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Sampling properties of estimators of nucleotide diversity at discovered SNP sites

Alexander Renwick, Penelope Bonnen, Dimitra Trikka, David Nelson, Ranajit Chakraborty, Marek Kimmel (2003)

International Journal of Applied Mathematics and Computer Science

SNP sites are generally discovered by sequencing regions of the human genome in a limited number of individuals. This may leave SNP sites present in the region, but containing rare mutant nucleotides, undetected. Consequently, estimates of nucleotide diversity obtained from assays of detected SNP sites are biased. In this research we present a statistical model of the SNP discovery process, which is used to evaluate the extent of this bias. This model involves the symmetric Beta distribution of...

Self-Assembly of Icosahedral Viral Capsids: the Combinatorial Analysis Approach

R. Kerner (2011)

Mathematical Modelling of Natural Phenomena

An analysis of all possible icosahedral viral capsids is proposed. It takes into account the diversity of coat proteins and their positioning in elementary pentagonal and hexagonal configurations, leading to definite capsid size. We show that the self-organization of observed capsids during their production implies a definite composition and configuration of elementary building blocks. The exact number of different protein dimers is related to the...

Spatio-Temporal Modelling of the p53–mdm2 Oscillatory System

K. E. Gordon, I. M.M. van Leeuwen, S. Laín, M. A.J. Chaplain (2009)

Mathematical Modelling of Natural Phenomena

In this paper we investigate the role of spatial effects in determining the dynamics of a subclass of signalling pathways characterised by their ability to demonstrate oscillatory behaviour. To this end, we formulate a simple spatial model of the p53 network that accounts for both a negative feedback and a transcriptional delay. We show that the formation of protein density patterns can depend on the shape of the cell, position of the nucleus, and the protein diffusion rates. The temporal...

Stability for a diffusive delayed predator-prey model with modified Leslie-Gower and Holling-type II schemes

Yanling Tian (2014)

Applications of Mathematics

A diffusive delayed predator-prey model with modified Leslie-Gower and Holling-type II schemes is considered. Local stability for each constant steady state is studied by analyzing the eigenvalues. Some simple and easily verifiable sufficient conditions for global stability are obtained by virtue of the stability of the related FDE and some monotonous iterative sequences. Numerical simulations and reasonable biological explanations are carried out to illustrate the main results and the justification...

Stationary solutions of aerotaxis equations

Piotr Knosalla, Tadeusz Nadzieja (2015)

Applicationes Mathematicae

We study the existence and uniqueness of the steady state in a model describing the evolution of density of bacteria and oxygen dissolved in water filling a capillary. The steady state is a stationary solution of a nonlinear and nonlocal problem which depends on the energy function and contains two parameters: the total mass of the colony of bacteria and the concentration (or flux) of oxygen at the end of the capillary. The existence and uniqueness of solutions depend on relations between these...

Statistical tools for discovering pseudo-periodicities in biological sequences

Bernard Prum, Élisabeth de Turckheim, Martin Vingron (2010)

ESAIM: Probability and Statistics


Many protein sequences present non trivial periodicities, such as cysteine signatures and leucine heptads. These known periodicities probably represent a small percentage of the total number of sequences periodic structures, and it is useful to have general tools to detect such sequences and their period in large databases of sequences. We compare three statistics adapted from those used in time series analysis: a generalisation of the simple autocovariance based on a similarity score and two statistics...

Statistical tools for discovering pseudo-periodicities in biological sequences

Bernard Prum, Élisabeth de Turckheim, Martin Vingron (2001)

ESAIM: Probability and Statistics

Many protein sequences present non trivial periodicities, such as cysteine signatures and leucine heptads. These known periodicities probably represent a small percentage of the total number of sequences periodic structures, and it is useful to have general tools to detect such sequences and their period in large databases of sequences. We compare three statistics adapted from those used in time series analysis: a generalisation of the simple autocovariance based on a similarity score and two statistics...

Stimuli-Responsive Polymers in Nanotechnology: Deposition and Possible Effect on Drug Release

A. L. Yarin (2008)

Mathematical Modelling of Natural Phenomena

Stimuli-responsive polymers result in on-demand regulation of properties and functioning of various nanoscale systems. In particular, they allow stimuli-responsive control of flow rates through membranes and nanofluidic devices with submicron channel sizes. They also allow regulation of drug release from nanoparticles and nanofibers in response to temperature or pH variation in the surrounding medium. In the present work two relevant mathematical models are introduced to address precipitation-driven...

Stippling the Skin: Generation of Anatomical Periodicity by Reaction-Diffusion Mechanisms

D. J. Headon, K. J. Painter (2009)

Mathematical Modelling of Natural Phenomena

During vertebrate development cells acquire different fates depending largely on their location in the embryo. The definition of a cell's developmental fate relies on extensive intercellular communication that produces positional information and ultimately generates an appropriately proportioned anatomy. Here we place reaction-diffusion mechanisms in the context of general concepts regarding the generation of positional information during development and then focus on these mechanisms as parsimonious...

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