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.

PhysiPKPD: A pharmacokinetics and pharmacodynamics module for PhysiCell.

Pharmacokinetics and pharmacodynamics (PKPD) are key considerations in any study of molecular therapies. It is thus imperative to factor their effects into any in silico model of biological tissue involving such therapies. Furthermore, creating a standardized and flexible framework will benefit the community by increasing access to such modules and enhancing their communicability. PhysiCell is an open-source physics-based cell simulator, i.e., a platform for modeling biological tissue, that is quickly being adopted and utilized by the mathematical biology community. We present here PhysiPKPD, an open-source PhysiCell-based package that allows users to include PKPD in PhysiCell models. Availability & Implementation: The source code for PhysiPKPD is located here: https://github.com/drbergman/PhysiPKPD.

Iterative community-driven development of a SARS-CoV-2 tissue simulator.

The 2019 novel coronavirus, SARS-CoV-2, is a pathogen of critical significance to international public health. Knowledge of the interplay between molecular-scale virus-receptor interactions, single-cell viral replication, intracellular-scale viral transport, and emergent tissue-scale viral propagation is limited. Moreover, little is known about immune system-virus-tissue interactions and how these can result in low-level (asymptomatic) infections in some cases and acute respiratory distress syndrome (ARDS) in others, particularly with respect to presentation in different age groups or pre-existing inflammatory risk factors. Given the nonlinear interactions within and among each of these processes, multiscale simulation models can shed light on the emergent dynamics that lead to divergent outcomes, identify actionable "choke points" for pharmacologic interventions, screen potential therapies, and identify potential biomarkers that differentiate patient outcomes. Given the complexity of the problem and the acute need for an actionable model to guide therapy discovery and optimization, we introduce and iteratively refine a prototype of a multiscale model of SARS-CoV-2 dynamics in lung tissue. The first prototype model was built and shared internationally as open source code and an online interactive model in under 12 hours, and community domain expertise is driving regular refinements. In a sustained community effort, this consortium is integrating data and expertise across virology, immunology, mathematical biology, quantitative systems physiology, cloud and high performance computing, and other domains to accelerate our response to this critical threat to international health. More broadly, this effort is creating a reusable, modular framework for studying viral replication and immune response in tissues, which can also potentially be adapted to related problems in immunology and immunotherapy.

Persistence as an Optimal Hedging Strategy.

Bacteria invest in a slow-growing subpopulation, called persisters, to ensure survival in the face of uncertainty. This hedging strategy is remarkably similar to financial hedging, where diversifying an investment portfolio protects against economic uncertainty. We provide a new, to our knowledge, theoretical foundation for understanding cellular hedging by unifying the study of biological population dynamics and the mathematics of financial risk management through optimal control theory. Motivated by the widely accepted role of volatility in the emergence of persistence, we consider several models of environmental volatility described by continuous-time stochastic processes. This allows us to study an emergent cellular hedging strategy that maximizes the expected per capita growth rate of the population. Analytical and simulation results probe the optimal persister strategy, revealing results that are consistent with experimental observations and suggest new opportunities for experimental investigation and design. Overall, we provide a new, to our knowledge, way of conceptualizing and modeling cellular decision making in volatile environments by explicitly unifying theory from mathematical biology and finance.

Trends of mutation accumulation across global SARS-CoV-2 genomes: Implications for the evolution of the novel coronavirus.

To understand SARS-CoV-2 microevolution, this study explored the genome-wide frequency, gene-wise distribution, and molecular nature of all point-mutations detected across its 71,703 RNA-genomes deposited in GISAID till 21 August 2020. Globally, nsp1/nsp2 and orf7a/orf3a were the most mutation-ridden non-structural and structural genes respectively. Phylogeny of 4618 spatiotemporally-representative genomes revealed that entities belonging to the early lineages are mostly spread over Asian countries, including India, whereas the recently-derived lineages are more globally distributed. Of the total 20,163 instances of polymorphism detected across global genomes, 12,594 and 7569 involved transitions and transversions, predominated by cytidine-to-uridine and guanosine-to-uridine conversions, respectively. Positive selection of nonsynonymous mutations (dN/dS >1) in most of the structural, but not the non-structural, genes indicated that SARS-CoV-2 has already harmonized its replication/transcription machineries with the host metabolism, while it is still redefining virulence/transmissibility strategies at the molecular level. Mechanistic bases and evolutionary/pathogenicity-related implications are discussed for the predominant mutation-types.

Aerobic microbial communities in the sediments of a marine oxygen minimum zone.

The ecology of aerobic microorganisms is never explored in marine oxygen minimum zone (OMZ) sediments. Here we reveal aerobic bacterial communities along ∼3 m sediment-horizons of the eastern Arabian Sea OMZ. Sulfide-containing sediment-cores retrieved from 530 mbsl (meters beneath the sea-level) and 580 mbsl were explored at 15-30 cm intervals, using metagenomics, pure-culture-isolation, genomics and metatranscriptomics. Genes for aerobic respiration, and oxidation of methane/ammonia/alcohols/thiosulfate/sulfite/organosulfur-compounds, were detected in the metagenomes from all 25 sediment-samples explored. Most probable numbers for aerobic chemolithoautotrophs and chemoorganoheterotrophs at individual sample-sites were up to 1.1 × 107 (g sediment)-1. The sediment-sample collected from 275 cmbsf (centimeters beneath the seafloor) of the 530-mbsl-core yielded many such obligately aerobic isolates belonging to Cereibacter, Guyparkeria, Halomonas, Methylophaga, Pseudomonas and Sulfitobacter which died upon anaerobic incubation, despite being provided with all possible electron acceptors and fermentative substrates. High percentages of metatranscriptomic reads from the 275 cmbsf sediment-sample, and metagenomic reads from all 25 sediment-samples, matched the isolates' genomic sequences including those for aerobic metabolisms, genetic/environmental information processing and cell division, thereby illustrating the bacteria's in-situ activity, and ubiquity across the sediment-horizons, respectively. The findings hold critical implications for organic carbon sequestration/remineralization, and inorganic compounds oxidation, within the sediment realm of global marine OMZs.

Administration of Defective Virus Inhibits Dengue Transmission into Mosquitoes.

The host-vector shuttle and the bottleneck in dengue transmission is a significant aspect with regard to the study of dengue outbreaks. As mosquitoes require 100-1000 times more virus to become infected than human, the transmission of dengue virus from human to mosquito is a vulnerability that can be targeted to improve disease control. In order to capture the heterogeneity in the infectiousness of an infected patient population towards the mosquito population, we calibrate a population of host-to-vector virus transmission models based on an experimentally quantified infected fraction of a mosquito population. Once the population of models is well-calibrated, we deploy a population of controls that helps to inhibit the human-to-mosquito transmission of the dengue virus indirectly by reducing the viral load in the patient body fluid. We use an optimal bang-bang control on the administration of the defective virus (transmissible interfering particles (TIPs)) to symptomatic patients in the course of their febrile period and observe the dynamics in successful reduction of dengue spread into mosquitoes.

Designing combination therapies using multiple optimal controls.

Strategic management of populations of interacting biological species routinely requires interventions combining multiple treatments or therapies. This is important in key research areas such as ecology, epidemiology, wound healing and oncology. Despite the well developed theory and techniques for determining single optimal controls, there is limited practical guidance supporting implementation of combination therapies. In this work we use optimal control theory to calculate optimal strategies for applying combination therapies to a model of acute myeloid leukaemia. We present a versatile framework to systematically explore the trade-offs that arise in designing combination therapy protocols using optimal control. We consider various combinations of continuous and bang-bang (discrete) controls, and we investigate how the control dynamics interact and respond to changes in the weighting and form of the pay-off characterising optimality. We demonstrate that the optimal controls respond non-linearly to treatment strength and control parameters, due to the interactions between species. We discuss challenges in appropriately characterising optimality in a multiple control setting and provide practical guidance for applying multiple optimal controls. Code used in this work to implement multiple optimal controls is available on GitHub.

Microbiome and ecology of a hot spring-microbialite system on the Trans-Himalayan Plateau.

Little is known about life in the boron-rich hot springs of Trans-Himalayas. Here, we explore the geomicrobiology of a 4438-m-high spring which emanates ~70 °C-water from a boratic microbialite called Shivlinga. Due to low atmospheric pressure, the vent-water is close to boiling point so can entropically destabilize biomacromolecular systems. Starting from the vent, Shivlinga's geomicrobiology was revealed along the thermal gradients of an outflow-channel and a progressively-drying mineral matrix that has no running water; ecosystem constraints were then considered in relation to those of entropically comparable environments. The spring-water chemistry and sinter mineralogy were dominated by borates, sodium, thiosulfate, sulfate, sulfite, sulfide, bicarbonate, and other macromolecule-stabilizing (kosmotropic) substances. Microbial diversity was high along both of the hydrothermal gradients. Bacteria, Eukarya and Archaea constituted >98%, ~1% and <1% of Shivlinga's microbiome, respectively. Temperature constrained the biodiversity at ~50 °C and ~60 °C, but not below 46 °C. Along each thermal gradient, in the vent-to-apron trajectory, communities were dominated by Aquificae/Deinococcus-Thermus, then Chlorobi/Chloroflexi/Cyanobacteria, and finally Bacteroidetes/Proteobacteria/Firmicutes. Interestingly, sites of >45 °C were inhabited by phylogenetic relatives of taxa for which laboratory growth is not known at >45 °C. Shivlinga's geomicrobiology highlights the possibility that the system's kosmotrope-dominated chemistry mitigates against the biomacromolecule-disordering effects of its thermal water.

Computational study of parameter sensitivity in DevR regulated gene expression.

The DevRS two-component system plays a pivotal role in signal transmission and downstream gene regulation in Mycobacterium tuberculosis. Under the hypoxic condition, phosphorylated DevR interacts with multiple binding sites at the promoter region of the target genes. In the present work, we carried out a detailed computational analysis to figure out the sensitivity of the kinetic parameters. The set of kinetic parameters takes care of the interaction among phosphorylated DevR and the binding sites, transcription and translation processes. We employ the method of stochastic optimization to quantitate the relevant kinetic parameter set necessary for DevR regulated gene expression. Measures of different correlation coefficients provide the relative ordering of kinetic parameters involved in gene regulation. Results obtained from correlation coefficients are further corroborated by sensitivity amplification.

A population of bang-bang switches of defective interfering particles makes within-host dynamics of dengue virus controllable.

The titre of virus in a dengue patient and the duration of this viraemia has a profound effect on whether or not a mosquito will become infected when it feeds on the patient and this, in turn, is a key driver of the magnitude of a dengue outbreak. The assessment of the heterogeneity of viral dynamics in dengue-infected patients and its precise treatment are still uncertain. Infection onset, patient physiology and immune response are thought to play major roles in the development of the viral load. Research has explored the interference and spontaneous generation of defective virus particles, but have not examined both the antibody and defective particles during natural infection. We explore the intrinsic variability in the within-host dynamics of viraemias for a population of patients using the method of population of models (POMs). A dataset from 208 patients is used to initially calibrate 20,000 models for the infection kinetics for each of the four dengue virus serotypes. The calibrated POMs suggests that naturally generated defective particles may interfere with the viraemia, but the generated defective virus particles are not adequate to reduce high fever and viraemia duration. The effect of adding excess defective dengue virus interfering particles to patients as a therapeutic is evaluated using the calibrated POMs in a bang-bang (on-off or two-step) optimal control setting. Bang-bang control is a class of binary feedback control that turns either 'ON' or 'OFF' at different time points, determined by the system feedback. Here, the bang-bang control estimates the mathematically optimal dose and duration of the intervention for each model in the POM set.

In silico modeling of phosphorylation dependent and independent c-Myc degradation.

BACKGROUND: c-Myc plays an important role in cell proliferation, cell growth and in differentiation, making it a key regulator for carcinogenesis and pluripotency. Tight control of c-myc turnover is required by ubiquitin-mediated degradation. This is achieved in the system by two F-box proteins Skp2 and FBXW7. RESULTS: Dynamic modelling technique was used to build two exclusive models for phosphorylation dependent degradation of Myc by FBXW7 (Model 1) and phosphorylation independent degradation by Skp2 (Model 2). Sensitivity analysis performed on these two models revealed that these models were corroborating experimental studies. It was also seen that Model 1 was more robust and perhaps more efficient in degrading c-Myc. These results questioned the existence of the two models in the system and to answer the question a combined model was hypothesised which had a decision making switch. The combined model had both Skp2 and FBXW7 mediated degradation where again the latter played a more important role. This model was able to achieve the lowest levels of ubiquitylated Myc and therefore functioned most efficiently in degradation of Myc. CONCLUSION: In this report, c-Myc degradation by two F-box proteins was mathematically evaluated based on the importance of c-Myc turnover. The study was performed in a homeostatic system and therefore, prompts the exploration of c-Myc degradation in cancer state and in pluripotent state.

Optimal control of acute myeloid leukaemia.

Acute myeloid leukaemia (AML) is a blood cancer affecting haematopoietic stem cells. AML is routinely treated with chemotherapy, and so it is of great interest to develop optimal chemotherapy treatment strategies. In this work, we incorporate an immune response into a stem cell model of AML, since we find that previous models lacking an immune response are inappropriate for deriving optimal control strategies. Using optimal control theory, we produce continuous controls and bang-bang controls, corresponding to a range of objectives and parameter choices. Through example calculations, we provide a practical approach to applying optimal control using Pontryagin's Maximum Principle. In particular, we describe and explore factors that have a profound influence on numerical convergence. We find that the convergence behaviour is sensitive to the method of control updating, the nature of the control, and to the relative weighting of terms in the objective function. All codes we use to implement optimal control are made available.

Enhanced carbon-sulfur cycling in the sediments of Arabian Sea oxygen minimum zone center.

Biogeochemistry of oxygen minimum zone (OMZ) sediments, which are characterized by high input of labile organic matter, have crucial bearings on the benthic biota, gas and metal fluxes across the sediment-water interface, and carbon-sulfur cycling. Here we couple pore-fluid chemistry and comprehensive microbial diversity data to reveal the sedimentary carbon-sulfur cycle across a water-depth transect covering the entire thickness of eastern Arabian Sea OMZ, off the west coast of India. Geochemical data show remarkable increase in average total organic carbon content and aerial sulfate reduction rate (JSO42-) in the sediments of the OMZ center coupled with shallowing of sulfate methane transition zone and hydrogen sulfide and ammonium build-up. Total bacterial diversity, including those of complex organic matter degraders, fermentative and exoelectrogenic bacteria, and sulfate-reducers (that utilize only simple carbon compounds) were also found to be highest in the same region. The above findings indicate that higher organic carbon sequestration from the water-columns (apparently due to lower benthic consumption, biodegradation and biotransformation) and greater bioavailability of simple organic carbon compounds (apparently produced by fermetative microflora of the sediments) are instrumental in intensifying the carbon-sulfur cycle in the sediments of the OMZ center.

Deciphering Parameter Sensitivity in the BvgAS Signal Transduction.

To understand the switching of different phenotypic phases of Bordetella pertussis, we propose an optimized mathematical framework for signal transduction through BvgAS two-component system. The response of the network output to the sensory input has been demonstrated in steady state. An analysis in terms of local sensitivity amplification characterizes the nature of the molecular switch. The sensitivity analysis of the model parameters within the framework of various correlation coefficients helps to decipher the contribution of the modular structure in signal propagation. Once classified, the model parameters are tuned to generate the behavior of some novel strains using simulated annealing, a stochastic optimization technique.

Effect of dielectric interface on charge aggregation in the voltage-gated K(+) ion channel.

BACKGROUND: There is experimental evidence of many cases of stable macromolecular conformations with charged amino-acids facing lipid, an arrangement thought to be energetically unfavourable. METHODS AND OBJECTIVES: Employing classical electrostatics, we show that, this is not necessarily the case and studied the physical basis of the specific role of proximity of charges to the dielectric interface between two different environments. We illustrate how self and induced energies due to the dielectric medium polarization, on either side of the interface, contribute differentially to the stability of a pair of charges and hence the mutual conformation of the S3b-S4 α-helix pair of the voltage-gated K(+) channel. RESULTS AND CONCLUSION: We show that (1) a pair of opposite charges on either side of lipid-protein interface confers significant stability; (2) hydrophobic media has an important role in holding together two similar repelling charges; (3) dielectric interface has stabilizing effect on a pair of charges, when an ion is closer to its interface than its neighboring charge; (4) in spite of the presence of dielectric interface, there is a nonexistence of any dielectric effect, when an ion is equidistant from its image and neighboring charge. We also demonstrate that, variation in dielectric media of the surrounding environment confers new mutual conformations to S3b-S4 α-helices of voltage sensor domain at zero potential, especially lipid environment on the helix side, which improved stability to the configuration by lowering the potential energy. Our results provide an answer to the long standing question of why charges face hydrophobic lipid membranes in the stable conformation of a protein.

Electrostatic interaction between dipoles and side chains in the voltage sensor domain of K(+) channel.

BACKGROUND: It is well known that α-helices of protein, possessing equal and opposite charged ends, behaves like a macrodipole, but the relative importance of such macrodipoles to the aggregation of a pair of helix in the voltage sensor domain (VSD) of K+ ion channel, has not been assessed. In the VSD, importance has been given primarily to the helically arranged Arginine residues of helix, but the role of the charged residues of S3b is less focused. METHOD AND OBJECTIVE: Applying electrostatic theory, we have studied the interaction between the charges of S3b-S4 α-helix pair of KvAP through virtual mutagenesis. RESULT AND CONCLUSION: We have shown that the terminal charges arising from the inherent dipolar property of α-helices play an important role in affecting the stability of the S3b-S4 pair, and in determining its spatial position at zero transmembrane potential. Moreover, the negatively charged side chain of S3b was found to be the primary stabilizing factor in holding S3b-S4 pair together as a "paddle". Comparison of sequences of S3b helix of K+ channels from different species showed a previously unreported positional conservation of negative residues, highlighting their functional importance. These charges may contribute to the energetic of α-helix movements in an electric field.

Role of terminal dipole charges in aggregation of α-helix pair in the voltage gated K(+) channel.

The voltage sensor domain (VSD) of the potassium ion channel KvAP is comprised of four (S1-S4) α-helix proteins, which are encompassed by several charged residues. Apart from these charges, each peptide α-helix having two inherent equal and opposite terminal dipolar charges behave like a macrodipole. The activity of voltage gated ion channel is electrostatic, where all the charges (charged residues and dipolar terminal charges) interact with each other and with the transmembrane potential. There are evidences that the role of the charged residues dominate the stabilization of the conformation and the gating process of the ion channel, but the role of the terminal dipolar charges are never considered in such analysis. Here, using electrostatic theory, we have studied the role of the dipolar terminal charges in aggregation of the S3b-S4 helix pair of KvAP in the absence of any external field (V=0). A system attains stability, when its potential energy reaches minimum values. We have shown that the presence of terminal dipole charges (1) change the total potential energy of the charges on S3b-S4, affecting the stabilization of the α-helix pair within the bilayer lipid membrane and (2) the C- and the N-termini of the α-helices favor a different dielectric medium for enhanced stability. Thus, the dipolar terminal charges play a significant role in the aggregation of the two neighboring α-helices.