Stability of a stochastically perturbed model of intracellular single-stranded RNA virus replication

Replication of single-stranded RNA virus can be complicated, compared to that of double-stranded virus, as it require production of intermediate antigenomic strands that then serve as template for the genomic-sense strands. Moreover, for ssRNA viruses, there is a variability of the molecular mechanism by which genomic strands can be replicated. A combination of such mechanisms can also occur: a fraction of the produced progeny may result from a stamping-machine type of replication that uses the parental genome as template, whereas others may result from the replication of progeny genomes. F. Mart\'{\i}nez et al. and J. Sardany\'{e}s at al. suggested a deterministic ssRNA virus intracellular replication model that allows for the variability in the replication mechanisms. To explore how stochasticity can affect this model principal properties, in this paper we consider the stability of a stochastically perturbed model of ssRNA virus replication within a cell. Using the direct Lyapunov method, we found sufficient conditions for the stability in probability of equilibrium states for this model. This result confirms that this heterogeneous model of single-stranded RNA virus replication is stable with respect to stochastic perturbations of the environment

A quantitative model of the initiation of DNA replication in Saccharomyces cerevisiae predicts the effects of system perturbations.

BackgroundEukaryotic cell proliferation involves DNA replication, a tightly regulated process mediated by a multitude of protein factors. In budding yeast, the initiation of replication is facilitated by the heterohexameric origin recognition complex (ORC). ORC binds to specific origins of replication and then serves as a scaffold for the recruitment of other factors such as Cdt1, Cdc6, the Mcm2-7 complex, Cdc45 and the Dbf4-Cdc7 kinase complex. While many of the mechanisms controlling these associations are well documented, mathematical models are needed to explore the network's dynamic behaviour. We have developed an ordinary differential equation-based model of the protein-protein interaction network describing replication initiation.ResultsThe model was validated against quantified levels of protein factors over a range of cell cycle timepoints. Using chromatin extracts from synchronized Saccharomyces cerevisiae cell cultures, we were able to monitor the in vivo fluctuations of several of the aforementioned proteins, with additional data obtained from the literature. The model behaviour conforms to perturbation trials previously reported in the literature, and accurately predicts the results of our own knockdown experiments. Furthermore, we successfully incorporated our replication initiation model into an established model of the entire yeast cell cycle, thus providing a comprehensive description of these processes.ConclusionsThis study establishes a robust model of the processes driving DNA replication initiation. The model was validated against observed cell concentrations of the driving factors, and characterizes the interactions between factors implicated in eukaryotic DNA replication. Finally, this model can serve as a guide in efforts to generate a comprehensive model of the mammalian cell cycle in order to explore cancer-related phenotypes

Kinetic model of DNA replication in eukaryotic organisms

We formulate a kinetic model of DNA replication that quantitatively describes recent results on DNA replication in the in vitro system of Xenopus laevis prior to the mid-blastula transition. The model describes well a large amount of different data within a simple theoretical framework. This allows one, for the first time, to determine the parameters governing the DNA replication program in a eukaryote on a genome-wide basis. In particular, we have determined the frequency of origin activation in time and space during the cell cycle. Although we focus on a specific stage of development, this model can easily be adapted to describe replication in many other organisms, including budding yeast.Comment: 10 pages, 6 figures: see also cond-mat/0306546 & physics/030615

Model Dependency of the Digital Option Replication – Replication under an Incomplete Model (in English)

The paper focuses on the replication of digital options under an incomplete model. Digital options are regularly applied in the hedging and static decomposition of many path-dependent options. The author examines the performance of static and dynamic replication. He considers the case of a market agent for whom the right model of the underlying asset-price evolution is not available. The observed price dynamic is supposed to follow four distinct models: (i) the Black and Scholes model, (ii) the Black and Scholes model with stochastic volatility driven by Hull and White model, (iii) the variance gamma model, defined as time changed Brownian motion, and (iv) the variance gamma model set in a stochastic environment modelled as the rate of time change via a Cox-Ingersoll-Ross model. Both static and dynamic replication methods are applied and examined within each of these settings. The author verifies the independence of the static replication on underlying processes.digital options, dynamic and static replication, internal time, Lévy models, replication error, stochastic environment, stochastic volatility, variance gamma process

Making Models Match: Replicating an Agent-Based Model

Scientists have increasingly employed computer models in their work. Recent years have seen a proliferation of agent-based models in the natural and social sciences. But with the exception of a few "classic" models, most of these models have never been replicated by anyone but the original developer. As replication is a critical component of the scientific method and a core practice of scientists, we argue herein for an increased practice of replication in the agent-based modeling community, and for widespread discussion of the issues surrounding replication. We begin by clarifying the concept of replication as it applies to ABM. Furthermore we argue that replication may have even greater benefits when applied to computational models than when applied to physical experiments. Replication of computational models affects model verification and validation and fosters shared understanding about modeling decisions. To facilitate replication, we must create standards for both how to replicate models and how to evaluate the replication. In this paper, we present a case study of our own attempt to replicate a classic agent-based model. We begin by describing an agent-based model from political science that was developed by Axelrod and Hammond. We then detail our effort to replicate that model and the challenges that arose in recreating the model and in determining if the replication was successful. We conclude this paper by discussing issues for (1) researchers attempting to replicate models and (2) researchers developing models in order to facilitate the replication of their results.Replication, Agent-Based Modeling, Verification, Validation, Scientific Method, Ethnocentrism

The Swr1 chromatin-remodeling complex prevents genome instability induced by replication fork progression defects.

Genome instability is associated with tumorigenesis. Here, we identify a role for the histone Htz1, which is deposited by the Swr1 chromatin-remodeling complex (SWR-C), in preventing genome instability in the absence of the replication fork/replication checkpoint proteins Mrc1, Csm3, or Tof1. When combined with deletion of SWR1 or HTZ1, deletion of MRC1, CSM3, or TOF1 or a replication-defective mrc1 mutation causes synergistic increases in gross chromosomal rearrangement (GCR) rates, accumulation of a broad spectrum of GCRs, and hypersensitivity to replication stress. The double mutants have severe replication defects and accumulate aberrant replication intermediates. None of the individual mutations cause large increases in GCR rates; however, defects in MRC1, CSM3 or TOF1 cause activation of the DNA damage checkpoint and replication defects. We propose a model in which Htz1 deposition and retention in chromatin prevents transiently stalled replication forks that occur in mrc1, tof1, or csm3 mutants from being converted to DNA double-strand breaks that trigger genome instability

DNAReplication: a database of information and resources for the eukaryotic DNA replication community

DNAReplication (at http://www.dnareplication.net) has been set up as a freely available single resource to facilitate access to information on eukaryotic DNA replication. This database summarizes organism-sorted data on replication proteins in the categories of nomenclature, biochemical properties, motifs, interactions, modifications, structure, cell localization and expression, and general comments. Replication concepts are defined and a general model of the steps in DNA replication is presented. Links to relevant websites and homepages of replication labs are provided. The site also has an interactive section where links to recent replication papers are posted and readers are provided with the facility to post comments about each paper. The interactive and links pages are modified weekly and the whole site is updated annually