A stochastic model of fragment formation when DNA replicates

The double-stranded molecule, DNA, has the unique property of replication and, because of this, it is the central molecule of life. The mechanism of replication for each single strand is intricate, involving enzymes which move along each of the single strands building a complementary copy. At the frontier of this action, the events have a strong stochastic character due to the random location on the DNA of key ‘sites' where copying commences. A model of this process is analysed. The central problem of interest is the mean length of certain ‘islands' of newly replicated DNA developed at the randomly located ‘sites'. These islands, which have been observed experimentally, are called Okazaki fragments.

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The global dynamics of stochastic Holling type II predator-prey models with non constant mortality rate

Filomat ◽

10.2298/fil1718811z ◽

2017 ◽

Vol 31 (18) ◽

pp. 5811-5825

Author(s):

Xinhong Zhang

Keyword(s):

Mortality Rate ◽

Stochastic Model ◽

Sufficient Conditions ◽

Positive Periodic Solution ◽

Global Dynamics ◽

Type Ii ◽

Predator Prey ◽

Persistence In The Mean ◽

The Mean ◽

Predator Prey Models

In this paper we study the global dynamics of stochastic predator-prey models with non constant mortality rate and Holling type II response. Concretely, we establish sufficient conditions for the extinction and persistence in the mean of autonomous stochastic model and obtain a critical value between them. Then by constructing appropriate Lyapunov functions, we prove that there is a nontrivial positive periodic solution to the non-autonomous stochastic model. Finally, numerical examples are introduced to illustrate the results developed.

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Distribution of the number of alleles in multigene families

Journal of Applied Probability ◽

10.1017/s0021900200043655 ◽

1992 ◽

Vol 29 (04) ◽

pp. 759-769

Author(s):

R. C. Griffiths

Keyword(s):

Stochastic Model ◽

Gene Conversion ◽

Lower Bounds ◽

Multigene Families ◽

Expected Number ◽

Allele Type ◽

The Mean

The distribution of the number of alleles in samples from r chromosomes is studied. The stochastic model used includes gene conversion within chromosomes and mutation at loci on the chromosomes. A method is described for simulating the distribution of alleles and an algorithm given for computing lower bounds for the mean number of alleles. A formula is derived for the expected number of samples from r chromosomes which contain the allele type of a locus chosen at random.

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A stochastic model for polymer degradation

Journal of Applied Probability ◽

10.2307/3212635 ◽

1972 ◽

Vol 9 (1) ◽

pp. 43-53 ◽

Cited By ~ 1

Author(s):

S. K. Srinivasan ◽

K. M. Mehata

Keyword(s):

Stochastic Model ◽

General Model ◽

Polymer Degradation ◽

Mean Square ◽

Product Density ◽

The Mean ◽

Number Of Segments

The stochastic model for breaking of molecular segments proposed by Bithell is analysed and some results relating to the distribution of the number of fragments are obtained by using a slightly more general model which allows multiple ruptures. The product density technique is employed to derive the mean and mean square number of segments at any time t and the number of segments with length greater than y at time of production.

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Statistics of nascent and mature RNA fluctuations in a stochastic model of transcriptional initiation, elongation, pausing, and termination

10.1101/2020.05.13.092650 ◽

2020 ◽

Author(s):

Tatiana Filatova ◽

Nikola Popovic ◽

Ramon Grima

Keyword(s):

Experimental Data ◽

Fluorescence Microscopy ◽

Stochastic Model ◽

Explicit Dependence ◽

Transcriptional Initiation ◽

Estimate Parameter ◽

Mean And Variance ◽

The Mean ◽

Nascent Rna ◽

Parameter Values

AbstractRecent advances in fluorescence microscopy have made it possible to measure the fluctuations of nascent (actively transcribed) RNA. These closely reflect transcription kinetics, as opposed to conventional measurements of mature (cellular) RNA, whose kinetics is affected by additional processes downstream of transcription. Here, we formulate a stochastic model which describes promoter switching, initiation, elongation, premature detachment, pausing, and termination while being analytically tractable. By computational binning of the gene into smaller segments, we derive exact closed-form expressions for the mean and variance of nascent RNA fluctuations in each of these segments, as well as for the total nascent RNA on a gene. We also derive exact expressions for the first two moments of mature RNA fluctuations, and approximate distributions for total numbers of nascent and mature RNA. Our results, which are verified by stochastic simulation, uncover the explicit dependence of the statistics of both types of RNA on transcriptional parameters and potentially provide a means to estimate parameter values from experimental data.

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Stochastic Model of the n-Stage Reversible First-Order Reaction: Relation between the Time of First Passage to the Most Probable Microstate and the Mean Equilibrium Fluctuations Lifetime

Zeitschrift für Physikalische Chemie ◽

10.1524/zpch.2002.216.7.869 ◽

2002 ◽

Vol 216 (7) ◽

Cited By ~ 4

Author(s):

M. Solc

Keyword(s):

Stochastic Model ◽

Order Reaction ◽

First Order Reaction ◽

First Passage ◽

Equilibrium Fluctuations ◽

First Order ◽

N Stage ◽

The Mean

Using the stochastic model of

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Fatigue of Metals as Stochastic Phenomena

Journal of Engineering Materials and Technology ◽

10.1115/1.3443399 ◽

1977 ◽

Vol 99 (1) ◽

pp. 26-28 ◽

Cited By ~ 3

Author(s):

C. Ihara ◽

A. Tsurui

Keyword(s):

Crack Initiation ◽

Stochastic Model ◽

Endurance Limit ◽

Recent Theory ◽

Mean Values ◽

Repeated Stress ◽

Coefficients Of Variation ◽

Cumulative Process ◽

The Mean ◽

Stochastic Phenomena

A stochastic model for the fatigue of metals under repeated stress or strain is proposed. Fatigue lives up to crack initiation are investigated with the aid of a recent theory on a cumulative process and the mean values are plotted versus stress amplitudes. Of interest is the fact that this curve behaves as if the endurance limit existed when the parameters are adequately taken. Except the neighborhood of the endurance limit, the coefficients of variation are also calculated approximately.

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On population-size-dependent branching processes

Advances in Applied Probability ◽

10.2307/1427223 ◽

1984 ◽

Vol 16 (1) ◽

pp. 30-55 ◽

Cited By ~ 53

Author(s):

F. C. Klebaner

Keyword(s):

Stochastic Model ◽

Asymptotic Behaviour ◽

Rate Of Convergence ◽

Population Size ◽

Gamma Distribution ◽

Branching Processes ◽

Independent Random Variables ◽

Size Dependent ◽

Offspring Distribution ◽

The Mean

We consider a stochastic model for the development in time of a population {Zn} where the law of offspring distribution depends on the population size. We are mainly concerned with the case when the mean mk and the variance of offspring distribution stabilize as the population size k grows to ∞, The process exhibits different asymptotic behaviour according to m < l, m = 1, m> l; moreover, the rate of convergence of mk to m plays an important role. It is shown that if m < 1 or m = 1 and mn approaches 1 not slower than n–2 then the process dies out with probability 1. If mn approaches 1 from above and the rate of convergence is n–1, then Zn/n converges in distribution to a gamma distribution, moreover a.s. both on a set of non-extinction and there are no constants an, such that Zn/an converges in probability to a non-degenerate limit. If mn approaches m > 1 not slower than n–α, α > 0, and do not grow to ∞ faster than nß, β <1 then Zn/mn converges almost surely and in L2 to a non-degenerate limit. A number of general results concerning the behaviour of sums of independent random variables are also given.

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Sensitivity of Perturbation Variance and Fluxes in Turbulent Jets to Changes in the Mean Jet

Journal of the Atmospheric Sciences ◽

10.1175/jas3256.1 ◽

2004 ◽

Vol 61 (21) ◽

pp. 2644-2652

Author(s):

Brian F. Farrell ◽

Petros J. Ioannou

Keyword(s):

Stochastic Model ◽

Storm Track ◽

Turbulent Jets ◽

Static Stability ◽

Structure Change ◽

Synoptic Scale ◽

Single Jet ◽

The Mean ◽

Arbitrary Change ◽

Jet Structure

Abstract Synoptic-scale eddy variance and fluxes of heat and momentum in midlatitude jets are sensitive to small changes in mean jet velocity, dissipation, and static stability. In this work the change in the jet producing the greatest increase in variance or flux is determined. Remarkably, a single jet structure change completely characterizes the sensitivity of a chosen quadratic statistical quantity to modification of the mean jet in the sense that an arbitrary change in the jet influences a chosen statistical quantity in proportion to the projection of the change on this single optimal structure. The method used extends previous work in which storm track statistics were obtained using a stochastic model of jet turbulence.

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