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Motivated by applications in systems biology, we seek a probabilistic framework based on Markov processes to represent intracellular processes. We review the formal relationships between different stochastic models referred to in the systems biology literature. As part of this review, we present a novel derivation of the differential Chapman-Kolmogorov equation for a general multidimensional Markov process made up of both continuous and jump processes. We start with the definition of a time-derivative for a probability density but place no restrictions on the probability distribution, in particular, we do not assume it to be confined to a region that has a surface (on which the probability is zero). In our derivation, the master equation gives the jump part of the Markov process while the Fokker-Planck equation gives the continuous part. We thereby sketch a {}``family tree for stochastic models in systems biology, providing explicit derivations of their formal relationship and clarifying assumptions involved.
Reproducibility and reusability of the results of data-based modeling studies are essential. Yet, there has been -- so far -- no broadly supported format for the specification of parameter estimation problems in systems biology. Here, we introduce PE
Computer simulations have become an important tool across the biomedical sciences and beyond. For many important problems several different models or hypotheses exist and choosing which one best describes reality or observed data is not straightforwa
Models of biological systems often have many unknown parameters that must be determined in order for model behavior to match experimental observations. Commonly-used methods for parameter estimation that return point estimates of the best-fit paramet
Although reproducibility is a core tenet of the scientific method, it remains challenging to reproduce many results. Surprisingly, this also holds true for computational results in domains such as systems biology where there have been extensive stand
1. Movement is the primary means by which animals obtain resources and avoid hazards. Most movement exhibits directional bias that is related to environmental features (taxis), such as the location of food patches, predators, ocean currents, or wind.