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At least 757 records · Page 42Linked to original sources

arXiv2004

DNA looping and physical constraints on transcription regulation

DNA looping participates in transcriptional regulation, for instance, by allowing distal binding sites to act synergistically. Here we study this process and compare different regulatory mechanisms based on repression with and without looping. Within a simple mathematical model for the lac operon, we show that regulation based on DNA looping, in addition to increasing the repression level, can reduce the fluctuations of transcription and, at the same time, decrease the sensitivity to changes in the number of regulatory proteins. Looping is thus able to circumvent some of the constraints inherent to mechanisms based solely on binding to a single operator site and provides a mechanism to regulate not only the average properties of transcription but also its fluctuations.

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arXiv2004

A one-dimensional Lattice Boltzmann method for modeling the dynamic pole-to-pole oscillations of Min proteins for determining the position of the midcell division plane

Determining the middle of the bacteria cell and the proper placement of the septum is essential to the division of the bacterial cell. In E. coli, this process depends on the proteins MinC, MinD, and MinE. Here, the Lattice Boltzmann method (LBM) is used to study the dynamics of the oscillations of the min proteins from pole to pole. This determines the midcell division plane at the cellular level. The LBM is applied to the set of the deterministic reaction diffusion equations proposed by Howard et. al. [1] to describe the dynamics of the Min proteins. The LBM results are in good agreement with those of Howard et al, and agree qualitatively with the experimental results. Our good results indicate that the LBM can be an alternative computational tool for simulating problems dealing with complex biological system which are described by the reaction-diffusion equations.

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arXiv2004

The dynamics of the min proteins of Escherichia coli under the constant external fields

In E. coli the determination of the middle of the cell and the proper placement of the septum is essential to the division of the cell. This step depends on the proteins MinC, MinD, and MinE. Exposure to a constant external field e.g., an electric field or magnetic field may cause the bacteria cell division mechanism to change resulting in an abnormal cytokinesis. To have insight into the effects of an external field on this process, we model the process using a set of the deterministic reaction diffusion equations, which incorporate the influence of an external field, min protein reactions, and diffusion of all species. Using the numerical method, we have found some changes in the dynamics of the oscillations of the min proteins from pole to pole when compared that of without the external field. The results show some interesting effects, which are qualitatively in good agreement with some experimental results.

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arXiv2005

Single Stranded DNA Translocation Through a Fluctuating Nanopore

We investigate the translocation of a single stranded DNA (ssDNA) through a pore, which fluctuates between two conformations, by using coupled master equations (ME). The probability density function (PDF) of the first passage times (FPT) of the translocation process is calculated, displaying a triple, double or mono-peaked behavior, depending on the system parameters. An analytical expression for the mean first passage time (MFPT) of the translocation process is derived, and provides an extensive characterization of the translocation process.

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arXiv2005

Uncorrelated two-state single molecule trajectories from reducible kinetic schemes

Trajectories of on-off events are the output of many single molecule experiments. Usually, one describes the underlying mechanism that generates the trajectory using a kinetic scheme, and by analyzing the trajectory aims at deducing this scheme. In a previous work [O. Flomenbom, J. Klafter, and A. Szabo, submitted (2004)], we showed that when successive events along a trajectory are uncorrelated, all the information in the trajectory is contained in two basic functions, which are the waiting time probability functions (PDFs) of the on state and of the off state. The kinetic schemes that lead to such uncorrelated trajectories were termed reducible. Here we discuss the reasons that lead to reducible schemes. In particular, the topology of reducible schemes is characterized and proven.

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arXiv2005

Release of Brain Mitochondrial Hexokinase by Acidic Proteins and Macromolecular Polyanions

Preparations of arachidonic acid binding and non-binding proteins from bovine brain, four acidic proteins (alpha-casein, phosvitin, beta-lactoglobulin A and B), the peptide polyglutamate, and two polyanions (heparin, dextran sulfate) enhanced both basal and glucose 6-phosphate induced solubilization of rat brain mitochondrial hexokinase (ATP:D-hexose 6-phosphotransferase, EC 2.7.1.1). In contrast, three other acidic proteins, had little (alpha-lactalbumin) or no effect (bovine serum albumin, ovalbumin) and five basic proteins inhibited release of the enzyme. Solubilizing activity therefore appears to require a net negative charge and one or more of the following structural features: extended conformation, random coil, and unordered or beta-structure, in the latter case, as the beta-barrel in the fatty acid binding proteins and beta-lactoglobulins. It is of interest that a difference of a single negative charge between beta-lactoglobulin A and B, resulted in a statistically significant difference in the stimulation of hexokinase release. Possible physiological and pathological roles of this hexokinase solubilizing effect are discussed briefly.

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arXiv2005

Kinetics of target site localization of a protein on DNA: a stochastic approach

It is widely recognized that the cleaving rate of a restriction enzyme on target DNA sequences is several orders of magnitude faster than the maximal one calculated from the diffusion--limited theory. It was therefore commonly assumed that the target site interaction of a restriction enzyme with DNA has to occur via two steps: one--dimensional diffusion along a DNA segment, and long--range jumps coming from association/dissociation events. We propose here a stochastic model for this reaction which comprises a series of 1D diffusions of a restriction enzyme on non-specific DNA sequences interrupted by 3D excursions in the solution until the target sequence is reached. This model provides an optimal finding strategy which explains the fast association rate. Modeling the excursions by uncorrelated random jumps, we recover the expression of the mean time required for target site association to occur given by Berg & al. \cite{berg81}, and we explicitly give several physical quantities describing the stochastic pathway of the enzyme. For competitive target sites we calculate two quantities: processivity and preference. By comparing these theoretical expressions to recent experimental data obtained for \textit{Eco}RV--DNA interaction, we quantify: i) the mean residence time per binding event of \textit{Eco}RV on DNA for a representative 1D diffusion coefficient, ii) the average lengths of DNA scanned during the 1D diffusion (during one binding event and during the overall process), iii) the mean time and the mean number of visits needed to go from one target site to the other. Further, we evaluate the dynamics of DNA cleavage with regard to the probability for the restriction enzyme to perform another 1D diffusion on the same DNA substrate following a 3D excursion.

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arXiv2005

Non-Maxwellian velocity distribution and anomalous diffusion of {\it in vitro} kidney cells

This manuscript uses a statistical mechanical approach to study the effect of the adhesion, through MOCA protein, on cell locomotion. The MOCA protein regulates cell-cell adhesion, and we explore its potential role in the cell movement. We present a series of statistical descriptions of the motion in order to characterize the cell movement, and found that MOCA affects the statistical scenario of cell locomotion. In particular, we observe that MOCA enhances the tendency of joint motion, inhibits super-diffusion, and decreases overall cell motion. These facts are compatible with the hypothesis that the cells move faster in a less cohesive environment. Furthermore, we observe that velocity distribution tails are longer than those predicted by Maxwell-Boltzmann in all cases studied here, indicating that cell movement is more complex than that of a liquid.

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arXiv2005

Metabolic Network Modelling: Including Stochastic Effects

We propose to model the dynamics of metabolic networks from a systems biology point of view by four dynamical structure elements: potential function, transverse matrix, degradation matrix, and stochastic force. These four elements are balanced to determine the network dynamics, which gives arise to a special stochastic differential equation supplemented by a relationship between the stochastic force and the degradation matrix. Important network behaviors can be obtained from the potential function without explicitly solving for the time-dependent solution. The existence of such a potential function suggests a global optimization principle, and the existence stochastic force corresponds natural to the hierarchical structure in metabolic networks. We provide theoretical evidences to justify our proposal by discussing its connections to others large-scale biochemical systems approaches, such as the network thermodynamics theory, biochemical systems theory, metabolic control analysis, and flux balance analysis. Experimental data displaying stochasticity are also pointed out.

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arXiv2005

On Myosin II dynamics in the presence of external loads

We address the controversial hot question concerning the validity of the loose coupling versus the lever-arm theories in the actomyosin dynamics by re-interpreting and extending the phenomenological washboard potential model proposed by some of us in a previous paper. In this new model a Brownian motion harnessing thermal energy is assumed to co-exist with the deterministic swing of the lever-arm, to yield an excellent fit of the set of data obtained by some of us on the sliding of Myosin II heads on immobilized actin filaments under various load conditions. Our theoretical arguments are complemented by accurate numerical simulations, and the robustness of the model is tested via different choices of parameters and potential profiles.

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arXiv2005

Modeling the dynamics of natural rotifer populations: phase-parametric analysis

A model of the dynamics of natural rotifer populations is described as a discrete nonlinear map depending on three parameters, which reflect characteristics of the population and environment. Model dynamics and their change by variation of these parameters were investigated by methods of bifurcation theory. A phase-parametric portrait of the model was constructed and domains of population persistence (stable equilibrium, periodic and a-periodic oscillations of population size) as well as population extinction were identified and investigated. The criteria for population persistence and approaches to determining critical parameter values are described. The results identify parameter values that lead to population extinction under various environmental conditions. They further illustrate that the likelihood of extinction can be substantially increased by small changes in environmental quality, which shifts populations into new dynamical regimes.

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arXiv2005

Budded membrane microdomains as regulators for cellular tension

We propose a mechanism for mechanical regulation at the membrane of living cells, based on the exchange of membrane area between the cell membrane and a membrane reservoir. The reservoir is composed of invaginated membrane microdomains which are liable to flatten upon increase of membrane strain, effectively controlling membrane tension. We show that the domain shape transition is first order, allowing for coexistence between flat and invaginated domains. During coexistence, the membrane tension is controlled by the domains elasticity and by the kinetics of the shape transition. We show that the tension of the plasma membrane of living cells is inherently transient and dynamical, and that valuable insights into the organization of the cell membrane can be obtained by studying the variation of the cell membrane tension upon mechanical perturbation.

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arXiv2005

Differential gene expression in Bacillus subtilis

Sporulation in Bacillus subtilis serves as a paradigm for the development of two different cell types (mother cell and prespore) from a single cell. The mechanism by which the two different developmental programs are initiated has been much studied but is not well understood. With the help of existing and new experimental results, a mathematical model has been developed that reproduces all published in vitro experiments and makes new predictions about the properties of the system in vivo.

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arXiv2005

Modelling and simulation of polycomb-dependent chromosomal interactions in drosophila

The conditions of the chromosomes inside the nucleus in the Rabl configuration have been modelled as self-avoiding polymer chains under restraining conditions. To ensure that the chromosomes remain stretched out and lined up, we fixed their end points to two opposing walls. The numbers of segments $N$, the distances $d_1$ and $d_2$ between the fixpoints, and the wall-to-wall distance $z$ (as measured in segment lengths) determine an approximate value for the Kuhn segment length $k_l$. We have simulated the movement of the chromosomes using molecular dynamics to obtain the expected distance distribution between the genetic loci in the absence of further attractive or repulsive forces. A comparison to biological experiments on \textit{Drosophila Melanogaster} yields information on the parameters for our model. With the correct parameters it is possible to draw conclusions on the strength and range of the attraction that leads to pairing.

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arXiv2006

Protocell Self-Reproduction in a Spatially Extended Metabolism-Vesicle System

Cellular life requires the presence of a set of biochemical mechanisms in order to maintain a predictable process of growth and division. Several attempts have been made towards the building of minimal protocells from a top-down approach, i.e. by using available biomolecules This type of synthetic approach has so far been unsuccesful, and the lack of appropriate models of the synthetic protocell cycle might be needed to guide future experiments. In this paper we present a simple biochemically and physically feasible model of cell replication involving a discrete semi-permeable vesicle with an internal minimal metabolism involving two reactive centers. It is shown that such a system can effectively undergo a whole cell replication cycle. The model can be used as a basic framework to model whole protocell dynamics including more complex sets of reactions. The possible implementation of our design in future synthetic protocells is outlined.

q-bio.CB↗

arXiv2006

Efficiency, Robustness and Stochasticity of Gene Regulatory Networks in Systems Biology: lambda Switch as a Working Example

Phage lambda is one of the most studied biological models in modern molecular biology. Over the past 50 years quantitative experimental knowledge on this biological model has been accumulated at all levels: physics, chemistry, genomics, proteomics, functions, and more. All its components have been known to a great detail. The theoretical task has been to integrate its components to make the organism working quantitatively in a harmonic manner. This would test our biological understanding and would lay a solid fundamental for further explorations and applications, an obvious goal of systems biology. One of the outstanding challenges in doing so has been the so-called stability puzzle of lambda switch: the biologically observed robustness and its difficult mathematical reconstruction based on known experimental values. In this chapter we review the recent theoretical and experimental efforts on tackling this problem. An emphasis is put on the minimum quantitative modeling where a successful numerical agreement between experiments and modeling has been achieved. A novel method tentatively named stochastic dynamical structure analysis emerged from such study is also discussed within a broad modeling perspective.

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arXiv2005

Cooperativity, sensitivity and noise in biochemical signaling

Cooperative interactions among the binding of multiple signaling molecules is a common mechanism for enhancing the sensitivity of biological signaling systems. It is widely assumed that this increase in sensitivity of the mean response implies the ability to detect smaller signals. We show that, quite generally, there is a component of the noise in such systems that can be traced to the random arrival of the signaling molecules at their receptor sites, and this diffusive noise is not reduced by cooperativity. Cooperativity makes it easier for real systems to reach this physical limit, but cannot reduce the limit itself.

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arXiv2006

Intracellular delay limits cyclic changes in gene expression

Based on previously published experimental observations and mathematical models for Hes1, p53 and NF-kB gene expression, we improve these models through a distributed delay formulation of the time lag between transcription factor binding and mRNA production. This description of natural variability for delays introduces a transition from a stable steady state to limit cycle oscillations and then a second transition back to a stable steady state which has not been observed in previously published models. On the basis of our results and following recent discussions about the role of delay-induced oscillations in gene transcription we establish the hypothesis that the period of the delay-induced cyclic changes should be characterized by an upper bound so that it cannot be greater then the period of fundamental biological cycles. We demonstrate our approach for two models. The first model describes Hes1 autorepression with equations for Hes1 mRNA production and Hes1 protein translation. The second model describes Hes1 repression by the protein complex Gro/TLE1/Hes1, where Gro/TLE1 is activated by Hes1 phosphorylation.

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