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Gene expression is the central process in cells, and is stochastic in nature. In this work, we study the mean expression level of, and the expression noise in, a population of isogenic cells, assuming that transcription is activated by two sequential exponential processes of rates κ and λ. We find that the mean expression level often displays oscillatory(More)
of Talks In the multiple authors case, the name with * is the speaker. Abstract: (Preliminary report) We examine the asymptotic states of symmetric solutions to ∆u − grad W (u) = 0, u : R n → R n constructed by Alikakos and Fusco. Here W is equivariant under a finite reflection group and has n + 1 nondegenerate minima. Passing to the limit as x → ∞ in(More)
We develop a general theorem concerning the existence of solutions to the periodic boundary value problem for the first-order impulsive differential equation,        x (t) = f (t, x(t)), t ∈ J \ {t 1 , t 2 , · · · , t k } x(t i) = I i (x(t i)), i = 1, 2 · · · k x(0) = x(T). And using it we get a concrete existence result. Moreover, to our knowledge(More)
How energy is consumed in gene expression is largely unknown mainly due to complexity of non-equilibrium mechanisms affecting expression levels. Here, by analyzing a representative gene model that considers complexity of gene expression, we show that negative feedback increases energy consumption but positive feedback has an opposite effect; promoter(More)
a r t i c l e i n f o a b s t r a c t This paper is concerned with the periodic boundary value problem u (t) = −Λu(t + r) − f t, u(t − r) , u(0) = −u(2r), u(0) = u(4r) (1) where r > 0 is a given constant, − π 2r < Λ < 3π 2r is a parameter, and f ∈ C (R 1 × R n , R n) satisfies f (t + r, z) = f (t, z) for all z ∈ R n. The variational principle is given and(More)