Dataset Information

Mathematical modelling of whole chromosome replication.

ABSTRACT: All chromosomes must be completely replicated prior to cell division, a requirement that demands the activation of a sufficient number of appropriately distributed DNA replication origins. Here we investigate how the activity of multiple origins on each chromosome is coordinated to ensure successful replication. We present a stochastic model for whole chromosome replication where the dynamics are based upon the parameters of individual origins. Using this model we demonstrate that mean replication time at any given chromosome position is determined collectively by the parameters of all origins. Combining parameter estimation with extensive simulations we show that there is a range of model parameters consistent with mean replication data, emphasising the need for caution in interpreting such data. In contrast, the replicated-fraction at time points through S phase contains more information than mean replication time data and allowed us to use our model to uniquely estimate many origin parameters. These estimated parameters enable us to make a number of predictions that showed agreement with independent experimental data, confirming that our model has predictive power. In summary, we demonstrate that a stochastic model can recapitulate experimental observations, including those that might be interpreted as deterministic such as ordered origin activation times.

SUBMITTER: de Moura AP

PROVIDER: S-EPMC2943597 | biostudies-literature | 2010 Sep

REPOSITORIES: biostudies-literature

ACCESS DATA

Publications

Mathematical modelling of whole chromosome replication.

de Moura Alessandro P S AP Retkute Renata R Hawkins Michelle M Nieduszynski Conrad A CA

Nucleic acids research 20100510 17

All chromosomes must be completely replicated prior to cell division, a requirement that demands the activation of a sufficient number of appropriately distributed DNA replication origins. Here we investigate how the activity of multiple origins on each chromosome is coordinated to ensure successful replication. We present a stochastic model for whole chromosome replication where the dynamics are based upon the parameters of individual origins. Using this model we demonstrate that mean replicati ...[more]

PMID: 20457753

Similar Datasets

Project description:Collective behaviour is of fundamental importance in the life sciences, where it appears at levels of biological complexity from single cells to superorganisms, in demography and the social sciences, where it describes the behaviour of populations, and in the physical and engineering sciences, where it describes physical phenomena and can be used to design distributed systems. Reasoning about collective behaviour is inherently difficult, as the non-linear interactions between individuals give rise to complex emergent dynamics. Mathematical techniques have been developed to analyse systematically collective behaviour in such systems, yet these frequently require extensive formal training and technical ability to apply. Even for those with the requisite training and ability, analysis using these techniques can be laborious, time-consuming and error-prone. Together these difficulties raise a barrier-to-entry for practitioners wishing to analyse models of collective behaviour. However, rigorous modelling of collective behaviour is required to make progress in understanding and applying it. Here we present an accessible tool which aims to automate the process of modelling and analysing collective behaviour, as far as possible. We focus our attention on the general class of systems described by reaction kinetics, involving interactions between components that change state as a result, as these are easily understood and extracted from data by natural, physical and social scientists, and correspond to algorithms for component-level controllers in engineering applications. By providing simple automated access to advanced mathematical techniques from statistical physics, nonlinear dynamical systems analysis, and computational simulation, we hope to advance standards in modelling collective behaviour. At the same time, by providing expert users with access to the results of automated analyses, sophisticated investigations that could take significant effort are substantially facilitated. Our tool can be accessed online without installing software, uses a simple programmatic interface, and provides interactive graphical plots for users to develop understanding of their models.

Project description:BackgroundGliomas are the most common types of brain cancer, well known for their aggressive proliferation and the invasive behavior leading to a high mortality rate. Several mathematical models have been developed for identifying the interactions between glioma cells and tissue microenvironment, which play an important role in the mechanism of the tumor formation and progression.MethodsBuilding and expanding on existing approaches, this paper develops a continuous three-dimensional model of avascular glioma spatio-temporal evolution. The proposed spherical model incorporates the interactions between the populations of four different glioma cell phenotypes (proliferative, hypoxic, hypoglychemic and necrotic) and their tissue microenvironment, in order to investigate how they affect tumor growth and invasion in an isotropic and homogeneous medium. The model includes two key variables involved in the proliferation and invasion processes of cancer cells; i.e. the extracellular matrix and the matrix-degradative enzymes concentrations inside the tumor and its surroundings. Additionally, the proposed model focuses on innovative features, such as the separate and independent impact of two vital nutrients, namely oxygen and glucose, in tumor growth, leading to the formation of cell populations with different metabolic profiles. The model implementation takes under consideration the variations of particular factors, such as the local cell proliferation rate, the variable conversion rates of cells from one category to another and the nutrient-dependent thresholds of conversion. All model variables (cell densities, ingredients concentrations) are continuous and described by reaction-diffusion equations.ResultsSeveral simulations were performed using combinations of growth and invasion rates, for different evolution times. The model results were evaluated by medical experts and validated on experimental glioma models available in the literature, revealing high agreement between simulated and experimental results.ConclusionsBased on the experimental validation, as well as the evaluation by clinical experts, the proposed model may provide an essential tool for the patient-specific simulation of different tumor evolution scenarios and reliable prognosis of glioma spatio-temporal progression.

Project description:In this paper, we develop a mathematical model for the spread and control of the coronavirus disease. An outbreak of COVID-19 has led to more than one million confirmed cases as of April 3rd, 2020. Understanding the early spread dynamics of the infection and evaluating the effectiveness of control measures is crucial for assessing the potential for sustained transmission to occur in new areas. Combining a mathematical model of severe COVID-19 spread with four datasets from within and outside of Wuhan, China; it is estimated how spread in Wuhan varied between January and February 2020. It is used these estimates to assess the potential for sustained human-to-human spread to occur in locations outside Wuhan if disease holders were introduced. It is combined SEIR framework model with data on cases of COVID-19 in China and International cases that originated in Wuhan to estimate how spread had varied over time during January and February 2020. Based on these estimates, it is calculated the probability that freshly introduced cases might produce outbreaks in other regions. Also, it is calculated approximately the median day by day basic reproduction number in Wuhan, refused from 2·45 (95% CI: 1·16-4·87) one week before travel restrictions were introduced on Jan 23rd, 2020, to 1.05 (0·42-2·40) one week after. Based on our estimates of, presumptuous SARS approximating disparity, it is computed that in locations with a similar spread potential to Wuhan in near the beginning of January, some time ago there are at least four independently set up cases, there is a more than fifty percent chance the infection will found within those inhabitants. COVID-19 spreading probably refused in Wuhan during delayed January 2020, corresponding with the prologue of voyage control channels. As more cases arrive in international locations with similar spread potential to Wuhan, before these organize measures, it is likely many chains of spread will fail to create initially but might lead to innovative outbreaks ultimately.

Dataset Information

Mathematical modelling of whole chromosome replication.

Publications

Mathematical modelling of whole chromosome replication.

Similar Datasets

OmicsDI is part of the ELIXIR infrastructure

Tweets