Fitness and entropy production in a cell population dynamics with epigenetic phenotype switching

Motivated by recent understandings in the stochastic natures of gene expression, biochemical signaling, and spontaneous reversible epigenetic switchings, we study a simple deterministic cell population dynamics in which subpopulations grow with different rates and individual cells can bi-directionally switch between a small number of different epigenetic phenotypes. Two theories in the past, the population dynamics and thermodynamics of master equations, separately defined two important concepts in mathematical terms: the fitness in the former and the (non-adiabatic) entropy production in the latter. Both of them play important roles in the evolution of the cell population dynamics. The switching sustains the variations among the subpopulation growth, thus sustains continuous natural selection. As a form of Price’s equation, the fitness increases with (i) natural selection through variations and (ii) a positive covariance between the per capita growth and switching, which represents a Lamarchian-like behavior. A negative covariance balances the natural selection in a fitness steady state --- “the red queen” scenario. At the same time the growth keeps the proportions of subpopulations away from the “intrinsic” switching equilibrium of individual cells, thus leads to a continuous entropy production. A covariance, between the per capita growth rate and the “chemical potential” of subpopulation, counteracts the entropy production. Analytical results are obtained for the limiting cases of growth dominating switching and vice versa.     

TOS9 regulates white-opaque switching in Candida albicans

In Candida albicans, the a1-alpha2 complex represses white-opaque switching, as well as mating. Based upon the assumption that the a1-alpha2 corepressor complex binds to the gene that regulates white-opaque switching, a chromatinimmunoprecipitation-microarray analysis strategy was used to identify 52 genes that bound to the complex. One of these genes, TOS9, exhibited an expression pattern consistent with a "master switch gene." TOS9 was only expressed in opaque cells, and its gene product, Tos9p, localized to the nucleus. Deletion of the gene blocked cells in the white phase, misexpression in the white phase caused stable mass conversion of cells to the opaque state, and misexpression blocked temperature-induced mass conversion from the opaque state to the white state. A model was developed for the regulation of spontaneous switching between the opaque state and the white state that includes stochastic changes of Tos9p levels above and below a threshold that induce changes in the chromatin state of an as-yet-unidentified switching locus. TOS9 has also been referred to as EAP2 and WOR1.     

Statistical Analysis of Lateral Diffusion and Multistate Kinetics in Single-Molecule Imaging

Single-molecule trajectories of molecules on the membrane of living cells have indicated the possibility that the lateral mobility of individual molecules is variable with time. Such temporal variation in mobility may indicate intrinsic kinetics of multiple molecular states. To clarify the mechanisms of signal processing on the membrane, quantitative characterizations of such temporal variations are necessary. Here we propose a method to analyze and characterize the multiple states in lateral mobility and their transition kinetics from single-molecule trajectories based on a displacement probability density function and an autocorrelation function of squared displacements. We performed our method for three cases: a molecule with a single diffusion coefficient (D), a mixture of molecules in two states with different D-values, and a molecule switching between two states with different D-values. Our analysis of numerically generated trajectories successfully distinguished the three cases and estimated the characteristic parameters for mobility and the kinetics of state transitions. This method is applicable to single-molecule tracking analysis of molecules in multiple functional states with different lateral mobility on the membrane of living cells.     

Med,a cell-surface localized protein regulating a competence transcription factor gene,comK, in Bacillus subtilis

Med was found as a positive regulator for comK, a master regulator for late competence genes. It was found by Western analysis that the ComK level was decreased in a med mutant. Experiments using an alkaline phosphatase fusion with Med and Western analysis of Med were done because a putative lipo-modification signal is found at the N-terminus of Med. The results obtained are consistent with the localization of Med at the cell surface. An implication of the cell-surface localization of Med is discussed in terms of comK regulation.     

Phosphate and ADP Differently Inhibit Coordinated Smooth Muscle Myosin Groups

Actin filaments propelled in vitro by groups of skeletal muscle myosin motors exhibit distinct phases of active sliding or arrest, whose occurrence depends on actin length (L) within a range of up to 1.0 μm. Smooth muscle myosin filaments are exponentially distributed with ≈150 nm average length in vivo—suggesting relevance of the L-dependence of myosin group kinetics. Here, we found L-dependent actin arrest and sliding in in vitro motility assays of smooth muscle myosin. We perturbed individual myosin kinetics with varying, physiological concentrations of phosphate (P_i, release associated with main power stroke) and adenosine diphosphate (ADP, release associated with minor mechanical step). Adenosine triphosphate was kept constant at physiological concentration. Increasing [P_i] lowered the fraction of time for which actin was actively sliding, reflected in reduced average sliding velocity (ν) and motile fraction (f_mot, fraction of time that filaments are moving); increasing [ADP] increased the fraction of time actively sliding and reduced the velocity while sliding, reflected in reduced ν and increased f_mot. We introduced specific P_i and ADP effects on individual myosin kinetics into our recently developed mathematical model of actin propulsion by myosin groups. Simulations matched our experimental observations and described the inhibition of myosin group kinetics. At low [P_i] and [ADP], actin arrest and sliding were reflected by two distinct chemical states of the myosin group. Upon [P_i] increase, the probability of the active state decreased; upon [ADP] increase, the probability of the active state increased, but the active state became increasingly similar to the arrested state.     

Metastable behavior in Markov processes with internal states

A perturbation framework is developed to analyze metastable behavior in stochastic processes with random internal and external states. The process is assumed to be under weak noise conditions, and the case where the deterministic limit is bistable is considered. A general analytical approximation is derived for the stationary probability density and the mean switching time between metastable states, which includes the pre exponential factor. The results are illustrated with a model of gene expression that displays bistable switching. In this model, the external state represents the number of protein molecules produced by a hypothetical gene. Once produced, a protein is eventually degraded. The internal state represents the activated or unactivated state of the gene; in the activated state the gene produces protein more rapidly than the unactivated state. The gene is activated by a dimer of the protein it produces so that the activation rate depends on the current protein level. This is a well studied model, and several model reductions and diffusion approximation methods are available to analyze its behavior. However, it is unclear if these methods accurately approximate long-time metastable behavior (i.e., mean switching time between metastable states of the bistable system). Diffusion approximations are generally known to fail in this regard.