Mathematical Biology

This is the prototype of an agent based model for a closed universe of a population experiencing a contagion-based epidemic, in which risk factors, movement, time of incubation and asymptomatic infection are all parameters. The model allows the operator to intervene at any step and change parameters, thus analytically visualizing the effect of policies like more testing, contract tracing, and shelter in place. Under current development, CovidSimMV is an ABM that supports a Multiverse of different environments, in which agents move from one to another according to ticket with stops. Each universe has its own characteristic mix of residents, transients and attached staff, and persons are able to adopt different roles and characteristics in different universes. The fundamental disease characteristics of incubation, asymptomatic infection, confirmed cases will be preserved. The Multiverse model will support a rich diversity of environments and interpersonal dynamics. These are JavaScript programs that can be run in a browser as HTML files. The code is open source, and available on github.com/ecsendmail.

Multiscale multicellular models combine representations of subcellular biological networks, cell behaviors, tissue level effects and whole body effects to describe tissue outcomes during development, homeostasis and disease. I will briefly introduce these simulation methodologies, the CompuCell3D simulation environment and their applications, then focus on a multiscale simulation of an acute primary infection of an epithelial tissue infected by a virus like SARS-CoV-2, a simplified cellular immune response and viral and immune-induced tissue damage. The model exhibits four basic parameter regimes: where the immune response fails to contain or significantly slow the spread of viral infection, where it significantly slows but fails to stop the spread of infection, where it eliminates all infected epithelial cells, but reinfection occurs from residual extracellular virus and where it clears the both infected cells and extracellular virus, leaving a substantial fraction of epithelial cells uninfected. Even this simplified model can illustrate the effects of a number of drug therapy concepts. Inhibition of viral internalization and faster immune-cell recruitment promote containment of infection. Fast viral internalization and slower immune response lead to uncontrolled spread of infection. Existing antivirals, despite blocking viral replication, show reduced clinical benefit when given later during the course of infection. Simulation of a drug which reduces the replication rate of viral RNA, shows that a low dosage that provides only a relatively limited reduction of viral RNA replication greatly decreases the total tissue damage and extracellular virus when given near the beginning of infection. However, even a high dosage that greatly reduces the rate of RNA replication rapidly loses efficacy when given later after infection. Many combinations of dosage and treatment time lead to distinct stochastic outcomes, with some replicas showing clearance or control of the virus (treatment success), while others show rapid infection of all epithelial cells (treatment failure). This switch between a regime of frequent treatment success and frequent failure occurs is quite abrupt as the time of treatment increases. The model is open-source and modular, allowing rapid development and extension of its components by groups working in parallel.

TBA

Until very recently most cancer biologists operated with the assumption that the most common route to metastasis involved cells of the primary tumor transforming to a motile single-cell phenotype via complete EMT (the epithelial-mesenchymal transition). This change allowed them to migrate individually to distant organs, eventually leading to clonal growths in other locations. But, a new more nuanced picture has been emerging, based on advanced measurements and on computational systems biology approaches. It has now been realized that cells can readily adopt states with hybrid properties, use these properties to move collectively and cooperatively, and reach distant niches as highly metastatic clusters. This talk will focus on the accumulating evidence for this revised perspective, the role of biological physics theory in instigating this whole line of investigation, and on open questions currently under investigation.

In this talk I will present a "dynamical paradigm" for modeling networks of interacting genes and proteins that regulate every aspect of cell physiology. The paradigm is based on dynamical systems theory of nonlinear ODEs, especially one- and two-parameter bifurcation diagrams. I will show how we have used this paradigm to unravel the mechanisms controlling "multiple fission" cycles in the photosynthetic green alga Chlamydomonas. While most eukaryotic cells maintain a characteristic size by executing binary division after each mass doubling, Chlamydomonas cells can grow more than eight-fold during daytime before undergoing rapid cycles of DNA replication, mitosis and cell division at night, which produce up to 16 daughter cells. We propose that this unusual strategy of growth and division (which is clearly advantageous for a photosynthetic organism) can be governed by a size-dependent bistable switch that turns on and off a limit cycle oscillator that drives cells through rapid cycles of DNA synthesis and mitosis. We show that this simple ‘sizer-oscillator’ arrangement reproduces the experimentally observed features of multiple-fission cycles and the response of Chlamydomonas cells to different light-dark regimes. Our model makes unexpected predictions about the size-dependence of the time of onset of cell-cycle oscillations after cells are transferred from light to dark conditions, and these predictions are confirmed by single-cell experiments.

Collaborators: Stefan Heldt and Bela Novak (Oxford Univ) on the modeling; Fred Cross (Rockefeller Univ) on the experiments.