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At least 73 records · Page 4Linked to original sources
arXiv2009

Quantitative interpretation of binding reactions of rapidly diffusing species using fluorescence recovery after photobleaching

Fluorescence recovery after photobleaching (FRAP) measurements offer an important tool for analyzing diffusion and binding processes. Confocal scanning laser microscopes that are used in FRAP experiments bleach regions with a radially Gaussian distributed profile. Previous attempts to derive analytical expressions in the case of processes governed by fast diffusion have overlooked the characteristics of the instruments used to perform FRAP measurements and therefore led to approximating solutions. In the present paper, bleaching laser beam characteristics are incorporated into an improved model to provide a more rigorous and accurate method. The proposed model simulates binding inside bounded regions, and it leads to FRAP curves that depend on the on and off rates that can be employed to determine the rate constants. It can be used in conjunction with experimental data acquired with confocal scanning laser microscopes to investigate the biophysical properties of proteins in living cells. The model aims to improve the accuracy when determining rate constants by taking into account amore realistic scenario of the light-matter interaction.

q-bio.SC↗
arXiv2009

Global Asymptotic Stability and Hopf Bifurcation for a Blood Cell Production Model

We analyze the asymptotic stability of a nonlinear system of two differential equations with delay describing the dynamics of blood cell production. This process takes place in the bone marrow where stem cells differentiate throughout divisions in blood cells. Taking into account an explicit role of the total population of hematopoietic stem cells on the introduction of cells in cycle, we are lead to study a characteristic equation with delay-dependent coefficients. We determine a necessary and sufficient condition for the global stability of the first steady state of our model, which describes the population's dying out, and we obtain the existence of a Hopf bifurcation for the only nontrivial positive steady state, leading to the existence of periodic solutions. These latter are related to dynamical diseases affecting blood cells known for their cyclic nature.

math.AP↗
arXiv2009

Epigenetic Tracking: Towards a Project for an Artificial Biology

This paper deals with a model of cellular growth called "Epigenetic Tracking", whose key features are: i) distinction bewteen "normal" and "driver" cells; ii) presence in driver cells of an epigenetic memory, that holds the position of the cell in the driver cell lineage tree and represents the source of differentiation during development. In the first part of the paper the model is proved able to generate arbitrary target shapes of unmatched size and variety by means of evo-devo techniques, thus being validated as a model of embryogenesis and cellular differentiation. In the second part of the paper it is shown how the model can produce artificial counterparts for some key aspects of multicellular biology, such as junk DNA, ageing and carcinogenesis. If individually each of these topics has been the subject of intense investigation and modelling effort, to our knowledge no single model or theory seeking to cover all of them under a unified framework has been put forward as yet: this work contains such a theory, which makes Epigenetic Tracking a potential basis for a project of Artificial Biology.

q-bio.CB↗
arXiv2009

General coarse-grained red blood cell models: I. Mechanics

We present a rigorous procedure to derive coarse-grained red blood cell (RBC) models, which lead to accurate mechanical properties of realistic RBCs. Based on a semi-analytic theory linear and non-linear elastic properties of the RBC membrane can be matched with those obtained in optical tweezers stretching experiments. In addition, we develop a nearly stress-free model which avoids a number of pitfalls of existing RBC models, such as non-biconcave equilibrium shape and dependence of RBC mechanical properties on the triangulation quality. The proposed RBC model is suitable for use in many existing numerical methods, such as Lattice Boltzmann, Multiparticle Collision Dynamics, Immersed Boundary, etc.

q-bio.CB↗
arXiv2009

A mathematical model for period-memorizing behavior in Physarum plasmodium

A mathematical model to describe period-memorizing behavior in Physarum plasmodium are reported. In constructing the model, we first examine the basic characteristics required for the class of models, then create a minimal linear model to fulfill these requirements. We also propose two modifications of the minimal model, nonlinearization and noise addition, which improve the reproducibility of experimental evidences. Differences in the mechanisms and in the reproducibility of experiments between our models and the previous models are discussed.

q-bio.CB↗
arXiv2009

Balance between cell survival and death: a minimal quantitative model of tumor necrosis factor alpha cytotoxicity

Tumor Necrosis Factor alpha (TNF) initiates a complex series of biochemical events in the cell upon binding to its type R1 receptor (TNF-R1). Recent experimental work has unravelled the molecular regulation of the recruitment of initial signaling complexes that lead either to cell survival or death. Survival signals are activated by direct binding of TNF to TNF-R1 at the cell membrane whereas apoptotic signals by endocytosed TNF/TNF-R1 complexes. Here we investigate these aspects by developing a quantitative mathematical model of TNF binding, internalization and intracellular signaling. Model outputs compare favorably with experimental data and allow to compute TNF-mediated cytotoxicity as observed in different cell systems. We extensively study the space of parameters to show that the model is structurally stable and robust over a broad range of parameter values. Thus, our model is suitable for implementation in multi-scale simulation programs that are presently under development to study the behavior of large tumor cell populations.

q-bio.MN↗
arXiv2009

An Optimization Algorithm for Finding Parameters for Bistability

Motivation: Many biochemical pathways are known, but the numerous parameters required to correctly explore the dynamics of the pathways are not known. For this reason, algorithms that can make inferences by looking at the topology of a network are desirable. In this work, we are particular interested in the question of whether a given pathway can potentially harbor multiple stable steady states. In other words, the challenge is to find the set of parameters such that the dynamical system defined by a set of ordinary differential equations will contain multiple stable steady states. Being able to find parameters that cause a network to be bistable may also be benefitial for engineering synthetic bistable systems where the engineer needs to know a working set of parameters. Result: We have developed an algorithm that optimizes the parameters of a dynamical system so that the system will contain at least one saddle or unstable point. The algorithm then looks at trajectories around this saddle or unstable point to see whether the different trajectories converge to different stable points. The algorithm returns the parameters that causes the system to exhibit multiple stable points. Since this is an optimization algorithm, it is not quaranteed to find a solution. Repeated runs are often required to find a solution for systems where only a narrow set of parameters exhibit bistability. Availability: The C code for the algorithm is available at http://tinkercell.googlecode.com

q-bio.MN↗
arXiv2009

Single--crossover recombination in discrete time

Modelling the process of recombination leads to a large coupled nonlinear dynamical system. Here, we consider a particular case of recombination in {\em discrete} time, allowing only for {\em single crossovers}. While the analogous dynamics in {\em continuous} time admits a closed solution, this no longer works for discrete time. A more general model (i.e. without the restriction to single crossovers) has been studied before and was solved algorithmically by means of Haldane linearisation. Using the special formalism introduced by Baake and Baake (2003), we obtain further insight into the single-crossover dynamics and the particular difficulties that arise in discrete time. We then transform the equations to a solvable system in a two-step procedure: linearisation followed by diagonalisation. Still, the coefficients of the second step must be determined in a recursive manner, but once this is done for a given system, they allow for an explicit solution valid for all times.

q-bio.PE↗
arXiv2009

Mathematical analysis of stochastic models for tumor-immune systems

In this paper we investigate some stochastic models for tumor-immune systems. To describe these models we used a Wiener process, as the noise has a stabilization effect. Their dynamics are studied in terms of stochastic stability in the equilibrium points, by constructing the Lyapunov exponent, depending on the parameters that describe the model. We have studied and analyzed a Kuznetsov-Taylor like stochastic model and a Bell stochastic model for tumor-immune systems. These stochastic models are studied from stability point of view and they were represented using the Euler second order scheme.

math.DS↗
arXiv2009

Robustness of the Drosophila segment polarity network to transient perturbations

Continuous and Boolean models for the Drosophila segment polarity network have shown that the system is able to maintain the wild-type pattern when subjected to sustained changes in the interaction parameters and initial conditions. Embryo development is likely to occur under fluctuating environmental conditions. We use a well-established Boolean model to explore the ability of the segment polarity network to resist transient changes. We identify paths along which alternate unviable states are reached, and hence critical nodes whose state changes lead the system away from the wild-type state. We find that the system appears to be more sensitive to changes that involve activation of normally inactive nodes. Through a simulation of the heat shock response, we show how a localized perturbation in one parasegment is more deleterious than a global perturbation affecting all parasegments. We identify the sequence of events involved in the recovery of the system from a global transient heat shock condition. Finally we discuss these results in terms of the robustness of the system response.

q-bio.CB↗
arXiv2009

Accuracy of direct gradient sensing by cell-surface receptors

Chemotactic cells of eukaryotic organisms are able to accurately sense shallow chemical concentration gradients using cell-surface receptors. This sensing ability is remarkable as cells must be able to spatially resolve small fractional differences in the numbers of particles randomly arriving at cell-surface receptors by diffusion. An additional challenge and source of uncertainty is that particles, once bound and released, may rebind the same or a different receptor, which adds to noise without providing any new information about the environment. We recently derived the fundamental physical limits of gradient sensing using a simple spherical-cell model, but not including explicit particle-receptor kinetics. Here, we use a method based on the fluctuation-dissipation theorem (FDT) to calculate the accuracy of gradient sensing by realistic receptors. We derive analytical results for two receptors, as well as two coaxial rings of receptors, e.g. one at each cell pole. For realistic receptors, we find that particle rebinding lowers the accuracy of gradient sensing, in line with our previous results.

q-bio.CB↗
arXiv2010

On the asymptotic behavior of the solutions to the replicator equation

Selection systems and the corresponding replicator equations model the evolution of replicators with a high level of abstraction. In this paper we apply novel methods of analysis of selection systems to the replicator equations. To be suitable for the suggested algorithm the interaction matrix of the replicator equation should be transformed; in particular the standard singular value decomposition allows us to rewrite the replicator equation in a convenient form. The original $n$-dimensional problem is reduced to the analysis of asymptotic behavior of the solutions to the so-called escort system, which in some important cases can be of significantly smaller dimension than the original system. The Newton diagram methods are applied to study the asymptotic behavior of the solutions to the escort system, when interaction matrix has rank 1 or 2. A general replicator equation with the interaction matrix of rank 1 is fully analyzed; the conditions are provided when the asymptotic state is a polymorphic equilibrium. As an example of the system with the interaction matrix of rank 2 we consider the problem from [Adams, M.R. and Sornborger, A.T., J Math Biol, 54:357-384, 2007], for which we show, for arbitrary dimension of the system and under some suitable conditions, that generically one globally stable equilibrium exits on the 1-skeleton of the simplex.

q-bio.PE↗
arXiv2010

Contractile prestress controls stiffening and fluidization of living cells in response to large external forces

We report the simultaneous characterization of time- and force-dependent mechanical properties of adherent cells in the physiologically relevant regime of large forces. We used magnetic tweezers to apply forces to magnetic beads bound to the cytoskeleton, and recorded the resulting deformation (creep response). The creep response followed a weak power law at all force levels. Stress stiffening and fluidization occurred simultaneously and were quantified by the force-dependence of the creep compliance and the power law exponent. The amount of stiffening and fluidization in response to force was controlled solely by the contractile prestress of the cell and followed a simple relationship. This behavior may be of fundamental importance in biological processes that involve a mechanical interaction between cells and their environment.

physics.bio-ph↗
arXiv2009

Phyllotaxis, a model

A model of the regular arrangement of leaves on a plant stem (phyllotactic patterns) is proposed, based on a new plant pattern algorithm. Tripartite patterning is proposed to occur by the interaction of two signaling pathways. Each pathway produces stimulated extracellular emission of like ligand upon activation of its respective receptor, as well as inhibiting such emission from the other pathway. Patterns arise spontaneously from zero density of activated receptor. All known phyllotactic patterns are reproduced, Fibonacci, distichous, decussate, and whorls, as well as the rare monostichy, with only one leaf directly above the previous.

q-bio.TO↗
arXiv2010

Coupling of cytoplasm and adhesion dynamics determines cell polarization and locomotion

Observations of single epidermal cells on flat adhesive substrates have revealed two distinct morphological and functional states, namely a non-migrating symmetric unpolarized state and a migrating asymmetric polarized state. These states are characterized by different spatial distributions and dynamics of important biochemical cell components: F-actin and myosin-II form the contractile part of the cytoskeleton, and integrin receptors in the plasma membrane connect F-actin filaments to the substratum. In this way, focal adhesion complexes are assembled, which determine cytoskeletal force transduction and subsequent cell locomotion. So far, physical models have reduced this phenomenon either to gradients in regulatory control molecules or to different mechanics of the actin filament system in different regions of the cell. Here we offer an alternative and self-organizational model incorporating polymerization, pushing and sliding of filaments, as well as formation of adhesion sites and their force dependent kinetics. All these phenomena can be combined into a non-linearly coupled system of hyperbolic, parabolic and elliptic differential equations. Aim of this article is to show how relatively simple relations for the small-scale mechanics and kinetics of participating molecules may reproduce the emergent behavior of polarization and migration on the large-scale cell level.

physics.bio-ph↗
arXiv2009

The rate of decline of CD4 T-cells in people infected with HIV

In people infected with HIV the RNA viral load is a good predictor of the rate of loss of CD4 cells at a population level but there is still great variability in the rate of decline of CD4 cells among individuals. Here we show that the pre-infection distribution of CD4 cell counts and the distribution of survival times together account for 87% of the variability in the observed rate of decline of CD4 cells among individuals. The challenge is to understand the variation in CD4 levels, among populations and individuals, and to establish the determinants of survival of which viral load may be the most important.

q-bio.CB↗
arXiv2009

Protein micro patterned lattices to probe a fundamental lengthscale involved in cell adhesion

Cell adhesion, a fundamental process of cell biology is involved in the embryo development and in numerous pathologies especially those related to cancers. We constrained cells to adhere on extracellular matrix proteins patterned in a micro lattices. The actin cytoskeleton is particularly sensitive to this constraint and reproducibly self organizes in simple geometrical patterns. Such highly organized cells are functional and proliferate. We performed statistical analysis of spread cells morphologies and discuss the existence of a fundamental lengthscale associated with active processes required for spreading.

physics.bio-ph↗