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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.

While active tuberculosis (TB) is a treatable disease, many complex factors prevent its global elimination. Part of the difficulty in developing optimal therapies is the large design space of antibiotic doses, regimens and combinations. Computational models that capture the spatial and temporal dynamics of antibiotics at the site of infection can aid in reducing the design space of costly and time-consuming animal pre-clinical and human clinical trials. The site of infection in TB is the granuloma, a collection of immune cells and bacteria that form in the lung, and new data suggest that penetration of drugs throughout granulomas is problematic. Here we integrate our computational model of granuloma formation and function with models for plasma pharmacokinetics, lung tissue pharmacokinetics and pharmacodynamics for two first line anti-TB antibiotics. The integrated model is calibrated to animal data. We make four predictions. First, antibiotics are frequently below effective concentrations inside granulomas, leading to bacterial growth between doses and contributing to the long treatment periods required for TB. Second, antibiotic concentration gradients form within granulomas, with lower concentrations toward their centers. Third, during antibiotic treatment, bacterial subpopulations are similar for INH and RIF treatment: mostly intracellular with extracellular bacteria located in areas non-permissive for replication (hypoxic areas), presenting a slowly increasing target population over time. Finally, we find that on an individual granuloma basis, pre-treatment infection severity (including bacterial burden, host cell activation and host cell death) is predictive of treatment outcome.

Tuberculosis (TB), one of the most common infectious diseases, requires treatment with multiple antibiotics taken over at least 6 months. This long treatment often results in poor patient-adherence, which can lead to the emergence of multi-drug resistant TB. New antibiotic treatment strategies are sorely needed. New antibiotics are being developed or repurposed to treat TB, but as there are numerous potential antibiotics, dosing sizes and potential schedules, the regimen design space for new treatments is too large to search exhaustively. Here we propose a method that combines an agent-based multi-scale model capturing TB granuloma formation with algorithms for mathematical optimization to identify optimal TB treatment regimens. We define two different single-antibiotic treatments to compare the efficiency and accuracy in predicting optimal treatment regimens of two optimization algorithms: genetic algorithms (GA) and surrogate-assisted optimization through radial basis function (RBF) networks. We also illustrate the use of RBF networks to optimize double-antibiotic treatments. We found that while GAs can locate optimal treatment regimens more accurately, RBF networks provide a more practical strategy to TB treatment optimization with fewer simulations, and successfully estimated optimal double-antibiotic treatment regimens. Our results indicate surrogate-assisted optimization can locate optimal TB treatment regimens from a larger set of antibiotics, doses and schedules, and could be applied to solve optimization problems in other areas of research using systems biology approaches. Our findings have important implications for the treatment of diseases like TB that have lengthy protocols or for any disease that requires multiple drugs.

The model herein aims to explore the dynamics of the spread of tuberculosis (TB) in an informal settlement or township. The population is divided into households of various sizes and also based on commuting status. The model dynamics distinguishes between three distinct social patterns: the exposure of commuters during travel, random diurnal interaction and familial exposure at night. Following the general SLIR models, the population is further segmented into susceptible (S), exposed/latently infected (L), active/infectious (I), and recovered (R) individuals. During the daytime, commuters travel on public transport, while non-commuters randomly interact in the community to mimic chance encounters with infectious persons. At night, each family interacts and sleeps together in the home. The risk of exposure to TB is based on the proximity, duration, and frequency of encounters with infectious persons. The model is applied to a hypothetical population to explore the effects of different intervention strategies including vaccination, wearing of masks or scarves during the commute, prophylactic treatment of latent infections and more effective case-finding and treatment. The most important findings of the model are: (1) members of larger families are responsible for more disease transmissions than those from smaller families, (2) daily commutes on public transport provide ideal conditions for transmission of the disease, (3) improved diagnosis and treatment has the greatest impact on the spread of the disease, and (4) detecting TB at the first clinic visit, when patients are still smear negative, is key.

It is generally accepted that the translation rate depends on the availability of cognate aa-tRNAs. In this study it is shown that the key factor that determines translation rate is the competition between near-cognate and cognate aa-tRNAs. The transport mechanism in the cytoplasm is diffusion, thus the competition between cognate, near-cognate and non-cognate aa-tRNAs to bind to the ribosome is a stochastic process. Two competition measures are introduced; C(i) and R(i) (i=1, 64) are quotients of the arrival frequencies of near-cognates vs. cognates and non-cognates vs. cognates, respectively. Furthermore, the reaction rates of bound cognates differ from those of bound near-cognates. If a near-cognate aa-tRNA binds to the A site of the ribosome, it may be rejected at the anti-codon recognition step or proofreading step or it may be accepted. Regardless of its fate, the near-cognates and non-cognates have caused delays of varying duration to the observed rate of translation. Rate constants have been measured at a temperature of 20 degrees C by (Gromadski, K.B., Rodnina, M.V., 2004. Kinetic determinants of high-fidelity tRNA discrimination on the ribosome. Mol. Cell 13, 191-200). These rate constants have been re-evaluated at 37 degrees C, using experimental data at 24.5 degrees C and 37 degrees C (Varenne, S., et al., 1984. Translation in a non-uniform process: effect of tRNA availability on the rate of elongation of nascent polypeptide chains. J. Mol. Biol. 180, 549-576). The key results of the study are: (i) the average time (at 37 degrees C) to add an amino acid, as defined by the ith codon, to the nascent peptide chain is: tau(i)=9.06+1.445x[10.48C(i)+0.5R(i)] (in ms); (ii) the misreading frequency is directly proportional to the near-cognate competition, E(i)=0.0009C(i); (iii) the competition from near-cognates, and not the availability of cognate aa-tRNAs, is the most important factor that determines the translation rate - the four codons with highest near-cognate competition (in the case of E. coli) are [GCC][CGG][AGG][GGA], which overlap only partially with the rarest codons: [AGG][CCA][GCC][CAC]; (iv) based on the kinetic rates at 37 degrees C, the average time to insert a cognate amino acid is 9.06ms and the average delay to process a near-cognate aa-tRNA is 10.45ms and (vii) the model also provides estimates of the vacancy times of the A site of the ribosome - an important factor in frameshifting.

Approximately one third of the world's population is infected with Mycobacterium tuberculosis. Limited information about how the immune system fights M. tuberculosis and what constitutes protection from the bacteria impact our ability to develop effective therapies for tuberculosis. We present an in vivo systems biology approach that integrates data from multiple model systems and over multiple length and time scales into a comprehensive multi-scale and multi-compartment view of the in vivo immune response to M. tuberculosis. We describe computational models that can be used to study (a) immunomodulation with the cytokines tumor necrosis factor and interleukin 10, (b) oral and inhaled antibiotics, and (c) the effect of vaccination.

Recently a theoretical analysis of PCR efficiency has been published by Booth et al. (2010). The PCR yield is the product of three efficiencies: (i) the annealing efficiency is the fraction of templates that form binary complexes with primers during annealing, (ii) the polymerase binding efficiency is the fraction of binary complexes that bind to polymerase to form ternary complexes and (iii) the elongation efficiency is the fraction of ternary complexes that extend fully. Yield is controlled by the smallest of the three efficiencies and control could shift from one type of efficiency to another over the course of a PCR experiment. Experiments have been designed that are specifically controlled by each one of the efficiencies and the results are consistent with the mathematical model. The experimental data has also been used to quantify six key parameters of the theoretical model. An important application of the fully characterized model is to calculate initial template concentration from real-time PCR data. Given the PCR protocol, the midpoint cycle number (where the template concentration is half that of the final concentration) can be theoretically determined and graphed for a variety of initial DNA concentrations. Real-time results can be used to calculate the midpoint cycle number and consequently the initial DNA concentration, using this graph. The application becomes particularly simple if a conservative PCR protocol is followed where only the annealing efficiency is controlling.

The polymerase chain reaction (PCR) has found wide application in biochemistry and molecular biology such as gene expression studies, mutation detection, forensic analysis and pathogen detection. Increasingly, quantitative real time PCR is used to assess copy numbers from overall yield. In this study the yield is analyzed as a function of several processes: (1) thermal damage of the template and polymerase occurring during the denaturing step, (2) competition existing between primers and templates to either anneal or form dsDNA, (3) polymerase binding to annealed products (primer/ ssDNA) to form ternary complexes and (4) extension of ternary complexes. Explicit expressions are provided for the efficiency of each process, therefore reaction conditions can be directly linked to the overall yield. Examples are provided where different processes play the yield-limiting role. The analysis will give researchers a unique understanding of the factors that control the reaction and will aid in the interpretation of experimental results.

The traditional diagnostic tests for tuberculosis consist of an acid fast stain and a culture test from a sputum sample. With the emergence of drug resistant strains of tuberculosis, nucleic acid amplification has become the diagnostic test of choice. The nucleic acid amplification test consists of four steps: sputum sample collection, lysis of bacilli to release DNA, DNA amplification by PCR and detection of PCR products. The DNA extraction step has been largely overlooked and this study describes a systematic approach to measure the kinetics of cell lysis in a Tris-EDTA buffer. Mycobacterium smegmatis is a saphorytic, fast-growing mycobacterium that is often used as a surrogate of Mycobacterium tuberculosis in laboratory studies. M. smegmatis cells have been transformed with green fluorescent protein (GFP) genes. Transformed cells are lysed in a temperature-controlled cuvette that is equipped with optical input/output. The fluorescence signal increases when the GFP is released from lysed cells, and the extent of lysis of the loaded cells can be followed in real time. The experimental results are complemented by two theoretical models. The first model is based on a Monte Carlo simulation of the lysis process and the accompanying probability density function as described by the Fokker-Planck equation. The second model follows a chemical reaction engineering approach: the cell wall is modeled as layers, where each layer is made up of ‘blocks’. Blocks can only be removed if they are exposed to the lysis solution and the model describes the rate of block exposure and removal. Both models are consistent with the experimental results. The main findings are: (1) the activation energy for M. smegmatis lysis by Tris-EDTA buffer is 22.1kcal/mole, (2) cells lyse on the average after 14–17% loss in cell wall thickness locally, (3) with the help of the models, the initial distribution in cell wall thickness of the population can be resolved, (4) near complete lysis of the cells is accomplished in 200 seconds at 80°C (90 seconds at 90°C). The results can be used to design an optimal lysis protocol that compromises between shorter processing times at higher temperature and reduced thermal damage to DNA at lower temperature.

Polymerase chain assembly (PCA) is a technique used to synthesize genes ranging from a few hundred base pairs to many kilobase pairs in length. In traditional PCA, equimolar concentrations of single stranded DNA oligonucleotides are repeatedly hybridized and extended by a polymerase enzyme into longer dsDNA constructs, with relatively few full-length sequences being assembled. Thus, traditional PCA is followed by a second primer-mediated PCR reaction to amplify the desired full-length sequence to useful, detectable quantities. Integration of assembly and primer-mediated amplification steps into a single reaction using a high-speed thermocycler is shown to produce similar results. For the integrated technique, the effects of oligo concentration, primer concentration, and number of oligonucleotides are explored. The technique is successfully demonstrated for the synthesis of two genes encoding EPCR-1 (653 bp) and pUC19 β-lactamase (929 bp) in under 20 min. However, rapid integrated PCA–PCR was found to be problematic when attempted with the TM-1 gene (1509 bp). Partial oligonucleotide sets of TM-1 could be assembled and amplified simultaneously, indicating that the technique may be limited to a maximum number of oligonucleotides due to competitive annealing and competition for primers.

The tri-frame model gives mathematical expression to the transcription and translation processes, and considers all three reading frames (RFs). RNA polymerases transcribe DNA in single nucleotide increments, but ribosomes translate mRNA in pairings of three (triplets or codons). The set of triplets in the mRNA, starting with the initiation codon (usually AUG) defines the open reading frame (ORF). Since ribosomes do not always translocate three nucleotide positions, two additional RFs are accessible. The −1 RF and the +1 RF are triplet pairings of the mRNA, which are accessed by shifting one nucleotide position in the 5′ and 3′ directions, respectively. Transcription is modeled as a linear operator that maps the initial codons in all three frames into other codon sets to account for possible transcriptional errors. Translational errors (missense errors) originate from misacylation of tRNAs and misreading of aa-tRNAs by the ribosome. Translation is modeled as a linear mapping from codons into aa-tRNA species, which includes misreading errors. A final transformation from aa-tRNA species into amino acids provides the probability distributions of possible amino acids into which the codons in all three frames could be translated. An important element of the tri-frame model is the ribosomal occupancy probability. It is a vector in R 3 that gives the probability to find the ribosome in the ORF, −1 or +1 RF at each codon position. The sequence of vectors, from the first to the final codon position, gives a history of ribosome frameshifting. The model is powerful: it provides explicit expressions for (1) yield of error-free protein, (2) fraction of prematurely terminated polypeptides, (3) number of transcription errors, (4) number of translation errors and (5) mutations due to frameshifting. The theory is demonstrated for the three genes rpsU , dnaG and rpoD of Escherichia coli , which lie on the same operon, as well as for the prfB gene.

The amplification of target DNA by the polymerase chain reaction (PCR) produces copies which may contain errors. Two sources of errors are associated with the PCR process: (1) editing errors that occur during DNA polymerase-catalyzed enzymatic copying and (2) errors due to DNA thermal damage. In this study a quantitative model of error frequencies is proposed and the role of reaction conditions is investigated. The errors which are ascribed to the polymerase depend on the efficiency of its editing function as well as the reaction conditions; specifically the temperature and the dNTP pool composition. Thermally induced errors stem mostly from three sources: A+G depurination, oxidative damage of guanine to 8-oxoG and cytosine deamination to uracil. The post-PCR modifications of sequences are primarily due to exposure of nucleic acids to elevated temperatures, especially if the DNA is in a single-stranded form. The proposed quantitative model predicts the accumulation of errors over the course of a PCR cycle. Thermal damage contributes significantly to the total errors; therefore consideration must be given to thermal management of the PCR process.