时间延迟和关联噪声对基因转录调节系统统计性质的影响

Effects of Time Delay and Cross-correlated Noises on Statistical Properties of a Gene Transcription Conditioning System

研究延迟时间τ和交叉关联噪声对基因转录调节系统关联函数C(s)和弛豫时间TC的影响.在小延迟近似下,利用微扰理论,得到了系统的定态概率分布函数Pst(x).基于Pst(x),通过Stratonovich解耦近似框架导出了C(s)和TC的近似表达式.数值计算结果表明,TC随乘性噪声强度D的变化曲线呈一单峰结构,τ和噪声间正关联时的关联强度λ的增大均使TC增大,而噪声间负关联时|λ|和加性噪声强度α的增大则使TC减小;系统态变量x(蛋白质浓度)的C(s)随时间s呈指数规律衰减,τ对C(s)的影响显示一个临界行为,即存在一个临界值τC,当τ<τC时,τ的增大使C(s)增大,而τ>τC时,使C(s)减小.λ>0时,λ增大使C(s)增大,而λ<0时,使其减小.D对C(s)的影响也显示一个临界行为,即D较小和较大时D的增大对C(s)的影响相反,然而,α的增大只会使C(s)值减小.

The correlation function C（s） and the associated relaxation time TC of the gene transcription conditioning system are investigated in the presence of the cross-correlated noises and time delay τ.Using the small time delay approximation and the perturbation theory,the stationary probability distribution function（SPDF） is obtained.Based on the SPDF,the expressions of C（s） and TC are derived by means of Stratonovich decoupling ansatz.The results of the numerical computations indicate as follows.（1） the curve of TC versus D（the multiplicative noise intensity） shows a one-peak structure.The peak height of TC increases as τ increases,while TC decreases as α（the additive noise intensity） increases.The increasing ｜λ｜（the cross-correlation strength between noises） plays an opposite role in TC for the cases of λ〉0 and λ〈0.（2） C（s） decreases exponentially as the decay time s increases.There is a critical value τC of τ,below which C（s） decreases as τ increases and above which C（s） increases as τ increases.The increasing ｜λ｜ plays an opposite role in C（s） when λ〉0 and λ〈0.Moreover,the increasing D also plays an opposite role in C（s） for small and large D,but C（s） only decreases as α increases.