Motor enzymes catalyze chemical reactions, like the hydrolysis of ATP, and in the process they also perform work. Recent studies indicate that motor enzymes perform work with specific intermediate steps in their catalyzed reactions, challenging the classic view (in Brownian motor models) that work can only be performed within biochemical states. An alternative class of models (chemical motor models) has emerged in which motors perform work with biochemical transitions, but many of these models lack a solid physicochemical foundation. In this paper, I develop a self consistent framework for chemical motor models. This novel framework accommodates multiple pathways for free energy transfer, predicts rich behaviors from the simplest multi motor systems, and provides important new insights into muscle and motor function.
We examine the dependence of the physical quantities of the rotatory molecular motor, such as the rotation velocity and the proton translocation rate, on the chemical reaction rate using the model based only on diffusion process. A peculiar behavior of proton translocation is found and the energy transduction efficiency of the motor protein is enhanced by this behavior. We give a natural explanation that this behavior is universal when certain inequalities between chemical reaction rates hold. That may give a clue to examine whether the motion of the molecular motor is dominated by diffusion p…
We have developed a novel method to evaluate the potential profile of a molecular motor at each chemical state from only the probe's trajectory and applied it to a rotary molecular motor F$_1$-ATPase. By using this method, we could also obtain the information regarding the mechanochemical coupling and energetics. We demonstrate that the position-dependent transition of the chemical states is the key feature for the highly efficient free-energy transduction by F$_1$-ATPase.
This note presents a self-contained and streamlined exposition of chemical-network results due to Feinberg, Horn, and Jackson. As an application, it shows the global asymptotic stability to equilibria of McKeithan's kinetic proofreading model for T-cell receptor signal transduction.
Recent experiments demonstrate that molecular motors from the Myosin II family serve as cross-links inducing active tension in the cytoskeletal network. Here we revise the Brownian ratchet model, previously studied in the context of active transport along polymer tracks, in setups resembling a motor in a polymer network, also taking into account the effect of electrostatic changes in the motor heads. We explore important mechanical quantities and show that such a model is also capable of mechanosensing. Finally, we introduce a novel efficiency based on excess heat production by the chemical cy…
Cells can be considered as systems that utilize changes in thermodynamic entropy as information. Therefore, they serve as useful models for investigating the relationships between entropy production and information transmission, i.e., signal transduction. Based on the hypothesis that cells apply a chemical reaction cascade for the most efficient transduction of information, we adopted a coding design that minimizes the number of bits per concentration of molecules that are employed for information transduction. As a result, the average rate of entropy production is uniform across all cycles in…
The pump process of the ratchet model inspired by the $F_o$ rotatory motor of ATP synthase is investigated. In this model there are two kinds of characteristic time. One is dynamical, the relaxation time of the system. Others are chemical, the chemical reaction rates at which a proton binds to or dissociates from the motor protein. The inequalities between them affect the behavior of the physical quantities, such as the rotation velocity and the proton pumping rates across the membrane. The energy transduction efficiency is calculated and the condition under which the efficiency can become hig…
We study the energetics of isothermal ratchets which are driven by a chemical reaction between two states and operate in contact with a single heat bath of constant temperature. We discuss generic aspects of energy transduction such as Onsager relations in the linear response regime as well as the efficiency and dissipation close to and far from equilibrium. In the linear response regime where the system operates reversibly the efficiency is in general nonzero. Studying the properties for specific examples of energy landscapes and transitions, we observe in the linear response regime that the …
We study the ensemble velocity of non-processive motor proteins, described with multiple chemical states. In particular, we discuss the velocity as a function of ATP concentration. Even a simple model which neglects the strain-dependence of transition rates, reverse transition rates and nonlinearities in the elasticity can show interesting functional dependencies, which deviate significantly from the frequently assumed Michaelis-Menten form. We discuss how the oder of events in the duty cycle can be inferred from the measured dependence. The model also predicts the possibility of velocity reve…
In living cells, molecular motors convert chemical energy into mechanical work. Its thermodynamic energy efficiency, i.e. the ratio of output mechanical work to input chemical energy, is usually high. However, using two-state models, we found the motion of molecular motors is loosely coupled to the chemical cycle. Only part of the input energy can be converted into mechanical work. Others is dissipated into environment during substeps without contributions to the macro scale unidirectional movement.
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…
Molecular motors convert chemical energy derived from the hydrolysis of ATP into mechanical energy. A well-studied model of a molecular motor is the flashing ratchet model. We show that this model exhibits a fluctuation relation known as the Gallavotti-Cohen symmetry. Our study highlights the fact that the symmetry is present only if the chemical and mechanical degrees of freedom are both included in the description.
A molecular motor is made of either a single macromolecule or a macromolecular complex. Just like their macroscopic counterparts, molecular motors "transduce" input energy into mechanical work. All the nano-motors considered here operate under isothermal conditions far from equilibrium. Moreover, one of the possible mechanisms of energy transduction, called Brownian ratchet, does not even have any macroscopic counterpart. But, molecular motor is not synonymous with Brownian ratchet; a large number of molecular motors execute a noisy power stroke, rather than operating as Brownian ratchet. We r…
Molecular motors transduce chemical energy obtained from hydrolizing ATP into mechanical work exerted against an external force. We calculate their efficiency at maximum power output for two simple generic models and show that the qualitative behaviour depends crucially on the position of the transition state. Specifically, we find a transition state near the initial state (sometimes characterized as a "power stroke") to be most favorable with respect to both high power output and high efficiency at maximum power. In this regime, driving the motor further out of equilibrium by applying higher …
Bacterial motility, and in particular repulsion or attraction towards specific chemicals, has been a subject of investigation for over 100 years, resulting in detailed understanding of bacterial chemotaxis and the corresponding sensory network in many bacterial species. For Escherichia coli most of the current understanding comes from the experiments with low levels of chemotactically-active ligands. However, chemotactically-inactive chemical species at concentrations found in the human gastrointestinal tract produce significant changes in E. coli's osmotic pressure, and have been shown to lea…
Molecular motors drive mechanical motions utilizing the free energy liberated from chemical reactions such as ATP hydrolysis. Although it is essential to know the efficiency of this free energy transduction, it has been a challenge due to the system's microscopic scale. Here, we evaluate the single-molecule energetics of a rotary molecular motor, F1-ATPase, by applying a recently derived nonequilibrium equality together with an electrorotation method. We show that the sum of the heat flow through the probe's rotational degree of freedom and the work against external load is almost equal to the…
In eukaryotic cells, many motor proteins can move simultaneously on a single microtubule track. This leads to interesting collective phenomena like jamming. Recently we reported ({\it Phys. Rev. Lett. {\bf 95}, 118101 (2005)}) a lattice-gas model which describes traffic of unconventional (single-headed) kinesins KIF1A. Here we generalize this model, introducing a novel interaction parameter $c$, to account for an interesting mechano-chemical process which has not been considered in any earlier model. We have been able to extract all the parameters of the model, except $c$, from experimentally …
ATP-dependent chromatin remodeling enzymes (CRE) are bio-molecular motors in eukaryotic cells. These are driven by a chemical fuel, namely, adenosine triphosphate (ATP). CREs actively participate in many cellular processes that require accessibility of specific segments of DNA which are packaged as chromatin. The basic unit of chromatin is a nucleosome where 146 bp $\sim$ 50 nm of a double stranded DNA (dsDNA) is wrapped around a spool formed by histone proteins. The helical path of histone-DNA contact on a nucleosome is also called "footprint". We investigate the mechanism of footprint traver…
Routinely navigating through an ever-changing and unsteady environment, and utilizing chemical energy, molecular motors transport the cell's crucial components, such as neurotransmitters and organelles. They generate force and pull cargo, as they literally walk along the polymeric tracts, e.g. microtubules. However, using experimental data one may derive that the energy needed for this pulling would take the most part of the 22 kT that ATP hydrolysis makes available. In such a case there would not be sufficient energy left to drive the conformational changes in the catalytic cycle of the prote…
Molecular motors belonging to the kinesin and myosin super family hydrolyze ATP by cycling through a sequence of chemical states. These cytoplasmic motors are dimers made up of two linked identical monomeric globular proteins. Fueled by the free energy generated by ATP hydrolysis, the motors walk on polar tracks (microtubule or filamentous actin) processively, which means that only one head detaches and executes a mechanical step while the other stays bound to the track. Thus, the one motor head must regulate chemical state of the other, referred to as "gating", a concept that is not fully und…
Inspired by active shape morphing in developing tissues and biomaterials, we investigate two generic mechanochemical models where the deformations of a thin elastic sheet are driven by, and in turn affect, the concentration gradients of a chemical signal. We develop numerical methods to study the coupled elastic deformations and chemical concentration kinetics, and illustrate with computations the formation of different patterns depending on shell thickness, strength of mechanochemical coupling and diffusivity. In the first model, the sheet curvature governs the production of a contractility i…
Cytoskeletal motor proteins move on filamentous tracks by converting input chemical energy that they derive by catalyzing the hydrolysis of ATP. The ATPase site is the analog of an engine and hydrolysis of ATP is the analog of burning of chemical fuel. Moreover, the functional role of a segment of the motor is analogous to that of the transmission system of an automobile that consists of shaft, gear, clutch, etc. The operation of the engine is intrinsically "noisy" and the motor faces a molecular "hailstorm" in the aqueous medium. In this commemorative article, we celebrate the centenary of Mi…
Molecular motors are single macromolecules that generate forces at the piconewton range and nanometer scale. They convert chemical energy into mechanical work by moving along filamentous structures. In this paper, we study the velocity of two-head molecular motors in the framework of a mechanochemical network theory. The network model, a generalization of the recently work of Liepelt and Lipowsky (PRL 98, 258102 (2007)), is based on the discrete mechanochemical states of a molecular motor with multiple cycles. By generalizing the mathematical method developed by Fisher and Kolomeisky for singl…
The design and synthesis of complex and large mimicked biochemical networks de novo is an unsolved problem in synthetic biology. To address this limitation without resorting to ad hoc computations and experiments, a predictive mathematical theory is required to reduce these complex chemical networks into natural physico-chemical expressions. Here we provide a theory that offers a physico-chemical expression for a large chemical network that is almost arbitrarily both nonlinear and complex. Unexpectedly, the theory demonstrates that such networks can be decomposed into reactions based solely on…
Quantitative understanding of the best possible performance of nanomotors allowed by physical laws pertains to study of nanomotors from biology as well as nanotechnology. Biological nanomotor F1-ATPase is the best available model system as it is the only nanomotor known for extreme energy conversion near the limit of energy conservation. Using a unified theoretical framework centred on a concept called directional fidelity, we analyze recent experiments in which F1-motor's performance was measured for controlled chemical potentials, and expose from the experiments quantitative evidence for the…
Molecular motors are found throughout the cells of the human body, and have many different and important roles. These micro-machines move along filament tracks, and have the ability to convert chemical energy into mechanical work that powers cellular motility. Different types of motors are characterized by different duty-ratios, which is the fraction of time that a motor is attached to its filament. In the case of myosin II - a non-processive molecular machine with a low duty ratio - cooperativity between several motors is essential to induce motion along its actin filament track. In this work…
RNA polymerase (RNAP) is an enzyme that synthesizes a messenger RNA (mRNA) strand which is complementary to a single-stranded DNA template. From the perspective of physicists, an RNAP is a molecular motor that utilizes chemical energy input to move along the track formed by a ssDNA. In some circumstances, which are described in this paper, a large number of RNAPs move simultaneously along the same track. We refer to such collective movements of the RNAPs as RNAP traffic because of the similarities between the collective dynamics of the RNAPs on ssDNA track and that of vehicles in highway traff…
RNA polymerase (RNAP) is an enzyme that synthesizes a messenger RNA (mRNA) strand which is complementary to a single-stranded DNA template. From the perspective of physicists, an RNAP is a molecular motor that utilizes chemical energy input to move along the track formed by a DNA. In many circumstances, which are described in this paper, a large number of RNAPs move simultaneously along the same track; we refer to such collective movements of the RNAPs as RNAP traffic. Here we develop a theoretical model for RNAP traffic by incorporating the steric interactions between RNAPs as well as the mec…
The Kinesin family of motor proteins are involved in a variety of cellular processes that transport materials and generate force. With recent advances in experimental techniques, such as optical tweezers which can probe individual molecules, there has been an increasing interest in understanding the mechanisms by which motor proteins convert chemical energy into mechanical work. Here we present a mathematical model for the chemistry and three dimensional mechanics of the Kinesin motor protein which captures many of the force dependent features of the motor. For the elasticity of the tether tha…
An electrical molecular motor driven by angular momentum transfer
Karlsruhe Institute of Technology（卡尔斯鲁厄理工学院）；Charles University（查理大学）；UPV/EHU（巴斯克国立大学）；CSIC-UPV/EHU（西班牙国家研究委员会-巴斯克国立大学）；University of Regensburg（雷根斯堡大学）；University of Basel（巴塞尔大学）
Nonequilibrium thermodynamics of a system situated in a sustained environment with influx and efflux is usually treated as a subsystem in a larger, closed "universe". It remains a question what the minimally required description for the surrounding of such an open driven system is, so that its nonequilibrium thermodynamics can be established solely based on the internal stochastic kinetics. We provide a solution to this problem using insights from studies of molecular motors in a chemical nonequilibrium steady state (NESS) with sustained external drive through a regenerating system, or in a qu…
FoF1-ATP synthase is the enzyme that provides the 'chemical energy currency' adenosine triphosphate, ATP, for living cells. The formation of ATP is accomplished by a stepwise internal rotation of subunits within the enzyme. We monitor subunit rotation by a single-molecule fluorescence resonance energy transfer (FRET) approach using two fluorophores specifically attached to the enzyme. To identify the stepsize of rotary movements by the motors of ATP synthase we simulated the confocal single-molecule FRET data of freely diffusing enzymes and developed a step finder algorithm based on 'Hidden Ma…
Modeling approaches of suspended, rod-like particles and recent experimental data have shown that depletion forces display different signatures depending on the orientation of these particles. It has been shown that axial attraction of two rods yields contractile forces of 0.1pN that are independent of the relative axial shift of the two rods. Here, we measured depletion-caused interactions of actin bundles extending the phase space of single pairs of rods to a multi-particle system. In contrast to a filament pair, we found forces up to 3pN . Upon bundle relaxation forces decayed exponentially…
