immune organs, head kidney, and spleen, and was sharply induced during bacterial infection. The in vitro tests suggested On-CD27 was involved in regulating inflammatory responses, activating immune-related signal pathways, and inducing apoptosis and pyroptosis progress. The scRNA data and in vivo experiments indicated that On-CD27 is mainly expressed in CD4⁺ T cells and involved in both innate and adaptive immunities. The present data provide a theoretical principle for further research on the mechanisms of CD27 in the innate and adaptive immunities of fish.

Drug Cocktail Formulation via Circuit Design

Electronic circuits intuitively visualize and quantitatively simulate biological systems with nonlinear differential equations that exhibit complicated dynamics. Drug cocktail therapies are a powerful tool against diseases that exhibit such dynamics. We show that just six key states, which are represented in a feedback circuit, enable drug-cocktail formulation: 1) healthy cell number; 2) infected cell number; 3) extracellular pathogen number; 4) intracellular pathogenic molecule number; 5) innate immune system strength; and 6) adaptive immune system strength. To enable drug cocktail formulation, the model represents the effects of the drugs in the circuit. For example, a nonlinear feedback circuit model fits measured clinical data, represents cytokine storm and adaptive autoimmune behavior, and accounts for age, sex, and variant effects for SARS-CoV-2 with few free parameters. The latter circuit model provided three quantitative insights on the optimal timing and dosage of drug components in a cocktail: 1) antipathogenic drugs should be given early in the infection, but immunosuppressant timing involves a tradeoff between controlling pathogen load and mitigating inflammation; 2) both within and across-class combinations of drugs have synergistic effects; 3) if they are administered sufficiently early in the infection, anti-pathogenic drugs are more effective at mitigating autoimmune behavior than immunosuppressant drugs.

The race to understand immunopathology in COVID-19: Perspectives on the impact of quantitative approaches to understand within-host interactions

The COVID-19 pandemic has revealed the need for the increased integration of modelling and data analysis to public health, experimental, and clinical studies. Throughout the first two years of the pandemic, there has been a concerted effort to improve our understanding of the within-host immune response to the SARS-CoV-2 virus to provide better predictions of COVID-19 severity, treatment and vaccine development questions, and insights into viral evolution and the impacts of variants on immunopathology. Here we provide perspectives on what has been accomplished using quantitative methods, including predictive modelling, population genetics, machine learning, and dimensionality reduction techniques, in the first 26 months of the COVID-19 pandemic approaches, and where we go from here to improve our responses to this and future pandemics.

The initial interplay between HIV and mucosal innate immunity

Human Immunodeficiency Virus (HIV) is still one of the major global health issues, and despite significant efforts that have been put into studying the pathogenesis of HIV infection, several aspects need to be clarified, including how innate immunity acts in different anatomical compartments. Given the nature of HIV as a sexually transmitted disease, one of the aspects that demands particular attention is the mucosal innate immune response. Given this scenario, we focused our attention on the interplay between HIV and mucosal innate response: the different mucosae act as a physical barrier, whose integrity can be compromised by the infection, and the virus-cell interaction induces the innate immune response. In addition, we explored the role of the mucosal microbiota in facilitating or preventing HIV infection and highlighted how its changes could influence the development of several opportunistic infections. Although recent progress, a proper characterization of mucosal innate immune response and microbiota is still missing, and further studies are needed to understand how they can be helpful for the formulation of an effective vaccine.

Biophysical models of early mammalian embryogenesis

Embryo development is a critical and fascinating stage in the life cycle of many organisms. Despite decades of research, the earliest stages of mammalian embryogenesis are still poorly understood, caused by a scarcity of high-resolution spatial and temporal data, the use of only a few model organisms, and a paucity of truly multidisciplinary approaches that combine biological research with biophysical modeling and computational simulation. Here, we explain the theoretical frameworks and biophysical processes that are best suited to modeling the early mammalian embryo, review a comprehensive list of previous models, and discuss the most promising avenues for future work.

Preparing for the next pandemic: Simulation-based deep reinforcement learning to discover and test multimodal control of systemic inflammation using repurposed immunomodulatory agents

Background

Preparation to address the critical gap in a future pandemic between non-pharmacological measures and the deployment of new drugs/vaccines requires addressing two factors: 1) finding virus/pathogen-agnostic pathophysiological targets to mitigate disease severity and 2) finding a more rational approach to repurposing existing drugs. It is increasingly recognized that acute viral disease severity is heavily driven by the immune response to the infection ("cytokine storm" or "cytokine release syndrome"). There exist numerous clinically available biologics that suppress various pro-inflammatory cytokines/mediators, but it is extremely difficult to identify clinically effective treatment regimens with these agents. We propose that this is a complex control problem that resists standard methods of developing treatment regimens and accomplishing this goal requires the application of simulation-based, model-free deep reinforcement learning (DRL) in a fashion akin to training successful game-playing artificial intelligences (AIs). This proof-of-concept study determines if simulated sepsis (e.g. infection-driven cytokine storm) can be controlled in the absence of effective antimicrobial agents by targeting cytokines for which FDA-approved biologics currently exist.

Methods

We use a previously validated agent-based model, the Innate Immune Response Agent-based Model (IIRABM), for control discovery using DRL. DRL training used a Deep Deterministic Policy Gradient (DDPG) approach with a clinically plausible control interval of 6 hours with manipulation of six cytokines for which there are existing drugs: Tumor Necrosis Factor (TNF), Interleukin-1 (IL-1), Interleukin-4 (IL-4), Interleukin-8 (IL-8), Interleukin-12 (IL-12) and Interferon-γ(IFNg).

Results

DRL trained an AI policy that could improve outcomes from a baseline Recovered Rate of 61% to one with a Recovered Rate of 90% over ~21 days simulated time. This DRL policy was then tested on four different parameterizations not seen in training representing a range of host and microbe characteristics, demonstrating a range of improvement in Recovered Rate by +33% to +56.

Discussion

The current proof-of-concept study demonstrates that significant disease severity mitigation can potentially be accomplished with existing anti-mediator drugs, but only through a multi-modal, adaptive treatment policy requiring implementation with an AI. While the actual clinical implementation of this approach is a projection for the future, the current goal of this work is to inspire the development of a research ecosystem that marries what is needed to improve the simulation models with the development of the sensing/assay technologies to collect the data needed to iteratively refine those models.

Multiscale modelling of desquamation in the interfollicular epidermis

Maintenance of epidermal thickness is critical to the barrier function of the skin. Decreased tissue thickness, specifically in the stratum corneum (the outermost layer of the tissue), causes discomfort and inflammation, and is related to several severe diseases of the tissue. In order to maintain both stratum corneum thickness and overall tissue thickness it is necessary for the system to balance cell proliferation and cell loss. Cell proliferation in the epidermis occurs in the basal layer and causes constant upwards movement in the tissue. Cell loss occurs when dead cells at the top of the tissue are lost to the environment through a process called desquamation. Desquamation is thought to occur through a gradual reduction in adhesion between cells, due to the cleaving of adhesion proteins by enzymes, in the stratum corneum.

In this paper we will investigate combining a (mass action) subcellular model of desquamation with a three dimensional (cell centre based) multicellular model of the interfollicular epidermis to better understand maintenance of epidermal thickness. Specifically, our aim is to determine if a hypothesised biological model for the degradation of cell-cell adhesion, from the literature, is sufficient to maintain a steady state tissue thickness. These investigations show the model is able to provide a consistent rate of cell loss in the multicellular model. This loss balances proliferation, and hence maintains a homeostatic tissue thickness. Moreover, we find that multiple proliferative cell populations in the basal layer can be represented by a single proliferative cell population, simplifying investigations with this model.

The model is used to investigate a disorder (Netherton Syndrome) which disrupts desquamation. The model shows how biochemical changes can cause disruptions to the tissue, resulting in a reduced tissue thickness and consequently diminishing the protective role of the tissue. A hypothetical treatment result is also investigated: we compare the cases of a partially effective homogeneous treatment (where all cells partially recover) and a totally effective heterogeneous treatment (in which a proportion of the cells totally recover) with the aim to determine the difference in the response of the tissue to these different scenarios. Results show an increased benefit to corneum thickness from the heterogeneous treatment over the homogeneous treatment.

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.

Building digital twins of the human immune system: toward a roadmap

Digital twins, customized simulation models pioneered in industry, are beginning to be deployed in medicine and healthcare, with some major successes, for instance in cardiovascular diagnostics and in insulin pump control. Personalized computational models are also assisting in applications ranging from drug development to treatment optimization. More advanced medical digital twins will be essential to making precision medicine a reality. Because the immune system plays an important role in such a wide range of diseases and health conditions, from fighting pathogens to autoimmune disorders, digital twins of the immune system will have an especially high impact. However, their development presents major challenges, stemming from the inherent complexity of the immune system and the difficulty of measuring many aspects of a patient’s immune state in vivo. This perspective outlines a roadmap for meeting these challenges and building a prototype of an immune digital twin. It is structured as a four-stage process that proceeds from a specification of a concrete use case to model constructions, personalization, and continued improvement.

Multiscale Model of Antiviral Timing, Potency, and Heterogeneity Effects on an Epithelial Tissue Patch Infected by SARS-CoV-2

We extend our established agent-based multiscale computational model of infection of lung tissue by SARS-CoV-2 to include pharmacokinetic and pharmacodynamic models of remdesivir. We model remdesivir treatment for COVID-19; however, our methods are general to other viral infections and antiviral therapies. We investigate the effects of drug potency, drug dosing frequency, treatment initiation delay, antiviral half-life, and variability in cellular uptake and metabolism of remdesivir and its active metabolite on treatment outcomes in a simulated patch of infected epithelial tissue. Non-spatial deterministic population models which treat all cells of a given class as identical can clarify how treatment dosage and timing influence treatment efficacy. However, they do not reveal how cell-to-cell variability affects treatment outcomes. Our simulations suggest that for a given treatment regime, including cell-to-cell variation in drug uptake, permeability and metabolism increase the likelihood of uncontrolled infection as the cells with the lowest internal levels of antiviral act as super-spreaders within the tissue. The model predicts substantial variability in infection outcomes between similar tissue patches for different treatment options. In models with cellular metabolic variability, antiviral doses have to be increased significantly (>50% depending on simulation parameters) to achieve the same treatment results as with the homogeneous cellular metabolism.

A multiscale multicellular spatiotemporal model of local influenza infection and immune response

Respiratory viral infections pose a serious public health concern, from mild seasonal influenza to pandemics like those of SARS-CoV-2. Spatiotemporal dynamics of viral infection impact nearly all aspects of the progression of a viral infection, like the dependence of viral replication rates on the type of cell and pathogen, the strength of the immune response and localization of infection. Mathematical modeling is often used to describe respiratory viral infections and the immune response to them using ordinary differential equation (ODE) models. However, ODE models neglect spatially-resolved biophysical mechanisms like lesion shape and the details of viral transport, and so cannot model spatial effects of a viral infection and immune response. In this work, we develop a multiscale, multicellular spatiotemporal model of influenza infection and immune response by combining non-spatial ODE modeling and spatial, cell-based modeling. We employ cellularization, a recently developed method for generating spatial, cell-based, stochastic models from non-spatial ODE models, to generate much of our model from a calibrated ODE model that describes infection, death and recovery of susceptible cells and innate and adaptive responses during influenza infection, and develop models of cell migration and other mechanisms not explicitly described by the ODE model. We determine new model parameters to generate agreement between the spatial and original ODE models under certain conditions, where simulation replicas using our model serve as microconfigurations of the ODE model, and compare results between the models to investigate the nature of viral exposure and impact of heterogeneous infection on the time-evolution of the viral infection. We found that using spatially homogeneous initial exposure conditions consistently with those employed during calibration of the ODE model generates far less severe infection, and that local exposure to virus must be multiple orders of magnitude greater than a uniformly applied exposure to all available susceptible cells. This strongly suggests a prominent role of localization of exposure in influenza A infection. We propose that the particularities of the microenvironment to which a virus is introduced plays a dominant role in disease onset and progression, and that spatially resolved models like ours may be important to better understand and more reliably predict future health states based on susceptibility of potential lesion sites using spatially resolved patient data of the state of an infection. We can readily integrate the immune response components of our model into other modeling and simulation frameworks of viral infection dynamics that do detailed modeling of other mechanisms like viral internalization and intracellular viral replication dynamics, which are not explicitly represented in the ODE model. We can also combine our model with available experimental data and modeling of exposure scenarios and spatiotemporal aspects of mechanisms like mucociliary clearance that are only implicitly described by the ODE model, which would significantly improve the ability of our model to present spatially resolved predictions about the progression of influenza infection and immune response.

Impairment of T cells' antiviral and anti-inflammation immunities may be critical to death from COVID-19

Clarifying dominant factors determining the immune heterogeneity from non-survivors to survivors is crucial for developing therapeutics and vaccines against COVID-19. The main difficulty is quantitatively analysing the multi-level clinical data, including viral dynamics, immune response and tissue damages. Here, we adopt a top-down modelling approach to quantify key functional aspects and their dynamical interplay in the battle between the virus and the immune system, yielding an accurate description of real-time clinical data involving hundreds of patients for the first time. The quantification of antiviral responses gives that, compared to antibodies, T cells play a more dominant role in virus clearance, especially for mild patients (96.5%). Moreover, the anti-inflammatory responses, namely the cytokine inhibition and tissue repair rates, also positively correlate with T cell number and are significantly suppressed in non-survivors. Simulations show that the lack of T cells can lead to more significant inflammation, proposing an explanation for the monotonic increase of COVID-19 mortality with age and higher mortality for males. We propose that T cells play a crucial role in the immunity against COVID-19, which provides a new direction-improvement of T cell number for advancing current prevention and treatment.

Spatially distributed infection increases viral load in a computational model of SARS-CoV-2 lung infection

A key question in SARS-CoV-2 infection is why viral loads and patient outcomes vary dramatically across individuals. Because spatial-temporal dynamics of viral spread and immune response are challenging to study in vivo, we developed Spatial Immune Model of Coronavirus (SIMCoV), a scalable computational model that simulates hundreds of millions of lung cells, including respiratory epithelial cells and T cells. SIMCoV replicates viral growth dynamics observed in patients and shows how spatially dispersed infections can lead to increased viral loads. The model also shows how the timing and strength of the T cell response can affect viral persistence, oscillations, and control. By incorporating spatial interactions, SIMCoV provides a parsimonious explanation for the dramatically different viral load trajectories among patients by varying only the number of initial sites of infection and the magnitude and timing of the T cell immune response. When the branching airway structure of the lung is explicitly represented, we find that virus spreads faster than in a 2D layer of epithelial cells, but much more slowly than in an undifferentiated 3D grid or in a well-mixed differential equation model. These results illustrate how realistic, spatially explicit computational models can improve understanding of within-host dynamics of SARS-CoV-2 infection.

Divergent COVID-19 Disease Trajectories Predicted by a DAMP-Centered Immune Network Model

COVID-19 presentations range from mild to moderate through severe disease but also manifest with persistent illness or viral recrudescence. We hypothesized that the spectrum of COVID-19 disease manifestations was a consequence of SARS-CoV-2-mediated delay in the pathogen-associated molecular pattern (PAMP) response, including dampened type I interferon signaling, thereby shifting the balance of the immune response to be dominated by damage-associated molecular pattern (DAMP) signaling. To test the hypothesis, we constructed a parsimonious mechanistic mathematical model. After calibration of the model for initial viral load and then by varying a few key parameters, we show that the core model generates four distinct viral load, immune response and associated disease trajectories termed “patient archetypes”, whose temporal dynamics are reflected in clinical data from hospitalized COVID-19 patients. The model also accounts for responses to corticosteroid therapy and predicts that vaccine-induced neutralizing antibodies and cellular memory will be protective, including from severe COVID-19 disease. This generalizable modeling framework could be used to analyze protective and pathogenic immune responses to diverse viral infections.

A hybrid PDE-ABM model for viral dynamics with application to SARS-CoV-2 and influenza

We propose a hybrid partial differential equation-agent-based (PDE-ABM) model to describe the spatio-temporal viral dynamics in a cell population. The virus concentration is considered as a continuous variable and virus movement is modelled by diffusion, while changes in the states of cells (i.e. healthy, infected, dead) are represented by a stochastic ABM. The two subsystems are intertwined: the probability of an agent getting infected in the ABM depends on the local viral concentration, and the source term of viral production in the PDE is determined by the cells that are infected. We develop a computational tool that allows us to study the hybrid system and the generated spatial patterns in detail. We systematically compare the outputs with a classical ODE system of viral dynamics, and find that the ODE model is a good approximation only if the diffusion coefficient is large. We demonstrate that the model is able to predict SARS-CoV-2 infection dynamics, and replicate the output of in vitro experiments. Applying the model to influenza as well, we can gain insight into why the outcomes of these two infections are different.

The Effects of Sperm and Seminal Fluid of Immunized Male Mice on In Vitro Fertilization and Surrogate Mother-Embryo Interaction

The latest vaccination campaign has actualized the potential impact of antigenic stimuli on reproductive functions. To address this, we mimicked vaccination’s effects by administering keyhole limpet hemocyanin (KLH ) to CD1 male mice and used their sperm for in vitro fertilization (IVF). Two-cell embryos after IVF with spermatozoa from control (C) or KLH-treated (Im) male mice were transferred to surrogate mothers mated with vasectomized control (C) or KLH-treated (Im) male mice, resulting in four experimental groups: C–C, Im–C, C–Im, and Im–Im. The pre-implantation losses were significantly lower in the Im–C group than in the C–Im group. At the same time, the resorption rates reduced markedly in the C–Im compared to the Im–C group. Embryo and placenta weights were significantly higher in the Im–Im group. Although the GM-CSF levels were lower in the amniotic fluid of the gestating surrogate mothers in the Im–Im group, they were strongly correlated with embryo mass. The number–size trade-off was only significant in the Im–Im group. This suggests a positive, cooperative effect of spermatozoa and seminal fluid from immune-primed males on embryo growth and the optimal distribution of surrogate mother maternal resources despite the negative impact of males’ antigenic challenge on the IVF success rate.

Generation of multicellular spatiotemporal models of population dynamics from ordinary differential equations, with applications in viral infection

BACKGROUND

The biophysics of an organism span multiple scales from subcellular to organismal and include processes characterized by spatial properties, such as the diffusion of molecules, cell migration, and flow of intravenous fluids. Mathematical biology seeks to explain biophysical processes in mathematical terms at, and across, all relevant spatial and temporal scales, through the generation of representative models. While non-spatial, ordinary differential equation (ODE) models are often used and readily calibrated to experimental data, they do not explicitly represent the spatial and stochastic features of a biological system, limiting their insights and applications. However, spatial models describing biological systems with spatial information are mathematically complex and computationally expensive, which limits the ability to calibrate and deploy them and highlights the need for simpler methods able to model the spatial features of biological systems.

RESULTS

In this work, we develop a formal method for deriving cell-based, spatial, multicellular models from ODE models of population dynamics in biological systems, and vice versa. We provide examples of generating spatiotemporal, multicellular models from ODE models of viral infection and immune response. In these models, the determinants of agreement of spatial and non-spatial models are the degree of spatial heterogeneity in viral production and rates of extracellular viral diffusion and decay. We show how ODE model parameters can implicitly represent spatial parameters, and cell-based spatial models can generate uncertain predictions through sensitivity to stochastic cellular events, which is not a feature of ODE models. Using our method, we can test ODE models in a multicellular, spatial context and translate information to and from non-spatial and spatial models, which help to employ spatiotemporal multicellular models using calibrated ODE model parameters. We additionally investigate objects and processes implicitly represented by ODE model terms and parameters and improve the reproducibility of spatial, stochastic models.

CONCLUSION

We developed and demonstrate a method for generating spatiotemporal, multicellular models from non-spatial population dynamics models of multicellular systems. We envision employing our method to generate new ODE model terms from spatiotemporal and multicellular models, recast popular ODE models on a cellular basis, and generate better models for critical applications where spatial and stochastic features affect outcomes.

Multiscale modeling in disease

Multiscale computational modeling aims to connect the complex networks of effects at different length and/or time scales. For example, these networks often include intracellular molecular signaling, crosstalk, and other interactions between neighboring cell populations, and higher levels of emergent phenomena across different regions of tissues and among collections of tissues or organs interacting with each other in the whole body. Recent applications of multiscale modeling across intracellular, cellular, and/or tissue levels are highlighted here. These models incorporated the roles of biochemical and biomechanical modulation in processes that are implicated in the mechanisms of several diseases including fibrosis, joint and bone diseases, respiratory infectious diseases, and cancers.

Intracellular Life Cycle Kinetics of SARS-CoV-2 Predicted Using Mathematical Modelling

SARS-CoV-2 infection represents a global threat to human health. Various approaches were employed to reveal the pathogenetic mechanisms of COVID-19. Mathematical and computational modelling is a powerful tool to describe and analyze the infection dynamics in relation to a plethora of processes contributing to the observed disease phenotypes. In our study here, we formulate and calibrate a deterministic model of the SARS-CoV-2 life cycle. It provides a kinetic description of the major replication stages of SARS-CoV-2. Sensitivity analysis of the net viral progeny with respect to model parameters enables the identification of the life cycle stages that have the strongest impact on viral replication. These three most influential parameters are (i) degradation rate of positive sense vRNAs in cytoplasm (negative effect), (ii) threshold number of non-structural proteins enhancing vRNA transcription (negative effect), and (iii) translation rate of non-structural proteins (positive effect). The results of our analysis could be used for guiding the search for antiviral drug targets to combat SARS-CoV-2 infection.

Advancing therapies for viral infections using mechanistic computational models of the dynamic interplay between the virus and host immune response

The COVID-19 pandemic has highlighted a need for improved frameworks for drug discovery, repurposing, clinical trial design and therapy optimization and personalization. Mechanistic computational models can play an important role in developing these frameworks. We discuss how mechanistic models, which consider viral entry, replication in target cells, viral spread in the body, immune response, and the complex factors involved in tissue and organ damage and recovery, can clarify the mechanisms of humoral and cellular immune responses to the virus, viral distribution and replication in tissues, the origins of pathogenesis and patient-to-patient heterogeneity in responses. These models are already improving our understanding of the mechanisms of action of antivirals and immune modulators. We discuss how closer collaboration between the experimentalists, clinicians and modelers could result in more predictive models which may guide therapies for viral infections, improving survival and leading to faster and more complete recovery.

Current and prospective computational approaches and challenges for developing COVID-19 vaccines

SARS-CoV-2, which causes COVID-19, was first identified in humans in late 2019 and is a coronavirus which is zoonotic in origin. As it spread around the world there has been an unprecedented effort in developing effective vaccines. Computational methods can be used to speed up the long and costly process of vaccine development. Antigen selection, epitope prediction, and toxicity and allergenicity prediction are areas in which computational tools have already been applied as part of reverse vaccinology for SARS-CoV-2 vaccine development. However, there is potential for computational methods to assist further. We review approaches which have been used and highlight additional bioinformatic approaches and PK modelling as in silico methods which may be useful for SARS-CoV-2 vaccine design but remain currently unexplored. As more novel viruses with pandemic potential are expected to arise in future, these techniques are not limited to application to SARS-CoV-2 but also useful to rapidly respond to novel emerging viruses.

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.