Properties Of Molecular Motors Research Articles

Molecular Motors–Nature’s Efficiency at Work

Nature has generated sophisticated and very efficient molecular motors, employed for nanoscale transport at the intracellular level. As a complementary tool to nanofluidics, these motors have been envisioned for nanotechnological devices. In order to pave the way for such applications, a thorough understanding of the mechanisms governing these motors is needed. Because of the complexity of their in vivo functions, this understanding is best acquired in vitro, where functional parameters can independently be controlled. I will report on work in my group that studies and harnesses the transport properties of molecular motors on functionalized structures of reduced dimensionality such as carbon nanotubes, 1 lithographically designed electrodes, 2 microwires, 3 loops 4 and swarms. 5 In addition, I will show results that demonstrate the potential of this work for biomedical advances. 6

Controlling rotary motion of molecular motors based on oxindole.

Molecular motors are essential components of artificial molecular machines, which can be used to manipulate and amplify mechanical motion at the nanoscale to create machine-like function. Since the discovery of light-driven rotary molecular motors, the field has been widely developed, including the introduction of molecular motors based on oxindole by our group in 2019. The rotational properties of molecular motors, e.g. absorption wavelength, quantum yield and rotation speed, often critically depend on substituent effects. Up to now, the substituent effects of oxindole-based molecular motors have not yet been investigated. Herein, we present a family of oxindole-based molecular motors functionalised at three different positions on the motor core, with either CN or OMe groups. The motors prepared in this work retain the favourable features of oxindole-based motors, i.e. simple synthesis and visible light addressability. We find that functionalisation has substantial effects on the absorption wavelength of the motors, meanwhile the rotation speed is unaffected. Furthermore, we found that functionalisation of the oxindole molecular motors increases their quantum efficiency considerably in comparison to previous motors of their class.

Temperature-Dependent Activity of Motor Proteins: Energetics and Their Implications for Collective Behavior.

Molecular motor proteins are an extremely important component of the cellular transport system that harness chemical energy derived from ATP hydrolysis to carry out directed mechanical motion inside the cells. Transport properties of these motors such as processivity, velocity, and their load dependence have been well established through single-molecule experiments. Temperature dependent biophysical properties of molecular motors are now being probed using single-molecule experiments. Additionally, the temperature dependent biochemical properties of motors (ATPase activity) are probed to understand the underlying mechanisms and their possible implications on the enzymatic activity of motor proteins. These experiments in turn have revealed their activation energies and how they compare with the thermal energy available from the surrounding medium. In this review, we summarize such temperature dependent biophysical and biochemical properties of linear and rotary motor proteins and their implications for collective function during intracellular transport and cellular movement, respectively.

Molecular Motors in Aqueous Environment.

Molecular motors are Nature’s solution for (supra)molecular transport and muscle functioning and are involved in most forms of directional motion at the cellular level. Their synthetic counterparts have also found a myriad of applications, ranging from molecular machines and smart materials to catalysis and anion transport. Although light-driven rotary molecular motors are likely to be suitable for use in an artificial cell, as well as in bionanotechnology, thus far they are not readily applied under physiological conditions. This results mainly from their inherently aromatic core structure, which makes them insoluble in aqueous solution. Here, the study of the dynamic behavior of these motors in biologically relevant media is described. Two molecular motors were equipped with solubilizing substituents and studied in aqueous solutions. Additionally, the behavior of a previously reported molecular motor was studied in micelles, as a model system for the biologically relevant confined environment. Design principles were established for molecular motors in these media, and insights are given into pH-dependent behavior. The work presented herein may provide a basis for the application of the remarkable properties of molecular motors in more advanced biohybrid systems.

Theoretical Investigation of Distributions of Run Lengths for Biological Molecular Motors

Motor proteins, also known as biological molecular motors, are active enzymatic molecules that support a variety of fundamental biological processes, including cellular transport, cell division, and cell motility. They usually function by transforming chemical energy into mechanical motion, which propels them along linear structures such as protein filaments and nucleic acids. Recent single-molecule experiments measured with high-precision distributions of various dynamic properties of molecular motors. However, it is difficult to utilize these observations to obtain a better description of molecular mechanisms in motor proteins because of the lack of corresponding theoretical methods. To fill this gap, we developed a new theoretical framework to describe the distributions of dynamic properties of biological molecular motors. It is based on the method of first-passage processes. To illustrate our approach, the distributions of run lengths of motor proteins are analyzed. It is found that these distributions depend on the finite length of linear tracks along which the motors move, on the initial position of the motor proteins along the filaments, and on the intermediate chemical transitions during the enzymatic cycle. The physical mechanisms of the observed phenomena are discussed.

Role of Cyclic Di-GMP and Exopolysaccharide in Type IV Pilus Dynamics.

For Pseudomonas aeruginosa, levels of cyclic di-GMP (c-di-GMP) govern the transition from the planktonic state to biofilm formation. Type IV pili (T4P) are crucial determinants of biofilm structure and dynamics, but it is unknown how levels of c-di-GMP affect pilus dynamics. Here, we scrutinized how c-di-GMP affects molecular motor properties and adhesive behavior of T4P. By means of retraction, T4P generated forces of ∼30 pN. Deletion mutants in the proteins with known roles in biofilm formation, swarming motility, and exopolysaccharide (EPS) production (specifically, the diguanylate cyclases sadC and roeA or the c-di-GMP phosphodiesterase bifA) showed only modest effects on velocity or force of T4P retraction. At high levels of c-di-GMP, the production of exopolysaccharides, particularly of Pel, is upregulated. We found that Pel production strongly enhances T4P-mediated surface adhesion of P. aeruginosa, suggesting that T4P-matrix interactions may be involved in biofilm formation by P. aeruginosa Finally, our data support the previously proposed model of slingshot-like "twitching" motility of P. aeruginosaIMPORTANCE Type IV pili (T4P) play various important roles in the transition of bacteria from the planktonic state to the biofilm state, including surface attachment and surface sensing. Here, we investigate adhesion, dynamics, and force generation of T4P after bacteria engage a surface. Our studies showed that two critical components of biofilm formation by Pseudomonas aeruginosa, T4P and exopolysaccharides, contribute to enhanced T4P-mediated force generation by attached bacteria. These data indicate a crucial role for the coordinated impact of multiple biofilm-promoting factors during the early stages of attachment to a surface. Our data are also consistent with a previous model explaining why pilus-mediated motility in P. aeruginosa results in characteristic "twitching" behavior.

Effect of Fluid Viscosity on the Cilia-Generated Flow on a Mouse Tracheal Lumen.

Mucous flow in a tracheal lumen is generated by the beat motion of ciliated cells to provide a clearance function by discharging harmful dust particles and viruses. Due to its physiological importance, the cilia-generated flow and the rheological properties of mucus have been investigated intensively. The effects of viscosity on the cilia-generated flow, however, have not been fully clarified. In this study, we measured bulk background velocity of ciliary flow using a micro particle tracking velocimetry method under various viscosity conditions in mice. The results showed that the flow velocity decreased as the increase with viscosity of ambient fluid. Moreover, no previous study has clarified the pump power generated by cilia, which provides important information with regard to understanding the molecular motor properties of cilia. Measurements of both the ciliary flow and the ciliary motion were conducted to determine the cilia pump power. Our results indicated that the cilia pump during the effective stroke did not drive the ciliary flow efficiently under high viscosity conditions; these findings are necessary to resolve the clearance function.

Visible-Light-Driven Photoisomerization and Increased Rotation Speed of a Molecular Motor Acting as a Ligand in a Ruthenium(II) Complex.

Toward the development of visible-light-driven molecular rotary motors, an overcrowded alkene-based ligand and the corresponding ruthenium(II) complex is presented. In our design, a 4,5-diazafluorenyl coordination motif is directly integrated into the motor function. The photochemical and thermal isomerization behavior has been studied by UV/Vis and NMR spectroscopy. Upon coordination to a Ru(II) bipyridine complex, the photoisomerization process can be driven by visible (λmax = 450 nm) instead of UV light and furthermore, a large increase of the speed of rotation is noted. DFT calculations point to a contraction of the diazafluorenyl lower half upon metal-coordination resulting in reduced steric hindrance in the "fjord region" of the molecule. Consequently, it is shown that metal-ligand interactions can play an important role in the adjustment of both photophysical and thermodynamic properties of molecular motors.

Visible‐Light‐Driven Photoisomerization and Increased Rotation Speed of a Molecular Motor Acting as a Ligand in a Ruthenium(II) Complex

AbstractToward the development of visible‐light‐driven molecular rotary motors, an overcrowded alkene‐based ligand and the corresponding ruthenium(II) complex is presented. In our design, a 4,5‐diazafluorenyl coordination motif is directly integrated into the motor function. The photochemical and thermal isomerization behavior has been studied by UV/Vis and NMR spectroscopy. Upon coordination to a RuII bipyridine complex, the photoisomerization process can be driven by visible (λmax=450 nm) instead of UV light and furthermore, a large increase of the speed of rotation is noted. DFT calculations point to a contraction of the diazafluorenyl lower half upon metal‐coordination resulting in reduced steric hindrance in the “fjord region” of the molecule. Consequently, it is shown that metal‐ligand interactions can play an important role in the adjustment of both photophysical and thermodynamic properties of molecular motors.

Correlations and symmetry of interactions influence collective dynamics of molecular motors

Enzymatic molecules that actively support many cellular processes, including transport, cell division and cell motility, are known as motor proteins or molecular motors. Experimental studies indicate that they interact with each other and they frequently work together in large groups. To understand the mechanisms of collective behavior of motor proteins we study the effect of interactions in the transport of molecular motors along linear filaments. It is done by analyzing a recently introduced class of totally asymmetric exclusion processes that takes into account the intermolecular interactions via thermodynamically consistent approach. We develop a new theoretical method that allows us to compute analytically all dynamic properties of the system. Our analysis shows that correlations play important role in dynamics of interacting molecular motors. Surprisingly, we find that the correlations for repulsive interactions are weaker and more short-range than the correlations for the attractive interactions. In addition, it is shown that symmetry of interactions affect dynamic properties of molecular motors. The implications of these findings for motor proteins transport are discussed. Our theoretical predictions are tested by extensive Monte Carlo computer simulations.

Theoretical analysis of dynamic processes for interacting molecular motors

Biological transport is supported by the collective dynamics of enzymatic molecules that are called motor proteins or molecular motors. Experiments suggest that motor proteins interact locally via short-range potentials. We investigate the fundamental role of these interactions by carrying out an analysis of a new class of totally asymmetric exclusion processes, in which interactions are accounted for in a thermodynamically consistent fashion. This allows us to explicitly connect microscopic features of motor proteins with their collective dynamic properties. A theoretical analysis that combines various mean-field calculations and computer simulations suggests that the dynamic properties of molecular motors strongly depend on the interactions, and that the correlations are stronger for interacting motor proteins. Surprisingly, it is found that there is an optimal strength of interactions (weak repulsion) that leads to a maximal particle flux. It is also argued that molecular motor transport is more sensitive to attractive interactions. Applications of these results for kinesin motor proteins are discussed.

Chaotic transport of fractional over-damped ratchet with fluctuation and periodic drive

The fractional over-damped ratchet model with thermal fluctuation and periodic drive is introduced by using the damping kernel function of general Langevin equation in the form of power law based on the assumption that cytosol in biological cells has characteristics of power-law memory. On basis of the Grunwald-Letnikov definition of fractional derivative, the numerical solution of this ratchet model is obtained. And furthermore, according to the numerical solution, the transport behaviors of stochastic ratchet and corresponding deterministic ratchet (especially when the deterministic ratchet has chaotic trajectory) are investigated, based on which we try to analyze how chaotic properties of the deterministic ratchet and the actions of noise influence the transport properties of molecular motors and moreover find the possible mechanism of current reversal of fractional molecular motor. Numerical results show that, as barrier height, barrier asymmetry and memorability of model change, the current reversal in deterministic ratchet is not necessarily required to appear when happening indeed in corresponding stochastic ratchet; moreover, with the decrease of order p, there exists a chaotic regime in deterministic ratchet model before current reversal, but with the disturbance of noise, current reversal will happen more earlier, namely, chaotic current direction in deterministic ratchet model can be reversed when disturbance of noise exists. This also demonstrates that noise can essentially change the transport behavior of a ratchet; current can change from chaotic state in a ratchet with no noise to directed transport with noise. This is a possible mechanism of current reversal of a fractional stochastic ratchet, and also a reflection that noise plays an active role in directed transport.

Functional diversity of axonemal dyneins as assessed by in vitro and in vivo motility assays of Chlamydomonas mutants.

This review outlines the current knowledge of the functional diversity of axonemal dyneins, as revealed by studies with the model organism Chlamydomonas. Axonemal dyneins, which comprise outer and inner dynein arms, power cilia and flagella beating by producing sliding movements between adjacent outer-doublet microtubules. Outer- and inner-arm dyneins have traditionally been considered similar in structure and function. However, recent evidence suggests that they differ rather strikingly in subunit composition, axonemal arrangement, and molecular motor properties. We posit that these arms make up two largely independent motile systems; whereas outer-arm dynein can generate axonemal beating by itself under certain conditions, inner-arm dynein can generate beating only in cooperation with the central pair/radial spokes. This conclusion is supported by genome analyses of various organisms. Outer-arm dynein appears to be particularly important for nodal cilia of mammalian embryos that function for determination of left-right body asymmetry.

Single-Molecule Motility: Statistical Analysis and the Effects of Track Length on Quantification of Processive Motion

In vitro, single-molecule motility assays allow for the direct characterization of molecular motor properties including stepping velocity and characteristic run length. Although application of these techniques in vivo is feasible, the challenges involved in sample preparation, as well as the added complexity of the cell and its systems, result in a reduced ability to collect large datasets, as well as difficulty in simultaneous observation of the components of the motility system, namely motor and track. To address these challenges, we have developed simulations to characterize motility datasets as a function of sample size, processive run length of the motor, and distribution of track lengths. We introduce the use of a simple bootstrapping technique that allows for the quantification of measurement uncertainty and a Monte Carlo permutation resampling scheme for the measurement of statistical significance and the estimation of required sample size. In addition, we have found that, despite conventional wisdom, the measured characteristic run length is directly coupled to the characteristic track length that describes the microtubule length distribution. To be able to make comparisons between motility experiments performed on different track populations as well as make measurements of motility when motors and tracks cannot be simultaneously resolved, we have developed a theoretical framework for the determination of the effect that track length has on observed characteristic run lengths. This shows good agreement with in vitro motility experiments on two kinesin constructs walking on microtubule populations of different characteristic track lengths.

Quantitative Assessment of Single Molecule Motility In Vivo

In vitro single molecule motility assays allow for the direct characterization of molecular motor properties including stepping velocity and characteristic run length. While application of these techniques in vivo is feasible, the challenges involved in sample preparation as well as the added complexity of the cell and its systems result in reduced ability to collect large datasets, as well as difficulty in simultaneous observation of the components of the motility system, namely motor and track. To address these challenges, we have developed simulations to characterize motility datasets in order to understand data behavior and the effects of undersampling. We introduce the use of a simple bootstrapping technique that allows for the quantification of measurement uncertainty and a Monte Carlo permutation resampling scheme for the measurement of statistical significance and the estimation of required sample size. In addition, we have modeled motility collected in the absence of simultaneous track observation and developed a theoretical framework for the determination of characteristic run length in systems where motility and track length must be characterized sequentially, which shows good agreement with in vitro motility experiments on two kinesin constructs walking on microtubules stabilized by either paclitaxel or the GTP analog GMPCPP.

Optical traps to study properties of molecular motors.

In vitro motility assays enabled the analysis of coupling between ATP hydrolysis and movement of myosin along actin filaments or kinesin along microtubules. Single-molecule assays using laser trapping have been used to obtain more detailed information about kinesins, myosins, and processive DNA enzymes. The combination of in vitro motility assays with laser-trap measurements has revealed detailed dynamic structural changes associated with the ATPase cycle. This article describes the use of optical traps to study processive and nonprocessive molecular motor proteins, focusing on the design of the instrument and the assays to characterize motility.

THE MEAN VELOCITY OF TWO-STATE MODELS OF MOLECULAR MOTOR

The motion of molecular motor is essential to the biophysical functioning of living cells. This motion can be regarded as a multiple chemical state process. So, mathematically, the motion of molecular motor can be described by several coupled one-dimensional hopping processes or by several coupled Fokker–Planck equations. To know the basic properties of molecular motor, in this paper, we will give detailed analysis about the simplest case in which there are only two chemical states. Actually, many of the existing models, such as the flashing ratchet model, can be regarded as a two-state model. From the explicit expression of the mean velocity, one can see that the mean velocity of molecular motor might be non-zero even if the potential in each state is periodic, which means that there is no energy input to the molecular motor in each of the two states. At the same time, the mean velocity might be zero even if there is non-trivial energy input. Generally, the velocity of molecular motor depends not only on the potentials (or corresponding forward and backward transition rates) in the two chemical states, but also on the transition rates between them.

Biased motion and molecular motor properties of bipedal spiders

Molecular spiders are synthetic molecular motors featuring multiple legs that each can interact with a substrate through binding and cleavage. Experimental studies suggest the motion of the spider in a matrix is biased toward uncleaved substrates and that spider properties such as processivity can be altered by changing the binding strength of the legs to substrate [R. Pei, S. K. Taylor, D. Stefanovic, S. Rudchenko, T. E. Mitchell, and M. N. Stojanovic, J. Am. Chem. Soc. 128, 12693 (2006)]. We investigate the origin of biased motion and molecular motor properties of bipedal spiders using Monte Carlo simulations. Our simulations combine a realistic chemical kinetic model, hand-over-hand or inchworm modes of stepping, and the use of a one-dimensional track. We find that stronger binding to substrate, cleavage and spider detachment from the track are contributing mechanisms to population bias. We investigate the contributions of stepping mechanism to speed, randomness parameter, processivity, coupling, and efficiency, and comment on how these molecular motor properties can be altered by changing experimentally tunable kinetic parameters.

Biased Motion and Molecular Motor Properties of Molecular Spiders

Molecular spiders are synthetic molecular motors featuring multiple legs that each can interact with a substrate through binding and cleavage. Experimental studies suggest the motion of the spider in a matrix is biased towards uncleaved substrates, and that spider properties such as processivity can be altered by changing the binding strength of the legs to substrate [R. Pei et al., J. Amer. Chem. Soc.128, 12693 (2006)]. We investigate the origin of biased motion and molecular motor properties of bipedal spiders using Monte Carlo simulations. Our simulations combine a realistic chemical kinetic model, hand-over-hand (HOH) or inchworm (IW) modes of stepping, and the use of a 1D track. We find that substrate cleavage and spider detachment from the track are both contributing mechanisms to population bias but are not necessary for biased motion on an asymmetric track. We investigate the contributions of stepping mechanism to speed, randomness parameter, processivity, coupling and efficiency, and comment on how these molecular motor properties can be altered by changing experimentally tunable kinetic parameters. We then consider the more general case where steps can occur by any mechanism, subject to steric constraints. We compare these results with the above for bipedal spiders and then simulate quadrupedal spiders to investigate the effect of leg number on motor performance.

Dynamics of molecular motors in reversible burnt-bridge models

Dynamic properties of molecular motors whose motion is powered by interactions with specic lattice bonds are studied theoretically with the help of discrete-state stochastic iburnt-bridgei models. Molecular motors are depicted as random walkers that can destroy or rebuild periodically distributed weak connections (ibridgesi) when crossing them, with probabilities p1 and p2 correspondingly. Dynamic properties, such as velocities and dispersions, are obtained in exact and explicit form for arbitrary values of parameters p1 and p2. For the unbiased random walker, reversible burning of the bridges results in a biased directed motion with a dynamic transition observed at very small concentrations of bridges. In the case of backward biased molecular motor its backward velocity is reduced and a reversal of the direction of motion is observed for some range of parameters. It is also found that the dispersion demonstrates a complex, non-monotonic behavior with large uctuations for some set of parameters. Complex dynamics of the system is discussed by analyzing the behavior of the molecular motors near burned bridges.