scholarly journals Theory of transcription bursting: Stochasticity in the transcription rates

2019 ◽  
Author(s):  
Rajamanickam Murugan
Keyword(s):  
Rna Polymerase ◽  
Stationary State ◽  
First Passage Time ◽  
Transcription Elongation ◽  
Random Variable ◽  
Fano Factor ◽  
Passage Time ◽  
Transcription Rate ◽  
Mrna Transcript ◽  
Transcription Machinery

ABSTRACTTranscription bursting creates variation among the individuals of a given population. Bursting emerges as the consequence of turning on and off the transcription process randomly. There are at least three sub-processes involved in the bursting phenomenon with different timescale regimes viz. flipping across the on-off state channels, microscopic transcription elongation events and the mesoscopic transcription dynamics along with the mRNA recycling. We demonstrate that when the flipping dynamics is coupled with the microscopic elongation events, then the distribution of the resultant transcription rates will be over-dispersed. This in turn reflects as the transcription bursting with over-dispersed non-Poisson type distribution of mRNA numbers. We further show that there exist optimum flipping rates (αC, βC) at which the stationary state Fano factor and variance associated with the mRNA numbers attain maxima. These optimum points are connected via . Here α is the rate of flipping from the on-state to the off-state, β is the rate of flipping from the off-state to the on-state and γr is the decay rate of mRNA. When α = β = χ with zero rate in the off-state channel, then there exist optimum flipping rates at which the non-stationary Fano factor and variance attain maxima. Here (here is the rate of transcription purely through the on-state elongation channel) is the optimum flipping rate at which the variance of mRNA attains a maximum and χC, κ ≃ 1.72/t is the optimum flipping rate at which the Fano factor attains a maximum. Close observation of the transcription mechanism reveals that the RNA polymerase performs several rounds of stall-continue type dynamics before generating a complete mRNA. Based on this observation, we model the transcription event as a stochastic trajectory of the transcription machinery across these on-off state elongation channels. Each mRNA transcript follows different trajectory. The total time taken by a given trajectory is the first passage time (FPT). Inverse of this FPT is the resultant transcription rate associated with the particular mRNA. Therefore, the time required to generate a given mRNA transcript will be a random variable. For a stall-continue type dynamics of RNA polymerase, we show that the overall average transcription rate can be expressed as where is the microscopic transcription elongation rate in the on-state channel and L is the length of a complete mRNA transcript and is the stationary state probability of finding the transcription machinery in the on-state.

scholarly journals Mycobacterial HelD is a nucleic acids-clearing factor for RNA polymerase

2020 ◽  
Vol 11 (1) ◽  
Author(s):  
Tomáš Kouba ◽  
Tomáš Koval’ ◽  
Petra Sudzinová ◽  
Jiří Pospíšil ◽  
Barbora Brezovská ◽  
...  
Keyword(s):  
Nucleic Acids ◽  
Rna Polymerase ◽  
Active Site ◽  
Mycobacterium Smegmatis ◽  
Rna Synthesis ◽  
Environmental Changes ◽  
Transcription Elongation ◽  
Specific Interactions ◽  
Inactive State ◽  
Transcription Machinery

AbstractRNA synthesis is central to life, and RNA polymerase (RNAP) depends on accessory factors for recovery from stalled states and adaptation to environmental changes. Here, we investigated the mechanism by which a helicase-like factor HelD recycles RNAP. We report a cryo-EM structure of a complex between the Mycobacterium smegmatis RNAP and HelD. The crescent-shaped HelD simultaneously penetrates deep into two RNAP channels that are responsible for nucleic acids binding and substrate delivery to the active site, thereby locking RNAP in an inactive state. We show that HelD prevents non-specific interactions between RNAP and DNA and dissociates stalled transcription elongation complexes. The liberated RNAP can either stay dormant, sequestered by HelD, or upon HelD release, restart transcription. Our results provide insights into the architecture and regulation of the highly medically-relevant mycobacterial transcription machinery and define HelD as a clearing factor that releases RNAP from nonfunctional complexes with nucleic acids.

scholarly journals Tools to Estimate the First Passage Time to a Convex Barrier

2005 ◽  
Vol 42 (1) ◽  
pp. 61-81
Author(s):  
Ola Hammarlid
Keyword(s):  
Limit Distribution ◽  
Sequential Analysis ◽  
Large Deviation ◽  
First Passage Time ◽  
Stopping Time ◽  
Random Variable ◽  
Passage Time ◽  
First Passage ◽  
Linear Barrier ◽  
Asymptotic Normal

The first passage time of a random walk to a barrier (constant or concave) is of great importance in many areas, such as insurance, finance, and sequential analysis. Here, we consider a sum of independent, identically distributed random variables and the convex barrier cb(n/c), where c is a scale parameter and n is time. It is shown, using large-deviation techniques, that the limit distribution of the first passage time decays exponentially in c. Under a tilt of measure, which changes the drift, four properties are proved: the limit distribution of the overshoot is distributed as an overshoot over a linear barrier; the stopping time is asymptotically normally distributed when it is properly normalized; the overshoot and the asymptotic normal part are asymptotically independent; and the overshoot over a linear barrier is bounded by an exponentially distributed random variable. The determination of the function that multiplies the exponential part is guided by consideration of these properties.

scholarly journals Tools to Estimate the First Passage Time to a Convex Barrier

2005 ◽  
Vol 42 (01) ◽  
pp. 61-81
Author(s):  
Ola Hammarlid
Keyword(s):  
Limit Distribution ◽  
Sequential Analysis ◽  
Large Deviation ◽  
First Passage Time ◽  
Stopping Time ◽  
Random Variable ◽  
Passage Time ◽  
First Passage ◽  
Linear Barrier ◽  
Asymptotic Normal

The first passage time of a random walk to a barrier (constant or concave) is of great importance in many areas, such as insurance, finance, and sequential analysis. Here, we consider a sum of independent, identically distributed random variables and the convex barrier cb(n/c), where c is a scale parameter and n is time. It is shown, using large-deviation techniques, that the limit distribution of the first passage time decays exponentially in c. Under a tilt of measure, which changes the drift, four properties are proved: the limit distribution of the overshoot is distributed as an overshoot over a linear barrier; the stopping time is asymptotically normally distributed when it is properly normalized; the overshoot and the asymptotic normal part are asymptotically independent; and the overshoot over a linear barrier is bounded by an exponentially distributed random variable. The determination of the function that multiplies the exponential part is guided by consideration of these properties.

scholarly journals Effects of restrained degradation on gene expression and regulation

2020 ◽  
Vol 34 (13) ◽  
pp. 2050132
Author(s):  
Y.-L. Feng ◽  
J. Sun ◽  
Y.-F. Liu ◽  
J.-G. Ren ◽  
J.-M. Dong
Keyword(s):  
Gene Expression ◽  
Stochastic Systems ◽  
First Passage Time ◽  
Genetic Regulation ◽  
Internal Noise ◽  
Planck Equation ◽  
Fano Factor ◽  
Passage Time ◽  
Regulation System ◽  
Constitutive Gene Expression

The effects of carrying capacity of environment [Formula: see text] for degradation (the [Formula: see text] effect for short) on the constitutive gene expression and a simple genetic regulation system are investigated by employing a stochastic Langevin equation combined with the corresponding Fokker–Planck equation for the two stochastic systems subjected to internal and external noises. This [Formula: see text] effect characterizes the limited degradation ability of the environment for RNA or proteins, such as insufficient catabolic enzymes. The [Formula: see text] effect could significantly change the distribution of mRNA copy-number in constitutive gene expression, and interestingly, it leads to the Fano factor slightly larger than one if only the internal noise exists. Therefore, that the recent experimental measurements suggest the Fano factor deviates from one slightly [D. L. Jones, R. C. Brewster and R. Phillips, Science 346 (2014) 1533], probably originates from the [Formula: see text] effect. The [Formula: see text] effects on the steady and transient properties of genetic regulation system, have been investigated in detail. It could enhance the mean first passage time significantly especially when the noises are weak and reduce the signal-to-noise ratio in stochastic resonance substantially.

scholarly journals Semi-Markov reliability model of two different units cold standby system

2017 ◽  
pp. 1-1
Author(s):  
Franciszek Grabski
Keyword(s):  
Markov Processes ◽  
First Passage Time ◽  
Random Variable ◽  
Reliability Function ◽  
Passage Time ◽  
Time To Failure ◽  
Operation Process ◽  
Cold Standby ◽  
Standby System ◽  
Semi Markov Processes

A semi-Markov stochastic process is used for solving in a reliability problem in the paper. The problem concerns of two different component cold standby system and a switch. To obtain the reliability characteristic and parameters of the system we construct so called an embedded semi-Markov process in the process describing operation process of the system. In the model the conditional time to failure of the system is represented by a random variable denoting the first passage time from the given state to the specified subset of states. We apply theorems of the semi-Markov processes theory concerning the conditional reliability functions to calculate the reliability function and mean time to failure of the system. Often an exact reliability function of the system by using Laplace transform is difficult to calculate, frequently impossible. The semi-Markov processes perturbation theory, allows to obtain an approximate reliability function of the system in that case.

scholarly journals Human Spt6 Stimulates Transcription Elongation by RNA Polymerase II In Vitro

2004 ◽  
Vol 24 (8) ◽  
pp. 3324-3336 ◽  
Author(s):  
Masaki Endoh ◽  
Wenyan Zhu ◽  
Jun Hasegawa ◽  
Hajime Watanabe ◽  
Dong-Ki Kim ◽  
...  
Keyword(s):  
Rna Polymerase ◽  
Rna Polymerase Ii ◽  
Transcription Elongation ◽  
Elongation Factor ◽  
Underlying Mechanism ◽  
Regulation Of Transcription ◽  
Mrna Synthesis ◽  
Transcription Machinery

ABSTRACT Recent studies have suggested that Spt6 participates in the regulation of transcription by RNA polymerase II (RNAPII). However, its underlying mechanism remains largely unknown. One possibility, which is supported by genetic and biochemical studies of Saccharomyces cerevisiae, is that Spt6 affects chromatin structure. Alternatively, Spt6 directly controls transcription by binding to the transcription machinery. In this study, we establish that human Spt6 (hSpt6) is a classic transcription elongation factor that enhances the rate of RNAPII elongation. hSpt6 is capable of stimulating transcription elongation both individually and in concert with DRB sensitivity-inducing factor (DSIF), comprising human Spt5 and human Spt4. We also provide evidence showing that hSpt6 interacts with RNAPII and DSIF in human cells. Thus, in vivo, hSpt6 may regulate multiple steps of mRNA synthesis through its interaction with histones, elongating RNAPII, and possibly other components of the transcription machinery.

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