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arXiv2014

Stepping and crowding of molecular motors: statistical kinetics from an exclusion process perspective

Motor enzymes are remarkable molecular machines that use the energy derived from the hydrolysis of a nucleoside triphosphate to generate mechanical movement, achieved through different steps that constitute their kinetic cycle. These macromolecules, nowadays investigated with advanced experimental techniques to unveil their molecular mechanisms and the properties of their kinetic cycles, are implicated in many biological processes, ranging from biopolymerisation (e.g. RNA polymerases and ribosomes) to intracellular transport (motor proteins such as kinesins or dyneins). Although the kinetics of individual motors is well studied on both theoretical and experimental grounds, the repercussions of their stepping cycle on the collective dynamics still remains unclear. Advances in this direction will improve our comprehension of transport process in the natural intracellular medium, where processive motor enzymes might operate in crowded conditions. In this work, we therefore extend the current statistical kinetic analysis to study collective transport phenomena of motors in terms of lattice gas models belonging to the exclusion process class. Via numerical simulations, we show how to interpret and use the randomness calculated from single particle trajectories in crowded conditions. Importantly, we also show that time fluctuations and non-Poissonian behavior are intrinsically related to spatial correlations and the emergence of large, but finite, clusters of co-moving motors. The properties unveiled by our analysis have important biological implications on the collective transport characteristics of processive motor enzymes in crowded conditions.

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arXiv2014

Residence times of receptors in dendritic spines analyzed by simulations in empirical domains

Analysis of high-density superresolution imaging of receptors reveal the organization of dendrites at the nano-scale resolution. We present here simulations in empirical live cell images, which allows converting local information extracted from short range trajectories into simulations of long range trajectories. Based on these empirical simulations, we compute the residence time of an AMPA receptor (AMPAR) in dendritic spines that accounts for receptors local interactions and geometrical organization. We report here that depending on the type of the spine, the residence time varies from one to five minutes. Moreover, we show that there exists transient organized structures, previously described as potential wells that can regulate the trafficking of AMPARs to dendritic spines.

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arXiv2014

The robustness of proofreading to crowding-induced pseudo-processivity in the MAPK pathway

Double phosphorylation of protein kinases is a common feature of signalling cascades. This motif may reduce cross-talk between signalling pathways, as the second phosphorylation site allows for proofreading, especially when phosphorylation is distributive rather than processive. Recent studies suggest that phosphorylation can be `pseudo-processive' in the crowded cellular environment, as rebinding after the first phosphorylation is enhanced by slow diffusion. Here, we use a simple model with unsaturated reactants to show that specificity for one substrate over another drops as rebinding increases and pseudo-processive behavior becomes possible. However, this loss of specificity with increased rebinding is typically also observed if two distinct enzyme species are required for phosphorylation, i.e. when the system is necessarily distributive. Thus the loss of specificity is due to an intrinsic reduction in selectivity with increased rebinding, which benefits inefficient reactions, rather than pseudo-processivity itself. We also show that proofreading can remain effective when the intended signalling pathway exhibits high levels of rebinding-induced pseudo-processivity, unlike other proposed advantages of the dual phosphorylation motif.

q-bio.MN↗

arXiv2014

Feedback Mechanism for Microtubule Length Regulation by Stathmin Gradients

We formulate and analyze a theoretical model for the regulation of microtubule (MT) polymerization dynamics by the signaling proteins Rac1 and stathmin. In cells, the MT growth rate is inhibited by cytosolic stathmin, which, in turn, is inactivated by Rac1. Growing MTs activate Rac1 at the cell edge, which closes a positive feedback loop. We investigate both tubulin sequestering and catastrophe promotion as mechanisms for MT growth inhibition by stathmin. For a homogeneous stathmin concentration in the absence of Rac1, we find a switch-like regulation of the MT mean length by stathmin. For constitutively active Rac1 at the cell edge, stathmin is deactivated locally, which establishes a spatial gradient of active stathmin. In this gradient, we find a stationary bimodal MT length distributions for both mechanisms of MT growth inhibition by stathmin. One subpopulation of the bimodal length distribution can be identified with fast growing and long pioneering MTs in the region near the cell edge, which have been observed experimentally. The feedback loop is closed through Rac1 activation by MTs. For tubulin sequestering by stathmin, this establishes a bistable switch with two stable states: one stable state corresponds to upregulated MT mean length and bimodal MT length distributions, i.e., pioneering MTs; the other stable state corresponds to an interrupted feedback with short MTs. Stochastic effects as well as external perturbations can trigger switching events. For catastrophe promoting stathmin we do not find bistability.

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arXiv2015

Quantifying protein diffusion and capture on filaments

The functional relevance of regulating proteins is often limited to specific binding sites such as the ends of microtubules or actin-filaments. A localization of proteins on these functional sites is of great importance. We present a quantitative theory for a diffusion and capture process, where proteins diffuse on a filament and stop diffusing when reaching the filament's end. It is found that end-association after one-dimensional diffusion is the main source for tip-localization of such proteins. As a consequence, diffusion and capture is highly efficient in enhancing the reaction velocity of enzymatic reactions, where proteins and filament ends are to each other as enzyme and substrate. We show that the reaction velocity can effectively be described within a Michaelis-Menten framework. Together one-dimensional diffusion and capture beats the (three-dimensional) Smoluchowski diffusion limit for the rate of protein association to filament ends.

physics.bio-ph↗

arXiv2016

Model for probing membrane-cortex adhesion by micropipette aspiration and fluctuation spectroscopy

We propose a model for membrane-cortex adhesion which couples membrane deformations, hydrodynamics and kinetics of membrane-cortex ligands. In its simplest form, the model gives explicit predictions for the critical pressure for membrane detachment and for the value of adhesion energy. We show that these quantities exhibit a significant dependence on the active acto-myosin stresses. The model provides a simple framework to access quantitative information on cortical activity by means of micropipette experiments. We also extend the model to incorporate fluctuations and show that detailed information on the stability of membrane-cortex coupling can be obtained by a combination of micropipette aspiration and fluctuation spectroscopy measurements.

physics.bio-ph↗

arXiv2016

Paradoxical signaling regulates structural plasticity in dendritic spines

Transient spine enlargement (3-5 min timescale) is an important event associated with the structural plasticity of dendritic spines. Many of the molecular mechanisms associated with transient spine enlargement have been identified experimentally. Here, we use a systems biology approach to construct a mathematical model of biochemical signaling and actin-mediated transient spine expansion in response to calcium-influx due to NMDA receptor activation. We have identified that a key feature of this signaling network is the paradoxical signaling loop. Paradoxical components act bifunctionally in signaling networks and their role is to control both the activation and inhibition of a desired response function (protein activity or spine volume). Using ordinary differential equation (ODE)-based modeling, we show that the dynamics of different regulators of transient spine expansion including CaMKII, RhoA, and Cdc42 and the spine volume can be described using paradoxical signaling loops. Our model is able to capture the experimentally observed dynamics of transient spine volume. Furthermore, we show that actin remodeling events provide a robustness to spine volume dynamics. We also generate experimentally testable predictions about the role of different components and parameters of the network on spine dynamics.

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arXiv2015

Molecular clustering digitizes signaling and increases fidelity

Many membrane-bound molecules in cells form small clusters. It has been hypothesized that these clusters convert an analog extracellular signal into a digital intracellular signal and that this conversion increases signaling fidelity. However, the mechanism by which clusters digitize a signal and the subsequent effects on fidelity remain poorly understood. Here we demonstrate using a stochastic model of cooperative cluster formation that sufficient cooperation leads to digital signaling. We show that despite reducing the number of output states, which decreases fidelity, digitization also reduces noise in the system, which increases fidelity. The tradeoff between these effects leads to an optimal cluster size that agrees with experimental measurements.

q-bio.MN↗

arXiv2016

Steric effects induce geometric remodeling of actin bundles in filopodia

Filopodia are ubiquitous fingerlike protrusions, spawned by many eukaryotic cells, to probe and interact with their environments. Polymerization dynamics of actin filaments, comprising the structural core of filopodia, largely determine their instantaneous lengths and overall lifetimes. The polymerization reactions at the filopodial tip require transport of G-actin, which enter the filopodial tube from the filopodial base and diffuse toward the filament barbed ends near the tip. Actin filaments are mechanically coupled into a tight bundle by cross-linker proteins. Interestingly, many of these proteins are relatively short, restricting the free diffusion of cytosolic G-actin throughout the bundle and, in particular, its penetration into the bundle core. To investigate the effect of steric restrictions on G-actin diffusion by the porous structure of filopodial actin filament bundle, we used a particle-based stochastic simulation approach. We discovered that excluded volume interactions result in partial and then full collapse of central filaments in the bundle, leading to a hollowed-out structure. The latter may further collapse radially due to the activity of cross-linking proteins, hence producing conical-shaped filament bundles. Interestingly, electron microscopy experiments on mature filopodia indeed frequently reveal actin bundles that are narrow at the tip and wider at the base. Overall, our work demonstrates that excluded volume effects in the context of reaction-diffusion processes in porous networks may lead to unexpected geometric growth patterns and complicated, history-dependent dynamics of intermediate metastable configurations.

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arXiv2016

Motor protein accumulation on antiparallel microtubule overlaps

Biopolymers serve as one-dimensional tracks on which motor proteins move to perform their biological roles. Motor protein phenomena have inspired theoretical models of one-dimensional transport, crowding, and jamming. Experiments studying the motion of Xklp1 motors on reconstituted antiparallel microtubule overlaps demonstrated that motors recruited to the overlap walk toward the plus end of individual microtubules and frequently switch between filaments. We study a model of this system that couples the totally asymmetric simple exclusion process (TASEP) for motor motion with switches between antiparallel filaments and binding kinetics. We determine steady-state motor density profiles for fixed-length overlaps using exact and approximate solutions of the continuum differential equations and compare to kinetic Monte Carlo simulations. Overlap motor density profiles and motor trajectories resemble experimental measurements. The phase diagram of the model is similar to the single-filament case for low switching rate, while for high switching rate we find a new low density-high density-low density-high density phase. The overlap center region, far from the overlap ends, has a constant motor density as one would naively expect. However, rather than following a simple binding equilibrium, the center motor density depends on total overlap length, motor speed, and motor switching rate. The size of the crowded boundary layer near the overlap ends is also dependent on the overlap length and switching rate in addition to the motor speed and bulk concentration. The antiparallel microtubule overlap geometry may offer a previously unrecognized mechanism for biological regulation of protein concentration and consequent activity.

physics.bio-ph↗

arXiv2016

Microtubule Defects Influence Kinesin-Based Transport In Vitro

Microtubules are protein polymers that form "molecular highways" for long-range transport within living cells. Molecular motors actively step along microtubules to shuttle cellular materials between the nucleus and the cell periphery; this transport is critical for the survival and health of all eukaryotic cells. Structural defects in microtubules exist, but whether these defects impact molecular motor-based transport remains unknown. Here, we report a new, to our knowledge, approach that allowed us to directly investigate the impact of such defects. Using a modified optical-trapping method, we examined the group function of a major molecular motor, conventional kinesin, when transporting cargos along individual microtubules. We found that microtubule defects influence kinesin-based transport in vitro. The effects depend on motor number: cargos driven by a few motors tended to unbind prematurely from the microtubule, whereas cargos driven by more motors tended to pause. To our knowledge, our study provides the first direct link between microtubule defects and kinesin function. The effects uncovered in our study may have physiological relevance in vivo.

q-bio.BM↗

arXiv2016

A Computational Model of YAP/TAZ Mechanosensing

In cell proliferation, stem cell differentiation, chemoresistance and tissue organization, the ubiquitous role of YAP/TAZ continues to impact our fundamental understanding in numerous physiological and disease systems. YAP/TAZ is an important signaling nexus integrating diverse mechanical and biochemical signals, such as ECM stiffness, adhesion ligand density, or cell-cell contacts, and thus strongly influences cell fate. Recent studies show that YAP/TAZ mechanical sensing is dependent on RhoA-regulated stress fibers. However, current understanding of YAP/TAZ still remains limited due to the unknown interaction between the canonical Hippo pathway and cell tension. To identify the roles of key signaling molecules in mechanical signal sensing and transduction, we present a novel computational model of the YAP/TAZ signaling pathway. This model converts ECM mechanical properties to biochemical signals via adhesion, and integrates intracellular signaling cascades associated with cytoskeleton dynamics. Adhesion molecules, such as FAK, are predicted to rescue YAP/TAZ activity in soft environments via the RhoA pathway. We found that changes of molecule concentrations result in different pattern of YAP/TAZ stiffness response. We also investigate the sensitivity of YAP/TAZ activity to ECM stiffness. In addition, the model shows that the unresolved synergistic effect of YAP/TAZ activity between the mechanosensing and the Hippo pathways can be explained by the interaction of LIMK and LATS. Overall, our model provides a novel platform for studying YAP/TAZ activity in the context of integrating different signaling pathways. This platform can be used to gain new fundamental insights into roles of key molecular and mechanical regulators on development, tissue engineering or tumor progression.

physics.bio-ph↗

arXiv2016

Quantitative Determination of the Probability of Multiple-Motor Transport in Bead-Based Assays

With their longest dimension typically being less than 100 nm, molecular motors are significantly below the optical-resolution limit. Despite substantial advances in fluorescence-based imaging methodologies, labeling with beads remains critical for optical-trapping-based investigations of molecular motors. A key experimental challenge in bead-based assays is that the number of motors on a bead is not well defined. Particularly for single-molecule investigations, the probability of single versus multiple-motor events has not been experimentally investigated. Here, we used bead travel distance as an indicator of multiple-motor transport and determined the lower-bound probability of bead transport by two or more motors. We limited the ATP concentration to increase our detection sensitivity for multiple- versus single-kinesin transport. Surprisingly, for all but the lowest motor number examined, our measurements exceeded estimations of a previous model by R2-fold. To bridge this apparent gap between theory and experiment, we derived a closed-form expression for the probability of bead transport by multiple motors, and constrained the only free parameter in this model using our experimental measurements. Our data indicate that kinesin extends to ~57 nm during bead transport, suggesting that kinesin exploits its conformational flexibility to interact with microtubules at highly curved interfaces such as those present for vesicle transport in cells. To our knowledge, our findings provide the first experimentally constrained guide for estimating the probability of multiple-motor transport in optical trapping studies. The experimental approach utilized here (limiting ATP concentration) may be generally applicable to studies in which molecular motors are labeled with cargos that are artificial or are purified from cellular extracts.

q-bio.BM↗

arXiv2015

The Limiting Speed of the Bacterial Flagellar Motor

Recent experiments on the bacterial flagellar motor have shown that the structure of this nanomachine, which drives locomotion in a wide range of bacterial species, is more dynamic than previously believed. Specifically, the number of active torque-generating units (stators) was shown to vary across applied loads. This finding invalidates the experimental evidence reporting that limiting (zero-torque) speed is independent of the number of active stators. Here, we propose that, contrary to previous assumptions, the maximum speed of the motor is not universal, but rather increases as additional torque-generators are recruited. This result arises from our assumption that stators disengage from the motor for a significant portion of their mechanochemical cycles at low loads. We show that this assumption is consistent with current experimental evidence and consolidate our predictions with arguments that a processive motor must have a high duty ratio at high loads.

physics.bio-ph↗

arXiv2016

Contributions of microtubule dynamic instability and rotational diffusion to kinetochore capture

Microtubule dynamic instability allows search and capture of kinetochores during spindle formation, an important process for accurate chromosome segregation during cell division. Recent work has found that microtubule rotational diffusion about minus-end attachment points contributes to kinetochore capture in fission yeast, but the relative contributions of dynamic instability and rotational diffusion are not well understood. We have developed a biophysical model of kinetochore capture in small fission-yeast nuclei using hybrid Brownian dynamics/kinetic Monte Carlo simulation techniques. With this model, we have studied the importance of dynamic instability and microtubule rotational diffusion for kinetochore capture, both to the lateral surface of a microtubule and at or near its end. Over a range of biologically relevant parameters, microtubule rotational diffusion decreased capture time, but made a relatively small contribution compared to dynamic instability. At most, rotational diffusion reduced capture time by 25%. Our results suggest that while microtubule rotational diffusion can speed up kinetochore capture, it is unlikely to be the dominant physical mechanism. In addition, we found that when microtubules undergo dynamic instability, lateral captures predominate even in the absence of rotational diffusion. Counterintuitively, adding rotational diffusion to a dynamic microtubule increases the probability of end-on capture.

physics.bio-ph↗

arXiv2016

The mitotic spindle in the one-cell C. elegans embryo is positioned with high precision and stability

Precise positioning of the mitotic spindle is important for specifying the plane of cell division, which in turn determines how the cytoplasmic contents are partitioned into the daughter cells, and how the daughters are positioned within the tissue. During metaphase in the early C. elegans embryo, the spindle is aligned and centered on the anterior-posterior axis by a microtubule-dependent machinery that exerts restoring forces when the spindle is displaced from the center. To investigate the accuracy and stability of centering, we tracked the position and orientation of the mitotic spindle during the first cell division with high temporal and spatial resolution. We found that the precision is remarkably high: the cell-to-cell variation in the transverse position of the center of the spindle during metaphase, as measured by the standard deviation, was only 1.5% of the length of the short axis of the cell. Spindle position is also very stable: the standard deviation of the fluctuations in transverse spindle position during metaphase was only 0.5% of the short axis of the cell. Assuming that stability is limited by fluctuations in the number of independent motor elements such as microtubules or dyneins underlying the centering machinery, we infer that the number is on the order of one thousand, consistent with the several thousand of astral microtubules in these cells. Astral microtubules grow out from the two spindle poles, make contact with the cell cortex, and then shrink back shortly thereafter. The high stability of centering can be accounted for quantitatively if, while making contact with the cortex, the astral microtubules buckle as they exert compressive, pushing forces. We thus propose that the large number of microtubules in the asters provides a highly precise mechanism for positioning the spindle during metaphase while assembly is completed prior to the onset of anaphase.

q-bio.SC↗

arXiv2016

Quantifying the Heat Dissipation from a Molecular Motor's Transport Properties in Nonequilibrium Steady States

Theoretical analysis, which maps single molecule time trajectories of a molecular motor onto unicyclic Markov processes, allows us to evaluate the heat dissipated from the motor and to elucidate its dependence on the mean velocity and diffusivity. Unlike passive Brownian particles in equilibrium, the velocity and diffusion constant of molecular motors are closely inter-related to each other. In particular, our study makes it clear that the increase of diffusivity with the heat production is a natural outcome of active particles, which is reminiscent of the recent experimental premise that the diffusion of an exothermic enzyme is enhanced by the heat released from its own catalytic turnover. Compared with freely diffusing exothermic enzymes, kinesin-1 whose dynamics is confined on one-dimensional tracks is highly efficient in transforming conformational fluctuations into a locally directed motion, thus displaying a significantly higher enhancement in diffusivity with its turnover rate. Putting molecular motors and freely diffusing enzymes on an equal footing, our study offers thermodynamic basis to understand the heat enhanced self-diffusion of exothermic enzymes.

q-bio.SC↗

arXiv2016

Small-volume effect enables the spine robust, sensitive and efficient information transfer

Why is the spine of a neuron so small that only small numbers of molecules can exist and reactions inevitably become stochastic? Despite such noisy conditions, we previously showed that the spine exhibits robust, sensitive and efficient features of information transfer using probability of Ca$^{2+}$ increase; however, their mechanisms remains unknown. Here we show that the small-volume effect enables robust, sensitive and efficient information transfer in the spine volume, but not in the cell volume. In the spine volume, intrinsic noise in reactions becomes larger than extrinsic noise of input, making robust information transfer against input fluctuation. Stochastic facilitation of Ca$^{2+}$ increase occurs in the spine volume, making higher sensitivity to lower intensity of input. Volume-dependency of information transfer enables efficient information transfer per input in the spine volume. Thus, we propose that the small-volume effect is the functional reasons why the spine has to be so small.

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