Biomolecular condensates provide distinct chemical environments, which control various cellular processes. The diffusive dynamics and chemical kinetics inside phase-separated condensates can be studied experimentally by fluorescently labeling molecules, providing key insights into cell biology. We discuss how condensates govern the kinetics of chemical reactions and how this is reflected in the stochastic dynamics of labeled molecules. This allows us to reveal how the physics of phase separation influences the evolution of single-molecule trajectories and governs their statistics. We find that, out of equilibrium, the interactions that enable phase separation can induce directed motion and transport at the level of single molecules. Our work provides a theoretical framework to quantitatively analyze single-molecule trajectories in phase-separated systems.
A common model of stochastic auto-regulatory gene expression describes promoter switching via cooperative protein binding, effective protein production in the active state and dilution of proteins. Here we consider an extension of this model whereby colored noise with a short correlation time is added to the reaction rate parameters -- we show that when the size and timescale of the noise is appropriately chosen it accounts for fast reactions that are not explicitly modelled, e.g., in models with no mRNA description, fluctuations in the protein production rate can account for rapid multiple stages of nuclear mRNA processing which precede translation in eukaryotes. We show how the unified colored noise approximation can be used to derive expressions for the protein number distribution that is in good agreement with stochastic simulations. We find that even when the noise in the rate parameters is small, the protein distributions predicted by our model can be significantly different than models assuming constant reaction rates.
Shreyas Bhaban, Rachit Srivastava, James Melbourne
et al.
Transport of intracellular cargo is often mediated by teams of molecular motors that function in a chaotic environment under varying conditions. We show that the motors have unique steady state behavior which enables transport modalities that are robust. Under reduced ATP concentrations, multi-motor configurations are preferred over single motors. Higher load force drives motors to cluster, but very high loads compel them to separate in a manner that promotes immediate cargo movement once the load subsides. These inferences, backed by analytical guarantees, provide unique insights into the coordination strategies adopted by molecular motors to transport intracellular cargo.
The adhesion of biomembranes is mediated by the binding of membrane-anchored receptor and ligand proteins. The proteins can only bind if the separation between apposing membranes is sufficiently close to the length of the protein complexes, which leads to an interplay between protein binding and membrane shape. In this article, we review current models of biomembrane adhesion and novel insights obtained from the models. Theory and simulations with elastic-membrane and coarse-grained molecular models of biomembrane adhesion indicate that the binding of proteins in membrane adhesion strongly depends on nanoscale shape fluctuations of the apposing membranes, which results in binding cooperativity. A length mismatch between protein complexes leads to repulsive interactions that are caused by membrane bending and act as a driving force for the length-based segregation of proteins during membrane adhesion.
Cells adapt to changing environments by sensing ligand concentrations using specific receptors. The accuracy of sensing is ultimately limited by the finite number of ligand molecules bound by receptors. Previously derived physical limits to sensing accuracy have assumed that the concentration was constant and ignored its temporal fluctuations. We formulate the problem of concentration sensing in a strongly fluctuating environment as a non-linear field-theoretic problem, for which we find an excellent approximate Gaussian solution. We derive a new physical bound on the relative error in concentration $c$ which scales as $δc/c \sim (Dacτ)^{-1/4}$ with ligand diffusivity $D$, receptor cross-section $a$, and characteristic fluctuation time scale $τ$, in stark contrast with the usual Berg and Purcell bound $δc/c \sim (DacT)^{-1/2}$ for a perfect receptor sensing concentration during time $T$. We show how the bound can be achieved by a simple biochemical network downstream the receptor that adapts the kinetics of signaling as a function of the square root of the sensed concentration.
Ryota Takaki, Mauro L. Mugnai, Yonathan Goldtzvik
et al.
Dimeric molecular motors walk on polar tracks by binding and hydrolyzing one ATP per step. Despite tremendous progress, the waiting state for ATP binding in the well-studied kinesin that walks on microtubule (MT), remains controversial. One experiment suggests that in the waiting state both heads are bound to the MT, while the other shows that ATP binds to the leading head after the partner head detaches. To discriminate between these two scenarios, we developed a theory to calculate accurately several experimentally measurable quantities as a function of ATP concentration and resistive force. In particular, we predict that measurement of the randomness parameter could discriminate between the two scenarios for the waiting state of kinesin, thereby resolving this standing controversy.
The plane of bacterial cell division must be precisely positioned. In the bacterium Myxococcus xanthus, the proteins PomX and PomY form a large cluster, which is tethered to the nucleoid by the ATPase PomZ and moves in a stochastic, but biased manner towards midcell, where it initiates cell division. Previously, a positioning mechanism based on the fluxes of PomZ on the nucleoid was proposed. However, the cluster dynamics was analyzed in a reduced, one-dimensional geometry. Here we introduce a mathematical model that accounts for the three-dimensional shape of the nucleoid, such that nucleoid-bound PomZ dimers can diffuse past the cluster without interacting with it. Using stochastic simulations, we find that the cluster still moves to and localizes at midcell. Redistribution of PomZ by diffusion in the cytosol is essential for this cluster dynamics. Our mechanism also positions two clusters equidistantly on the nucleoid. We conclude that a flux-based mechanism allows for cluster positioning in a biologically realistic three-dimensional cell geometry.
Understanding the mechanisms responsible for the formation and growth of FtsZ polymers and their subsequent formation of the $Z$-ring is important for gaining insight into the cell division in prokaryotic cells. In this work, we present a minimal stochastic model that qualitatively reproduces {\it in vitro} observations of polymerization, formation of dynamic contractile ring that is stable for a long time and depolymerization shown by FtsZ polymer filaments. In this stochastic model, we explore different mechanisms for ring breaking and hydrolysis. In addition to hydrolysis, which is known to regulate the dynamics of other tubulin polymers like microtubules, we find that the presence of the ring allows for an additional mechanism for regulating the dynamics of FtsZ polymers. Ring breaking dynamics in the presence of hydrolysis naturally induce rescue and catastrophe events in this model irrespective of the mechanism of hydrolysis.
Via a concomitant communication (the first part of my work), I have conclusively debunked the prevailing explanations for mitochondrial oxidative phosphorylation and established the need for a novel rationale to account for the reaction paradigm. Towards the same, murburn concept is hereby floated as a viable explanation (in the second part of my work). It is proposed that the inner mitochondrial membrane (harboring the various metal and flavin enzyme complexes) serves as means to confine and stabilize radical reactions, which effectively couple and bring about ATP synthesis in the proton-deficient microcosm. The proposed scheme is un-ordered and favored by Ockham's razor and evolutionary perspectives. Murburn concept is a paradigm-shift in biochemistry because it advocates that diffusible reactive (oxygen) species are mainstay of routine cellular metabolic process within the mitochondria.
Yoram Zarai, Michael Margaliot, Anatoly B. Kolomeisky
Natural phenomena frequently involve a very large number of interacting molecules moving in confined regions of space. Cellular transport by motor proteins is an example of such collective behavior. We derive a deterministic compartmental model for the unidirectional flow of particles along a one-dimensional lattice of sites with nearest-neighbor interactions between the particles. The flow between consecutive sites is governed by a soft simple exclusion principle and by attracting or repelling forces between neighboring particles. Using tools from contraction theory, we prove that the model admits a unique steady-state and that every trajectory converges to this steady-state. Analysis and simulations of the effect of the attracting and repelling forces on this steady-state highlight the crucial role that these forces may play in increasing the steady-state flow, and reveal that this increase stems from the alleviation of traffic jams along the lattice. Our theoretical analysis clarifies microscopic aspects of complex multi-particle dynamic processes.
During the lifecycle of a virus, viral proteins and other components self-assemble to form a symmetric protein shell called a capsid. This assembly process is subject to multiple competing constraints, including the need to form a thermostable shell while avoiding kinetic traps. It has been proposed that viral assembly satisfies these constraints through allosteric regulation, including the interconversion of capsid proteins among conformations with different propensities for assembly. In this article we use computational and theoretical modeling to explore how such allostery affects the assembly of icosahedral shells. We simulate assembly under a wide range of protein concentrations, protein binding affinities, and two different mechanisms of allosteric control. We find that, above a threshold strength of allosteric control, assembly becomes robust over a broad range of subunit binding affinities and concentrations, allowing the formation of highly thermostable capsids. Our results suggest that allostery can significantly shift the range of protein binding affinities that lead to successful assembly, and thus should be accounted for in models that are used to estimate interaction parameters from experimental data.
Adam J. M. Wollman, Aisha H. Syeda, Peter McGlynn
et al.
The method of action of many antibiotics is to interfere with DNA replication - quinolones trap DNA gyrase and topoisomerase proteins onto DNA while metronidazole causes single and double stranded breaks in DNA. To understand how bacteria respond to these drugs, it is important to understand the repair processes utilised when DNA replication is blocked. We have used tandem lac operators inserted into the chromosome bound by fluorescently labelled lac repressors as a model protein block to replication in E. coli. We have used dual-colour, alternating-laser, single-molecule narrowfield microscopy to quantify the amount of operator at the block and simultaneously image fluorescently labelled DNA polymerase. We anticipate use of this system as a quantitative platform to study replication stalling and repair proteins.
Claudia Cecchetto, Marta Maschietto, Pasquale Boccaccio
et al.
Theoretical and experimental evidences support the hypothesis that extremely low-frequency electromagnetic fields can affect voltage-gated channels. Little is known, however, about their effect on potassium channels. Kv1.3, a member of the voltage-gated potassium channels family originally discovered in the brain, is a key player in important biological processes including antigen-dependent activation of T-cells during the immune response. We report that Kv1.3 expressed in CHO-K1 cells can be modulated in cell subpopulations by extremely low frequency and relatively low intensity electromagnetic fields. In particular, we observed that field exposure can cause an enhancement of Kv1.3 potassium conductance and that the effect lasts for several minutes after field removal. The results contribute to put immune and nervous system responses to extremely low-frequency electromagnetic fields into a new perspective, with Kv1.3 playing a pivotal molecular role. Keywords: immunotherapy, immunomodulation, potassium channels, gating, electromagnetic fields
Thibault Lagache, Christian Sieben, Tim Meyer
et al.
Influenza viruses enter a cell via endocytosis after binding to the surface. During the endosomal journey, acidification triggers a conformational change of the virus spike protein hemagglutinin (HA) that results in escape of the viral genome from the endosome to the cytoplasm. A quantitative understanding of the processes involved in HA mediated fusion with the endosome is still missing. We develop here a stochastic model to estimate the change of conformation of HAs inside the endosome nanodomain. Using a Markov-jump process to model the arrival of protons to HA binding sites, we compute the kinetics of their accumulation and the mean first time for HAs to be activated. This analysis reveals that HA proton binding sites possess a high chemical barrier, ensuring a stability of the spike protein at sub-acidic pH. Finally, we predict that activating more than 3 adjacent HAs is necessary to prevent a premature fusion.
Anand Banerjee, Alexander Berzhkovskii, Ralph Nossal
Experiments show that cellular uptake of nanoparticles, via receptor-mediated endocytosis, strongly depends on nanoparticle size. There is an optimal size, approximately 50 nm in diameter, at which cellular uptake is the highest. In addition, there is a maximum size, approximately 200 nm, beyond which uptake via receptor-mediated endocytosis does not occur. By comparing results from different experiments, we found that these sizes weakly depend on the type of cells, nanoparticles, and ligands used in the experiments. Here, we argue that these observations are consequences of the energetics and assembly dynamics of the protein coat that forms on the cytoplasmic side of the outer cell membrane during receptor-mediated endocytosis. Specifically, we show that the energetics of coat formation imposes an upper bound on the size of the nanoparticles that can be internalized, whereas the nanoparticle-size-dependent dynamics of coat assembly results in the optimal nanoparticle size. The weak dependence of the optimal and maximum sizes on cell-nanoparticle-ligand type also follows naturally from our analysis.