A modified Gillespie algorithm for E.coli gene regulation systems

The dynamics of complex gene regulation systems can be simulated by the Gillespie algorithm. The classic Gillespie algorithm is appropriate to simulate a stochastic

Modeling stochastic noise in gene regulatory systems

The Master equation is considered the gold standard for modeling the stochastic mechanisms of gene regulation in molecular detail, but it is too complex to solve exactly in most cases, so approximation and simulation methods are essential. However, there is still a lack of consensus about the best way to carry these out. To help clarify the situation, we review Master equation models of gene regulation, theoretical approximations based on an expansion method due to N.G. van Kampen and R. Kubo, and simulation algorithms due to D.T. Gillespie and P. Langevin. Expansion of the Master equation shows that for systems with a single stable steady-state, the stochastic model reduces to a deterministic model in a first-order approximation. Additional theory, also due to van Kampen, describes the asymptotic behavior of multistable systems. To support and illustrate the theory and provide further insight into the complex behavior of multistable systems, we perform a detailed simulation study comparing the various approximation and simulation methods applied to synthetic gene regulatory systems with various qualitative characteristics. The simulation studies show that for large stochastic systems with a single steady-state, deterministic models are quite accurate, since the probability distribution of the solution has a single peak tracking the deterministic trajectory whose variance is inversely proportional to the system size. In multistable stochastic systems, large fluctuations can cause individual trajectories to escape from the domain of attraction of one steady-state and be attracted to another, so the system eventually reaches a multimodal probability distribution in which all stable steady- states are represented proportional to their relative stability. However, since the escape time scales exponentially with system size, this process can take a very long time in large systems.

Three-dimensional cytoplasmic calcium propagation with boundaries

Ca^(2+)plays an important role in cell signal transduction.Its intracellular propagation is the most basic process of Ca^(2+)signaling,such as calcium wave and double messenger system.In this work,with both numerical simulation and mean field ansatz,the three-dimensional probability distribution of Ca^(2+),which is read out by phosphorylation,is studied in two scenarios with boundaries.The coverage of distribution of Ca^(2+)is found at an order of magnitude ofμm,which is consistent with experimental observed calcium spike and wave.Our results suggest that the double messenger system may occur in the ER-PM junction to acquire great efficiency.The buffer effect of kinase is also discussed by calculating the average position of phosphorylations and free Ca^(2+).The results are helpful to understand the mechanism of Ca^(2+)signaling.

Corrigendum to“Silent circulation of poliovirus in small populations”[Infectious Disease Modeling 2(2017)431e440]

An error in a previous publication in the calculation of the average age at first infection for the model is corrected here.The average age at first infection for the effective contact rates used to generate the data ranges from 1.2 to 3.3 years of age instead of 3e5 years of age as advertised in the previous version of the paper.This change has an effect on the force of infection generated by this model.In this corrigendum,we demonstrate the correct method to calculate the average age at first infection for the model.We compare the forces of infection that correspond to these ages in our model with the forces of infection in other endemic populations.We show that the modified age range corresponds to forces of infection which are higher than those that are known to exist in historical studies of polioendemic regions.Thus,the results in the paper have limited applicability to real-world endemic situations.

Silent circulation of poliovirus in small populations

Background:Small populations that have been isolated by conflict make vaccination and surveillance difficult,threatening polio eradication.Silent circulation is caused by asymptomatic infections.It is currently not clear whether the dynamics of waning immunity also influence the risk of silent circulation in the absence of vaccination.Such circulation can,nevertheless,be present following a declaration of elimination as a result of inadequate acute flaccid paralysis surveillance(AFPS)or environmental surveillance(ES).Methods:We have constructed a stochastic model to understand how stochastic effects alter the ability of small populations to sustain virus circulation in the absence of vaccination.We analyzed how the stochastic process determinants of the duration of silent circulation that could have been detected by ES were affected by R0,waning dynamics,population size,and AFPS sensitivity in a discrete individual stochastic model with homogeneous contagiousness and random mixing.We measured the duration of silent circulation both by the interval between detected acute flaccid paralysis(AFP)cases and the duration of circulation until elimination.Results:As R0 increased and population size increased,the interval between detected AFP cases and the duration of circulation until elimination increased.As AFPS detection rates decreased,the interval between detected AFP cases increased.There was up to a 22%chance of silent circulation lasting for more than 3 years with 100%AFP detection.The duration of silent circulation was not affected by the waning immunity dynamics.Conclusion:We demonstrated that small populations have the potential to sustain prolonged silent circulation.Surveillance in these areas should be intensified before declaring elimination.To further validate these conclusions,it is necessary to realistically relax the simplifying assumptions about mixing and waning.