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Full-Text Articles in Physical Sciences and Mathematics
Discrete-State Stochastic Models Of Calcium-Regulated Calcium Influx And Subspace Dynamics Are Not Well-Approximated By Odes That Neglect Concentration Fluctuations, Seth H. Weinberg, Gregory D. Smith
Discrete-State Stochastic Models Of Calcium-Regulated Calcium Influx And Subspace Dynamics Are Not Well-Approximated By Odes That Neglect Concentration Fluctuations, Seth H. Weinberg, Gregory D. Smith
Arts & Sciences Articles
Cardiac myocyte calcium signaling is often modeled using deterministic ordinary differential equations (ODEs) and mass-action kinetics. However, spatially restricted “domains” associated with calcium influx are small enough (e.g., 10−17 liters) that local signaling may involve 1–100 calcium ions. Is it appropriate to model the dynamics of subspace calcium using deterministic ODEs or, alternatively, do we require stochastic descriptions that account for the fundamentally discrete nature of these local calcium signals? To address this question, we constructed a minimal Markov model of a calcium-regulated calcium channel and associated subspace. We compared the expected value of fluctuating subspace calcium concentration (a result …
Generating A Close-To-Reality Synthetic Population Of Ghana, Tyler Frazier, Andreas Alfons
Generating A Close-To-Reality Synthetic Population Of Ghana, Tyler Frazier, Andreas Alfons
Arts & Sciences Articles
The purpose of this research is to generate a close-to-reality synthetic human population for use in a geosimulation of urban dynamics. Two commonly accepted approaches to generating synthetic human populations are Iterative Proportional Fitting (IPF) and Resampling with Replacement. While these methods are effective at reproducing one instance of the probability model describing the survey, it is an instance with extremely small variability amongst subgroups and is very unlikely to be the real population. IPF and Resampling with Replacement also rely on pure replication of units from the underlying sample which can increase unrealistic model behavior. In this work we …
Automated Reductions Of Markov Chain Models Of Calcium Release Site Models, Yan Hao
Automated Reductions Of Markov Chain Models Of Calcium Release Site Models, Yan Hao
Dissertations, Theses, and Masters Projects
Markov chain models have played an important role in understanding the relationship between single channel gating of intracellular calcium (Ca2+) channels, specifically 1,4,5-trisphosphate receptors (IP3Rs) and ryanodine receptors (RyRs), and the stochastic dynamics of Ca2+ release events, known as Ca2+ puffs and sparks. Mechanistic Ca2+ release site models are defined by the composition of single channel models whose transition probabilities depend on the local calcium concentration and thus the state of the other channels. Unfortunately, the large state space of such compositional models impedes simulation and computational analysis of the whole cell Ca2+ signaling in which the stochastic dynamics of …