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arXiv2020

The fitness landscapes of translation

Motivated by recent experiments on an antibiotic resistance gene, we investigate genetic interactions between synonymous mutations in the framework of exclusion models of translation. We show that the range of possible interactions is markedly different depending on whether translation efficiency is assumed to be proportional to ribosome current or ribosome speed. In the first case every mutational effect has a definite sign that is independent of genetic background, whereas in the second case the effect-sign can vary depending on the presence of other mutations. The latter result is demonstrated using configurations of multiple translational bottlenecks induced by slow codons.

q-bio.SC↗

arXiv2004

Discreteness-induced Stochastic Steady State in Reaction Diffusion Systems: Self-consistent Analysis and Stochastic Simulations

A self-consistent equation to derive a discreteness-induced stochastic steady state is presented for reaction-diffusion systems. For this formalism, we use the so-called Kuramoto length, a typical distance over which a molecule diffuses in its lifetime, as was originally introduced to determine if local fluctuations influence globally the whole system. We show that this Kuramoto length is also relevant to determine whether the discreteness of molecules is significant or not. If the number of molecules of a certain species within the Kuramoto length is small and discrete, localization of some other chemicals is brought about, which can accelerate certain reactions. When this acceleration influences the concentration of the original molecule species, it is shown that a novel, stochastic steady state is induced that does not appear in the continuum limit. A theory to obtain and characterize this state is introduced, based on the self-consistent equation for chemical concentrations. This stochastic steady state is confirmed by numerical simulations on a certain reaction model, which agrees well with the theoretical estimation. Formation and coexistence of domains with different stochastic states are also reported, which is maintained by the discreteness. Relevance of our result to intracellular reactions is briefly discussed.

physics.chem-ph↗

arXiv2009

Stochastic Eulerian-Lagrangian Methods for Fluid-Structure Interactions with Thermal Fluctuations and Shear Boundary Conditions

A computational approach is introduced for the study of the rheological properties of complex fluids and soft materials. The approach allows for a consistent treatment of microstructure elastic mechanics, hydrodynamic coupling, thermal fluctuations, and externally driven shear flows. A mixed description in terms of Eulerian and Lagrangian reference frames is used for the physical system. Microstructure configurations are represented in a Lagrangian reference frame. Conserved quantities, such as momentum of the fluid and microstructures, are represented in an Eulerian reference frame. The mathematical formalism couples these different descriptions using general operators subject to consistency conditions. Thermal fluctuations are taken into account in the formalism by stochastic driving fields introduced in accordance with the principles of statistical mechanics. To study the rheological responses of materials subject to shear, generalized periodic boundary conditions are developed where periodic images are shifted relative to the unit cell to induce shear. Stochastic numerical methods are developed for the formalism. As a demonstration of the methods, results are presented for the shear responses of a polymeric fluid, lipid vesicle fluid, and a gel-like material.

cond-mat.soft↗

arXiv2005

Movements of molecular motors: Ratchets, random walks and traffic phenomena

Processive molecular motors which drive the traffic of organelles in cells move in a directed way along cytoskeletal filaments. On large time scales, they perform motor walks, i.e., peculiar random walks which arise from the repeated unbinding from and rebinding to filaments. Unbound motors perform Brownian motion in the surrounding fluid. In addition, the traffic of molecular motors exhibits many cooperative phenomena. In particular, it faces similar problems as the traffic on streets such as the occurrence of traffic jams and the coordination of (two-way) traffic. These issues are studied here theoretically using lattice models.

cond-mat.stat-mech↗

arXiv2004

Collective charge excitations along cell membranes

A significant part of the thin layers of counter-ions adjacent to the exterior and interior surfaces of a cell membrane form quasi-two-dimensional (2D) layers of mobile charge. Collective charge density oscillations, known as plasmon modes, in these 2D charged systems of counter-ions are predicted in the present paper. This is based on a calculation of the self-consistent response of this system to a fast electric field fluctuation. The possibility that the membrane channels might be using these excitations to carry out fast communication is suggested and experiments are proposed to reveal the existence of such excitations.

q-bio.SC↗

arXiv2010

Renewal-anomalous-heterogeneous files

Renewal-anomalous-heterogeneous files are solved. A simple file is made of Brownian hard spheres that diffuse stochastically in an effective 1D channel. Generally, Brownian files are heterogeneous: the spheres' diffusion coefficients are distributed and the initial spheres' density is non-uniform. In renewal-anomalous files, the distribution of waiting times for individual jumps is exponential as in Brownian files, yet obeys: ψ_α (t)~t^(-1-α), 0<α<1. The file is renewal as all the particles attempt to jump at the same time. It is shown that the mean square displacement (MSD) in a renewal-anomalous-heterogeneous file, , obeys, ~[ _{nrml}]^α, where _{nrml} is the MSD in the corresponding Brownian file. This scaling is an outcome of an exact relation (derived here) connecting probability density functions of Brownian files and renewal-anomalous files. It is also shown that non-renewal-anomalous files are slower than the corresponding renewal ones.

cond-mat.soft↗

arXiv2012

Coagulation-fragmentation for a finite number of particles and application to telomere clustering in the yeast nucleus

We develop a coagulation-fragmentation model to study a system composed of a small number of stochastic objects moving in a confined domain, that can aggregate upon binding to form local clusters of arbitrary sizes. A cluster can also dissociate into two subclusters with a uniform probability. To study the statistics of clusters, we combine a Markov chain analysis with a partition number approach. Interestingly, we obtain explicit formulas for the size and the number of clusters in terms of hypergeometric functions. Finally, we apply our analysis to study the statistical physics of telomeres (ends of chromosomes) clustering in the yeast nucleus and show that the diffusion-coagulation-fragmentation process can predict the organization of telomeres.

q-bio.SC↗

arXiv2017

A mechanical model of bacteriophage DNA ejection

Single molecule experiments on bacteriophages show an exponential scaling for the dependence of mobility on the length of DNA within the capsid. It has been suggested that this could be due to the "capstan mechanism" -- the exponential amplification of friction forces that result when a rope is wound around a cylinder as in a ship's capstan. Here we describe a desktop experiment that illustrates the effect. Though our model phage is a million times larger, it exhibits the same scaling observed in single molecule experiments.

physics.bio-ph↗

arXiv2015

Intracellular transport driven by cytoskeletal motors: General mechanisms and defects

Cells are strongly out-of-equilibrium systems driven by continuous energy supply. They carry out many vital functions requiring active transport of various ingredients and organelles, some being small, others being large. The cytoskeleton, composed of three types of filaments, determines the shape of the cell and plays a role in cell motion. It also serves as a road network for the so-called cytoskeletal motors. These molecules can attach to a cytoskeletal filament, perform directed motion, possibly carrying along some cargo, and then detach. It is a central issue to understand how intracellular transport driven by molecular motors is regulated, in particular because its breakdown is one of the signatures of some neuronal diseases like the Alzheimer. We give a survey of the current knowledge on microtubule based intracellular transport. We first review some biological facts obtained from experiments, and present some modeling attempts based on cellular automata. We start with background knowledge on the original and variants of the TASEP (Totally Asymmetric Simple Exclusion Process), before turning to more application oriented models. After addressing microtubule based transport in general, with a focus on in vitro experiments, and on cooperative effects in the transportation of large cargos by multiple motors, we concentrate on axonal transport, because of its relevance for neuronal diseases. It is a challenge to understand how this transport is organized, given that it takes place in a confined environment and that several types of motors moving in opposite directions are involved. We review several features that could contribute to the efficiency of this transport, including the role of motor-motor interactions and of the dynamics of the underlying microtubule network. Finally, we discuss some still open questions.

physics.bio-ph↗

arXiv2019

Quantitative Immunology for Physicists

The adaptive immune system is a dynamical, self-organized multiscale system that protects vertebrates from both pathogens and internal irregularities, such as tumours. For these reason it fascinates physicists, yet the multitude of different cells, molecules and sub-systems is often also petrifying. Despite this complexity, as experiments on different scales of the adaptive immune system become more quantitative, many physicists have made both theoretical and experimental contributions that help predict the behaviour of ensembles of cells and molecules that participate in an immune response. Here we review some recent contributions with an emphasis on quantitative questions and methodologies. We also provide a more general methods section that presents some of the wide array of theoretical tools used in the field.

q-bio.QM↗

arXiv2022

Length control of long cell protrusions: rulers, timers and transport

A living cell uses long tubular appendages for locomotion and sensory purposes. Hence, assembling and maintaining a protrusion of correct length is crucial for its survival and overall performance. Usually the protrusions lack the machinery for the synthesis of building blocks and imports them from the cell body. What are the unique features of the transport logistics which facilitate the exchange of these building blocks between the cell and the protrusion? What kind of `rulers' and `timers' does the cell use for constructing its appendages of correct length on time? How do the multiple appendages coordinate and communicate among themselves during different stages of their existence? How frequently do the fluctuations drive the length of these dynamic protrusions out of the acceptable bounds? These questions are addressed from a broad perspective in this review which is organized in three parts. In part-I the list of all known cell protrusions is followed by a comprehensive list of the mechanisms of length control of cell protrusions reported in the literature. We review not only the dynamics of the genesis of the protrusions, but also their resorption and regrowth as well as regeneration after amputation. As a case study in part-II, the specific cell protrusion that has been discussed in detail is eukaryotic flagellum (also known as cilium); this choice was dictated by the fact that flagellar length control mechanisms have been studied most extensively over more than half a century in cells with two or more flagella. Although limited in scope, brief discussions on a few non-flagellar cell protrusions in part-III of this review is intended to provide a glimpse of the uncharted territories and challenging frontiers of research on subcellular length control phenomena that awaits vigorous investigations.

physics.bio-ph↗

arXiv2006

DNA looping: the consequences and its control

The formation of DNA loops by proteins and protein complexes is ubiquitous to many fundamental cellular processes, including transcription, recombination, and replication. Here we review recent advances in understanding the properties of DNA looping in its natural context and how they propagate to the cellular behavior through gene regulation. The results of connecting the molecular properties with cellular physiology indicate that looping of DNA in vivo is much more complex and easier than predicted from current models and reveals a wealth of previously unappreciated details.

q-bio.BM↗

arXiv2021

Spatial and temporal dynamics of RhoA activities of single breast tumor cells in a 3D environment revealed by a machine learning-assisted FRET technique

One of the hallmarks of cancer cells is their exceptional ability to migrate within the extracellular matrix (ECM) for gaining access to the circulatory system, a critical step of cancer metastasis. RhoA, a small GTPase, is known to be a key molecular switch that toggles between actomyosin contractility and lamellipodial protrusion during cell migration. Current understanding of RhoA activity in cell migration has been largely derived from studies of cells plated on a two-dimensional (2D) substrate using a FRET biosensor. There has been increasing evidence that cells behave differently in a more physiologically relevant three-dimensional (3D) environment, however, studies of RhoA activities in 3D have been hindered by low signal-to-noise ratio in fluorescence imaging. In this paper, we present a machine learning-assisted FRET technique to follow the spatiotemporal dynamics of RhoA activities of single breast tumor cells (MDA-MB-231) migrating in a 3D as well as a 2D environment using a RhoA biosensor. We found that RhoA activity is more polarized along the long axis of the cell for single cells migrating on 2D fibronectin-coated glass versus those embedded in 3D collagen matrices. In particular, RhoA activities of cells in 2D exhibit a distinct front-to-back and back-to-front movement during migration in contrast to those in 3D. Finally, regardless of dimensionality, RhoA polarization is found to be correlated with cell shape.

q-bio.CB↗

arXiv2003

Ribosome recycling, diffusion, and mRNA loop formation in translational regulation

We explore and quantify the physical and biochemical mechanisms that may be relevant in the regulation of translation. After elongation and detachment from the 3' termination site of mRNA, parts of the ribosome machinery can diffuse back to the initiation site, especially if it is held nearby, enhancing overall translation rates. The elongation steps of the mRNA-bound ribosomes are modeled using exact and asymptotic results of the totally asymmetric exclusion process (TASEP).Since the ribosome injection rates of the TASEP depend on the local concentrations at the initiation site, a source of ribosomes emanating from the termination end can feed back to the initiation site, leading to a self-consistent set of equations for the steady-state ribosome throughput. Additional mRNA binding factors can also promote loop formation, or cyclization, bringing the initiation and termination sites into close proximity. The probability distribution of the distance between the initiation and termination sites is described using simple noninteracting polymer models. We find that the initiation, or initial ribosome adsorption binding required for maximal throughput can vary dramatically depending on certain values of the bulk ribosome concentration and diffusion constant. If cooperative interactions among the loop-promoting proteins and the initiation/termination sites are considered, the throughput can be further regulated in a nonmonotonic manner. Potential experiments to test the hypothesized physical mechanisms are discussed.

cond-mat.soft↗

arXiv2002

A Simple Kinetic Model Describes the Processivity of Myosin-V

Myosin-V is a motor protein responsible for organelle and vesicle transport in cells. Recent single-molecule experiments have shown that it is an efficient processive motor that walks along actin filaments taking steps of mean size close to 36 nm. A theoretical study of myosin-V motility is presented following an approach used successfully to analyze the dynamics of conventional kinesin but also taking some account of step-size variations. Much of the present experimental data for myosin-V can be well described by a two-state chemical kinetic model with three load-dependent rates. In addition, the analysis predicts the variation of the mean velocity and of the randomness -- a quantitative measure of the stochastic deviations from uniform, constant-speed motion -- with ATP concentration under both resisting and assisting loads, and indicates a {\it sub}step of size $d_{0} \simeq$ 13-14 nm (from the ATP-binding site) that appears to accord with independent observations.

cond-mat.stat-mech↗

arXiv2003

Mobility of Taxol in Microtubule Bundles

Mobility of taxol inside microtubules was investigated using fluorescence recovery after photobleaching (FRAP) on flow-aligned bundles. Bundles were made of microtubules with either GMPCPP or GTP at the exchangeable site on the tubulin dimer. Recovery times were sensitive to bundle thickness and packing, indicating that taxol molecules are able to move laterally through the bundle. The density of open binding sites along a microtubule was varied by controlling the concentration of taxol in solution for GMPCPP samples. With > 63% sites occupied, recovery times were independent of taxol concentration and, therefore, inversely proportional to the microscopic dissociation rate, k_{off}. It was found that 10*k_{off} (GMPCPP) ~ k_{off} (GTP), consistent with, but not fully accounting for, the difference in equilibrium constants for taxol on GMPCPP and GTP microtubules. With < 63% sites occupied, recovery times decreased as ~ [Tax]^{-1/5} for both types of microtubules. We conclude that the diffusion of taxol along the microtubule interior is hindered by rebinding events when open sites are within ~7 nm of each other.

q-bio.SC↗

arXiv2004

Increased Concentration of Polyvalent Phospholipids in the Adsorption Domain of a Charged Protein

We studied the adsorption of a charged protein onto an oppositely charged membrane, composed of mobile phospholipids of differing valence, using a statistical-thermodynamical approach. A two-block model was employed, one block corresponding to the protein-affected region on the membrane, referred to as the adsorption domain, and the other to the unaffected remainder of the membrane. We calculated the protein-induced lipid rearrangement in the adsorption domain as arising from the interplay between the electrostatic interactions in the system and the mixing entropy of the lipids. Equating the electrochemical potentials of the lipids in the two blocks yields an expression for the relations among the various lipid fractions in the adsorption domain, indicating a sensitive dependence of lipid fraction on valence. This expression is a result of the two-block picture but does not depend on further details of the protein-membrane interaction. We subsequently calculated the lipid fractions themselves using the Poisson-Boltzmann theory. We examined the dependence of lipid enrichment, i.e., the ratio between the lipid fractions inside and outside the adsorption domain, on various parameters such as ionic strength and lipid valence. Maximum enrichment was found for lipid valence of about (-3) to (-4) in physiological conditions. Our results are in qualitative agreement with recent experimental studies on the interactions between peptides having a domain of basic residues and membranes containing a small fraction of the polyvalent phosphatidylinositol 4,5-bisphosphate (PIP2). This study provides theoretical support for the suggestion that proteins adsorbed onto membranes through a cluster of basic residues may sequester PIP2 and other polyvalent lipids.

physics.bio-ph↗

arXiv2004

Simulation of Drosophila Circadian Oscillations, Mutations, and Light Responses by a Model with VRI, PDP-1, and CLK

A model of Drosophila circadian rhythm generation was developed to represent feedback loops based on transcriptional regulation of per, Clk (dclock), Pdp-1, and vri (vrille). The model postulates that histone acetylation kinetics make transcriptional activation a nonlinear function of [CLK]. Such a nonlinearity is essential to simulate robust circadian oscillations of transcription in our model and in previous models. Simulations suggest two positive feedback loops involving Clk are not essential for oscillations, because oscillations of [PER] were preserved when Clk, vri, or Pdp-1 expression was fixed. Eliminating the negative feedback loop in which PER represses per expression abolished oscillations. Simulations of per or Clk null mutations and of vri, Clk, or Pdp-1 heterozygous null mutations altered model behavior in ways similar to experimental data. The model simulated a photic phase-response curve resembling experimental curves, and oscillations entrained to simulated light-dark cycles. The model makes experimental predictions, some of which could be tested in transgenic Drosophila.

q-bio.MN↗