Mean-field theory accurately captures the variation of copy number distributions across the mRNA life cycle

2022 ◽  
Vol 105 (1) ◽  
Author(s):  
Juraj Szavits-Nossan ◽  
Ramon Grima
2021 ◽  
Author(s):  
Juraj Szavits-Nossan ◽  
Ramon Grima

We consider a stochastic model where a gene switches between two states, an mRNA transcript is released in the active state and subsequently it undergoes an arbitrary number of sequential unimolecular steps before being degraded. The reactions effectively describe various stages of the mRNA life cycle such as initiation, elongation, termination, splicing, export and degradation. We construct a novel mean-field approach that leads to closed-form steady-state distributions for the number of transcript molecules at each stage of the mRNA life cycle. By comparison with stochastic simulations, we show that the approximation is highly accurate over all of parameter space, independent of the type of expression (constitutive or bursty) and of the shape of the distribution (unimodal, bimodal and nearly bimodal). The theory predicts that in a population of identical cells, any bimodality is gradually washed away as the mRNA progresses through its life cycle.


1993 ◽  
Vol 3 (3) ◽  
pp. 385-393 ◽  
Author(s):  
W. Helfrich

2000 ◽  
Vol 61 (17) ◽  
pp. 11521-11528 ◽  
Author(s):  
Sergio A. Cannas ◽  
A. C. N. de Magalhães ◽  
Francisco A. Tamarit

2021 ◽  
Vol 104 (1) ◽  
Author(s):  
Qinghong Yang ◽  
Zhesen Yang ◽  
Dong E. Liu

Materials ◽  
2021 ◽  
Vol 14 (4) ◽  
pp. 778
Author(s):  
Yingli Niu ◽  
Xiangyu Bu ◽  
Xinghua Zhang

The application of single chain mean-field theory (SCMFT) on semiflexible chain brushes is reviewed. The worm-like chain (WLC) model is the best mode of semiflexible chain that can continuously recover to the rigid rod model and Gaussian chain (GC) model in rigid and flexible limits, respectively. Compared with the commonly used GC model, SCMFT is more applicable to the WLC model because the algorithmic complexity of the WLC model is much higher than that of the GC model in self-consistent field theory (SCFT). On the contrary, the algorithmic complexity of both models in SCMFT are comparable. In SCMFT, the ensemble average of quantities is obtained by sampling the conformations of a single chain or multi-chains in the external auxiliary field instead of solving the modified diffuse equation (MDE) in SCFT. The precision of this calculation is controlled by the number of bonds Nm used to discretize the chain contour length L and the number of conformations M used in the ensemble average. The latter factor can be well controlled by metropolis Monte Carlo simulation. This approach can be easily generalized to solve problems with complex boundary conditions or in high-dimensional systems, which were once nightmares when solving MDEs in SCFT. Moreover, the calculations in SCMFT mainly relate to the assemble averages of chain conformations, for which a portion of conformations can be performed parallel on different computing cores using a message-passing interface (MPI).


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