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arXiv2022

Microtubule organization and cell geometry

We present a systematic study of the influence of cell geometry on the orientational distribution of microtubules (MTs) nucleated from a single microtubule organizing center (MTOC). For simplicity we consider an elliptical cell geometry, a setting appropriate to a generic non-spherical animal cell. Within this context we introduce four models of increasing complexity, in each case introducing additional mechanisms that govern the interaction of the MTs with the cell boundary. In order, we consider the cases: MTs that can bind to the boundary with a fixed mean residence time (M0), force-producing MTs that can slide on the boundary towards the cell poles (MS), MTs that interact with a generic polarity factor that is transported and deposited at the boundary, and which in turn stabilizes the MTs at the boundary (MP), and a final model in which both sliding and stabilization by polarity factors is taken into account (MSP). In the baseline model (M0), the exponential length distribution of MTs causes most of the interactions at the cell boundary to occur along the shorter transverse direction in the cell, leading to transverse biaxial order. MT sliding (MS) is able to reorient the main axis of this biaxial order along the longitudinal axis. The polarization mechanism introduced in MP and MSP overrules the geometric bias towards bipolar order observed in M0 and MS, and allows the establishment of unipolar order either along the short- (MP) or the long cell axis (MSP). The behavior of the latter two models can be qualitatively reproduced by a very simple toy model with discrete MT orientations.

q-bio.BM↗

arXiv2023

Calcium oscillation on homogeneous and heterogeneous networks of ryanodine receptor

Calcium oscillation is an important calcium homeostasis, imbalance of which is the key mechanism of initiation and progression of many major diseases. The formation and maintenance of calcium homeostasis are closely related to the spatial distribution of calcium channels. In the current paper, a theoretical framework is established by abstracting the spatial distribution of the calcium channels as a nonlinear biological complex network with calcium channels as nodes and Ca$^{2+}$ as edges. A dynamical model for a RyR is adopted to investigate the effect of spatial distribution on calcium oscillation. The mean-field model can be well reproduced from the complete graph and dense Erdös-Rényi network. The synchronization of RyRs is found important to generate a global calcium oscillation. The clique graph with a cluster structure can not produce a global oscillation due to the failure of synchronization between clusters. A more realistic geometric network is constructed in a two-dimensional plane based on the experimental information about the RyR arrangement of clusters and the frequency distribution of cluster sizes. Different from the clique graph, the global oscillation can be generated with reasonable parameters on the geometric network. The simulation also suggests that existence of small clusters and rogue RyR's plays an important role in the maintenance of global calcium oscillation through keeping synchronization between large clusters. Such results support the heterogeneous distribution of RyR's with different-size clusters, which is helpful to understand recent observations with super resolution nanoscale imaging techniques. The current theoretical framework can also be extent to investigate other phenomena in calcium signal transduction.

q-bio.SC↗

arXiv2022

Population heterogeneity in the fractional master equation, ensemble self-reinforcement and strong memory effects

We formulate a fractional master equation in continuous time with random transition probabilities across the population of random walkers such that the effective underlying random walk exhibits ensemble self-reinforcement. The population heterogeneity generates a random walk with conditional transition probabilities that increase with the number of steps taken previously (self-reinforcement). Through this, we establish the connection between random walks with a heterogeneous ensemble and those with strong memory where the transition probability depends on the entire history of steps. We find the ensemble averaged solution of the fractional master equation through subordination involving the fractional Poisson process counting the number of steps at a given time and the underlying discrete random walk with self-reinforcement. We also find the exact solution for the variance which exhibits superdiffusion even as the fractional exponent tends to 1.

cond-mat.stat-mech↗

arXiv2023

Noise-induced transitions in gene circuits: a perturbative approach for slow noise

We consider a generic class of gene circuits affected by nonlinear extrinsic noise. To address this nonlinearity we introduce a general perturbative methodology based on assuming timescale separation between noise and genes dynamics, with fluctuations exhibiting a large but finite correlation time. We apply this methodology to the case of the toggle switch, and by considering biologically relevant log-normal fluctuations, we find that the system exhibits noise-induced transitions. The system becomes bimodal in regions of the parameter space where it would be deterministically monostable. We show that by including higher order corrections our methodology allows one to obtain correct predictions for the occurrence of transitions even for not so large correlation time of the fluctuations, overcoming thereby limitations of previous theoretical approaches. Interestingly we find that at intermediate noise intensities the noise-induced transition in the toggle switch affects one of the genes involved, but not the other one.

q-bio.MN↗

arXiv2023

Models of Vimentin Organization Under Actin-Driven Transport

Intermediate filaments form an essential structural network, spread throughout the cytoplasm and play a key role in cell mechanics, intracellular organization and molecular signaling. The maintenance of the network and its adaptation to the cell's dynamic behavior relies on several mechanisms implicating cytoskeletal crosstalk which are not fully understood. Mathematical modeling allows us to compare several biologically realistic scenarios to help us interpret experimental data. In this study, we observe and model the dynamics of the vimentin intermediate filaments in single glial cells seeded on circular micropatterns following microtubule disruption by nocodazole treatment. In these conditions, the vimentin filaments move towards the cell center and accumulate before eventually reaching a steady-state. In absence of microtubule-driven transport, the motion of the vimentin network is primarily driven by actin-related mechanisms. To model these experimental findings, we hypothesize that vimentin may exist in two states, mobile and immobile, and switches between the states at unknown (either constant or non-constant) rates. Mobile vimentin are assumed to advect with either constant or non-constant velocity. We introduce several biologically realistic scenarios using this set of assumptions. For each scenario, we use differential evolution to find the best parameter sets resulting in a solution that most closely matches the experimental data, then the assumptions are evaluated using the Akaike Information Criterion. This modeling approach allows us to conclude that our experimental data are best explained by a spatially dependent trapping of intermediate filaments or a spatially dependent speed of actin-dependent transport.

q-bio.SC↗

arXiv2022

Herding of proteins by the ends of shrinking polymers

The control of biopolymer length is mediated by proteins that localize to polymer ends and regulate polymerization dynamics. Several mechanisms have been proposed to achieve end localization. Here, we propose a novel mechanism by which a protein that binds to a shrinking polymer and slows its shrinkage will be spontaneously enriched at the shrinking end through a "herding" effect. We formalize this process using both a lattice-gas model and a continuum description, and we present experimental evidence that the microtubule regulator spastin employs this mechanism. Our findings extend to more general problems involving diffusion within shrinking domains.

physics.bio-ph↗

arXiv2021

Universal energy-accuracy tradeoffs in nonequilibrium cellular sensing

We combine stochastic thermodynamics, large deviation theory, and information theory to derive fundamental limits on the accuracy with which single cell receptors can estimate external concentrations. As expected, if estimation is performed by an ideal observer of the entire trajectory of receptor states, then no energy consuming non-equilibrium receptor that can be divided into bound and unbound states can outperform an equilibrium two-state receptor. However, when estimation is performed by a simple observer that measures the fraction of time the receptor is bound, we derive a fundamental limit on the accuracy of general nonequilibrium receptors as a function of energy consumption. We further derive and exploit explicit formulas to numerically estimate a Pareto-optimal tradeoff between accuracy and energy. We find this tradeoff can be achieved by nonuniform ring receptors with a number of states that necessarily increases with energy. Our results yield a novel thermodynamic uncertainty relation for the time a physical system spends in a pool of states, and generalize the classic 1977 Berg-Purcell limit on cellular sensing along multiple dimensions.

physics.bio-ph↗

arXiv2023

Sorting of multiple molecular species on cell membranes

Eukaryotic cells maintain their inner order by a hectic process of distillation of molecular factors taking place on the surface of their lipid membranes. To understand the properties of this molecular sorting process, a physical model of the process has been recently proposed [arXiv:1811.06760], based on (a) the phase separation of a single, initially dispersed molecular species into spatially localized sorting domains on the lipid membrane, and (b) domain-induced membrane bending leading to the nucleation of submicrometric lipid vesicles, naturally enriched in the molecules of the engulfed sorting domain. The analysis of the model has shown the existence of an optimal region of the parameter space where sorting is most efficient. Here, the model is extended to account for the simultaneous distillation of a pool of distinct molecular species. We find that the mean time spent by sorted molecules on the membrane increases with the heterogeneity of the pool (i.e., the number of distinct molecular species sorted) according to a simple scaling law, and that a large number of distinct molecular species can in principle be sorted in parallel on a typical cell membrane region without significantly interfering with each other. Moreover, sorting is found to be most efficient when the distinct molecular species have comparable homotypic affinities. We also consider how valence (i.e., the average number of interacting neighbors of a molecule in a sorting domain) affects the sorting process, finding that higher-valence molecules can be sorted with greater efficiency than lower-valence molecules.

cond-mat.soft↗

arXiv2022

Physical limits to membrane curvature sensing by a single protein

Membrane curvature sensing is essential for a diverse range of biological processes. Recent experiments have revealed that a single nanometer-sized septin protein can distinguish between membrane-coated glass beads of one micron and three micron diameters, even though the septin is orders of magnitude smaller than the beads. This sensing ability is especially surprising since curvature-sensing proteins must deal with persistent thermal fluctuations of the membrane, leading to discrepancies between the bead's curvature and the local membrane curvature sensed instantaneously by a protein. Using continuum models of fluctuating membranes, we investigate whether it is feasible for a protein acting as a perfect observer of the membrane to sense micron-scale curvature either by measuring local membrane curvature or by using bilayer lipid densities as a proxy. To do this, we develop algorithms to simulate lipid density and membrane shape fluctuations. We derive physical limits to the sensing efficacy of a protein in terms of protein size, membrane thickness, membrane bending modulus, membrane-substrate adhesion strength, and bead size. To explain the experimental protein-bead association rates, we develop two classes of predictive models: i) for proteins that maximally associate to a preferred curvature, and ii) for proteins with enhanced association rates above a threshold curvature. We find that the experimentally observed sensing efficacy is close to the theoretical sensing limits imposed on a septin-sized protein, and that the variance in membrane curvature fluctuations sensed by a protein determines how sharply the association rate depends on the curvature of the bead.

physics.bio-ph↗

arXiv2023

A mean-field theory approach to 3D nematic phase transitions in microtubules

Microtubules are dynamic intracellular fibers that have been observed experimentally to undergo spontaneous self-alignment. We formulate a 3D mean-field theory model to analyze the nematic phase transition of microtubules growing and interacting within a 3D space then make a comparison with computational simulations. We identify a control parameter $G_\text{eff}$ and predict a unique critical value $G_\text{eff}=1.56$ for which a phase transition can occur. Furthermore, we show both analytically and using simulations that this predicted critical value does not depend on the presence of zippering. The mean-field theory developed here provides an analytical estimate of microtubule patterning characteristics without running time-consuming simulations and is a step towards bridging scales from microtubule behavior to multicellular simulations.

physics.bio-ph↗

arXiv2023

The effect of loops on the mean square displacement of Rouse-model chromatin

Many researchers have been encouraged to describe the dynamics of chromosomal loci in chromatin using the classical Rouse model of polymer dynamics by the agreement between the measured mean square displacement (MSD) versus time of fluorescently-labelled loci and the Rouse-model predictions. However, the discovery of intermediate-scale chromatin organization, known as topologically associating domains (TADs), together with the proposed explanation of TADs in terms of chromatin loops and loop extrusion, is at odds with the classical Rouse model, which does not contain loops. Accordingly, we introduce an extended Rouse model that incorporates chromatin loop configurations from loop-extrusion-factor-model simulations. Specifically, we extend the classical Rouse model by modifying the polymer's dynamical matrix to incorporate extra springs that represent loop bases. We also theoretically generalize the friction coefficient matrix so that the Rouse beads with non-uniform friction coefficients are compatible with our Rouse model simulation method. This extended Rouse model allowes us to investigate the impact of loops and loop extrusion on the dynamics of chromatin. We show that loops significantly suppress the averaged MSD of a chromosomal locus, consistent with recent experiments that track fluorescently-labelled chromatin loci in fission yeast [M. L. P. Bailey, I. Surovtsev, J. F. Williams, H. Yan, T. Yuan, S. G. Mochrie, and M. C. King, Mol. Biol. Cell (in press)]. We also find that loops slightly reduce the MSD's stretching exponent from the classical Rouse-model value of 0.5 to a loop-density-dependent value in the 0.45-0.40 range. Remarkably, stretching exponent values in this range have also been reported in recent experiments [S. C. Weber, A. J. Spakowitz, and J. A. Theriot, Phys. Rev. Lett. 104, 238102 (2010) and Bailey et al., Mol. Biol. Cell (in press)].

physics.bio-ph↗

arXiv2024

Coat stiffening can explain invagination of clathrin-coated membranes

Clathrin-mediated endocytosis is the main pathway used by eukaryotic cells to take up extracellular material, but the dominant physical mechanisms driving this process are still elusive. Recently several high-resolution imaging techniques have been used on different cell lines to measure the geometrical properties of clathrin-coated pits over their whole lifetime. Here we first show that the combination of all datasets with the recently introduced cooperative curvature model defines a consensus pathway, which is characterized by a flat to-curved transition at finite area, followed by linear growth and subsequent saturation of curvature. We then apply an energetic model for the composite of plasma membrane and clathrin coat to this consensus pathway to show that the dominant mechanism for invagination could be coat stiffening, which might originate from cooperative interactions between the different clathrin molecules and progressively drives the system towards its intrinsic curvature. Our theory predicts that two length scales determine the invagination pathway, namely the patch size at which the flat-to-curved transition occurs and the final pit radius.

q-bio.SC↗

arXiv2003

Spatial curvature effects on molecular transport by diffusion

For a substance diffusing on a curved surface, we obtain an explicit relation valid for very small values of the time, between the local concentration, the diffusion coefficient, the intrinsic spatial curvature and the time. We recover the known solution of Fick's law of diffusion in the flat space limit. In the biological context, this result would be useful in understanding the variations in the diffusion rates of integral proteins and other molecules on membranes.

physics.bio-ph↗

arXiv2003

Recursiveness, Switching, and Fluctuations in a Replicating Catalytic Network

A protocell model consisting of mutually catalyzing molecules is studied in order to investigate how chemical compositions are transferred recursively through cell divisions under replication errors. Depending on the path rate, the numbers of molecules and species, three phases are found: fast switching state without recursive production, recursive production, and itinerancy between the above two states. The number distributions of the molecules in the recursive states are shown to be log-normal except for those species that form a core hypercycle, and are explained with the help of a heuristic argument.

cond-mat↗

arXiv2003

Single Stranded DNA Translocation Through A Nanopore: A Master Equation Approach

We study voltage driven translocation of a single stranded (ss) DNA through a membrane channel. Our model, based on a master equation (ME) approach, investigates the probability density function (pdf) of the translocation times, and shows that it can be either double or mono-peaked, depending on the system parameters. We show that the most probable translocation time is proportional to the polymer length, and inversely proportional to the first or second power of the voltage, depending on the initial conditions. The model recovers experimental observations on hetro-polymers when using their properties inside the pore, such as stiffness and polymer-pore interaction.

cond-mat.stat-mech↗

arXiv2004

Rupture of a liposomal vesicle

We discuss pore dynamics in osmotically stressed vesicles. A set of equations which govern the liposomal size, internal solute concentration, and pore diameter is solved numerically. We find that dependent on the internal solute concentration and vesicle size, liposomes can stay pore-free, nucleate a short lived pore, or nucleate a long-lived pore. The phase diagram of pore stability is constructed, and the different scaling regimes are deduced analytically.

cond-mat.soft↗

arXiv2004

Nucleosome interactions in chromatin: fiber stiffening and hairpin formation

We use Monte Carlo simulations to study attractive and excluded volume interactions between nucleosome core particles in 30 nm-chromatin fibers. The nucleosomes are treated as disk-like objects having an excluded volume and short range attraction modelled by a variant of the Gay-Berne potential. The nucleosomes are connected via bendable and twistable linker DNA in the crossed linker fashion. We investigate the influence of the nucleosomal excluded volume on the stiffness of the fiber. For parameter values that correspond to chicken erythrocyte chromatin we find that the persistence length is governed to a large extent by that excluded volume whereas the soft linker backbone elasticity plays only a minor role. We further find that internucleosomal attraction can induce the formation of hairpin configurations. Tension-induced opening of such configurations into straight fibers manifests itself in a quasi-plateau in the force-extension curve that resembles results from recent micromanipulation experiments. Such hairpins may play a role in the formation of higher order structures in chromosomes like chromonema fibers.

q-bio.SC↗

arXiv2004

Molecular Discreteness in Reaction-Diffusion Systems Yields Steady States Not Seen in the Continuum Limit

We investigate the effects of spatial discreteness of molecules in reaction-diffusion systems. It is found that discreteness within the so called Kuramoto length can lead to a localization of molecules, resulting in novel steady states that do not exist in the continuous case. These novel states are analyzed theoretically as the fixed points of accelerated localized reactions, an approach that was verified to be in good agreement with stochastic particle simulations. The relevance of this discreteness-induced state to biological intracellular processes is discussed.

physics.chem-ph↗