Mechano-chemical kinetics of DNA replication: identification of the translocation step of a replicative DNA polymerase

During DNA replication replicative polymerases move in discrete mechanical steps along the DNA template. To address how the chemical cycle is coupled to mechanical motion of the enzyme, here we use optical tweezers to study the translocation mechanism of individual bacteriophage Phi29 DNA polymerases during processive DNA replication. We determine the main kinetic parameters of the nucleotide incorporation cycle and their dependence on external load and nucleotide (dNTP) concentration. The data is inconsistent with power stroke models for translocation, instead supports a loose-coupling mechanism between chemical catalysis and mechanical translocation during DNA replication. According to this mechanism the DNA polymerase works by alternating between a dNTP/PPi-free state, which diffuses thermally between pre- and post-translocated states, and a dNTP/PPi-bound state where dNTP binding stabilizes the post-translocated state. We show how this thermal ratchet mechanism is used by the polymerase to generate work against large opposing loads (∼50 pN).     

A modified active Brownian dynamics model using asymmetric energy conversion and its application to the molecular motor system

We consider a modified energy depot model in the overdamped limit using an asymmetric energy conversion rate, which consists of linear and quadratic terms in an active particle’s velocity. In order to analyze our model, we adopt a system of molecular motors on a microtubule and employ a flashing ratchet potential synchronized to a stochastic energy supply. By performing an active Brownian dynamics simulation, we investigate effects of the active force, thermal noise, external load, and energy-supply rate. Our model yields the stepping and stalling behaviors of the conventional molecular motor. The active force is found to facilitate the forwardly processive stepping motion, while the thermal noise reduces the stall force by enhancing relatively the backward stepping motion under external loads. The stall force in our model decreases as the energy-supply rate is decreased. Hence, assuming the Michaelis–Menten relation between the energy-supply rate and the an ATP concentration, our model describes ATP-dependent stall force in contrast to kinesin-1.     

Single molecule processes on the stepwise movement of ATP-driven molecular motors

Movement is a fundamental characteristic of all living things. This biogenic function that is attributed to the molecular motors such as kinesin, dynein and myosin. Molecular motors generate forces by using chemical energy derived from the hydrolysis reaction of ATP molecules. Despite a large number of studies on this topic, the chemomechanical energy transduction mechanism is still unsolved. In this study, we have investigated the chemomechanical coupling of the ATPase cycle to the mechanical events of the molecular motor kinesin using single molecule detection (SMD) techniques. The SMD techniques allowed to detection of the movement of single kinesin molecules along a microtubule and showed that kinesin steps mainly in the forward direction, but occasionally in the backward. The stepping direction is determined by a certain load-dependent process, on which the stochastic behavior is well characterized by Feynman's thermal ratchet model. The driving force of the stepwise movement is essentially Brownian motion, but it is biased in the forward direction by using the free energy released from the hydrolysis of ATP.     

Active Nucleosome Displacement: A Theoretical Approach

Three-quarters of eukaryotic DNA are wrapped around protein cylinders forming so-called nucleosomes that block the access to the genetic information. Nucleosomes need therefore to be repositioned, either passively (by thermal fluctuations) or actively (by molecular motors). Here we introduce a theoretical model that allows us to study the interplay between a motor protein that moves along DNA (e.g., an RNA polymerase) and a nucleosome that it encounters on its way. We aim at describing the displacement mechanisms of the nucleosome and the motor protein on a microscopic level to understand better the intricate interplay between the active step of the motor and the nucleosome-repositioning step. Different motor types (Brownian ratchet versus power-stroke mechanism) that perform very similarly under a constant load are shown to have very different nucleosome repositioning capacities.     

Fluctuation driven transport and models of molecular motors and pumps

Non-equilibrium fluctuations can drive vectorial transport along an anisotropic structure in an isothermal medium by biasing the effect of thermal noise (k _B T). Mechanisms based on this principle are often called Brownian ratchets and have been invoked as a possible explanation for the operation of biomolecular motors and pumps. We discuss the thermodynamics and kinetics for the operation of microscopic ratchet motors under conditions relevant to biology, showing how energy provided by external fluctuations or a non-equilibrium chemical reaction can cause unidirectional motion or uphill pumping of a substance. Our analysis suggests that molecular pumps such as Na,K-ATPase and molecular motors such as kinesin and myosin may share a common underlying mechanism. Received: 18 February 1998 / Revised version: 5 May 1998 / Accepted: 14 May 1998     

Force and motion generation of myosin motors: muscle contraction

Brownian ratchet theory refers to the phenomenon that non-equilibrium fluctuations in an isothermal medium and anisotropic system can induce mechanical force and motion. This concept of noise-induced transport has motivated an abundance of theoretical and applied research. One of the exciting applications of the ratchet theory lies in the possible explanation of the operating mode of biological molecular motors. Biomolecular motors are proteins able of converting chemical reactions into mechanical motion and force. Operating at energy levels only a few times greater than the energy levels of thermal baths, their operating mode has to be stochastic in nature. Here, we review the theoretical concepts of the Brownian ratchet theory and its possible link to the operation of the myosin II motors involved in muscle contraction.     

Rotary DNA motors.

Many molecular motors move unidirectionally along a DNA strand powered by nucleotide hydrolysis. These motors are multimeric ATPases with more than one hydrolysis site. We present here a model for how these motors generate the requisite force to process along their DNA track. This novel mechanism for force generation is based on a fluctuating electrostatic field driven by nucleotide hydrolysis. We apply the principle to explain the motion of certain DNA helicases and the portal protein, the motor that bacteriophages use to pump the genome into their capsids. The motor can reverse its direction without reversing the polarity of its electrostatic field, that is, without major structural modifications of the protein. We also show that the motor can be driven by an ion gradient; thus the mechanism may apply as well to the bacterial flagellar motor and to ATP synthase.     

Mechanical transduction mechanisms of RecA-like molecular motors

A majority of ATP-dependent molecular motors are RecA-like proteins, performing diverse functions in biology. These RecA-like molecular motors consist of a highly conserved core containing the ATP-binding site. Here I examined how ATP binding within this core is coupled to the conformational changes of different RecA-like molecular motors. Conserved hydrogen bond networks and conformational changes revealed two major mechanical transduction mechanisms: (1) intra-domain conformational changes and (2) inter-domain conformational changes. The intra-domain mechanism has a significant hydrogen bond rearrangement within the domain containing the P-loop, causing relative motion between two parts of the protein. The inter-domain mechanism exhibits little conformational change in the P-loop domain. Instead, the major conformational change is observed between the P-loop domain and an adjacent domain or subunit containing the arginine finger. These differences in the mechanical transduction mechanisms may link to the underlying energy surface governing a Brownian ratchet or a power stroke.     

A chemically reversible Brownian motor: application to kinesin and Ncd.

Kinesin and nonclaret disjunctional protein (ncd) are two microtubule-based molecular motors that use energy from ATP hydrolysis to drive motion in opposite directions. They are structurally very similar and bind with similar orientations on microtubule. What is the origin of the different directionality? Is it some subtle feature of the structure of the motor domains, not apparent in x-ray diffraction studies, or possibly some difference near the neck regions far from the microtubule binding site? Perhaps because the motors function as dimers, the explanation involves differences in the strength of the interaction between the two motor monomers themselves. Here we present another possibility, based on a Brownian ratchet, in which the direction of motion of the motor is controlled by the chemical mechanism of ATP hydrolysis and is an inherent property of a single head. In contrast to conventional power stroke models, dissociation of the individual heads is not obligatory in the chemomechanical cycle, and the steps during which motion and force generation occurs are best described as one-dimensional thermally activated transitions that take place while both heads are attached to the microtubule. We show that our model is consistent with experiments on kinesin in which the velocity is measured as a function of external force and with the observed stiochiometry of one ATP/8-nm step at low load. Further, the model provides a way of understanding recent experiments on the ATP dependence of the variance (randomness) of the distance moved in a given time.     

Cell motility driven by actin polymerization.

Certain kinds of cellular movements are apparently driven by actin polymerization. Examples include the lamellipodia of spreading and migrating embryonic cells, and the bacterium Listeria monocytogenes, that propels itself through its host's cytoplasm by constructing behind it a polymerized tail of cross-linked actin filaments. Peskin et al. (1993) formulated a model to explain how a polymerizing filament could rectify the Brownian motion of an object so as to produce unidirectional force (Peskin, C., G. Odell, and G. Oster. 1993. Cellular motions and thermal fluctuations: the Brownian ratchet. Biophys. J. 65:316-324). Their "Brownian ratchet" model assumed that the filament was stiff and that thermal fluctuations affected only the "load," i.e., the object being pushed. However, under many conditions of biological interest, the thermal fluctuations of the load are insufficient to produce the observed motions. Here we shall show that the thermal motions of the polymerizing filaments can produce a directed force. This "elastic Brownian ratchet" can explain quantitatively the propulsion of Listeria and the protrusive mechanics of lamellipodia. The model also explains how the polymerization process nucleates the orthogonal structure of the actin network in lamellipodia.     

One axon,many kinesins: What's the logic?

A large number of membrane-bounded organelles, protein complexes, and mRNAs are transported along microtubules to different locations within the neuronal axon. Axonal transport in the anterograde direction is carried out by members of a superfamily of specialized motor proteins, the kinesins. All kinesins contain a conserved motor domain that hydrolyses ATP to generate movement along microtubules. Regions outside the motor domain are responsible for cargo binding and regulation of motor activity. Present in a soluble, inactive form in the cytoplasm, kinesins are activated upon cargo binding. Selective targeting of different types of kinesin motors to specific cargoes is directed by amino acid sequences situated in their variable tails. Cargo proteins with specific function at their destination, bind directly to specific kinesins for transport. Whereas most kinesins move to microtubule plus-ends, a small number of them move to microtubule minus-ends, and may participate in retrograde axonal transport. Axonal transport by kinesins has a logic: Fully assembled, multisubunit, functional complexes (e.g., ion channel complexes, signaling complexes, RNA-protein complexes) are transported to their destination by kinesin motors that interact transiently (i.e., during transport only) with one of the complexes' subunits.     

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 biopolymerization (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 contemporary 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 comoving motors. The properties unveiled by our analysis have important biological implications on the collective transport characteristics of processive motor enzymes in crowded conditions.     

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 biopolymerization (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 contemporary 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 comoving motors. The properties unveiled by our analysis have important biological implications on the collective transport characteristics of processive motor enzymes in crowded conditions.     

Kin I kinesins: insights into the mechanism of depolymerization

Kin I kinesins are members of the diverse kinesin superfamily of molecular motors. Whereas most kinesins use ATP to move along microtubules, Kin I kinesins depolymerize microtubules rather than walk along them. Functionally, this distinct subfamily of kinesins is important in regulating cellular microtubule dynamics and plays a crucial role in spindle assembly and chromosome segregation. The molecular mechanism of Kin I-induced microtubule destabilization is as yet unclear. It is generally believed that Kin Is induce a structural change on the microtubule that leads to microtubule destabilization. Recently, much progress has been made towards understanding how Kin Is may cause this structural change, and how ATPase activity is employed in the catalytic cycle.     

Stepping, strain gating, and an unexpected force-velocity curve for multiple-motor-based transport

BACKGROUND: Intracellular transport via processive kinesin, dynein, and myosin molecular motors plays an important role in maintaining cell structure and function. In many cases, cargoes move distances longer than expected for single motors; there is significant evidence that this increased travel is in part due to multiple motors working together to move the cargoes. Although we understand single motors experimentally and theoretically, our understanding of multiple motors working together is less developed. RESULTS: We theoretically investigate how multiple kinesin motors function. Our model includes stochastic fluctuations of each motor as it proceeds through its enzymatic cycle. Motors dynamically influence each other and function in the presence of thermal noise and viscosity. We test the theory via comparison with the experimentally observed distribution of step sizes for two motors moving a cargo, and by predicting slightly subadditive stalling force for two motors relative to one. In the presence of load, our predictions for travel distances and mean velocities are different from the steady-state model: with high motor-motor coupling, we predict a form of strain-gating, where-because of the underlying motor's dynamics-the motors share load unevenly, leading to increased mean travel distance of the multiple-motor system under load. Surprisingly, we predict that in the presence of small load, two-motor cargoes move slightly slower than do single-motor cargoes. Unpublished data from G.T. Shubeita, B.C. Carter, and S.P.G. confirm this prediction in vivo. CONCLUSIONS: When only a few motors are active, fluctuations and unequal load sharing between motors can result in significant alterations of ensemble function.     

Chemomechanical coupling of the forward and backward steps of single kinesin molecules

The molecular motor kinesin travels processively along a microtubule in a stepwise manner. Here we have studied the chemomechanical coupling of the hydrolysis of ATP to the mechanical work of kinesin by analysing the individual stepwise movements according to the directionality of the movements. Kinesin molecules move primarily in the forward direction and only occasionally in the backward direction. The hydrolysis of a single ATP molecule is coupled to either the forward or the backward movement. This bidirectional movement is well described by a model of Brownian motion assuming an asymmetric potential of activation energy. Thus, the stepwise movement along the microtubule is most probably due to Brownian motion that is biased towards the forward direction by chemical energy stored in ATP molecules.     

Molecular motors: thermodynamics and the random walk

The biochemical cycle of a molecular motor provides the essential link between its thermodynamics and kinetics. The thermodynamics of the cycle determine the motor's ability to perform mechanical work, whilst the kinetics of the cycle govern its stochastic behaviour. We concentrate here on tightly coupled, processive molecular motors, such as kinesin and myosin V, which hydrolyse one molecule of ATP per forward step. Thermodynamics require that, when such a motor pulls against a constant load f, the ratio of the forward and backward products of the rate constants for its cycle is exp [-(DeltaG + u(0)f)/kT], where -DeltaG is the free energy available from ATP hydrolysis and u(0) is the motor's step size. A hypothetical one-state motor can therefore act as a chemically driven ratchet executing a biased random walk. Treating this random walk as a diffusion problem, we calculate the forward velocity v and the diffusion coefficient D and we find that its randomness parameter r is determined solely by thermodynamics. However, real molecular motors pass through several states at each attachment site. They satisfy a modified diffusion equation that follows directly from the rate equations for the biochemical cycle and their effective diffusion coefficient is reduced to D-v(2)tau, where tau is the time-constant for the motor to reach the steady state. Hence, the randomness of multistate motors is reduced compared with the one-state case and can be used for determining tau. Our analysis therefore demonstrates the intimate relationship between the biochemical cycle, the force-velocity relation and the random motion of molecular motors.     

Kin I Kinesins: Insights into the Mechanism of Depolymerization

ABSTRACT

Kin I kinesins are members of the diverse kinesin superfamily of molecular motors. Whereas most kinesins use ATP to move along microtubules, Kin I kinesins depolymerize microtubules rather than walk along them. Functionally, this distinct subfamily of kinesins is important in regulating cellular microtubule dynamics and plays a crucial role in spindle assembly and chromosome segregation. The molecular mechanism of Kin I-induced microtubule destabilization is as yet unclear. It is generally believed that Kin Is induce a structural change on the microtubule that leads to microtubule destabilization. Recently, much progress has been made towards understanding how Kin Is may cause this structural change, and how ATPase activity is employed in the catalytic cycle.