Transmission dynamics of Covid-19 in Italy, Germany and Turkey considering social distancing, testing and quarantine

INTRODUCTION

There are significant differences in the active cases and fatality rates of Covid-19 for different European countries.

METHODOLOGY

The present study employs Monte Carlo based transmission growth simulations for Italy, Germany and Turkey. The probabilities of transmission at home, work and social networks and the number of initial cases have been calibrated to match the basic reproduction number and the reported fatality curves. Parametric studies were conducted to observe the effect of social distancing, work closure, testing and quarantine of the family and colleagues of positively tested individuals.

RESULTS

It is observed that estimates of the number of initial cases in Italy compared to Turkey and Germany are higher. Turkey will probably experience about 30% less number of fatalities than Germany due its smaller elderly population. If social distancing and work contacts are limited to 25% of daily routines, Germany and Turkey may limit the number of fatalities to a few thousands as the reproduction number decreases to about 1.3 from 2.8. Random testing may reduce the number of fatalities by 10% upon testing least 5/1000 of the population. Quarantining of family and workmates of positively tested individuals may reduce the total number of fatalities by about 50%.

CONCLUSIONS

The fatality rate of Covid-19 is estimated to be about 1.5% based on the simulation results. This may further be reduced by limiting the number of non-family contacts to two, conducting tests more than 0.5% of the population and immediate quarantine of the contacts for positively tested individuals.

Modeling biogeochemical dynamics in porous media: Practical considerations of pore scale variability, reaction networks, and microbial population dynamics in a sandy aquifer

Prediction of the fate and environmental impacts of groundwater contaminants requires the identification of relevant biogeochemical processes and necessitates the macroscopic representation of microbial activity occurring at the microscale. Using a well-studied sandy aquifer environment, we evaluate the importance of pore distribution on organic matter respiration in a porous medium environment by performing spatially explicit simulations of microbial metabolism at the sub-millimeter scale. Model results using an idealized porous medium under non-biofilm forming conditions indicate that while some heterogeneity is observed for flow rates, distributions of microbes and dissolved organic substrates remain relatively homogenous at the grain scale. At the macroscale in the same environment, we assess the impact of a comprehensive reaction network description for a phenolic contaminant plume, and compare the findings to a setting describing organic matter breakdown in a coastal marine sediment. This comparison reveals the importance of reactions recycling reduced metabolites at redox interfaces, leading to a competition for oxidants. When the spatio-temporal dynamics of microbial groups are accounted for, our simulations show the importance of reaction energetics and nutrient limitations such as microbial nitrogen demands.

In silico Geobacter sulfurreducens metabolism and its representation in reactive transport models

Microbial activity governs elemental cycling and the transformation of many anthropogenic substances in aqueous environments. Through the development of a dynamic cell model of the well-characterized, versatile, and abundant Geobacter sulfurreducens, we showed that a kinetic representation of key components of cell metabolism matched microbial growth dynamics observed in chemostat experiments under various environmental conditions and led to results similar to those from a comprehensive flux balance model. Coupling the kinetic cell model to its environment by expressing substrate uptake rates depending on intra- and extracellular substrate concentrations, two-dimensional reactive transport simulations of an aquifer were performed. They illustrated that a proper representation of growth efficiency as a function of substrate availability is a determining factor for the spatial distribution of microbial populations in a porous medium. It was shown that simplified model representations of microbial dynamics in the subsurface that only depended on extracellular conditions could be derived by properly parameterizing emerging properties of the kinetic cell model.

Chromosome segregation in Escherichia coli division: a free energy-driven string model

Although the mechanisms of eukaryotic chromosome segregation and cell division have been elucidated to a certain extent, those for bacteria remain largely unknown. Here we present a computational string model for simulating the dynamics of Escherichia coli chromosome segregation. A novel thermal-average force field accounting for stretching, bending, volume exclusion, friction and random fluctuation is introduced. A Langevin equation is used to simulate the chromosome structural changes. The mechanism of chromosome segregation is thereby postulated as a result of free energy-driven structural optimization with replication introduced chromosomal mass increase. Predictions of the model agree well with observations of fluorescence labeled chromosome loci movement in living cells. The results demonstrate the possibility of a mechanism of chromosome segregation that does not involve cytoskeletal guidance or advanced apparatus in an E. coli cell. The model also shows that DNA condensation of locally compacted domains is a requirement for successful chromosome segregation. Simulations also imply that the shape-determining protein MreB may play a role in the segregation via modification of the membrane pressure.

Cancer onset and progression: A genome-wide, nonlinear dynamical systems perspective on onconetworks

It is hypothesized that the many human cell types corresponding to multiple states is supported by an underlying nonlinear dynamical system (NDS) of transcriptional regulatory network (TRN) processes. This hypothesis is validated for epithelial cells whose TRN is found to support an extremely complex array of states that we term a "bifurcation nexus", for which we introduce a quantitative measure of complexity. The TRN used is constructed and analyzed by integrating a database of TRN information, cDNA microarray data analyzers, bioinformatics modules, a transcription/translation/post-translation kinetic model, and NDS analysis software. Results of this genome-wide approach suggest that a cell can be induced to persist in one state or to transition between distinct states; apparently irreversible transitions can be reversed when the high dimensional space of extracellular and intracellular parameters is understood. As conditions change, certain cellular states (cell lines) are no longer supported, new ones emerge, and transitions (cell differentiation or death) occur. The accumulation of simulated point mutations (minor changes which individually are insignificant) lead to occasional dramatic transitions. The genome-wide scope of many of these transitions is shown to arise from the cross-linked TRN structure. These notions imply that studying individual oncogenes may not be sufficient to understand cancer; rather, "onconetworks" (subsets of strongly coupled genes supporting multiple cell states) should be considered. Our approach reveals several epithelial onconetworks, each involving oncogenes and anti-tumor and supporting genes.

Transcriptional regulatory network discovery via multiple method integration: application to e. coli K12

Transcriptional regulatory network (TRN) discovery from one method (e.g. microarray analysis, gene ontology, phylogenic similarity) does not seem feasible due to lack of sufficient information, resulting in the construction of spurious or incomplete TRNs. We develop a methodology, TRND, that integrates a preliminary TRN, microarray data, gene ontology and phylogenic similarity to accurately discover TRNs and apply the method to E. coli K12. The approach can easily be extended to include other methodologies. Although gene ontology and phylogenic similarity have been used in the context of gene-gene networks, we show that more information can be extracted when gene-gene scores are transformed to gene-transcription factor (TF) scores using a preliminary TRN. This seems to be preferable over the construction of gene-gene interaction networks in light of the observed fact that gene expression and activity of a TF made of a component encoded by that gene is often out of phase. TRND multi-method integration is found to be facilitated by the use of a Bayesian framework for each method derived from its individual scoring measure and a training set of gene/TF regulatory interactions. The TRNs we construct are in better agreement with microarray data. The number of gene/TF interactions we discover is actually double that of existing networks.

Transcriptional regulatory networks via gene ontology and expression data

Transcriptional regulatory network (TRN) discovery using information from a single source does not seem feasible due to lack of sufficient information, resulting in the construction of spurious or incomplete TRNs. A methodology, TRND, that integrates a preliminary TRN, gene expression data and gene ontology is developed to discover TRNs. The method is applied to a comprehensive set of expression data on B cell and a preliminary TRN that included 1,335 genes, 443 transcription factors (TFs) and 4032 gene/TF interactions. Predictions were obtained for 443 TFs and 9,589 genes. 14,616 of 4,247,927 possible gene/TF interactions scored higher than the imposed threshold. Results for three TFs, E2F-4, p130 and c-Myc, were examined in more detail to assess the accuracy of the integrated methodology. Although the training sets for E2F-4 and p130 were rather limited, the activities of these two TFs were found to be highly correlated and a large set of coregulated genes is predicted. These predictions were confirmed with published experimental results not used in the training set. A similar test was run for the c-Myc TF using the comprehensive resource www.myccancergene.org. In addition, correlations between expression of genes that encode TFs and TF activities were calculated and showed that the assumption of TF activity correlates with encoding gene expression might be misleading. The constructed B cell TRN, and scores for individual methodologies and the integrated approach are available at systemsbiology.indiana.edu/trndresults.

The Karyote physico-chemical genomic, proteomic, metabolic cell modeling system

Modeling approaches to the dynamics of a living cell are presented that are strongly based on its underlying physical and chemical processes and its hierarchical spatio-temporal organization. Through the inclusion of a broad spectrum of processes and a rigorous analysis of the multiple scale nature of cellular dynamics, we are attempting to advance cell modeling and its applications. The presentation focuses on our cell modeling system, which integrates data archiving and quantitative physico-chemical modeling and information theory to provide a seamless approach to the modeling/data analysis endeavor. Thereby the rapidly growing mess of genomic, proteomic, metabolic, and cell physiological data can be automatically used to develop and calibrate a predictive cell model. The discussion focuses on the Karyote cell modeling system and an introduction to the CellX and VirusX models. The Karyote software system integrates three elements: (1) a model-building and data archiving module that allows one to define a cell type to be modeled through its reaction network, structure, and transport processes as well as to choose the surrounding medium and other parameters of the phenomenon to be modeled; (2) a genomic, proteomic, metabolic cell simulator that solves the equations of metabolic reaction, transcription/translation polymerization and the exchange of molecules between parts of the cell and with the surrounding medium; and (3) an information theory module (ITM) that automates model calibration and development, and integrates a variety of data types with the cell dynamic computations. In Karyote, reactions may be fast (equilibrated) or slow (finite rate), and the special effects of enzymes and other minority species yielding steady-state cycles of arbitrary complexities are accounted for. These features of the dynamics are handled via rigorous multiple scale analysis. A user interface allows for an automated generation and solution of the equations of multiple timescale, compartmented dynamics. Karyote is based on a fixed intracellular structure. However, cell response to changes in the host medium, damage, development or transformation to abnormality can involve dramatic changes in intracellular structure. As this changes the nature of the cellular dynamics, a new model, CellX, is being developed based on the spatial distribution of concentration and other variables. This allows CellX to capture the self-organizing character of cellular behavior. The self-assembly of organelles, viruses, and other subcellular bodies is being addressed in a second new model, VirusX, that integrates molecular mechanics and continuum theory. VirusX is designed to study the influence of a host medium on viral self-assembly, structural stability, infection of a single cell, and transmission of disease.

Classical density functional theory of orientational order at interfaces: Application to water

A classical density functional formalism has been developed to predict the position-orientation number density of structured fluids. It is applied to the liquid-vapor interface of pure water, where it consists of a classical term, a gradient correction, and an anisotropic term that yields order through density gradients. The model is calibrated to predict that water molecules have their dipole moments almost parallel to a planar interface, while the molecular plane is parallel to it on the liquid side and perpendicular to it on the vapor side. For a planar interface, the surface tension obtained is twice its experimental value, while the surface potential is in qualitative agreement with that calculated by others. The model is also used to predict the orientation of water molecules near the surface of droplets, as well as the dependence of equilibrium vapor pressure around them on their size.

Efficient solution technique for solving the Poisson-Boltzmann equation

The Poisson-Boltzmann (PB) equation has been extensively used to analyze the energetics and structure of proteins and other significant biomolecules immersed in electrolyte media. A new highly efficient approach for solving PB-type equations that allows for the modeling of many-atoms structures such as encountered in cell biology, virology, and nanotechnology is presented. We accomplish these efficiencies by reformulating the elliptic PB equation as the long-time solution of an advection-diffusion equation. An efficient modified, memory optimized, alternating direction implicit scheme is used to integrate the reformulated PB equation. Our approach is demonstrated on protein composites (a polio virus capsid protomer and a pentamer). The approach has great potential for the analysis of supramillion atoms immersed in a host electrolyte.