Study On Nonlinear Stochastic Dynamics Of Epigenetic Gene Regulatory Networks

Epigenetic gene regulation is the regulation of gene expression at the transcriptional and post-transcriptional levels without altering DNA sequence.A large and complex gene regulatory network is formed owing to the interaction among various gene expression products in biological systems.The study of gene regulatory networks dynamics and mechanism,especial for core network motifs,has become an important issue in systems biology and bioinformatics.The gene regulatory networks of biological systems are influenced by many nonlinear stochastic dynamics factors,i.e.the significant fluctuation in the biochemical reaction due to the few number of involved molecules,the stochastic disturbance in the cell microenvironment and the time-delay effect during the signal transmission processes of gene regulation.Therefore,nonlinear stochastic dynamics should be fully considered in the study of gene regulatory networks.In this paper,based on nonlinear stochastic dynamics and numerical simulation,the cascaded feedforward gene regulatory model of somatic reprogramming and the double negative feedback regulatory model of the sternness characteristic phenotypic transition of lung carcinoma cells were further studied.The main results are as follows:(1)Based on the cascaded feedforward kinetic model with"AND gate"describing the somatic cell reprogramming process of iPSCs,the numerical simulation results of the expressions of each key factor under continuous expression of exogenous pluripotent factors can be consistent with the delayed effect of the activation of each factor in the somatic reprogramming experiment.The parameter sensitivity analysis indicate that the increase of the transcriptional regulation intensity can accelerate the expression of pluripotency factors,thereby accelerating the process of somatic cell reprogramming.The formulas of Fano factor for three key gene expression level are analytically derived from the kinetic model of somatic cell reprogramming process around steady-state by virtue of the Langevin theory,and the susceptibility is used to measure the sensitivity of response to variation in systemic parameters.It is found that the internal fluctuation of the expression levels of three key genes are not observably changed with the increasing of activated ratios(ks2 and kY),and there is a minimum for the internal fluctuation of the expression level of gene Y when the activated ratio kx by the upstream transcription factor X is around 0.25.With the increasing of the self-activation ratio(or self-degradation ratio),the internal fluctuations of the expression level of three key genes mainly depend on itself activation ratio and degradation ratio.The Fano factor approaches one for low values of the self-activation ratio(or self-degradation ratio),reaches a maximum when the self-activation ratio(or self-degradation ratio)is increased,and then decreases for high values of self-activation ratio(or self-degradation ratio).Above theoretical results obtained by Langevin theory are coincident with those obtained by the Gillespie algorithm.Under a fixed activated ratio by the upstream transcription factor,with the increasing of self-activation ratio(or self-degradation ratio),the susceptibility of steady-state increases first,reaches a maximum,and then decreases.The magnitude of maximum is decreased with the increasing of the activated ratio by the upstream transcription factor.In summary,the results imply that(?)the dynamics of coherent feedforward transcription regulation loops can be used to explain the observed delay kinetics and irreversible switch behavior of reprogramming induced pluripotency by exogenous OSKM factors;(?)the intrinsic noise of upstream transcription factor can not be transmitted to the expression of downstream transcription factor in the cascade of genes regulation motifs;(?)the susceptibility of steady-state response to the variation in systemic parameters has a nonmonotonic behavior,and the reprogramming process of somatic cells might be triggered through forced expression of a set of transcription factors.Our results might provide new insights into the roles of internal fluctuation and susceptibility in the dynamics of induced pluripotency and the behaviors captured of somatic cell reprogramming.(2)Based on the double-negative feedback loop of genes Lin28 and Let7 under the inhibitory regulation of miR200,a simplified kinetic model is proposed to describe the mechanism of sternness characteristic phenotypic transition of lung cancer cells.We identify three phenotypes(high-stemness U state,medium-sternness P state,low-stemness D state)of tumor cells by vitue of bifurcation diagram,then find that the increase of Let7 expression and the reduction of self-degradation rates can enhance the robustness of P state,while the decrease of Lin28 expression can intensify the irreversibility of phenotypic transition between D state and U state by using parameter sensitivity analysis for the saddle node bifurcation point.We compare five kinds of phenotypic distributions under different miR200 expression levels with major clinical types of lung cancer trying to make a possible connection between them.Then,we explore the influences of various regulatory factors(such as noise intensity,self-regulation intensity,and mutual inhibition intensity)on the probability distribution of the three phenotypes and the MFPT of phenotypic transition,and find that activation of Lin28 or inhibition of Let7 can promote the phenotype transitioning to U state,conversely to D state.The numerical simulation of Lin28 and Let7 expression under the combined action of internal noise and time-delay suggests that the increase of noise intensity improve the frequency of the transition between cell phenotypes and promotes phenotypic transition to the phenotype with the highest probability,moreover the increase of the time-delay of the self-activation regulation of Lin28 can enhance the stability of the cell phenotype,so as to reduce the frequency of the transition between phenotypes caused by the increase of noise intensity,and the cell phenotypes are inclined to the low-Lin28 state.Finally,we explore the mechanism of therapeutic resistance for non-small cell lung cancer and possible countermeasures by simulating the development of therapeutic resistance.In conclusion,our model provides new insights into the heterogeneity and phenotypic transition of lung cancer from the perspective of sternness,and new ideas for the diagnosis and treatment of lung cancer and other cancers.