Dynamics Of Biological System Including Hidden Variables: From Single Molecule To Cell

Biological system is a very complex system. In di?erent scales, there area lot of special phenomena need us to understand. In this thesis, we studied thedynamics of several representative phenomena in single molecule, sub-cell and cellscales, including multi-exponential waiting time distribution in the single-moleculeenzyme reaction, non-monotonic characteristic of the mean catalytic rate of thesingle-molecule enzyme reaction under stretching force, the abortive initiation oftranscription, thermotaxis of bacteria, and the fitness of cell population in ?uctuatingenvironment. We find that, although these phenomena seem quite di?erent, all ofthem can be well understood by dynamic models with hidden variables. These hiddenvariables include the conformation coordinate of biomacromolecule, such as protein,the state energy under di?erent conformation, and the stochastic gene expressionand the time delay in gene regulation network. In addition, based on a coarse-grainphysical model of the folding and unfolding of single forced RNAs conducted in lighttweezer experiments, we also proposed a Bayesian statistic approach to infer intrinsickinetic parameters from noisy single molecule experimental data. These e?orts notonly deepen our understanding of the dynamic behaviors of the biological systems,but also provide the foundation to study other biological phenomena.