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Microtubule-based actin transport and localization in a spherical cell

The interaction between actin filaments and microtubules is crucial for many eukaryotic cellular processes, such as, among others, cell polarization, cell motility and cellular wound healing. The importance of this interaction has long been recognised, yet very little is understood about both the underlying mechanisms and the consequences for the spatial (re)organization of the cellular cytoskeleton. At the same time, understanding the causes and the consequences of the interaction between different biomolecular components are key questions for \emph{in vitro} research involving reconstituted biomolecular systems, especially in the light of current interest in creating minimal synthetic cells. In this light, recent \emph{in vitro} experiments have shown that the actin-microtubule interaction mediated by the cytolinker TipAct, which binds to actin lattice and microtubule tip, causes the directed transport of actin filaments. We develop an analytical theory of dynamically unstable microtubules, nucleated from the center of a spherical cell, in interaction with actin filaments. We show that, depending on the balance between the diffusion of unbound actin filaments and propensity to bind microtubules, actin is either concentrated in the center of the cell, where the density of microtubules is highest, or becomes localized to the cell cortex.

q-bio.SC↗

Variability in mRNA Translation: A Random Matrix Theory Approach

The rate of mRNA translation depends on the initiation, elongation, and termination rates of ribosomes along the mRNA. These rates depend on many "local" factors like the abundance of free ribosomes and tRNA molecules in the vicinity of the mRNA molecule. All these factors are stochastic and their experimental measurements are also noisy. An important question is how protein production in the cell is affected by this considerable variability. We develop a new theoretical framework for addressing this question by modeling the rates as identically and independently distributed random variables and using tools from random matrix theory to analyze the steady-state production rate. The analysis reveals a principle of universality: the average protein production rate depends only on the of the set of possible values that the random variable may attain. This explains how total protein production can be stabilized despite the overwhelming stochasticticity underlying cellular processes.

q-bio.SC↗

Extrusion without a motor: a new take on the loop extrusion model of genome organization

Chromatin loop extrusion is a popular model for the formation of CTCF loops and topological domains. Recent HiC data have revealed a strong bias in favour of a particular arrangement of the CTCF binding motifs that stabilize loops, and extrusion is the only model to date which can explain this. However, the model requires a motor to generate the loops, and although cohesin is a strong candidate for the extruding factor, a suitable motor protein (or a motor activity in cohesin itself) has yet to be found. Here we explore a new hypothesis: that there is no motor, and thermal motion within the nucleus drives extrusion. Using theoretical modelling and computer simulations we ask whether such diffusive extrusion could feasibly generate loops. Our simulations uncover an interesting ratchet effect (where an osmotic pressure promotes loop growth), and suggest, by comparison to recent in vitro and in vivo measurements, that diffusive extrusion can in principle generate loops of the size observed in the data. Extra View on : C. A. Brackley, J. Johnson, D. Michieletto, A. N. Morozov, M. Nicodemi, P. R. Cook, and D. Marenduzzo "Non-equilibrium chromosome looping via molecular slip-links", Physical Review Letters 119, 138101 (2017)

physics.bio-ph↗

Computation of single-cell metabolite distributions using mixture models

Metabolic heterogeneity is widely recognised as the next challenge in our understanding of non-genetic variation. A growing body of evidence suggests that metabolic heterogeneity may result from the inherent stochasticity of intracellular events. However, metabolism has been traditionally viewed as a purely deterministic process, on the basis that highly abundant metabolites tend to filter out stochastic phenomena. Here we bridge this gap with a general method for prediction of metabolite distributions across single cells. By exploiting the separation of time scales between enzyme expression and enzyme kinetics, our method produces estimates for metabolite distributions without the lengthy stochastic simulations that would be typically required for large metabolic models. The metabolite distributions take the form of Gaussian mixture models that are directly computable from single-cell expression data and standard deterministic models for metabolic pathways. The proposed mixture models provide a systematic method to predict the impact of biochemical parameters on metabolite distributions. Our method lays the groundwork for identifying the molecular processes that shape metabolic heterogeneity and its functional implications in disease.

q-bio.MN↗

Bridging-induced microphase separation: photobleaching experiments, chromatin domains, and the need for active reactions

We review the mechanism and consequences of the "bridging-induced attraction", a generic biophysical principle which underpins some existing models for chromosome organisation in 3-D. This attraction, which was revealed in polymer physics-inspired computer simulations, is a generic clustering tendency arising in multivalent chromatin-binding proteins, and it provides an explanation for the biogenesis of nuclear bodies and transcription factories via microphase separation. Including post-translational modification reactions involving these multivalent proteins can account for the fast dynamics of the ensuing clusters, as is observed via microscopy and photobleaching experiments. The clusters found in simulations also give rise to chromatin domains which conform well with the observation of A/B compartments in HiC experiments.

cond-mat.soft↗

Mechanistic Modelling of Chromatin Folding to Understand Function

Experimental approaches have been applied to address questions in understanding three-dimensional chromatin organisation and function. As datasets increase in size and complexity, it becomes a challenge to reach a mechanistic interpretation of experimental results. Polymer simulations and mechanistic modelling have been applied to explain experimental observations, and the links to different aspects of genome function. Here, we provide a guide for biologists, explaining different simulation approaches and the contexts in which they have been used.

physics.bio-ph↗

Polymer Modelling Predicts Chromosome Reorganisation in Senescence

Lamina-associated domains (LADs) cover a large part of the human genome and are thought to play a major role in shaping the nuclear architectural landscape. Here, we perform polymer simulations, microscopy and mass spectrometry to dissect the roles played by heterochromatin- and lamina-mediated interactions in nuclear organisation. Our model explains the conventional organisation of heterochromatin and euchromatin in growing cells and the pathological organisation found in oncogene-induced senescence and progeria. We show that the experimentally observed changes in the locality of contacts in senescent and progeroid cells can be explained as arising due to phase transitions in the system. Within our simulations LADs are highly stochastic, as in experiments. Our model suggests that, once established, the senescent phenotype should be metastable even if lamina-mediated interactions were reinstated. Overall, our simulations uncover a generic physical mechanism that can regulate heterochromatin segregation and LAD formation in a wide range of mammalian nuclei.

physics.bio-ph↗

The role of liquid-liquid phase separation in regulating enzyme activity

Liquid-liquid phase separation is now recognized as a common mechanism for regulating enzyme activity in cells. Insights from studies in cells are complemented by in vitro studies aimed at developing better understanding of mechanisms underlying such control. These mechanisms are often based on the influence of LLPS on the physicochemical properties of the enzyme's environment. Biochemical mechanisms underlying such regulation include the potential for concentrating reactants together, tuning reaction rates, and controlling competing metabolic pathways. LLPS is thus a powerful tool with extensive utilities for the cell, e.g. for consolidating cell survival under stress or rerouting metabolic pathways in response to the energy state of the cell. By examining the evidence of how LLPS affects enzyme catalysis, we can begin to understand emerging concepts and expand our understanding of enzyme catalysis in living cells.

q-bio.BM↗

Localization microscopy: a review of the progress in methods and applications

Here, we report analysis and summary of research in the field of localization microscopy for optical imaging. We introduce the basic elements of super-resolved localization microscopy methods for PALM and STORM, commonly used both in vivo and in vitro, discussing the core essentials of background theory, instrumentation and computational algorithms. We discuss the resolution limit of light microscopy and the mathematical framework for localizing fluorescent dyes in space beyond this limit, including the precision obtainable as a function of the amount of light emitted from a dye, and how it leads to a fundamental compromise between spatial and temporal precision. The properties of a "good dye" are outlined, as are the features of PALM and STORM super-resolution microscopy and adaptations that may need to be made to experimental protocols to perform localization determination. We analyse briefly some of the methods of modern super-resolved optical imaging that work through reshaping point spread functions and how they utilize aspects of localization microscopy, such as stimulated depletion (STED) methods and MINFLUX, and summarize modern methods that push localization into 3D using non-Gaussian point spread functions. We report on current methods for analyzing localization data including determination of 2D and 3D diffusion constants, molecular stoichiometries, and performing cluster analysis with cutting-edge techniques, and finally discuss how these techniques may be used to enable important insight into a range of biological processes.

physics.optics↗

A Linear Reciprocal Relationship Between Robustness and Plasticity in Homeostatic Biological Networks

In physics of living systems, a search for relationships of a few macroscopic variables that emerge from many microscopic elements is a central issue. We evolved gene regulatory networks so that the expression of target genes (partial system) is insensitive to environmental changes. Then, we found the expression levels of the remaining genes autonomously increase as a plastic response. Negative proportionality was observed between the average changes in target and remnant genes, reflecting reciprocity between the macroscopic robustness of homeostatic genes and plasticity of regulator genes. This reciprocity follows the lever principle, which was satisfied throughout the evolutionary course, imposing an evolutionary constraint.

physics.bio-ph↗

An enzymatic hormesis box

We present a simple enzymatic system that is capable of a biphasic response under competitive inhibition. This is arguably the simplest system that can be said to be hormetic

q-bio.BM↗

Membrane Trafficking of Integral Cell Junction Proteins and its Functional Consequences

Though membrane trafficking of cell junction proteins has been studied extensively for more than two decades, the accumulated knowledge remains fragmentary. The goal of this review is to synthesize published studies on the membrane trafficking of the five major junction transmembrane proteins: claudins, occludin, and junction adhesion molecules (JAMs) in tight junctions; cadherins and nectins in adherens junctions; to identify underlying common mechanisms; to highlight their functional consequences on barrier function; and to identify knowledge gaps. Clathrin-mediated endocytosis appears to be the main, but not exclusive, mode of internalization. Caveolin-mediated endocytosis and macropinocytosis are employed less frequently. PDZ-domain binding is the predominant mode of interaction between junction protein cytoplasmic tails and scaffold proteins. It is shared by claudins, the largest family of junction integral proteins, by junction adhesion molecules A, B, and C, and by the three nectins. All eight proteins are destined to either recycling via Rab4/Rab11 GTPases or to degradation. The sorting mechanisms that underlie the specificity of their endocytic pathways and determine their fates are not fully known. New data is presented to introduce an emerging role of junction-associated scaffold proteins in claudin membrane trafficking.

q-bio.SC↗

In silico model of infection of a CD4(+) T-cell by a human immunodeficiency type 1 virus, and a mini-review on its molecular pathophysiology

Introduction. Can the infection due to the human immunodeficiency virus type 1 induce a change in the differentiation status or process in T cells?. Methods. We will consider two stochastic Markov chain models, one which will describe the T-helper cell differentiation process, and another one describing that process of infection of the T-helper cell by the virus; in these Markov chains, we will consider a set of states $\{X_t \}$ comprised of those proteins involved in each of the processes and their interactions (either differentiation or infection of the cell), such that we will obtain two stochastic transition matrices ($A,B$), one for each process; afterwards, the computation of their eigenvalues shall be performed, in which, should the eigenvalue $λ_i=1$ exist, the computation for the equilibrium distribution $π^n$ will be obtained for each of the matrices, which will inform us on the trends of interactions amongst the proteins in the long-term. Results. The stochastic processes considered possess an equilibrium distribution, when reaching their equilibrium distribution, there exists an increase in their informational entropy, and their log-rank distributions can be modeled as discrete beta generalized distributions (DGBD). Discussion. The equilibrium distributions of both process can be regarded as states in which the cell is well-differentiated, ergo there exists an induction of a novel HIV-dependent differentiated state in the T-cell; these processes due to their DGBD distribution can be considered complex processes; due to the increasing entropy, the equilibrium states are stable ones. Conclusion. The HIV virus can promote a novel differentiated state in the T-cell, which can give account for clinical features seen in patients; this model, notwithstanding does not give account of YES/NO logical switches involved in the regulatory networks.

q-bio.MN↗

A mathematical modelling framework for the regulation of intra-cellular OCT4 in human pluripotent stem cells

Human pluripotent stem cells (hPSCs) have promising clinical applications in regenerative medicine, drug-discovery and personalised medicine due to their potential to differentiate into all cell types, a property know as pluripotency. A deeper understanding of how pluripotency is regulated is required to assist in controlling pluripotency and differentiation trajectories experimentally. Mathematical modelling provides a non-invasive tool through which to explore, characterise and replicate the regulation of pluripotency and the consequences on cell fate. Here we use experimental data of the expression of the pluripotency transcription factor OCT4 in a growing hPSC colony to develop and evaluate mathematical models for temporal pluripotency regulation. We consider fractional Brownian motion and the stochastic logistic equation and explore the effects of both additive and multiplicative noise. We illustrate the use of time-dependent carrying capacities and the introduction of Allee effects to the stochastic logistic equation to describe cell differentiation. This mathematical framework for describing intra-cellular OCT4 regulation can be extended to other transcription factors and developed into sophisticated predictive models.

q-bio.SC↗

Diffusive search and trajectories on spatial networks: a propagator approach

Several organelles in eukaryotic cells, including mitochondria and the endoplasmic reticulum, form interconnected tubule networks extending throughout the cell. These tubular networks host many biochemical pathways that rely on proteins diffusively searching through the network to encounter binding partners or localized target regions. In this work we develop both exact analytical methods to compute mean first passage times and efficient kinetic Monte Carlo algorithms to simulate trajectories of particles diffusing in a tubular network. Our approach leverages exact propagator functions for the distribution of transition times between network nodes and allows large simulation time steps determined by the network structure. The methodology is applied to both synthetic planar networks and organelle network structures, demonstrating key general features such as the heterogeneity of search times in different network regions and the functional advantage of broadly distributing target sites throughout the network. The proposed algorithms pave the way for future exploration of the interrelationship between tubular network structure and biomolecular reaction kinetics.

physics.bio-ph↗

Analytic solution of chemical master equations involving gene switching. I: Representation theory and diagrammatic approach to exact solution

The chemical master equation (CME), which describes the discrete and stochastic molecule number dynamics associated with biological processes like transcription, is difficult to solve analytically. It is particularly hard to solve for models involving bursting/gene switching, a biological feature that tends to produce heavy-tailed single cell RNA counts distributions. In this paper, we present a novel method for computing exact and analytic solutions to the CME in such cases, and use these results to explore approximate solutions valid in different parameter regimes, and to compute observables of interest. Our method leverages tools inspired by quantum mechanics, including ladder operators and Feynman-like diagrams, and establishes close formal parallels between the dynamics of bursty transcription, and the dynamics of bosons interacting with a single fermion. We focus on two problems: (i) the chemical birth-death process coupled to a switching gene/the telegraph model, and (ii) a model of transcription and multistep splicing involving a switching gene and an arbitrary number of downstream splicing steps. We work out many special cases, and exhaustively explore the special functionology associated with these problems. This is Part I in a two-part series of papers; in Part II, we explore an alternative solution approach that is more useful for numerically solving these problems, and apply it to parameter inference on simulated RNA counts data.

q-bio.SC↗

Metabolic limits on classical information processing by biological cells

Biological information processing is generally assumed to be classical. Measured cellular energy budgets of both prokaryotes and eukaryotes, however, fall orders of magnitude short of the power required to maintain classical states of protein conformation and localization at the Å, fs scales predicted by single-molecule decoherence calculations and assumed by classical molecular dynamics models. We suggest that decoherence is limited to the immediate surroundings of the cell membrane and of intercompartmental boundaries within the cell, and that bulk cellular biochemistry implements quantum information processing. Detection of Bell-inequality violations in responses to perturbation of recently-separated sister cells would provide a sensitive test of this prediction. If it is correct, modeling both intra- and intercellular communication requires quantum theory.

quant-ph↗

Monostability and bistability of biological switches

Cell-fate transition can be modeled by ordinary differential equations (ODEs) which describe the behavior of several molecules in interaction, and for which each stable equilibrium corresponds to a possible phenotype (or 'biological trait'). In this paper, we focus on simple ODE systems modeling two molecules which each negatively (or positively) regulate the other. It is well-known that such models may lead to monostability or multistability, depending on the selected parameters. However, extensive numerical simulations have led systems biologists to conjecture that in the vast majority of cases, there cannot be more than two stable points. Our main result is a proof of this conjecture. More specifically, we provide a criterion ensuring at most bistability, which is indeed satisfied by most commonly used functions. This includes Hill functions, but also a wide family of convex and sigmoid functions. We also determine which parameters lead to monostability, and which lead to bistability, by developing a more general framework encompassing all our results.

math.DS↗