Boundary conditions and reversibility in diffusion controlled reactions. II. A three state model for steady state evaporation of a spherical drop

Gene transcription is a stochastic process manifested by fluctuations in mRNA copy numbers in individual isogenic cells. Together with mathematical models of stochastic transcription, the massive mRNA distribution data that can be used to quantify fluctuations in mRNA levels can be fitted by Pm(t), which is the probability of producing m mRNA molecules at time t in a single cell. Tremendous efforts have been made to derive analytical forms of Pm(t), which rely on solving infinite arrays of the master equations of models. However, current approaches focus on the steady-state (t→∞) or require several parameters to be zero or infinity. Here, we present an approach for calculating Pm(t) with time, where all parameters are positive and finite. Our approach was successfully implemented for the classical two-state model and the widely used three-state model and may be further developed for different models with constant kinetic rates of transcription. Furthermore, the direct computations of Pm(t) for the two-state model and three-state model showed that the different regulations of gene activation can generate discriminated dynamical bimodal features of mRNA distribution under the same kinetic rates and similar steady-state mRNA distribution.

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Retarded potentials and the expansion of the universe

Proceedings of the Royal Society of London Series A - Mathematical and Physical Sciences ◽

10.1098/rspa.1963.0104 ◽

1963 ◽

Vol 273 (1355) ◽

pp. 484-495 ◽

Cited By ~ 11

Keyword(s):

Steady State ◽

Boundary Conditions ◽

State Model ◽

De Sitter ◽

Maxwell Theory ◽

Steady State Model ◽

Expansion Of The Universe ◽

Sitter Model ◽

Radiation Processes ◽

De Sitter Model

The observed irreversibility of radiation processes is traced to the asymmetry in time of the expanding universe. A similar idea has recently been proposed by Hogarth (1962), who applied the Wheeler-Feynman (1945) theory to various world-models in an attempt to discriminate between advanced and retarded potentials. Hogarth found that, while the steady-state model leads to the required retarded potentials, the Einstein-de Sitter model leads to advanced potentials. In addition to disagreeing with observation, this latter result implies that a uniform distribution of galaxies can give rise to an infinite intensity of radiation. By contrast, we work with the conventional Maxwell theory. By using Kirchhoff’s boundary-value formulation of this theory, the boundary conditions appropriate to nonstatic world-models can be introduced. Among the consequences of these boundary conditions are: (i) In the Einstein-de Sitter model there exist distributions of sources for which Maxwell’s theory leads to retarded potentials (but, in addition, to an arbitrary amount of source-free radiation). In these cases the Wheeler-Feynman theory breaks down. The actual galaxies may constitute such a distribution. (ii) In the steady-state model Maxwell’s theory is equivalent to the Wheeler-Feynman theory, and leads to retarded potentials. In this case there is no source-free radiation, in agreement with the (somewhat crude) observational data.

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