Parameter Estimation in Mathematical Models of Viral Infections Using R

Biophysical Analysis of Potential Inhibitors of SARS-CoV-2 Cell Recognition and Their Effect on Viral Dynamics in Different Cell Types: A Computational Prediction from In Vitro Experimental Data

Recent reports have suggested that the susceptibility of cells to SARS-CoV-2 infection can be influenced by various proteins that potentially act as receptors for the virus. To investigate this further, we conducted simulations of viral dynamics using different cellular systems (Vero E6, HeLa, HEK293, and CaLu3) in the presence and absence of drugs (anthelmintic, ARBs, anticoagulant, serine protease inhibitor, antimalarials, and NSAID) that have been shown to impact cellular recognition by the spike protein based on experimental data. Our simulations revealed that the susceptibility of the simulated cell systems to SARS-CoV-2 infection was similar across all tested systems. Notably, CaLu3 cells exhibited the highest susceptibility to SARS-CoV-2 infection, potentially due to the presence of receptors other than ACE2, which may account for a significant portion of the observed susceptibility. Throughout the study, all tested compounds showed thermodynamically favorable and stable binding to the spike protein. Among the tested compounds, the anticoagulant nafamostat demonstrated the most favorable characteristics in terms of thermodynamics, kinetics, theoretical antiviral activity, and potential safety (toxicity) in relation to SARS-CoV-2 spike protein-mediated infections in the tested cell lines. This study provides mathematical and bioinformatic models that can aid in the identification of optimal cell lines for compound evaluation and detection, particularly in studies focused on repurposed drugs and their mechanisms of action. It is important to note that these observations should be experimentally validated, and this research is expected to inspire future quantitative experiments.

Comparative study of SARS-CoV-2 infection in different cell types: Biophysical-computational approach to the role of potential receptors

Cellular susceptibility to SARS-CoV-2 infection in the respiratory tract has been associated with the ability of the virus to interact with potential receptors on the host membrane. We have modeled viral dynamics by simulating various cellular systems and artificial conditions, including macromolecular crowding, based on experimental and transcriptomic data to infer parameters associated with viral growth and predict cell susceptibility. We have accomplished this based on the type, number and level of expression of the angiotensin-converting enzyme 2 (ACE2), transmembrane serine 2 (TMPRSS2), basigin2 (CD147), FURIN protease, neuropilin 1 (NRP1) or other less studied candidate receptors such as heat shock protein A5 (HSPA5) and angiotensin II receptor type 2 (AGTR2). In parallel, we studied the effect of simulated artificial environments on the accessibility to said proposed receptors. In addition, viral kinetic behavior dependent on the degree of cellular susceptibility was predicted. The latter was observed to be more influenced by the type of proteins and expression level, than by the number of potential proteins associated with the SARS CoV-2 infection. We predict a greater theoretical propensity to susceptibility in cell lines such as NTERA-2, SCLC-21H, HepG2 and Vero6, and a lower theoretical propensity in lines such as CaLu3, RT4, HEK293, A549 and U-251MG. An important relationship was observed between expression levels, protein diffusivity, and thermodynamically favorable interactions between host proteins and the viral spike, suggesting potential sites of early infection other than the lungs. This research is expected to stimulate future quantitative experiments and promote systematic investigation of the effect of crowding presented here.

PDEparams: parameter fitting toolbox for partial differential equations in python

MOTIVATION

Partial differential equations (PDEs) is a well-established and powerful tool to simulate multi-cellular biological systems. However, available free tools for validation against data are on development.

RESULTS

The PDEparams module provides a flexible interface and readily accommodates different parameter analysis tools in PDE models such as computation of likelihood profiles, and parametric bootstrapping, along with direct visualization of the results. To our knowledge, it is the first open, freely available tool for parameter fitting of PDE models.

AVAILABILITY AND IMPLEMENTATION

PDEparams is distributed under the MIT license. The source code, usage instructions and examples are freely available on GitHub at github.com/systemsmedicine/PDE_params.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.