scholarly journals Density- and elongation speed-dependent error correction in RNA polymerization

2021 ◽  
Author(s):  
Xinzhe Zuo ◽  
Tom Chou
Keyword(s):  
Stochastic Model ◽  
Rna Polymerase ◽  
Error Correction ◽  
Analytic Solutions ◽  
Dna Transcription ◽  
Exact Analytic Solutions ◽  
Rna Polymerization ◽  
Simplifying Assumptions ◽  
The Mean ◽  
Dependent Error

Abstract Backtracking of RNA polymerase (RNAP) is an important pausing mechanism during DNA transcription that is part of the error correction process that enhances transcription fidelity. We model the backtracking mechanism of RNA polymerase, which usually happens when the polymerase tries to incorporate a noncognate or "mismatched" nucleotide triphosphate. Previous models have made simplifying assumptions such as neglecting the trailing polymerase behind the backtracking polymerase or assuming that the trailing polymerase is stationary. We derive exact analytic solutions of a stochastic model that includes locally interacting RNAPs by explicitly showing how a trailing RNAP influences the probability that an error is corrected or incorporated by the leading backtracking RNAP. We also provide two related methods for computing the mean times for error correction and incorporation given an initial local RNAP configuration. Using these results, we propose an effective interacting-RNAP lattice that can be readily simulated.

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

Filomat ◽  
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.

Distribution of the number of alleles in multigene families

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.

CRYSTALLINE GRAVITY

2009 ◽  
Vol 24 (18n19) ◽  
pp. 3243-3255 ◽  
Author(s):  
GERARD 't HOOFT
Keyword(s):  
Finite Number ◽  
Lorentz Group ◽  
Degrees Of Freedom ◽  
Holonomy Group ◽  
Discrete Subgroup ◽  
Analytic Solutions ◽  
Space Time ◽  
Exact Analytic Solutions ◽  
Finite Domains ◽  
Dimensional Crystal

Matter interacting classically with gravity in 3+1 dimensions usually gives rise to a continuum of degrees of freedom, so that, in any attempt to quantize the theory, ultraviolet divergences are nearly inevitable. Here, we investigate a theory that only displays a finite number of degrees of freedom in compact sections of space-time. In finite domains, one has only exact, analytic solutions. This is achieved by limiting ourselves to straight pieces of string, surrounded by locally flat sections of space-time. Next, we suggest replacing in the string holonomy group, the Lorentz group by a discrete subgroup, which turns space-time into a 4-dimensional crystal with defects.

Estimation of Site Amplification from Geotechnical Array Data Using Neural Networks

2021 ◽  
Author(s):  
Daniel Roten ◽  
Kim B. Olsen
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Site Response ◽  
Site Amplification ◽  
Data Driven ◽  
Vertical Array ◽  
The Neural Network ◽  
Simplifying Assumptions ◽  
The Mean ◽  
Fully Connected

ABSTRACT We use deep learning to predict surface-to-borehole Fourier amplification functions (AFs) from discretized shear-wave velocity profiles. Specifically, we train a fully connected neural network and a convolutional neural network using mean AFs observed at ∼600 KiK-net vertical array sites. Compared with predictions based on theoretical SH 1D amplifications, the neural network (NN) results in up to 50% reduction of the mean squared log error between predictions and observations at sites not used for training. In the future, NNs may lead to a purely data-driven prediction of site response that is independent of proxies or simplifying assumptions.

Theoretical analysis of RNA polymerase fidelity: a steady-state copolymerization approach

2021 ◽  
Author(s):  
Wenbo Fu ◽  
Qiushi Li ◽  
Yongshun Song ◽  
Yaogen Shu ◽  
Zhongcan Ouyang ◽  
...  
Keyword(s):  
Steady State ◽  
Dna Replication ◽  
Theoretical Analysis ◽  
Rna Polymerase ◽  
Higher Order ◽  
Simplified Models ◽  
Rna Transcription ◽  
Dna Transcription ◽  
Polymerase Fidelity ◽  
Neighbor Effects

Abstract The fidelity of DNA transcription catalyzed by RNA polymerase (RNAP) has long been an important issue in biology. Experiments have revealed that RNAP can incorporate matched nucleotides selectively and proofread the incorporated mismatched nucleotides. However, systematic theoretical researches on RNAP fidelity are still lacking. In the last decade, several theories on RNA transcription have been proposed, but they only handled highly simplified models without considering the high-order neighbor effects and the oligonucleotides cleavage both of which are critical for the overall fidelity. In this paper, we regard RNA transcription as a binary copolymerization process and calculate the transcription fidelity by the steady-state copolymerization theory recently proposed by us for DNA replication. With this theory, the more realistic models considering higher-order neighbor effects, oligonucleotides cleavage, multi-step incorporation and multi-step cleavage can be rigorously handled.

A stochastic model for polymer degradation

1972 ◽  
Vol 9 (1) ◽  
pp. 43-53 ◽  
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.

scholarly journals RNA-Dependent RNA Polymerase from Heterobasidion RNA Virus 6 Is an Active Replicase In Vitro

Viruses ◽  
2021 ◽  
Vol 13 (9) ◽  
pp. 1738
Author(s):  
Alesia A. Levanova ◽  
Eeva J. Vainio ◽  
Jarkko Hantula ◽  
Minna M. Poranen
Keyword(s):  
Rna Polymerase ◽  
Rna Synthesis ◽  
Rna Virus ◽  
Polymerization Reaction ◽  
Rna Dependent Rna Polymerase ◽  
Independent Manner ◽  
Nucleotidyl Transferase ◽  
Rna Polymerization ◽  
The Family

Heterobasidion RNA virus 6 (HetRV6) is a double-stranded (ds)RNA mycovirus and a member of the recently established genus Orthocurvulavirus within the family Orthocurvulaviridae. The purpose of the study was to determine the biochemical requirements for RNA synthesis catalyzed by HetRV6 RNA-dependent RNA polymerase (RdRp). HetRV6 RdRp was expressed in Escherichia coli and isolated to near homogeneity using liquid chromatography. The enzyme activities were studied in vitro using radiolabeled UTP. The HetRV6 RdRp was able to initiate RNA synthesis in a primer-independent manner using both virus-related and heterologous single-stranded (ss)RNA templates, with a polymerization rate of about 46 nt/min under optimal NTP concentration and temperature. NTPs with 2′-fluoro modifications were also accepted as substrates in the HetRV6 RdRp-catalyzed RNA polymerization reaction. HetRV6 RdRp transcribed viral RNA genome via semi-conservative mechanism. Furthermore, the enzyme demonstrated terminal nucleotidyl transferase (TNTase) activity. Presence of Mn2+ was required for the HetRV6 RdRp catalyzed enzymatic activities. In summary, our study shows that HetRV6 RdRp is an active replicase in vitro that can be potentially used in biotechnological applications, molecular biology, and biomedicine.

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

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.

scholarly journals Exact analytical solutions of continuously graded models of flat lenses based on transformation optics

2017 ◽  
Vol 30 (4) ◽  
pp. 639-646 ◽  
Author(s):  
Mariana Dalarsson ◽  
Raj Mittra
Keyword(s):  
Magnetic Fields ◽  
Longitudinal Direction ◽  
Middle Layer ◽  
Analytic Solutions ◽  
Transformation Optics ◽  
Confluent Hypergeometric Functions ◽  
Graded Index ◽  
Exact Analytic Solutions ◽  
Electric And Magnetic Fields ◽  
Physical Insight

We present a study of exact analytic solutions for electric and magnetic fields in continuously graded flat lenses designed utilizing transformation optics. The lenses typically consist of a number of layers of graded index dielectrics in both the radial and longitudinal directions, where the central layer in the longitudinal direction primarily contributes to a bulk of the phase transformation, while other layers act as matching layers and reduce the reflections at the interfaces of the middle layer. Such lenses can be modeled as compact composites with continuous permittivity (and if needed) permeability functions which asymptotically approach unity at the boundaries of the composite cylinder. We illustrate the proposed procedures by obtaining the exact analytic solutions for the electric and magnetic fields for one simple special class of composite designs with radially graded parameters. To this purpose we utilize the equivalence between the Helmholtz equation of our graded flat lens and the quantum-mechanical radial Schr?dinger equation with Coulomb potential, furnishing the results in the form of Kummer confluent hypergeometric functions. Our approach allows for a better physical insight into the operation of our transformation optics-based graded lenses and opens a path toward novel designs and approaches.

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