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At least 1,351 records · Page 75Linked to original sources

arXiv2004

Turbulence near cyclic fold bifurcations in birhythmic media

We show that at the onset of a cyclic fold bifurcation, a birhythmic medium composed of glycolytic oscillators displays turbulent dynamics. By computing the largest Lyapunov exponent, the spatial correlation function, and the average transient lifetime, we classify it as a weak turbulence with transient nature. Virtual heterogeneities generating unstable fast oscillations are the mechanism of the transient turbulence. In the presence of wavenumber instability, unstable oscillations can be reinjected leading to stationary turbulence. We also find similar turbulence in a cell cycle model. These findings suggest that weak turbulence may be universal in biochemical birhythmic media exhibiting cyclic fold bifurcations.

q-bio.SC↗

arXiv2003

Self-organized Pattern Formation in Motor-Microtubule Mixtures

We propose and study a hydrodynamic model for pattern formation in mixtures of molecular motors and microtubules. The steady state patterns we obtain in different regimes of parameter space include arrangements of vortices and asters separately as well as aster-vortex mixtures and fully disordered states. Such stable steady states are observed in experiments in vitro. The sequence of patterns obtained in the experiments can be associated with smooth trajectories in a non-equilibrium phase diagram for our model.

cond-mat.stat-mech↗

arXiv2004

Novel steady state of a microtubule assembly in a confined geometry

We study the steady state of an assembly of microtubules in a confined volume, analogous to the situation inside a cell where the cell boundary forms a natural barrier to growth. We show that the dynamical equations for growing and shrinking microtubules predict the existence of two steady states, with either exponentially decaying or exponentially increasing distribution of microtubule lengths. We identify the regimes in parameter space corresponding to these steady states. In the latter case, the apparent catastrophe frequency near the boundary was found to be significantly larger than that in the interior. Both the exponential distribution of lengths and the increase in the catastrophe frequency near the cell margin is in excellent agreement with recent experimental observations.

q-bio.SC↗

arXiv2004

Self-assembly of polyhedral shells: A molecular dynamics study

The use of reduced models for investigating the self-assembly dynamics underlying protein shell formation in spherical viruses is described. The spontaneous self-assembly of these polyhedral, supramolecular structures, in which icosahedral symmetry is a conspicuous feature, is a phenomenon whose dynamics remain unexplored; studying the growth process by means of computer simulation provides access to the mechanisms underlying assembly. In order to capture the more universal aspects of self-assembly, namely the manner in which component shapes influence structure and assembly pathway, in this exploratory study low-resolution approximations are used to represent the basic protein building blocks. Alternative approaches involving both irreversible and reversible assembly are discussed, models based on both schemes are introduced, and examples of the resulting behavior described.

cond-mat.soft↗

arXiv2004

How does the chromatin fiber deal with topological constraints?

In the nuclei of eukaryotic cells, DNA is packaged through several levels of compaction in an orderly retrievable way that enables the correct regulation of gene expression. The functional dynamics of this assembly involves the unwinding of the so-called 30 nm chromatin fiber and accordingly imposes strong topological constraints. We present a general method for computing both the twist and the writhe of any winding pattern. An explicit derivation is implemented for the chromatin fiber which provides the linking number of DNA in eukaryotic chromosomes. We show that there exists one and only one unwinding path which satisfies both topological and mechanical constraints that DNA has to deal with during condensation/decondensation processes.

q-bio.SC↗

arXiv2004

Electrostatics and the Assembly of an RNA Virus

Electrostatic interactions play a central role in the assembly of single-stranded RNA viruses. Under physiological conditions of salinity and acidity, virus capsid assembly requires the presence of genomic material that is oppositely charged to the core proteins. In this paper we apply basic polymer physics and statistical mechanics methods to the self-assembly of a synthetic virus encapsidating generic polyelectrolyte molecules. We find that (i) the mean concentration of the encapsidated polyelectrolyte material depends on the surface charge density, the radius of the capsid, and the linear charge density of the polymer but neither on the salt concentration or the Kuhn length, (ii) the total charge of the capsid interior is equal but opposite to that of the empty capsid, a form of charge reversal. Unlike natural viruses, synthetic viruses are predicted not to be under an osmotic swelling pressure. The design condition that self-assembly only produces filled capsids is shown to coincide with the condition that the capsid surface charge exceeds the desorption threshold of polymer surface adsorption. We compare our results with studies on the self-assembly of both synthetic and natural viruses.

q-bio.BM↗

arXiv2007

Dynamic instability of microtubules: effect of catastrophe-suppressing drugs

Microtubules are stiff filamentary proteins that constitute an important component of the cytoskeleton of cells. These are known to exhibit a dynamic instability. A steadily growing microtubule can suddenly start depolymerizing very rapidly; this phenomenon is known as ``catastrophe''. However, often a shrinking microtubule is ``rescued'' and starts polymerizing again. Here we develope a model for the polymerization-depolymerization dynamics of microtubules in the presence of {\it catastrophe-suppressing drugs}. Solving the dynamical equations in the steady-state, we derive exact analytical expressions for the length distributions of the microtubules tipped with drug-bound tubulin subunits as well as those of the microtubules, in the growing and shrinking phases, tipped with drug-free pure tubulin subunits. We also examine the stability of the steady-state solutions.

cond-mat.stat-mech↗

arXiv2005

First passage times and asymmetry of DNA translocation

Motivated by experiments in which single-stranded DNA with a short hairpin loop at one end undergoes unforced diffusion through a narrow pore, we study the first passage times for a particle, executing one-dimensional brownian motion in an asymmetric sawtooth potential, to exit one of the boundaries. We consider the first passage times for the case of classical diffusion, characterized by a mean-square displacement of the form $< (Δx)^2> \sim t$, and for the case of anomalous diffusion or subdiffusion, characterized by a mean-square displacement of the form $< (Δx)^2> \sim t^γ$ with $0<γ<1$. In the context of classical diffusion, we obtain an expression for the mean first passage time and show that this quantity changes when the direction of the sawtooth is reversed or, equivalently, when the reflecting and absorbing boundaries are exchanged. We discuss at which numbers of `teeth' $N$ (or number of DNA nucleotides) and at which heights of the sawtooth potential this difference becomes significant. For large $N$, it is well known that the mean first passage time scales as $N^2$. In the context of subdiffusion, the mean first passage time does not exist. Therefore we obtain instead the distribution of first passage times in the limit of long times. We show that the prefactor in the power relation for this distribution is simply the expression for the mean first passage time in classical diffusion. We also describe a hypothetical experiment to calculate the average of the first passage times for a fraction of passage events that each end within some time $t^*$. We show that this average first passage time scales as $N^{2/γ}$ in subdiffusion.

q-bio.BM↗

arXiv2006

Detection of confinement and jumps in single molecule membrane trajectories

We propose a novel variant of the algorithm by Simson et al. [R. Simson, E.D. Sheets, K. Jacobson, Biophys. J. 69, 989 (1995)]. Their algorithm was developed to detect transient confinement zones in experimental single particle tracking trajectories of diffusing membrane proteins or lipids. We show that our algorithm is able to detect confinement in a wider class of confining potential shapes than Simson et al.'s one. Furthermore it enables to detect not only temporary confinement but also jumps between confinement zones. Jumps are predicted by membrane skeleton fence and picket models. In the case of experimental trajectories of $μ$-opioid receptors, which belong to the family of G-protein-coupled receptors involved in a signal transduction pathway, this algorithm confirms that confinement cannot be explained solely by rigid fences.

q-bio.QM↗

arXiv2006

Min-protein oscillations in Escherichia coli with spontaneous formation of two-stranded filaments in a three-dimensional stochastic reaction-diffusion model

We introduce a three-dimensional stochastic reaction-diffusion model to describe MinD/MinE dynamical structures in Escherichia coli. This model spontaneously generates pole-to-pole oscillations of the membrane-associated MinD proteins, MinE ring, as well as filaments of the membrane-associated MinD proteins. Experimental data suggest MinD filaments are two-stranded. In order to model them we assume that each membrane-associated MinD protein can form up to three bonds with adjacent membrane associated MinD molecules and that MinE induced hydrolysis strongly depends on the number of bonds MinD has established.

q-bio.SC↗

arXiv2006

Force generation in small ensembles of Brownian motors

The motility of certain gram-negative bacteria is mediated by retraction of type IV pili surface filaments, which are essential for infectivity. The retraction is powered by a strong molecular motor protein, PilT, producing very high forces that can exceed 150 pN. The molecular details of the motor mechanism are still largely unknown, while other features have been identified, such as the ring-shaped protein structure of the PilT motor. The surprisingly high forces generated by the PilT system motivate a model investigation of the generation of large forces in molecular motors. We propose a simple model, involving a small ensemble of motor subunits interacting through the deformations on a circular backbone with finite stiffness. The model describes the motor subunits in terms of diffusing particles in an asymmetric, time-dependent binding potential (flashing ratchet potential), roughly corresponding to the ATP hydrolysis cycle. We compute force-velocity relations in a subset of the parameter space and explore how the maximum force (stall force) is determined by stiffness, binding strength, ensemble size, and degree of asymmetry. We identify two qualitatively different regimes of operation depending on the relation between ensemble size and asymmetry. In the transition between these two regimes, the stall force depends nonlinearly on the number of motor subunits. Compared to its constituents without interactions, we find higher efficiency and qualitatively different force-velocity relations. The model captures several of the qualitative features obtained in experiments on pilus retraction forces, such as roughly constant velocity at low applied forces and insensitivity in the stall force to changes in the ATP concentration.

q-bio.SC↗

arXiv2006

Analysis of a microscopic stochastic model of microtubule dynamic instability

A novel theoretical model of dynamic instability of a system of linear (1D) microtubules (MTs) in a bounded domain is introduced for studying the role of a cell edge in vivo and analyzing the effect of competition for a limited amount of tubulin. The model differs from earlier models in that the evolution of MTs is based on the rates of single unit (e.g., a heterodimer per protofilament) transformations, in contrast to postulating effective rates/frequencies of larger-scale changes, extracted, e.g., from the length history plots of MTs. Spontaneous GTP hydrolysis with finite rate after polymerization is assumed, and theoretical estimates of an effective catastrophe frequency as well as other parameters characterizing MT length distributions and cap size are derived. We implement a simple cap model which does not include vectorial hydrolysis. We demonstrate that our theoretical predictions, such as steady state concentration of free tubulin, and parameters of MT length distributions, are in agreement with the numerical simulations. The present model establishes a quantitative link between microscopic parameters governing the dynamics of MTs and macroscopic characteristics of MTs in a closed system. Lastly, we use a computational Monte Carlo model to provide an explanation for non-exponential MT length distributions observed in experiments. In particular, we show that appearance of such non-exponential distributions in the experiments can occur because the true steady state has not been reached, and/or due to the presence of a cell edge.

q-bio.SC↗

arXiv2006

Finite-size domains in membranes with active two-state inclusions

The distribution of inclusion-rich domains in membranes with active two-state inclusions is studied by simulations. Our study shows that typical size of inclusion-rich domains ($L$) can be controlled by inclusion activities in several ways. When there is effective attraction between state-1 inclusions, we find: (i) Small domains with only several inclusions are observed for inclusions with time scales ($\sim 10^{-3} {\rm s}$) and interaction energy [$\sim \mathcal{O}({\rm k_BT})$] comparable to motor proteins. (ii) $L$ scales as 1/3 power of the lifetime of state-1 for a wide range of parameters. (iii) $L$ shows a switch-like dependence on state-2 lifetime $k_{12}^{-1}$. That is, $L$ depends weakly on $k_{12}$ when $k_{12} < k_{12}^*$ but increases rapidly with $k_{12}$ when $k_{12} > k_{12}^*$, the crossover $k_{12}^*$ occurs when the diffusion length of a typical state-2 inclusion within its lifetime is comparable to $L$. (iv) Inclusion-curvature coupling provides another length scale that competes with the effects of transition rates.

q-bio.SC↗

arXiv2008

Effective charge and free energy of DNA inside an ion channel

Translocation of a single stranded DNA (ssDNA) through an alpha-hemolysin channel in a lipid membrane driven by applied transmembrane voltage V was extensively studied recently. While the bare charge of the ssDNA piece inside the channel is approximately 12 (in units of electron charge) measurements of different effective charges resulted in values between one and two. We explain these challenging observations by a large self-energy of a charge in the narrow water filled gap between ssDNA and channel walls, related to large difference between dielectric constants of water and lipid, and calculate effective charges of ssDNA. We start from the most fundamental stall charge $q_s$, which determines the force $F_s= q_s V/L$ stalling DNA against the voltage V (L is the length of the channel). We show that the stall charge $q_s$ is proportional to the ion current blocked by DNA, which is small due to the self-energy barrier. Large voltage V reduces the capture barrier which DNA molecule should overcome in order to enter the channel by $|q_c|V$, where $q_c$ is the effective capture charge. We expressed it through the stall charge $q_s$. We also relate the stall charge $q_s$ to two other effective charges measured for ssDNA with a hairpin in the back end: the charge $q_u$ responsible for reduction of the barrier for unzipping of the hairpin and the charge $q_e$ responsible for DNA escape in the direction of hairpin against the voltage. At small V we explain reduction of the capture barrier with the salt concentration.

cond-mat.soft↗

arXiv2007

A model of hyphal tip growth involving microtubule-based transport

We propose a simple model for mass transport within a fungal hypha and its subsequent growth. Inspired by the role of microtubule-transported vesicles, we embody the internal dynamics of mass inside a hypha with mutually excluding particles progressing stochastically along a growing one-dimensional lattice. The connection between long range transport of materials for growth, and the resulting extension of the hyphal tip has not previously been addressed in the modelling literature. We derive and analyse mean-field equations for the model and present a phase diagram of its steady state behaviour, which we compare to simulations. We discuss our results in the context of the filamentous fungus, Neurospora crassa.

q-bio.SC↗

arXiv2007

Intra-cellular transport by single-headed kinesin KIF1A: effects of single-motor mechano-chemistry and steric interactions

In eukaryotic cells, many motor proteins can move simultaneously on a single microtubule track. This leads to interesting collective phenomena like jamming. Recently we reported ({\it Phys. Rev. Lett. {\bf 95}, 118101 (2005)}) a lattice-gas model which describes traffic of unconventional (single-headed) kinesins KIF1A. Here we generalize this model, introducing a novel interaction parameter $c$, to account for an interesting mechano-chemical process which has not been considered in any earlier model. We have been able to extract all the parameters of the model, except $c$, from experimentally measured quantities. In contrast to earlier models of intra-cellular molecular motor traffic, our model assigns distinct ``chemical'' (or, conformational) states to each kinesin to account for the hydrolysis of ATP, the chemical fuel of the motor. Our model makes experimentally testable theoretical predictions. We determine the phase diagram of the model in planes spanned by experimentally controllable parameters, namely, the concentrations of kinesins and ATP. Furthermore, the phase-separated regime is studied in some detail using analytical methods and simulations to determine e.g. the position of shocks. Comparison of our theoretical predictions with experimental results is expected to elucidate the nature of the mechano-chemical process captured by the parameter $c$.

physics.bio-ph↗

arXiv2007

Model for Osteosarcoma-9 as a Potent Factor in Cell Survivor and Resistance to Apoptosis

In this paper we use a simple toy model to explore the function of the gene Osteosarcoma-9. We are in particular interested in understanding the role of this gene as a potent anti-apoptotic factor. The theoretical description is constrained by experimental data from induction of apoptosis in cells where OS-9 is overexpressed. The data available suggest that OS-9 promotes cell viability and confers resistance to apoptosis, potentially implicating OS-9 in the survival of cancer cells. Three different apoptosis inducing mechanisms were tested and are here modelled. More complex and realistic models are also discussed.

q-bio.SC↗

arXiv2007

Steady-state MreB helices inside bacteria: dynamics without motors

Within individual bacteria, we combine force-dependent polymerization dynamics of individual MreB protofilaments with an elastic model of protofilament bundles buckled into helical configurations. We use variational techniques and stochastic simulations to relate the pitch of the MreB helix, the total abundance of MreB, and the number of protofilaments. By comparing our simulations with mean-field calculations, we find that stochastic fluctuations are significant. We examine the quasi-static evolution of the helical pitch with cell growth, as well as timescales of helix turnover and denovo establishment. We find that while the body of a polarized MreB helix treadmills towards its slow-growing end, the fast-growing tips of laterally associated protofilaments move towards the opposite fast-growing end of the MreB helix. This offers a possible mechanism for targeted polar localization without cytoplasmic motor proteins.

q-bio.SC↗