Search results for "Quantitative Biology"
showing 10 items of 1025 documents
An Extended Filament Based Lamellipodium Model Produces Various Moving Cell Shapes in the Presence of Chemotactic Signals
2015
The Filament Based Lamellipodium Model (FBLM) is a two-phase two-dimensional continuum model, describing the dynamcis of two interacting families of locally parallel actin filaments (C.Schmeiser and D.Oelz, How do cells move? Mathematical modeling of cytoskeleton dynamics and cell migration. Cell mechanics: from single scale-based models to multiscale modeling. Chapman and Hall, 2010). It contains accounts of the filaments' bending stiffness, of adhesion to the substrate, and of cross-links connecting the two families. An extension of the model is presented with contributions from nucleation of filaments by branching, from capping, from contraction by actin-myosin interaction, and from a pr…
The Concept of Duality and Applications to Markov Processes Arising in Neutral Population Genetics Models
1999
One possible and widely used definition of the duality of Markov processes employs functions H relating one process to another in a certain way. For given processes X and Y the space U of all such functions H, called the duality space of X and Y, is studied in this paper. The algebraic structure of U is closely related to the eigenvalues and eigenvectors of the transition matrices of X and Y. Often as for example in physics (interacting particle systems) and in biology (population genetics models) dual processes arise naturally by looking forwards and backwards in time. In particular, time-reversible Markov processes are self-dual. In this paper, results on the duality space are presented f…
Dynamics of the Selkov oscillator.
2018
A classical example of a mathematical model for oscillations in a biological system is the Selkov oscillator, which is a simple description of glycolysis. It is a system of two ordinary differential equations which, when expressed in dimensionless variables, depends on two parameters. Surprisingly it appears that no complete rigorous analysis of the dynamics of this model has ever been given. In this paper several properties of the dynamics of solutions of the model are established. With a view to studying unbounded solutions a thorough analysis of the Poincar\'e compactification of the system is given. It is proved that for any values of the parameters there are solutions which tend to inf…
Tuning active Brownian motion with shot noise energy pulses
2009
The main aim of this work is to explore the possibility of modeling the biological energy support mediated by absorption of ATP (adenosine triphosphate) as an energetic shot noise. We develop a general model with discrete input of energy pulses and study shot-noise-driven ratchets. We consider these ratchets as prototypes of Brownian motors driven by energy-rich ATP molecules. Our model is a stochastic machine able to acquire energy from the environment and convert it into kinetic energy of motion. We present characteristic features and demonstrate the possibility of tuning these motors by adapting the mean frequency of the discrete energy inputs, which are described as a special shot noise…
Noise driven translocation of short polymers in crowded solutions
2008
In this work we study the noise induced effects on the dynamics of short polymers crossing a potential barrier, in the presence of a metastable state. An improved version of the Rouse model for a flexible polymer has been adopted to mimic the molecular dynamics by taking into account both the interactions between adjacent monomers and introducing a Lennard-Jones potential between all beads. A bending recoil torque has also been included in our model. The polymer dynamics is simulated in a two-dimensional domain by numerically solving the Langevin equations of motion with a Gaussian uncorrelated noise. We find a nonmonotonic behaviour of the mean first passage time and the most probable tran…
A nonstationary cylinder-based model describing group dispersal in a fragmented habitat
2014
International audience; A doubly nonstationary cylinder-based model is built to describe the dispersal of a population from a point source. In this model, each cylinder represents a fraction of the population, i.e., a group. Two contexts are considered: The dispersal can occur in a uniform habitat or in a fragmented habitat described by a conditional Boolean model. After the construction of the models, we investigate their properties: the first and second order moments, the probability that the population vanishes, and the distribution of the spatial extent of the population.
Ancestral processes in population genetics-the coalescent.
2000
A special stochastic process, called the coalescent, is of fundamental interest in population genetics. For a large class of population models this process is the appropriate tool to analyse the ancestral structure of a sample of n individuals or genes, if the total number of individuals in the population is sufficiently large. A corresponding convergence theorem was first proved by Kingman in 1982 for the Wright-Fisher model and the Moran model. Generalizations to a large class of exchangeable population models and to models with overlying mutation processes followed shortly later. One speaks of the "robustness of the coalescent, as this process appears in many models as the total populati…
Global stability of protein folding from an empirical free energy function
2013
The principles governing protein folding stand as one of the biggest challenges of Biophysics. Modeling the global stability of proteins and predicting their tertiary structure are hard tasks, due in part to the variety and large number of forces involved and the difficulties to describe them with sufficient accuracy. We have developed a fast, physics-based empirical potential, intended to be used in global structure prediction methods. This model considers four main contributions: Two entropic factors, the hydrophobic effect and configurational entropy, and two terms resulting from a decomposition of close-packing interactions, namely the balance of the dispersive interactions of folded an…
Remarks on ergodicity and invariant occupation measure in branching diffusions with immigration☆
2005
Abstract We give a necessary and sufficient condition for ergodicity with finite invariant occupation measure for branching diffusions with immigration. We do not assume uniformly subcritial reproduction means. We discuss the structure of the invariant occupation measure and of its density.
A Bayesian SIRS model for the analysis of respiratory syncytial virus in the region of Valencia, Spain
2014
We present a Bayesian stochastic susceptible-infected-recovered-susceptible (SIRS) model in discrete time to understand respiratory syncytial virus dynamics in the region of Valencia, Spain. A SIRS model based on ordinary differential equations has also been proposed to describe RSV dynamics in the region of Valencia. However, this continuous-time deterministic model is not suitable when the initial number of infected individuals is small. Stochastic epidemic models based on a probability of disease transmission provide a more natural description of the spread of infectious diseases. In addition, by allowing the transmission rate to vary stochastically over time, the proposed model provides…