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A mathematical model for the regulation of induction in the lac operon in Escherichia coli is presented. This model takes into account the dynamics of the permease facilitating the internalization of external lactose; internal lactose; beta-galactosidase, which is involved in the conversion of lactose to allolactose, glucose and galactose; the allolactose(More)
The period (in the order of 40 to 80 days) in periodic chronic myelogenous leukemia (PCML) oscillations is quite long compared with the duration of the cell cycle of the hematopoietic stem cells from which the oscillations are presumed to originate (in the order of one or two days). Our objective is to understand the origin of these long-period oscillations(More)
This paper analyzes the dynamics of a G 0 cell cycle model of pluripotential stem cells to understand the origin of the long period oscillations of blood cell levels observed in periodic chronic myelogenous leukemia (PCML). The model dynamics are described by a system of two delayed differential equations. We give conditions for the local stability of the(More)
The transcriptional repressor Hes1, a basic helix-loop-helix family protein, periodically changes its expression in the presomitic mesoderm. Its periodic pattern of expression is retained in a number of cultured murine cell lines. In this paper, we introduce an extended mathematical model for Hes1 oscillatory expression that includes regulation of Hes1(More)
We develop a mathematical model of the phage lambda lysis/lysogeny switch, taking into account recent experimental evidence demonstrating enhanced cooperativity between the left and right operator regions. Model parameters are estimated from available experimental data. The model is shown to have a single stable steady state for these estimated parameter(More)
We study a class of delay differential equations which have been used to model hematological stem cell regulation and dynamics. Under certain circumstances the model exhibits self-sustained oscillations, with periods which can be significantly longer than the basic cell cycle time. We show that the long periods in the oscillations occur when the cell(More)
Understanding the regulation of gene control networks and their ensuing dynamics will be a critical component in the understanding of the mountain of genomic data being currently collected. This paper reviews recent mathematical modeling work on the tryptophan and lactose operons which are, respectively, the classical paradigms for repressible and inducible(More)
We have formulated and analysed a dynamic model for recurrent inhibition that takes into account the state dependence of the delayed feedback signal (due to the variation in threshold of fibres with their size) and the distribution of these delays (due to the distribution of fibre diameters in the feedback pathway). Using a combination of analytic and(More)
BACKGROUND Recent discoveries in the field of somitogenesis have confirmed, for the most part, the feasibility of the clock and wavefront model. There are good candidates for both the clock (various genes expressed cyclically in the tail bud of vertebrate embryos have been discovered) and the wavefront (there are at least three different substances, whose(More)
We study the moment stability of the trivial solution of a linear differential delay equation in the presence of additive and multiplicative white noise. The results established here are applied to examining the local stability of the hematopoietic stem cell (HSC) regulation system in the presence of noise. The stability of the first moment for the(More)