Intra-cellular traffic: bio-molecular motors on filamentary tracks
Debashish Chowdhury, Aakash Basu, Ashok Garai, Philip Greulich, Katsuhiro Nishinari, Andreas Schadschneider, Tripti Tripathi
备注：
9 pages, 11 figures; Based on the invited talk delivered by the first author (DC) at the IUPAP International Conference STATPHYS23, Genoa (Italy), July, 2007
发表信息：
European Physical Journal B, vol. 64, p. 593 (2008).
Molecular motors are macromolecular complexes which use some form of input energy to perform mechanical work. The filamentary tracks, on which these motors move, are made of either proteins (e.g., microtubules) or nucleic acids (DNA or RNA). Often, many such motors move simultaneously on the same track and their collective properties have superficial similarities with vehicular traffic on highways. The models we have developed provide ``unified'' description: in the low-density limit, a model captures the transport properties of a single motor while, at higher densities the same model accounts for the collective spatio-temporal organization of interacting motors. By drawing analogy with vehicular traffic, we have introduced novel quantities for characterizing the nature of the spatio-temporal organization of molecular motors on their tracks. We show how the traffic-like intracellular collective phenomena depend on the mechano-chemistry of the corresponding individual motors.
Understanding the operation of biological molecular motors, nanoscale machines that transduce electrochemical energy into mechanical work, is enhanced by bottom-up strategies to synthesize novel motors.
Regulating physical size is an essential problem that biological organisms must solve from the subcellular to the organismal scales, but it is not well understood what physical principles and mechanisms organisms use to sense and regulate their size. Any biophysical size-regulation scheme operates in a noisy environment and must be robust to other cellular dynamics and fluctuations. This work develops theory of filament length regulation inspired by recent experiments on kinesin-8 motor proteins, which move with directional bias on microtubule filaments and alter microtubule dynamics. Purified…
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 o…
We study the mechanical and thermodynamic properties of different traffic models for kinesin which are relevant in biological and experimental contexts. We find that motor-motor interactions play a fundamental role by enhancing the thermodynamic efficiency at maximum power of the motors, as compared to the non-interacting system, in a wide range of biologically compatible scenarios. We furthermore consider the case where the motor-motor interaction directly affects the internal chemical cycle and investigate the effect on the system dynamics and thermodynamics.
We introduce a two-species exclusion model to describe the key features of the conflict between the RNA polymerase (RNAP) motor traffic, engaged in the transcription of a segment of DNA, concomitant with the progress of two DNA replication forks on the same DNA segment. One of the species of particles ($P$) represents RNAP motors while the other ($R$) represents replication forks. Motivated by the biological phenomena that this model is intended to capture, a maximum of only two $R$ particles are allowed to enter the lattice from two opposite ends whereas the unrestricted number of $P$ particl…
The mechanical properties of the cell depend crucially on the tension of its cytoskeleton, a biopolymer network that is put under stress by active motor proteins. While the fibrous nature of the network is known to strongly affect the transmission of these forces to the cellular scale, our understanding of this process remains incomplete. Here we investigate the transmission of forces through the network at the individual filament level, and show that active forces can be geometrically amplified as a transverse motor-generated force force "plucks" the fiber and induces a nonlinear tension. In …
Molecular motors play pivotal roles in organizing the interior of cells. A motor efficient in cargo transport would move along cytoskeletal filaments with a high speed and a minimal error in transport distance (or time) while consuming a minimal amount of energy. The travel distance of the motor and its variance are, however, physically constrained by the free energy being consumed. A recently formulated \emph{thermodynamic uncertainty relation} offers a theoretical framework for the energy-accuracy trade-off relation ubiquitous in biological processes. According to the relation, a measure $\m…
We experimentally showed that biological molecular motor F$_1$-ATPase (F$_1$) implements an optimal rectification mechanism. F$_1$ hardly suppresses adenosine triphosphate (ATP) synthesis, which is the F$_1$'s physiological role while inhibiting unfavorable hydrolysis of ATP. This optimal rectification is a high contrast to a simple ratchet model, where the inhibition of the backward current is inevitably accompanied by the suppression of the forward current. The detailed analysis of single-molecule trajectories demonstrated a novel but simple rectification mechanism of F$_1$ with parallel lan…
Molecular motors do not work in isolation {\it in-vivo}. We highlight some of the coordinations, cooperations and competitions that determine the collective properties of molecular motors in eukaryotic cells. In the context of traffic-like movement of motors on a track, we emphasize the importance of single-motor bio-chemical cycle and enzymatic activity on their collective spatio-temporal organisation. Our modelling strategy is based on a synthesis- the same model describes the single-motor mechano-chemistry at sufficiently low densities whereas at higher densities it accounts for the collect…
Linear bio-molecular motors move unidirectionally along a track by coordinating several different processes, such as fuel (ATP) capture, hydrolysis, conformational changes, binding and unbinding from a track, and center-of-mass diffusion. A better understanding of the interdependencies between these processes, which take place over a wide range of different time scales, would help elucidate the general operational principles of molecular motors. Artificial molecular motors present a unique opportunity for such a study because motor structure and function are a priori known. Here we describe us…
Traffic-like collective movements are observed at almost all levels of biological systems. Molecular motor proteins like, for example, kinesin and dynein, which are the vehicles of almost all intra-cellular transport in eukayotic cells, sometimes encounter traffic jam that manifests as a disease of the organism. Similarly, traffic jam of collagenase MMP-1, which moves on the collagen fibrils of the extracellular matrix of vertebrates, has also been observed in recent experiments. Traffic-like movements of social insects like ants and termites on trails are, perhaps, more familiar in our everyd…
We have studied the elastic response of actin networks with both compliant and rigid crosslinks by modeling molecular motors as force dipoles. Our finite element simulations show that for compliant crosslinkers such as filamin A, the network can be stiffened by two orders of magnitude while stiffening achieved with incompliant linkers such as scruin is significantly smaller, typically a factor of two, in excellent agreement with recent experiments. We show that the differences arise from the fact that the motors are able to stretch the compliant crosslinks to the fullest possible extent, which…
Efficient capture and detection of minute amount of deoxyribonucleic acid (DNA) molecules are pivotal for an array of modern gene technologies which are widely utilized in medical, forensic and defense applications, including DNA extraction, preconcentration, and separation. In this work, we propose a rational mechanism to substantially accelerate the capture and detection efficiency of DNA molecules by actively motorizing designed Raman microsensors. At least 4-fold enhancement has been achieved on the microsensors rotating at 1200 rpm. The process is monitored dynamically and in-situ from th…
Biomolecular systems like molecular motors or pumps, transcription and translation machinery, and other enzymatic reactions can be described as Markov processes on a suitable network. We show quite generally that in a steady state the dispersion of observables like the number of consumed/produced molecules or the number of steps of a motor is constrained by the thermodynamic cost of generating it. An uncertainty $ε$ requires at least a cost of $2k_BT/ε^2$ independent of the time required to generate the output.
This paper describes a design of a molecular propagation system in molecular communication. Molecular communication is a new communication paradigm where biological and artificially-created nanomachines communicate over a short distance using molecules. A molecular propagation system in molecular communication directionally transports molecules from a sender to a receiver. In the design described in this paper, protein filaments glide over immobilized motor proteins along preconfigured microlithographic tracks, and the gliding protein filaments carry and transport molecules from a sender to a …
Autonomous oscillations in biological systems may have a biochemical origin or result from an interplay between force-generating and visco-elastic elements. In molecular motor assemblies the force-generating elements are molecular engines and the visco-elastic elements are stiff cytoskeletal polymers. The physical mechanism leading to oscillations depends on the particular architecture of the assembly. Existing models can be grouped into two distinct categories: systems with a delayed force activation and anomalous force-velocity relations. We discuss these systems within phase plane analysis …
Traffic-like collective movements are observed at almost all levels of biological systems. Molecular motor proteins like, for example, kinesin and dynein, which are the vehicles of almost all intra-cellular transport in eukayotic cells, sometimes encounter traffic jam that manifests as a disease of the organism. Similarly, traffic jam of collagenase MMP-1, which moves on the collagen fibrils of the extracellular matrix of vertebrates, has also been observed in recent experiments. Traffic-like movements of social insects like ants and termites on trails are, perhaps, more familiar in our everyd…
Molecular motors are essential components for the biophysical functions of the cell. Our current quantitative understanding of how multiple motors move along a single track is not complete; even though models and theories for single motor chemomechanics abound. Recently, M.J.I. M$\ddot{\rm u}$ller {\em et al.} have developed a tug-of-war model to describe the bidirectional movement of the cargo (PNAS(2008) 105(12) P4609-4614). Through Monte Carlo simulations, they discovered that the tug-of-war model exhibits several qualitative different motility regimes, which depend on the precise value of …
In cells and in vitro assays the number of motor proteins involved in biological transport processes is far from being unlimited. The cytoskeletal binding sites are in contact with the same finite reservoir of motors (either the cytosol or the flow chamber) and hence compete for recruiting the available motors, potentially depleting the reservoir and affecting cytoskeletal transport. In this work we provide a theoretical framework to study, analytically and numerically, how motor density profiles and crowding along cytoskeletal filaments depend on the competition of motors for their binding si…
The transportation of the cargoes in biological cells is primarily driven by the motor proteins on filamentous protein tracks. The stochastic nature of the motion of motor protein often leads to its spontaneous detachment from the track. Using the available experimental data, we demonstrate a tradeoff between the speed of the motor and its rate of spontaneous detachment from the track. Further, it is also shown that this speed-detachment relation follows a power law where its exponent dictates the nature of the motor protein processivity. We utilize this information to study the motion of moto…
Recent experiments reveal both passive subdiffusion of various nanoparticles and anomalous active transport of such particles by molecular motors in the molecularly crowded environment of living biological cells. Passive and active microrheology reveals that the origin of this anomalous dynamics is due to the viscoelasticity of the intracellular fluid. How do molecular motors perform in such a highly viscous, dissipative environment? Can we explain the observed co-existence of the anomalous transport of relatively large particles of 100 to 500 nm in size by kinesin motors with the normal trans…
We propose a biochemical model providing the kinetic and energetic descriptions of the processivity dynamics of kinesin and dinein molecular motors. Our approach is a modified version of a well known model describing kinesin dynamics and considers the presence of a competitive inhibition reaction by ADP. We first reconstruct a continuous free-energy landscape of the cycle catalyst process that allows us to calculate the number of steps given by a single molecular motor. Then, we calculate an analytical expression associated to the translational velocity and the stopping time of the molecular m…
Biological functions in each animal cell depend on coordinated operations of a wide variety of molecular motors. Some of the these motors transport cargo to their respective destinations whereas some others are mobile workshops which synthesize macromolecules while moving on their tracks. Some other motors are designed to function as packers and movers. All these motors require input energy for performing their mechanical works and operate under conditions far from thermodynamic equilibrium. The typical size of these motors and the forces they generate are of the order of nano-meters and pico-…
We review the properties of biological motor proteins which move along linear filaments that are polar and periodic. The physics of the operation of such motors can be described by simple stochastic models which are coupled to a chemical reaction. We analyze the essential features of force and motion generation and discuss the general properties of single motors in the framework of two-state models. Systems which contain large numbers of motors such as muscles and flagella motivate the study of many interacting motors within the framework of simple models. In this case, collective effects can …
The cytoskeleton in eukaryotic cells plays several crucial roles. In terms of intracellular transport, motor proteins use the cytoskeletal filaments as a backbone along which they can actively transport biological cargos such as vesicles carrying biochemical reactants. Crossings between such filaments constitute a key element, as they may serve to alter the destination of such payload. Although motor proteins are known to display a rich behaviour at such crossings, the latter have so far only been modelled as simple branching points. Here we explore a model for a crossing between two microtubu…
We investigate the efficiency of systems of molecular motors operating at maximum power. We consider two models of kinesin motors on a microtubule: for both the simplified and the detailed model, we find that the many-body exclusion effect enhances the efficiency at maximum power of the many-motor system, with respect to the single motor case. Remarkably, we find that this effect occurs in a limited region of the system parameters, compatible with the biologically relevant range.
We describe a system of stochastic differential equations (SDEs) which model the interaction between processive molecular motors, such as kinesin and dynein, and the biomolecular cargo they tow as part of microtubule-based intracellular transport. We show that the classical experimental environment fits within a parameter regime which is qualitatively distinct from conditions one expects to find in living cells. Through an asymptotic analysis of our system of SDEs, we develop a means for applying in vitro observations of the nonlinear response by motors to forces induced on the attached cargo …
We have developed a two dimensional stochastic molecular dynamics model for the description of intra cellular collective motion of bio motors, in particular Kinesins, on a microtubular track. The model is capable or reproducing the hand-over-hand mechanism of the directed motion along the microtubule. The model gives the average directed velocity and the current of Kinesins along the microtubule. It is shown that beyond a certain density of Kinesins, the average velocity and current undergo notable decrease which is due to formation of traffic jams in the system.
One of the causes of high fidelity of copying in biological systems is kinetic discrimination. In this mechanism larger dissipation and copying velocity result in improved copying accuracy. We consider a model of a polymerase which simultaneously copies a single stranded RNA and opens a single- to double-stranded junction serving as an obstacle. The presence of the obstacle slows down the motor, resulting in a change of its fidelity, which can be used to gain information about the motor and junction dynamics. We find that the motor's fidelity does not depend on details of the motor-junction in…
Many biological processes involve the action of molecular motors that interact with the cell cytoskeleton. Some processes, such as the transport of cargoes is achieved mainly by the action of individual motors. Other, such as cell motility and division, require the cooperative work of many motors. Collective motor dynamics can be quite complex and unexpected. One beautiful example is the bidirectional ("back and forth") motion of filaments which is induced when the motors within a group exert forces in opposite directions. This review tackles the puzzle emerging from a recent experimental work…
Bacteria can adjust the structure of colonies and biofilms to enhance their survival rate under external stress. Here, we explore the link between bacterial interaction forces and colony structure. We show that the activity of extracellular pilus motors enhances local ordering and accelerates fusion dynamics of bacterial colonies. The radial distribution function of mature colonies shows local fluid-like order. The degree and dynamics of ordering are dependent on motor activity. At a larger scale, the fusion dynamics of two colonies shows liquid-like behavior whereby motor activity strongly af…
We analyze the collective behavior of hydrodynamically coupled molecular motors. We show that the local fluxes induced by motors displacement can induce the experimentally observed bidirectional motion of cargoes and vesicles. By means of a mean--field approach we show that sustained oscillations as well as bistable collective motor motion arise even for very large collection of motors, when thermal noise is irrelevant. The analysis clarifies the physical mechanisms responsible for such dynamics by identifying the relevant coupling parameter and its dependence on the geometry of the hydrodynam…
Reconstituted filamentous actin networks with myosin motor proteins form active gels, in which motor proteins generate forces that drive the network far from equilibrium. This motor activity can also strongly affect the network elasticity; experiments have shown a dramatic stiffening in in vitro networks with molecular motors. Here we study the effects of motor generated forces on the mechanics of simulated 2D networks of athermal stiff filaments. We show how heterogeneous internal motor stresses can lead to stiffening in networks that are governed by filament bending modes. The motors are mod…
As a complementary tool to nanofluidics, biomolecular based transport is envisioned for nanotechnological devices. We report a new method for guiding microtubule shuttles on multi-walled carbon nanotube tracks, aligned by dielectrophoresis on a functionalized surface. In the absence of electric field and in fluid flow, alignment is maintained. The directed translocation of kinesin propelled microtubules has been investigated using fluorescence microscopy. To our knowledge, this is the first demonstration of microtubules gliding along carbon nanotubes.
Micro/nano-scale propulsion has attracted considerable recent attention due to its promise for biomedical applications such as targeted drug delivery. In this paper, we report on a new experimental design and theoretical modelling of high-speed fuel-free magnetically-driven propellers which exploit the flexibility of nanowires for propulsion. These readily prepared nanomotors display both high dimensional propulsion velocities (up to ~ 21 micrometer per second) and dimensionless speeds (in body lengths per revolution) when compared with natural microorganisms and other artificial propellers. T…
The cytoskeleton -- a collection of polymeric filaments, molecular motors, and crosslinkers -- is a foundational example of active matter, and in the cell assembles into organelles that guide basic biological functions. Simulation of cytoskeletal assemblies is an important tool for modeling cellular processes and understanding their surprising material properties. Here we present aLENS, a novel computational framework to surmount the limits of conventional simulation methods. We model molecular motors with crosslinking kinetics that adhere to a thermodynamic energy landscape, and integrate the…
The motion of molecular motor is essential to the biophysical functioning of living cells. In principle, this motion can be regraded as a multiple chemical states process. In which, the molecular motor can jump between different chemical states, and in each chemical state, the motor moves forward or backward in a corresponding potential. So, mathematically, the motion of molecular motor can be described by several coupled one-dimensional hopping models or by several coupled Fokker-Planck equations. To know the basic properties of molecular motor, in this paper, we will give detailed analysis a…
Hepatitis C virus helicase is a molecular motor that splits nucleic acid duplex structures during viral replication, therefore representing a promising target for antiviral treatment. Hence, a detailed understanding of the mechanism by which it operates would facilitate the development of efficient drug-assisted therapies aiming to inhibit helicase activity. Despite extensive investigations performed in the past, a thorough understanding of the activity of this important protein was lacking since the underlying internal conformational motions could not be resolved. Here we review investigation…
We present a model of an ATP-fueled molecular machine which push a polymer through a pore channel. The machine acts between two levels (working-waiting), and the working one remains active for a fixed time giving a constant force. The machine activation rate can be put in relationship with the available ATP concentration in the solution, which gives the necessary energy supply. The translocation time shows a monotonic behavior as a function of the activation frequency and the velocity follows a Michaelis-Menten law that arises naturally in this description. The estimation of the stall force of…
Evaporation-Induced Pattern Formation and Wetting in Active Microtubule-Kinesin Droplets
Harvard University（哈佛大学）；Max Planck Institute for Dynamics and Self-Organization（马克斯·普朗克动力学与自组织研究所）；University of Surrey（萨里大学）；Universität Konstanz（康斯坦茨大学）
Transport of molecular motors along protein filaments in a half-closed geometry is a common feature of biologically relevant processes in cellular protrusions. Using a lattice gas model we study how the interplay between active and diffusive transport and mass conservation leads to localised domain walls and tip localisation of the motors. We identify a mechanism for task sharing between the active motors (maintaining a gradient) and the diffusive motion (transport to the tip), which ensures that energy consumption is low and motor exchange mostly happens at the tip. These features are attribu…
Cells accomplish diverse functions using the same molecular building blocks, from setting up cytoplasmic flows to generating mechanical forces. In particular, transitions between these non-equilibrium states are triggered by regulating the expression and activity of cytoskeletal proteins. However, how these proteins set the large-scale mechanics of the cytoskeleton and drive such non-equilibrium phase transitions remain poorly understood. Here, we show that a minimal network of biopolymers, molecular motors, and crosslinkers exhibits two distinct emergent behaviors depending on its composition…
