Introducing prescribed biases in out of equilibrium Markov models

Markov models are often used in modeling complex out of equilibrium chemical and biochemical systems. However, many times their predictions do not agree with experiments. We need a systematic framework to update Markov models to make them consistent with constraints that are derived from experiments. Here, we present a framework based on the principle of maximum path entropy to update Markov models using stationary state and dynamical trajectory-based constraints. We illustrate the framework using a biochemical model network of growth factors-based signaling. We also show how to find the closest detailed balanced Markov model to a given Markov model. Further applications and generalizations are discussed.