scholarly journals Exact and WKB-approximate distributions in a gene expression model with feedback in burst frequency, burst size, and protein stability

2020 ◽  
Author(s):  
Pavol Bokes
Keyword(s):  
Protein Stability ◽  
Kinetic Monte Carlo ◽  
Burst Size ◽  
Dynamical Process ◽  
Protein Distribution ◽  
Functional Protein ◽  
Burst Frequency ◽  
Jump Size ◽  
Kinetic Monte Carlo Simulations ◽  
The Difference

AbstractThe expression of individual genes into functional protein molecules is a noisy dynamical process. Here we model the protein concentration as a jump-drift process which combines discrete stochastic production bursts (jumps) with continuous deterministic decay (drift). We allow the drift rate, the jump rate, and the jump size to depend on the current protein level in an arbitrary fashion to implement feedback in protein stability, burst frequency, and burst size. Two versions of feedback in burst size are considered: in the “infinitesimally delayed” version, only those molecules of protein that have been present before a burst started can regulate the size of the burst; in the “undelayed” version, newly produced molecules also partake in the regulation of the further growth of a burst. Excluding the infinitesimal delay in burst size, the model is explicitly solvable. With the inclusion of the infinitesimal delay, an exact distribution to the model is no longer available, but we are able to construct a WKB approximation that applies in the asymptotic regime of small but frequent bursts. Comparing the asymptotic behaviour of the two model versions, we report that they yield the same WKB quasi-potential but a different exponential prefactor. We illustrate the difference on the case of a bimodal protein distribution sustained by a sigmoid feedback in burst size: we show that the omission of the infinitesimal delay overestimates the weight of the upper mode of the protein distribution. The analytic results are supported by kinetic Monte-Carlo simulations.

scholarly journals Noise induced bimodality in genetic circuits with monostable positive feedback

2018 ◽  
Author(s):  
Pavol Bokes ◽  
Abhyudai Singh
Keyword(s):  
Positive Feedback ◽  
Kinetic Monte Carlo ◽  
Burst Size ◽  
Gene Activation ◽  
Genetic Circuits ◽  
Burst Frequency ◽  
Modelling Framework ◽  
Low Copy Number ◽  
Kinetic Monte Carlo Simulations ◽  
Noise Amplification

AbstractThe expression of individual genes can be maintained through positive feedback loop mechanisms. If genes are expressed in bursts, then feedback either affects the frequency with which bursts occur or their size. Here we use a tractable hybrid modelling framework to evaluate how noncooperative positive feedback in burst frequency or burst size impacts the protein-level distribution. We confirm the results of previous studies that noncooperative positive feedback in burst frequency can support bimodal distributions. Intriguingly, bimodal distributions are unavailable in the case of feedback in burst size in the hybrid framework. However, kinetic Monte Carlo simulations of a full discrete model show that bimodality can reappear due to low-copy number effects. The two types of feedbacks lead to dramatically different values of protein mean and noise. We show that small values of leakage imply a small protein mean for feedback in burst frequency but not necessarily for feedback in burst size. We also show that protein noise decreases in response to gene activation if feedback is in burst frequency but there is a transient noise amplification if feedback acts on burst size. Our results suggest that feedback in burst size and feedback in burst frequency may play fundamentally different roles in maintaining and controlling stochastic gene expression.

Effective Interactions Approach to Phase Stability in Alloys Under Irradiation

1998 ◽  
Vol 538 ◽  
Author(s):  
Raúl A. Enrique ◽  
Pascal Bellon
Keyword(s):  
Phase Diagram ◽  
Phase Stability ◽  
Kinetic Monte Carlo ◽  
Theoretical Frameworks ◽  
Effective Interactions ◽  
Dynamical Phase ◽  
Thermodynamic Potentials ◽  
Simple Kinetic Model ◽  
Kinetic Monte Carlo Simulations ◽  
Competing Dynamics

AbstractPhase stability in alloys under irradiation is studied considering effective thermodynamic potentials. A simple kinetic model of a binary alloy with phase separation is investigated. Time evolution in the alloy results from two competing dynamics: thermal diffusion, and irradiation induced ballistic exchanges. The dynamical (steady state) phase diagram is evaluated exactly performing Kinetic Monte Carlo simulations. The solution is then compared to two theoretical frameworks: the effective quasi-interactions model as proposed by Vaks and Kamishenko, and the effective free energy model as proposed by Martin. New developments of these models are proposed to allow for quantitative comparisons. Both theoretical frameworks yield fairly good approximations to the dynamical phase diagram.

Kinetic Monte Carlo Simulation of Impurity Effects on Nucleation and Growth of SiC Clusters on Si(100)

2013 ◽  
Vol 740-742 ◽  
pp. 393-396
Author(s):  
Maxim N. Lubov ◽  
Jörg Pezoldt ◽  
Yuri V. Trushin
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Cluster Size ◽  
Kinetic Monte Carlo ◽  
Nucleation And Growth ◽  
Nucleation Density ◽  
Nucleation Process ◽  
Impurity Effects ◽  
Kinetic Monte Carlo Simulations ◽  
The Mean

The influence of attractive and repulsive impurities on the nucleation process of the SiC clusters on Si(100) surface was investigated. Kinetic Monte Carlo simulations of the SiC clusters growth show that that increase of the impurity concentration (both attractive and repulsive) leads to decrease of the mean cluster size and rise of the nucleation density of the clusters.

Trapping Effect on the Kinetic Critical Radius in Nucleation and Growth Processes

2014 ◽  
Vol 790-791 ◽  
pp. 97-102
Author(s):  
Zoltán Erdélyi ◽  
Zoltán Balogh ◽  
Gabor L. Katona ◽  
Dezső L. Beke
Keyword(s):  
Critical Nucleus ◽  
Solid Phase ◽  
Kinetic Monte Carlo ◽  
Mean Field ◽  
Transformation Process ◽  
Nucleus Size ◽  
Critical Nucleus Size ◽  
Acta Mater ◽  
Order Of Magnitude ◽  
The Difference

The critical nucleus size—above which nuclei grow, below dissolve—during diffusion controlled nucleation in binary solid-solid phase transformation process is calculated using kinetic Monte Carlo (KMC). If atomic jumps are slower in an A-rich nucleus than in the embedding B-rich matrix, the nucleus traps the A atoms approaching its surface. It doesn’t have enough time to eject A atoms before new ones arrive, even if it would be favourable thermodynamically. In this case the critical nucleus size can be even by an order of magnitude smaller than expected from equilibrium thermodynamics or without trapping. These results were published in [Z. Erdélyi et al., Acta Mater. 58 (2010) 5639]. In a recent paper M. Leitner [M. Leitner, Acta Mater. 60 (2012) 6709] has questioned our results based on the arguments that his simulations led to different results, but he could not point out the reason for the difference. In this paper we summarize our original results and on the basis of recent KMC and kinetic mean field (KMF) simulations we show that Leitner’s conclusions are not valid and we confirm again our original results.

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