RNA polymerase as a molecular machine

Structure and function of DNA-dependent RNA polymerase is considered in terms of a conveying molecular machine. The use of mechanical energy and mechanical devices, such as "power-stroke motor", is supposed unlikely in the conveying function of RNA polymerase, as well as other molecular machines. Brownian motion and thermal mobility of macromolecules and their parts are postulated as the only motive impulse at the molecular level. Binding of substrates and subsequent chemical reaction as the energy input may provide successive selection and fixation of alternative conformational states of the enzyme complex thus providing the directionality of the conveyance ("Brownian ratchet mechanism"). The following sequence of events "substrate binding--fixation of a certain conformational state--chemical reaction--fixation of an alternative conformational state--translocation (dissociation and downstream reassociation) of product-template duplex" is proposed as the principal scheme of the forward movement of RNA polymerase along DNA template.     

Ribosome as a molecular machine

General principles of structure and function of the ribosome are surveyed, and the translating ribosome is regarded as a molecular conveying machine. Two coupled conveying processes, the passing of compact tRNA globules and the drawing of linear mRNA chain through intraribosomal channel, are considered driven by discrete acts of translocation during translation. Instead of mechanical transmission mechanisms and power-stroke 'motors', thermal motion and chemically induced changes in affinities of ribosomal binding sites for their ligands (tRNAs, mRNA, elongation factors) are proposed to underlie all the directional movements within the ribosomal complex. The GTP-dependent catalysis of conformational transitions by elongation factors during translation is also discussed.     

Plausible view on the biological molecular energy machines.

A qualitative picture of operation modes of biological molecular energy machines is presented. It is suggested that there is mutual control between the flow of molecular energy stored in a biological molecular energy machine and the sequence of nonequilibrium conformational states through which the machine passes in doing work. If the structure of the conformational space is favorable, the set of trajectories in this space decomposes into two families, each of which accomplishes another task. This divergence of trajectories enables to distinguish molecular objects according to differences in interaction between the machine and the object, i.e., to perform a measurement on a molecular object and process the object according to the result of that measurement.     

A structural perspective on the dynamics of kinesin motors

Despite significant fluctuation under thermal noise, biological machines in cells perform their tasks with exquisite precision. Using molecular simulation of a coarse-grained model and theoretical arguments, we envisaged how kinesin, a prototype of biological machines, generates force and regulates its dynamics to sustain persistent motor action. A structure-based model, which can be versatile in adapting its structure to external stresses while maintaining its native fold, was employed to account for several features of kinesin dynamics along the biochemical cycle. This analysis complements our current understandings of kinesin dynamics and connections to experiments. We propose a thermodynamic cycle for kinesin that emphasizes the mechanical and regulatory role of the neck linker and clarify issues related to the motor directionality, and the difference between the external stalling force and the internal tension responsible for the head-head coordination. The comparison between the thermodynamic cycle of kinesin and macroscopic heat engines highlights the importance of structural change as the source of work production in biomolecular machines.     

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.     

Maximum likelihood estimation of molecular motor kinetics from staircase dwell-time sequences

Molecular motors, such as kinesin, myosin, or dynein, convert chemical energy into mechanical energy by hydrolyzing ATP. The mechanical energy is used for moving in discrete steps along the cytoskeleton and carrying a molecular load. High resolution single molecule recordings of motor steps appear as a stochastic sequence of dwells, resembling a staircase. Staircase data can also be obtained from other molecular machines such as F1 -ATPase, RNA polymerase, or topoisomerase. We developed a maximum likelihood algorithm that estimates the rate constants between different conformational states of the protein, including motor steps. We model the motor with a periodic Markov model that reflects the repetitive chemistry of the motor step. We estimated the kinetics from the idealized dwell-sequence by numerical maximization of the likelihood function for discrete-time Markov models. This approach eliminates the need for missed event correction. The algorithm can fit kinetic models of arbitrary complexity, such as uniform or alternating step chemistry, reversible or irreversible kinetics, ATP concentration and mechanical force-dependent rates, etc. The method allows global fitting across stationary and nonstationary experimental conditions, and user-defined a priori constraints on rate constants. The algorithm was tested with simulated data, and implemented in the free QuB software.     

RNA Polymerase As a Molecular Machine

Structure and function of DNA-dependent RNA polymerase is considered in terms of a conveying molecular machine. It is unlikely that mechanical energy and mechanical devices such as power-stroke motor are used in the conveying function of RNA polymerase, as well as other molecular machines. Brownian motion and thermal mobility of macromolecules and their parts are postulated as the only motive impulse at the molecular level. Binding of substrates and subsequent chemical reaction as the energy input may provide successive selection and fixation of alternative conformational states of the enzyme complex, thus providing the directionality of the conveyance (Brownian ratchet mechanism). The following sequence of events: substrate binding fixation of a certain conformational state chemical reaction fixation of an alternative conformational state translocation (dissociation and downstream reassociation) of the product–template duplex is proposed as the principal scheme of the forward movement of RNA polymerase along the DNA template.     

Running backwards: soft landing–hard takeoff,a less efficient rebound

Human running at low and intermediate speeds is characterized by a greater average force exerted after ‘landing’, when muscle–tendon units are stretched (‘hard landing’), and a lower average force exerted before ‘takeoff’, when muscle–tendon units shorten (‘soft takeoff’). This landing–takeoff asymmetry is consistent with the force–velocity relation of the ‘motor’ (i.e. with the basic property of muscle to resist stretching with a force greater than that developed during shortening), but it may also be due to the ‘machine’ (e.g. to the asymmetric lever system of the foot operating during stance). Hard landing and soft takeoff—never the reverse—were found in running, hopping and trotting animals using diverse lever systems, suggesting that the different machines evolved to comply with the basic force–velocity relation of the motor. Here we measure the mechanical energy of the centre of mass of the body in backward running, an exercise where the normal coupling between motor and machine is voluntarily disrupted, in order to see the relevance of the motor–machine interplay in human running. We find that the landing–takeoff asymmetry is reversed. The resulting ‘soft landing’ and ‘hard takeoff’ are associated with a reduced efficiency of positive work production. We conclude that the landing–takeoff asymmetry found in running, hopping and trotting is the expression of a convenient interplay between motor and machine. More metabolic energy must be spent in the opposite case when muscle is forced to work against its basic property (i.e. when it must exert a greater force during shortening and a lower force during stretching).     

Entropy and barrier-controlled fluctuations determine conformational viscoelasticity of single biomolecules

Biological macromolecules have complex and nontrivial energy landscapes, endowing them with a unique conformational adaptability and diversity in function. Hence, understanding the processes of elasticity and dissipation at the nanoscale is important to molecular biology and emerging fields such as nanotechnology. Here we analyze single molecule fluctuations in an atomic force microscope, using a generic model of biopolymer viscoelasticity that includes local "internal" conformational dissipation. Comparing two biopolymers, dextran and cellulose (polysaccharides with and without local bistable transitions), demonstrates that signatures of simple conformational change are minima in both the elastic and internal friction constants around a characteristic force. A novel analysis of dynamics on a bistable energy landscape provides a simple explanation: an elasticity driven by the entropy, and friction by a barrier-controlled hopping time of populations between states, which is surprisingly distinct to the well-known relaxation time. This nonequilibrium microscopic analysis thus provides a means of quantifying new dynamical features of the energy landscape of the glucopyranose ring, revealing an unexpected underlying roughness and information on the shape of the barrier of the chair-boat transition in dextran. The results presented herein provide a basis toward probing the viscoelasticity of macromolecular conformational transitions on more complex energy landscapes, such as during protein folding.     

Force generation, work, and coupling in molecular motors.

A mechanism is proposed for molecular motors in which force is generated by a protein conformational change driven by binding energy (in muscle, that of myosin with actin as well as with ATP, ADP, or Pi). Work, the product of the force generated by one myosin or kinesin molecule (F) and the distance over which it acts (d), is a function of a ratio of dissociation constants before and after the contractile step: F.d < RT ln(KAe/KAc). From published data the ratio is > 2 x 10(4), which can be explained by conversion of a surface complex to an enclosed, or partly enclosed, complex. Although the complex performing the work stroke is in unstrained conformation, the complex after the work stroke is much more stable, owing to binding forces; the latter, however, is destabilized by the load, which thereby opposes the contractile conformational change, countering the force-generating reaction. The connection between the free energy release and work is implicit in the mechanism, inasmuch as coupling, like force generation, depends on conformational changes driven by binding energy (internal rather than external work being involved in coupling). The principles apply whether ATP or an ion gradient drives the system. At high load, in muscle, the mechanism allows for a summation of the forces generated by several myosin molecules.     

Electrostatic Ratchet in the Protective Antigen Channel Promotes Anthrax Toxin Translocation

Central to the power-stroke and Brownian-ratchet mechanisms of protein translocation is the process through which nonequilibrium fluctuations are rectified or ratcheted by the molecular motor to transport substrate proteins along a specific axis. We investigated the ratchet mechanism using anthrax toxin as a model. Anthrax toxin is a tripartite toxin comprised of the protective antigen (PA) component, a homooligomeric transmembrane translocase, which translocates two other enzyme components, lethal factor (LF) and edema factor (EF), into the cytosol of the host cell under the proton motive force (PMF). The PA-binding domains of LF and EF (LF_N and EF_N) possess identical folds and similar solution stabilities; however, EF_N translocates ∼10–200-fold slower than LF_N, depending on the electrical potential (Δψ) and chemical potential (ΔpH) compositions of the PMF. From an analysis of LF_N/EF_N chimera proteins, we identified two 10-residue cassettes comprised of charged sequence that were responsible for the impaired translocation kinetics of EF_N. These cassettes have nonspecific electrostatic requirements: one surprisingly prefers acidic residues when driven by either a Δψ or a ΔpH; the second requires basic residues only when driven by a Δψ. Through modeling and experiment, we identified a charged surface in the PA channel responsible for charge selectivity. The charged surface latches the substrate and promotes PMF-driven transport. We propose an electrostatic ratchet in the channel, comprised of opposing rings of charged residues, enforces directionality by interacting with charged cassettes in the substrate, thereby generating forces sufficient to drive unfolding.     

Theory of molecular machines. I. Channel capacity of molecular machines

Like macroscopic machines, molecular-sized machines are limited by their material components, their design, and their use of power. One of these limits is the maximum number of states that a machine can choose from. The logarithm to the base 2 of the number of states is defined to be the number of bits of information that the machine could "gain" during its operation. The maximum possible information gain is a function of the energy that a molecular machine dissipates into the surrounding medium (Py), the thermal noise energy which disturbs the machine (Ny) and the number of independently moving parts involved in the operation (dspace): Cy = dspace log2 [( Py + Ny)/Ny] bits per operation. This "machine capacity" is closely related to Shannon's channel capacity for communications systems. An important theorem that Shannon proved for communication channels also applies to molecular machines. With regard to molecular machines, the theorem states that if the amount of information which a machine gains is less than or equal to Cy, then the error rate (frequency of failure) can be made arbitrarily small by using a sufficiently complex coding of the molecular machine's operation. Thus, the capacity of a molecular machine is sharply limited by the dissipation and the thermal noise, but the machine failure rate can be reduced to whatever low level may be required for the organism to survive.     

Dynamics of the bacterial flagellar motor: the effects of stator compliance, back steps, temperature, and rotational asymmetry

The rotation of a bacterial flagellar motor (BFM) is driven by multiple stators tethered to the cell wall. Here, we extend a recently proposed power-stroke model to study the BFM dynamics under different biophysical conditions. Our model explains several key experimental observations and reveals their underlying mechanisms. 1), The observed independence of the speed at low load on the number of stators is explained by a force-dependent stepping mechanism that is independent of the strength of the stator tethering spring. Conversely, without force-dependent stepping, an unrealistically weak stator spring is required. 2), Our model with back-stepping naturally explains the observed absence of a barrier to backward rotation. Using the same set of parameters, it also explains BFM behaviors in the high-speed negative-torque regime. 3), From the measured temperature dependence of the maximum speed, our model shows that stator-stepping is a thermally activated process with an energy barrier. 4), The recently observed asymmetry in the torque-speed curve between counterclockwise- and clockwise-rotating BFMs can be quantitatively explained by the asymmetry in the stator-rotor interaction potentials, i.e., a quasilinear form for the counterclockwise motor and a quadratic form for the clockwise motor.     

Reverse engineering of force integration during mitosis in the Drosophila embryo

The mitotic spindle is a complex macromolecular machine that coordinates accurate chromosome segregation. The spindle accomplishes its function using forces generated by microtubules (MTs) and multiple molecular motors, but how these forces are integrated remains unclear, since the temporal activation profiles and the mechanical characteristics of the relevant motors are largely unknown. Here, we developed a computational search algorithm that uses experimental measurements to ‘reverse engineer’ molecular mechanical machines. Our algorithm uses measurements of length time series for wild‐type and experimentally perturbed spindles to identify mechanistic models for coordination of the mitotic force generators in Drosophila embryo spindles. The search eliminated thousands of possible models and identified six distinct strategies for MT–motor integration that agree with available data. Many features of these six predicted strategies are conserved, including a persistent kinesin‐5‐driven sliding filament mechanism combined with the anaphase B‐specific inhibition of a kinesin‐13 MT depolymerase on spindle poles. Such conserved features allow predictions of force–velocity characteristics and activation–deactivation profiles of key mitotic motors. Identified differences among the six predicted strategies regarding the mechanisms of prometaphase and anaphase spindle elongation suggest future experiments.     

Protein Unfolding by Biological Unfoldases: Insights from Modeling

The molecular determinants of the high efficiency of biological machines like unfoldases (e.g., the proteasome) are not well understood. We propose a model to study protein translocation into the chamber of biological unfoldases represented as a funnel. It is argued that translocation is a much faster way of unfolding a protein than end-to-end stretching, especially in a low-force regime, because it allows for a conformational freedom while concentrating local tension on consecutive regions of a protein chain and preventing refolding. This results in a serial unfolding of the protein structures dominated by unzipping. Thus, pulling against the unfoldase pore is an efficient catalyst of the unfolding reaction. We also show that the presence of the funnel makes the tension along the backbone of the substrate protein nonuniform even when the protein gets unfolded. Hence, the stalling force measured by single-molecule force spectroscopy techniques may be smaller than the traction force of the unfoldase motor.     

Protein Unfolding by Biological Unfoldases: Insights from Modeling

The molecular determinants of the high efficiency of biological machines like unfoldases (e.g., the proteasome) are not well understood. We propose a model to study protein translocation into the chamber of biological unfoldases represented as a funnel. It is argued that translocation is a much faster way of unfolding a protein than end-to-end stretching, especially in a low-force regime, because it allows for a conformational freedom while concentrating local tension on consecutive regions of a protein chain and preventing refolding. This results in a serial unfolding of the protein structures dominated by unzipping. Thus, pulling against the unfoldase pore is an efficient catalyst of the unfolding reaction. We also show that the presence of the funnel makes the tension along the backbone of the substrate protein nonuniform even when the protein gets unfolded. Hence, the stalling force measured by single-molecule force spectroscopy techniques may be smaller than the traction force of the unfoldase motor.     

A model for the interaction of muscle cross-bridges with ligands which compete with ATP

A model is presented to describe the inhibition of muscle fiber contraction by ligands that compete with MgATP. Two ligands, adenosine 5' (beta, gamma-imido) triphosphate (AMPPNP) and pyrophosphate (PPi), decrease the force developed in isometric contractions and act as weak competitive inhibitors of the maximum velocity of contraction (Pate & Cooke, 1985). These observations provide information on the energetics of actomyosin ligand states at the end of the power-stroke where MgATP dissociates the myosin cross-bridge from actin, and they are analysed in terms of a seven state model of cross-bridge kinetics. The model can reconcile the observations that these ligands bind tightly to fibers, Kd = 10(-4) M, while they are only weak inhibitors of fiber velocity, Ki = 2 X 10(-3) M. It provides a reasonable fit to the data and leads to several conclusions concerning the properties of the cross-bridge states. The states with bound ligand are shifted axially so that they occur earlier in the power-stroke than the nucleotide-free rigor state. This shift also explains the axial lengthening seen upon addition of ligands to rigor fibers. We can conclude that these ligands cause small perturbations in the cross-bridge configuration rather than large shifts. A second conclusion is that cross-bridges do not detach from actin during their power-strokes. Instead they traverse the entire length of the power stroke and are detached only at the end, leading to the suggestion that the cycling of bridges in isometric fibers is due to fluctuations in the relative positions of thick and thin filaments. With some further assumptions, the model also explains many of the rate constants and equilibrium constants of the actin-myosin-ligand interaction that have been measured in solution.     

Ionic channels with conformational substates.

Recent studies of protein dynamics suggest that ionic channels can assume many conformational substates. Long-lived substates have been directly observed in single-channel current records. In many cases, however, the lifetimes of conformational states will be far below the theoretical limit of time resolution of single-channel experiments. The existence of such hidden substates may strongly influence the observable (time-averaged) properties of a channel, such as the concentration dependence of conductance. A channel exhibiting fast, voltage-dependent transitions between different conductance states may behave as an intrinsic rectifier. In the presence of more than one permeable ion species, coupling between ionic fluxes may occur, even when the channel has only a single ion-binding site. In special situations the rate of ion translocation becomes limited by the rate of conformational transitions, meaning that the channel approaches the kinetic behavior of a carrier. As a result of the strong coulombic interaction between an ion in a binding site and polar groups of the protein, rate constants of conformational transitions may depend on the occupancy of the binding site. Under this condition a nonequilibrium distribution of conformational states is created when ions are driven through the channel by an external force. This may lead to an apparent violation of microscopic reversibility, i.e., to a situation in which the frequency of transitions from state A to state B is no longer equal to the transition frequency from state B to state A.     

How myosin motors power cellular functions: an exciting journey from structure to function: based on a lecture delivered at the 34th FEBS Congress in Prague, Czech Republic, July 2009

Molecular motors such as myosins are allosteric enzymes that power essential motility functions in the cell. Structural biology is an important tool for deciphering how these motors work. Myosins produce force upon the actin-driven conformational changes controlling the sequential release of the hydrolysis products of ATP (Pi followed by ADP). These conformational changes are amplified by a 'lever arm', which includes the region of the motor known as the converter and the adjacent elongated light chain binding region. Analysis of four structural states of the motor provides a detailed understanding of the rearrangements and pathways of communication in the motor that are necessary for detachment from the actin track and repriming of the motor. However, the important part of the cycle in which force is produced remains enigmatic and awaits new high-resolution structures. The value of a structural approach is particularly evident from clues provided by the structural states of the reverse myosin VI motor. Crystallographic structures have revealed that rearrangements within the converter subdomain occur, which explains why this myosin can produce a large stroke in the opposite direction to all other myosins, despite a very short lever arm. By providing a detailed understanding of the motor rearrangements, structural biology will continue to reveal essential information and help solve current enigma, such as how actin promotes force production, how motors are tuned for specific cellular roles or how motor/cargo interactions regulate the function of myosin in the cell.     

Controlling kinesin by reversible disulfide cross-linking. Identifying the motility-producing conformational change

Conventional kinesin, a dimeric molecular motor, uses ATP-dependent conformational changes to move unidirectionally along a row of tubulin subunits on a microtubule. Two models have been advanced for the major structural change underlying kinesin motility: the first involves an unzippering/zippering of a small peptide (neck linker) from the motor catalytic core and the second proposes an unwinding/rewinding of the adjacent coiled-coil (neck coiled-coil). Here, we have tested these models using disulfide cross-linking of cysteines engineered into recombinant kinesin motors. When the neck linker motion was prevented by cross-linking, kinesin ceased unidirectional movement and only showed brief one-dimensional diffusion along microtubules. Motility fully recovered upon adding reducing agents to reverse the cross-link. When the neck linker motion was partially restrained, single kinesin motors showed biased diffusion towards the microtubule plus end but could not move effectively against a load imposed by an optical trap. Thus, partial movement of the neck linker suffices for directionality but not for normal processivity or force generation. In contrast, preventing neck coiled-coil unwinding by disulfide cross-linking had relatively little effect on motor activity, although the average run length of single kinesin molecules decreased by 30-50%. These studies indicate that conformational changes in the neck linker, not in the neck coiled-coil, drive processive movement by the kinesin motor.