Fluctuations And Noise Propagation In Phenotypic Transition Cascades Around Steady State

Stochastic phenotype switching is a common feature of living systems. It plays an impor-tant role for organisms to adapt to sudden changes in local temperature, chemical composition, or illumination. The noise is ubiquitous due to random births and deaths of individual molecules and the fluctuations in reaction rates. A lot of experiments show that the number of cell involved in a biochemical reaction is often very small, which can lead to large intrinsic fluctuations in the cell population; Additionally, an individual can transform between diverse phenotypic states in a fluctuating environment. Therefore, it is a challenging and significant task to understand the impacts of noise on the stochastic phenotype switching.In this paper, the stochastic dynamics of the cell population and noise propagation around the steady state in phenotypic transition cascades are investigated by virtue of the stochastic dynamic theory and the computer simulation technology. The stochastic dynamics behaviors of two system, including three cell phenotypes (stem cells, transit-amplifying cells, and fully differentiated cells) conversion model in colonic crypt and two species (species A and species B) interconversion model in bacterial community with exploitative competition are investigated numerically and theoretically, respectively. The main results are presented as following:First, fluctuations of cell population in colonic crypt are studied. In a colonic crypt, stem cells differentiate into transit-amplifying cells, and then transit-amplifying cells differentiate into fully differentiated cells. Two differentiation rates are regulated by linear feedbacks mechanism to maintain the homeostasis. Based on this model, the Fano factor, covariance and susceptibility formulae of cell population around the steady state are derived by using of Langevin theory. According to the simulation, we find the stationary populations of TACs and FDCs exhibit an approximately threshold behavior as a function of the net growth rate of TACs, and the repro-ductions of TACs and FDCs can be classified into three regimens:controlled, crossover, and uncontrolled; Moreover, with the increasing of net growth rate of TACs, there is a maximum of the relative intrinsic fluctuations (i.e. the Fano factors) of TACs and FDCs in the crossover region. For a fixed differentiation rate and net growth rate of SCs, the covariance of fluctuations between SCs and TACs has a maximum in the crossover region. However, the susceptibilities of both TACs and FDCs to the net growth rate of TACs have a minimum in the crossover region.Second, fluctuations and noise propagation in different phenotypic transition cascades around steady state are studied. A general model of the phenotypic transition cascade is constructed firstly. Then, a general formulae for investigating fluctuations and noise propagation in the di-verse phenotypic transition cascades is presented by normalizing the fluctuation-dissipation the- orem which is gained by the linear noise approximation for the master equation of the general model. Applying the results on the various phenotypic transition cascades, we find:(i) In bacterial community with exploitative competition, the interconversions between species A and species B form a bidirectional phenotypic transition cascade. In this cascade, a systemic fluctuation environment is provided by all phenotypes. Therefore, the total noise of each phenotype include its intrinsic noise, transmitted noise from other phenotypes, and inter-conversion noise. The interconversion between different phenotypes leads to an added intrinsic noise, that is, the intrinsic noise is enlarged by the interconversion. Because the interconversion noises are little enough to be omitted, the total noise of each phenotype depends mainly on its intrinsic noise and transmitted noise.(ii) In a colonic crypt, the directional differentiations from stem cells to transit-amplifying cells and from transit-amplifying cells to fully differentiated cells form a unidirectional phe-notypic transition cascade. In this cascade, the fluctuation environment in each downstream phenotype is provided by the upstream phenotypes. Therefore, there is only the intrinsic noise in the upstream phenotype. Whereas, the total noise of each downstream phenotype is composed by its intrinsic noise, transmitted noise from other phenotypes, and conversion noise. Because the intrinsic noises and conversion noises are too little to be comparable, the total noise of each downstream phenotype depends mainly on its transmitted noises from upstream phenotypes.