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The first experimental evidence of the Turing pattern was observed by De Kepper and her associates (1990) on the CIMA reaction in an open unstirred gel reactor, almost 40 years after Turing’s prediction. Lengyel and Epstein characterized this famous experiment using a system of reactiondiffusion equations. In this paper we report some fundamental analytic(More)
Gene transcription in single cells is inherently a probabilistic process. Even in a hypothetically homogeneous intracellular environment, the stochasticity of transcription would produce fluctuations in the number of transcripts, constituting the phenotypic heterogeneity in cell population. Noise, the variance normalized by the square of the mean, has(More)
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)
The recent in vivo RNA detection technique has allowed real-time monitoring of gene transcription in individual living cells, revealing that genes can be transcribed randomly in a bursting fashion that short periods of rapid production of multiple transcripts are interspersed with relatively long periods of no production. In this work, we utilize the three(More)
Dengue fever is a mosquito-borne viral disease with 100 million people infected annually. A novel strategy for dengue control uses the bacterium Wolbachia to invade dengue vector Aedes mosquitoes. As the impact of environmental heterogeneity on Wolbachia spread dynamics in natural areas has been rarely quantified, we develop a model of differential(More)
Gene transcription is a central cellular process and is stochastic in nature. The stochasticity has been studied in real cells and in theory, but often for the transcription activated by a single signaling pathway at steady-state. As transcription of many genes is involved with multiple pathways, we investigate how the transcription efficiency and noise is(More)
Gene transcription is a stochastic process, and is often activated by multiple signal transduction pathways. In this work, we study gene transcription activated randomly by two cross-talking pathways, with the messenger RNA (mRNA) molecules being produced in a simple birth and death process. We derive the analytical formulas for the mean and the second(More)
Sequence specific transcription factors (TFs) are critical to ensuring that genes are transcribed in the right cell at the right time. Often, the gene promoter is flanked by multiple binding sites, some of which can be bound by different types of TFs in the cell. To investigate how the transcription noise is modulated by the competition of these TFs at(More)