Modeling identifies variability in SARS-CoV-2 uptake and eclipse phase by infected cells as principal drivers of extreme variability in nasal viral load in the 48 h post infection.

The SARS-CoV-2 coronavirus continues to evolve with scores of mutations of the spike, membrane, envelope, and nucleocapsid structural proteins that impact pathogenesis. Infection data from nasal swabs, nasal PCR assays, upper respiratory samples, ex vivo cell cultures and nasal epithelial organoids reveal extreme variabilities in SARS-CoV-2 RNA titers within and between the variants. Some variabilities are naturally prone to clinical testing protocols and experimental controls. Here we focus on nasal viral load sensitivity arising from the timing of sample collection relative to onset of infection and from heterogeneity in the kinetics of cellular infection, uptake, replication, and shedding of viral RNA copies. The sources of between-variant variability are likely due to SARS-CoV-2 structural protein mutations, whereas within-variant population variability is likely due to heterogeneity in cellular response to that particular variant. With the physiologically faithful, agent-based mechanistic model of inhaled exposure and infection from (Chen et al., 2022), we perform statistical sensitivity analyses of the progression of nasal viral titers in the first 0-48 h post infection, focusing on three kinetic mechanisms. Model simulations reveal shorter latency times of infected cells (including cellular uptake, viral RNA replication, until the onset of viral RNA shedding) exponentially accelerate nasal viral load. Further, the rate of infectious RNA copies shed per day has a proportional influence on nasal viral load. Finally, there is a very weak, negative correlation of viral load with the probability of infection per virus-cell encounter, the model proxy for spike-receptor binding affinity.

Disrupting the ciliary gradient of active Arl3 affects rod photoreceptor nuclear migration.

The small GTPase Arl3 is important for the enrichment of lipidated proteins to primary cilia, including the outer segment of photoreceptors. Human mutations in the small GTPase Arl3 cause both autosomal recessive and dominant inherited retinal dystrophies. We discovered that dominant mutations result in increased active G-protein-Arl3-D67V has constitutive activity and Arl3-Y90C is fast cycling-and their expression in mouse rods resulted in a displaced nuclear phenotype due to an aberrant Arl3-GTP gradient. Using multiple strategies, we go on to show that removing or restoring the Arl3-GTP gradient within the cilium is sufficient to rescue the nuclear migration defect. Together, our results reveal that an Arl3 ciliary gradient is involved in proper positioning of photoreceptor nuclei during retinal development.

Antibody protection from SARS-CoV-2 respiratory tract exposure and infection.

The COVID-19 pandemic has underscored the need to understand the dynamics of SARS-CoV-2 respiratory infection and protection provided by the immune response. SARS-CoV-2 infections are characterized by a particularly high viral load, and further by the small number of inhaled virions sufficient to generate a high viral titer in the nasal passage a few days after exposure. SARS-CoV-2 specific antibodies (Ab), induced from vaccines, previous infection, or inhaled monoclonal Ab, have proven effective against SARS-CoV-2 infection. Our goal in this work is to model the protective mechanisms that Ab can provide and to assess the degree of protection from individual and combined mechanisms at different locations in the respiratory tract. Neutralization, in which Ab bind to virion spikes and inhibit them from binding to and infecting target cells, is one widely reported protective mechanism. A second mechanism of Ab protection is muco-trapping, in which Ab crosslink virions to domains on mucin polymers, effectively immobilizing them in the mucus layer. When muco-trapped, the continuous clearance of the mucus barrier by coordinated ciliary propulsion entrains the trapped viral load toward the esophagus to be swallowed. We model and simulate the protection provided by either and both mechanisms at different locations in the respiratory tract, parametrized by the Ab titer and binding-unbinding rates of Ab to viral spikes and mucin domains. Our results illustrate limits in the degree of protection by neutralizing Ab alone, the powerful protection afforded by muco-trapping Ab, and the potential for dual protection by muco-trapping and neutralizing Ab to arrest a SARS-CoV-2 infection. This manuscript was submitted as part of a theme issue on "Modelling COVID-19 and Preparedness for Future Pandemics".

Computational Modeling Insights into Extreme Heterogeneity in COVID-19 Nasal Swab Data.

Throughout the COVID-19 pandemic, an unprecedented level of clinical nasal swab data from around the globe has been collected and shared. Positive tests have consistently revealed viral titers spanning six orders of magnitude! An open question is whether such extreme population heterogeneity is unique to SARS-CoV-2 or possibly generic to viral respiratory infections. To probe this question, we turn to the computational modeling of nasal tract infections. Employing a physiologically faithful, spatially resolved, stochastic model of respiratory tract infection, we explore the statistical distribution of human nasal infections in the immediate 48 h of infection. The spread, or heterogeneity, of the distribution derives from variations in factors within the model that are unique to the infected host, infectious variant, and timing of the test. Hypothetical factors include: (1) reported physiological differences between infected individuals (nasal mucus thickness and clearance velocity); (2) differences in the kinetics of infection, replication, and shedding of viral RNA copies arising from the unique interactions between the host and viral variant; and (3) differences in the time between initial cell infection and the clinical test. Since positive clinical tests are often pre-symptomatic and independent of prior infection or vaccination status, in the model we assume immune evasion throughout the immediate 48 h of infection. Model simulations generate the mean statistical outcomes of total shed viral load and infected cells throughout 48 h for each "virtual individual", which we define as each fixed set of model parameters (1) and (2) above. The "virtual population" and the statistical distribution of outcomes over the population are defined by collecting clinically and experimentally guided ranges for the full set of model parameters (1) and (2). This establishes a model-generated "virtual population database" of nasal viral titers throughout the initial 48 h of infection of every individual, which we then compare with clinical swab test data. Support for model efficacy comes from the sampling of infection dynamics over the virtual population database, which reproduces the six-order-of-magnitude clinical population heterogeneity. However, the goal of this study is to answer a deeper biological and clinical question. What is the impact on the dynamics of early nasal infection due to each individual physiological feature or virus-cell kinetic mechanism? To answer this question, global data analysis methods are applied to the virtual population database that sample across the entire database and de-correlate (i.e., isolate) the dynamic infection outcome sensitivities of each model parameter. These methods predict the dominant, indeed exponential, driver of population heterogeneity in dynamic infection outcomes is the latency time of infected cells (from the moment of infection until onset of viral RNA shedding). The shedding rate of the viral RNA of infected cells in the shedding phase is a strong, but not exponential, driver of infection. Furthermore, the unknown timing of the nasal swab test relative to the onset of infection is an equally dominant contributor to extreme population heterogeneity in clinical test data since infectious viral loads grow from undetectable levels to more than six orders of magnitude within 48 h.

Modeling insights into SARS-CoV-2 respiratory tract infections prior to immune protection.

Mechanistic insights into human respiratory tract (RT) infections from SARS-CoV-2 can inform public awareness as well as guide medical prevention and treatment for COVID-19 disease. Yet the complexity of the RT and the inability to access diverse regions pose fundamental roadblocks to evaluation of potential mechanisms for the onset and progression of infection (and transmission). We present a model that incorporates detailed RT anatomy and physiology, including airway geometry, physical dimensions, thicknesses of airway surface liquids (ASLs), and mucus layer transport by cilia. The model further incorporates SARS-CoV-2 diffusivity in ASLs and best-known data for epithelial cell infection probabilities, and, once infected, duration of eclipse and replication phases, and replication rate of infectious virions. We apply this baseline model in the absence of immune protection to explore immediate, short-term outcomes from novel SARS-CoV-2 depositions onto the air-ASL interface. For each RT location, we compute probability to clear versus infect; per infected cell, we compute dynamics of viral load and cell infection. Results reveal that nasal infections are highly likely within 1-2 days from minimal exposure, and alveolar pneumonia occurs only if infectious virions are deposited directly into alveolar ducts and sacs, not via retrograde propagation to the deep lung. Furthermore, to infect just 1% of the 140 m2 of alveolar surface area within 1 week, either 103 boluses each with 106 infectious virions or 106 aerosols with one infectious virion, all physically separated, must be directly deposited. These results strongly suggest that COVID-19 disease occurs in stages: a nasal/upper RT infection, followed by self-transmission of infection to the deep lung. Two mechanisms of self-transmission are persistent aspiration of infected nasal boluses that drain to the deep lung and repeated rupture of nasal aerosols from infected mucosal membranes by speaking, singing, or cheering that are partially inhaled, exhaled, and re-inhaled, to the deep lung.

A PBPK model recapitulates early kinetics of anti-PEG antibody-mediated clearance of PEG-liposomes.

PEGylation is routinely used to extend the systemic circulation of various protein therapeutics and nanomedicines. Nonetheless, mounting evidence is emerging that individuals exposed to select PEGylated therapeutics can develop antibodies specific to PEG, i.e., anti-PEG antibodies (APA). In turn, APA increase both the risk of hypersensitivity to the drug as well as potential loss of efficacy due to accelerated blood clearance of the drug. Despite the broad implications of APA, the timescales and systemic specificity by which APA can alter the pharmacokinetics and biodistribution of PEGylated drugs remain not well understood. Here, we developed a physiologically based pharmacokinetic (PBPK) model designed to resolve APA's impact on both early- and late-phase pharmacokinetics and biodistribution of intravenously administered PEGylated drugs. Our model accurately recapitulates PK and biodistribution data obtained from PET/CT imaging of radiolabeled PEG-liposomes and PEG-uricase in mice with and without APA, as well as serum levels of PEG-uricase in humans. Our work provides another illustration of the power of high-resolution PBPK models for understanding the pharmacokinetic impacts of anti-drug antibodies and the dynamics with which antibodies can mediate clearance of foreign species.

Experimental Data and PBPK Modeling Quantify Antibody Interference in PEGylated Drug Carrier Delivery.

Physiologically-based pharmacokinetic (PBPK) modeling is a popular drug development tool that integrates physiology, drug physicochemical properties, preclinical data, and clinical information to predict drug systemic disposition. Since PBPK models seek to capture complex physiology, parameter uncertainty and variability is a prevailing challenge: there are often more compartments (e.g., organs, each with drug flux and retention mechanisms, and associated model parameters) than can be simultaneously measured. To improve the fidelity of PBPK modeling, one approach is to search and optimize within the high-dimensional model parameter space, based on experimental time-series measurements of drug distributions. Here, we employ Latin Hypercube Sampling (LHS) on a PBPK model of PEG-liposomes (PL) that tracks biodistribution in an 8-compartment mouse circulatory system, in the presence (APA+) or absence (naïve) of anti-PEG antibodies (APA). Near-continuous experimental measurements of PL concentration during the first hour post-injection from the liver, spleen, kidney, muscle, lung, and blood plasma, based on PET/CT imaging in live mice, are used as truth sets with LHS to infer optimal parameter ranges for the full PBPK model. The data and model quantify that PL retention in the liver is the primary differentiator of biodistribution patterns in naïve versus APA+ mice, and spleen the secondary differentiator. Retention of PEGylated nanomedicines is substantially amplified in APA+ mice, likely due to PL-bound APA engaging specific receptors in the liver and spleen that bind antibody Fc domains. Our work illustrates how applying LHS to PBPK models can further mechanistic understanding of the biodistribution and antibody-mediated clearance of specific drugs.

A computational model tracks whole-lung Mycobacterium tuberculosis infection and predicts factors that inhibit dissemination.

Mycobacterium tuberculosis (Mtb), the causative infectious agent of tuberculosis (TB), kills more individuals per year than any other infectious agent. Granulomas, the hallmark of Mtb infection, are complex structures that form in lungs, composed of immune cells surrounding bacteria, infected cells, and a caseous necrotic core. While granulomas serve to physically contain and immunologically restrain bacteria growth, some granulomas are unable to control Mtb growth, leading to bacteria and infected cells leaving the granuloma and disseminating, either resulting in additional granuloma formation (local or non-local) or spread to airways or lymph nodes. Dissemination is associated with development of active TB. It is challenging to experimentally address specific mechanisms driving dissemination from TB lung granulomas. Herein, we develop a novel hybrid multi-scale computational model, MultiGran, that tracks Mtb infection within multiple granulomas in an entire lung. MultiGran follows cells, cytokines, and bacterial populations within each lung granuloma throughout the course of infection and is calibrated to multiple non-human primate (NHP) cellular, granuloma, and whole-lung datasets. We show that MultiGran can recapitulate patterns of in vivo local and non-local dissemination, predict likelihood of dissemination, and predict a crucial role for multifunctional CD8+ T cells and macrophage dynamics for preventing dissemination.

An Agent-Based Systems Pharmacology Model of the Antibody-Drug Conjugate Kadcyla to Predict Efficacy of Different Dosing Regimens.

The pharmaceutical industry has invested significantly in antibody-drug conjugates (ADCs) with five FDA-approved therapies and several more showing promise in late-stage clinical trials. The FDA-approved therapeutic Kadcyla (ado-trastuzumab emtansine or T-DM1) can extend the survival of patients with tumors overexpressing HER2. However, tumor histology shows that most T-DM1 localizes perivascularly, but coadministration with its unconjugated form (trastuzumab) improves penetration of the ADC into the tumor and subsequent treatment efficacy. ADC dosing schedule, e.g., dose fractionation, has also been shown to improve tolerability. However, it is still not clear how coadministration with carrier doses impacts efficacy in terms of receptor expression, dosing regimens, and payload potency. Here, we develop a hybrid agent-based model (ABM) to capture ADC and/or antibody delivery and to predict tumor killing and growth kinetics. The results indicate that a carrier dose improves efficacy when the increased number of cells targeted by the ADC outweighs the reduced fractional killing of the targeted cells. The threshold number of payloads per cell required for killing plays a pivotal role in defining this cutoff. Likewise, fractionated dosing lowers ADC efficacy due to lower tissue penetration from a reduced maximum plasma concentration. It is only beneficial when an increase in tolerability from fractionation allows a higher ADC/payload dose that more than compensates for the loss in efficacy from fractionation. Overall, the multiscale model enables detailed depictions of heterogeneous ADC delivery, cancer cell death, and tumor growth to show how carrier dosing impacts efficacy to design the most efficacious regimen.

Overcoming anti-PEG antibody mediated accelerated blood clearance of PEGylated liposomes by pre-infusion with high molecular weight free PEG.

Antibodies that specifically bind polyethylene glycol (PEG), i.e. anti-PEG antibodies (APA), are associated with reduced efficacy and increased risk of serious adverse events for several PEGylated therapeutics. Here, we explored the concept of using free PEG molecules to saturate circulating APA. Surprisingly, we found that 40 kDa free PEG effectively restored the prolonged circulation of PEGylated liposomes in the presence of high titers of pre-existing APA for at least 48 h in mice. In contrast, lower molecular weight free PEG (≤10 kDa) failed to restore circulation beyond a few hours. These in vivo results were consistent with estimates from a minimal physiologically based pharmacokinetic model. Importantly, the infusion of free PEG appeared to be safe in mice previously sensitized by injection of PEGylated liposomes, and free PEG did not elicit excess APA production even in mice with pre-existing adaptive immunity against PEG. Our results support further investigation of high molecular weight free PEG as a potential method to control and overcome high titers of APA, restoring the prolonged circulation of PEGylated liposomes and possibly other PEGylated therapeutics.

Modeling Barrier Properties of Intestinal Mucus Reinforced with IgG and Secretory IgA against Motile Bacteria.

The gastrointestinal (GI) tract is lined with a layer of viscoelastic mucus gel, characterized by a dense network of entangled and cross-linked mucins together with an abundance of antibodies (Ab). Secretory IgA (sIgA), the predominant Ab isotype in the GI tract, is a dimeric molecule with 4 antigen-binding domains capable of inducing efficient clumping of bacteria, or agglutination. IgG, another common Ab at mucosal surfaces, can cross-link individual viruses to the mucin mesh through multiple weak bonds between IgG-Fc and mucins, a process termed muco-trapping. Relative contributions by agglutination versus muco-trapping in blocking permeation of motile bacteria through mucus remain poorly understood. Here, we developed a mathematical model that takes into account physiologically relevant spatial dimensions and time scales, binding and unbinding rates between Ab and bacteria as well as between Ab and mucins, the diffusivities of Ab, and run-tumble motion of active bacteria. Our model predicts both sIgA and IgG can accumulate on the surface of individual bacteria at sufficient quantities and rates to enable trapping individual bacteria in mucins before they penetrate the mucus layer. Furthermore, our model predicts that agglutination only modestly improves the ability for antibodies to block bacteria permeation through mucus. These results suggest that while sIgA is the most potent Ab isotype overall at stopping bacterial penetration, IgG may represent a practical alternative for mucosal prophylaxis and therapy. Our work improves the mechanistic understanding of Ab-enhanced barrier properties of mucus and highlights the ability for muco-trapping Ab to protect against motile pathogens at mucosal surfaces.

Data-Driven Model Validation Across Dimensions.

Data-driven model validation across dimensions in mathematical and computational biology assumptions are often made (e.g., symmetry) to reduce the problem from three spatial dimensions (3D) to two (2D). However, some experimental datasets, such as cell counts obtained via flow cytometry, represent the entire 3D biological object. For purpose of model calibration and validation, it is sometimes necessary to compare these biological datasets with model outputs. We propose a methodology for scaling 2D model outputs to compare with 3D experimental datasets, and we discuss the application of this methodology to two examples: agent-based models of granuloma formation and skeletal muscle tissue. The accuracy of the method is evaluated in artificially generated scenarios.

Dynamic balance of pro- and anti-inflammatory signals controls disease and limits pathology.

Immune responses to pathogens are complex and not well understood in many diseases, and this is especially true for infections by persistent pathogens. One mechanism that allows for long-term control of infection while also preventing an over-zealous inflammatory response from causing extensive tissue damage is for the immune system to balance pro- and anti-inflammatory cells and signals. This balance is dynamic and the immune system responds to cues from both host and pathogen, maintaining a steady state across multiple scales through continuous feedback. Identifying the signals, cells, cytokines, and other immune response factors that mediate this balance over time has been difficult using traditional research strategies. Computational modeling studies based on data from traditional systems can identify how this balance contributes to immunity. Here we provide evidence from both experimental and mathematical/computational studies to support the concept of a dynamic balance operating during persistent and other infection scenarios. We focus mainly on tuberculosis, currently the leading cause of death due to infectious disease in the world, and also provide evidence for other infections. A better understanding of the dynamically balanced immune response can help shape treatment strategies that utilize both drugs and host-directed therapies.

A blueprint for robust crosslinking of mobile species in biogels with weakly adhesive molecular anchors.

Biopolymeric matrices can impede transport of nanoparticulates and pathogens by entropic or direct adhesive interactions, or by harnessing "third-party" molecular anchors to crosslink nanoparticulates to matrix constituents. The trapping potency of anchors is dictated by association rates and affinities to both nanoparticulates and matrix; the popular dogma is that long-lived, high-affinity bonds to both species facilitate optimal trapping. Here we present a contrasting paradigm combining experimental evidence (using IgG antibodies and Matrigel®), a theoretical framework (based on multiple timescale analysis), and computational modeling. Anchors that bind and unbind rapidly from matrix accumulate on nanoparticulates much more quickly than anchors that form high-affinity, long-lived bonds with matrix, leading to markedly greater trapping potency of multiple invading species without saturating matrix trapping capacity. Our results provide a blueprint for engineering molecular anchors with finely tuned affinities to effectively enhance the barrier properties of biogels against diverse nanoparticulate species.Biological polymeric matrices often use molecular anchors, such as antibodies, to trap nanoparticulates. Here, the authors find that anchor-matrix bonds that are weak and short-lived confer superior trapping potency, contrary to the prevailing belief that effective molecular anchors should form strong bonds to both the matrix and the nanoparticulates.

Modeling the Excess Cell Surface Stored in a Complex Morphology of Bleb-Like Protrusions.

Cells transition from spread to rounded morphologies in diverse physiological contexts including mitosis and mesenchymal-to-amoeboid transitions. When these drastic shape changes occur rapidly, cell volume and surface area are approximately conserved. Consequently, the rounded cells are suddenly presented with a several-fold excess of cell surface whose area far exceeds that of a smooth sphere enclosing the cell volume. This excess is stored in a population of bleb-like protrusions (BLiPs), whose size distribution is shown by electron micrographs to be skewed. We introduce three complementary models of rounded cell morphologies with a prescribed excess surface area. A 2D Hamiltonian model provides a mechanistic description of how discrete attachment points between the cell surface and cortex together with surface bending energy can generate a morphology that satisfies a prescribed excess area and BLiP number density. A 3D random seed-and-growth model simulates efficient packing of BLiPs over a primary rounded shape, demonstrating a pathway for skewed BLiP size distributions that recapitulate 3D morphologies. Finally, a phase field model (2D and 3D) posits energy-based constitutive laws for the cell membrane, nematic F-actin cortex, interior cytosol, and external aqueous medium. The cell surface is equipped with a spontaneous curvature function, a proxy for the cell surface-cortex couple, that is a priori unknown, which the model "learns" from the thin section transmission electron micrograph image (2D) or the "seed and growth" model image (3D). Converged phase field simulations predict self-consistent amplitudes and spatial localization of pressure and stress throughout the cell for any posited stationary morphology target and cell compartment constitutive properties. The models form a general framework for future studies of cell morphological dynamics in a variety of biological contexts.

Using Computational Modeling To Optimize the Design of Antibodies That Trap Viruses in Mucus.

Immunoglobulin G (IgG) antibodies that trap viruses in cervicovaginal mucus (CVM) via adhesive interactions between IgG-Fc and mucins have recently emerged as a promising strategy to block vaginally transmitted infections. The array of IgG bound to a virus particle appears to trap the virus by making multiple weak affinity bonds to the fibrous mucins that form the mucus gel. However, the antibody characteristics that maximize virus trapping and minimize viral infectivity remain poorly understood. Toward this goal, we developed a mathematical model that takes into account physiologically relevant spatial dimensions and time scales, binding, and unbinding rates between IgG and virions and between IgG and mucins, as well as the respective diffusivities of virions and IgG in semen and CVM. We then systematically explored the IgG-antigen and IgG-mucin binding and unbinding rates that minimize the flux of infectious HIV arriving at the vaginal epithelium. Surprisingly, contrary to common intuition that infectivity would drop monotonically with increasing affinities between IgG and HIV, and between IgG and mucins, our model suggests maximal trapping of HIV and minimal flux of HIV to the epithelium are achieved with IgG molecules that exhibit (i) rapid antigen binding (high kon) rather than very slow unbinding (low koff), that is, high-affinity binding to the virion, and (ii) relatively weak affinity with mucins. These results provide important insights into the design of more potent "mucotrapping" IgG for enhanced protection against vaginally transmitted infections. The model is adaptable to other pathogens, mucosal barriers, geometries, and kinetic and diffusional effects, providing a tool for hypothesis testing and producing quantitative insights into the dynamics of immune-mediated protection.