Motor proteins and molecular motors: how to operate machines at the nanoscale

Stiffening of the Cytoplasm in Response to Intracellularly Applied Forces

Cells constantly encounter mechanical forces that regulate various cellular functions, such as migration, division, and differentiation. Understanding how cells respond to forces at the intracellular level is essential for elucidating the mechanical adaptability of living cells. This study investigates how the cytoplasm alters its mechanical properties in response to forces applied inside a cell. The mechanical properties were measured through in situ characterization using magnetic tweezers to apply mechanical forces on magnetic beads internalized into cells. The findings reveal that the cytoplasm stiffens within seconds when force is applied to the cytoplasm. Macromolecular crowding and cytoskeletal structures, particularly F-actin, were found to significantly contribute to cytoplasm stiffening. The stiffening response was also observed across multiple length scales by using magnetic beads of varying diameters. These results highlight the rapid adaptation of the cytoplasm to mechanical forces applied to the inside of a cell.

CARD14 signalosome formation is associated with its endosomal relocation and mTORC1-induced keratinocyte proliferation

Rare mutations in CARD14 promote psoriasis by inducing CARD14-BCL10-MALT1 complexes that activate NF-κB and MAP kinases. Here, the downstream signalling mechanism of the highly penetrant CARD14E138A alteration is described. In addition to BCL10 and MALT1, CARD14E138A associated with several proteins important in innate immune signalling. Interactions with M1-specific ubiquitin E3 ligase HOIP, and K63-specific ubiquitin E3 ligase TRAF6 promoted BCL10 ubiquitination and were essential for NF-κB and MAP kinase activation. In contrast, the ubiquitin binding proteins A20 and ABIN1, both genetically associated with psoriasis development, negatively regulated signalling by inducing CARD14E138A turnover. CARD14E138A localized to early endosomes and was associated with the AP2 adaptor complex. AP2 function was required for CARD14E138A activation of mTOR complex 1 (mTORC1), which stimulated keratinocyte metabolism, but not for NF-κB nor MAP kinase activation. Furthermore, rapamycin ameliorated CARD14E138A-induced keratinocyte proliferation and epidermal acanthosis in mice, suggesting that blocking mTORC1 may be therapeutically beneficial in CARD14-dependent psoriasis.

Myosin-Catalyzed ATP Hydrolysis in the Presence of Disease-Causing Mutations: Mavacamten as a Way to Repair Mechanism

Hypertrophic cardiomyopathy is one of the most common forms of genetic cardiomyopathy. Mavacamten is a first-in-class myosin modulator that was identified via activity screening on the wild type, and it is FDA-approved for the treatment of obstructive hypertrophic cardiomyopathy (HCM). The drug selectively binds to the cardiac β-myosin, inhibiting myosin function to decrease cardiac contractility. Though the drug is thought to affect multiple steps of the myosin cross-bridge cycle, its detailed mechanism of action is still under investigation. Individual steps in the overall cross-bridge cycle must be queried to elucidate the full mechanism of action. In this study, we utilize the rare-event method of transition path sampling to generate reactive trajectories to gain insights into the action of the drug on the dynamics and rate of the ATP hydrolysis step for human cardiac β-myosin. We study three known HCM causative myosin mutations: R453C, P710R, and R712L to observe the effect of the drug on the alterations caused by these mutations in the chemical step. Since the crystal structure of the drug-bound myosin was not available at the time of this work, we created a model of the drug-bound system utilizing a molecular docking approach. We find a significant effect of the drug in one case, where the actual mechanism of the reaction is altered from the wild type by mutation. The drug restores both the rate of hydrolysis to the wildtype level and the mechanism of the reaction. This is a way to check the effect of the drug on untested mutations.

Unlocking the potential of information flow: Maximizing free-energy transduction in a model of an autonomous rotary molecular motor

Molecular motors fulfill critical functions within all living beings. Understanding their underlying working principles is therefore of great interest. Here we develop a simple model inspired by the two-component biomolecular motor F_{o}-F_{1} ATP synthase. We analyze its energetics and characterize information flows between the machine's components. At maximum output power we find that information transduction plays a minor role for free-energy transduction. However, when the two components are coupled to different environments (e.g., when in contact with heat baths at different temperatures), we show that information flow becomes a resource worth exploiting to maximize free-energy transduction. Our findings suggest that real-world powerful and efficient information engines could be found in machines whose components are subjected to fluctuations of different strength, since in this situation the benefit gained from using information for work extraction can outweigh the costs of information generation.

Single-file transport of binary hard-sphere mixtures through periodic potentials

Single-file transport occurs in various scientific fields, including diffusion through nanopores, nanofluidic devices, and cellular processes. We here investigate the impact of polydispersity on particle currents for single-file Brownian motion of hard spheres when they are driven through periodic potentials by a constant drag force. Through theoretical analysis and extensive Brownian dynamics simulations, we unveil the behavior of particle currents for random binary mixtures. The particle currents show a recurring pattern in dependence of the hard-sphere diameters and mixing ratio. We explain this recurrent behavior by showing that a basic unit cell exists in the space of the two hard-sphere diameters. Once the behavior of an observable inside the unit cell is determined, it can be inferred for any diameter. The overall variation of particle currents with the mixing ratio and hard-sphere diameters is reflected by their variation in the limit where the system is fully covered by hard spheres. In this limit, the currents can be predicted analytically. Our analysis explains the occurrence of pronounced maxima and minima of the currents by changes in the effective potential barrier for the center-of-mass motion.

Roughness induced current reversal in fractional hydrodynamic memory

The existence of a corrugated surface is of great importance and ubiquity in biological systems, exhibiting diverse dynamic behaviors. However, it has remained unclear whether such rough surface leads to the current reversal in fractional hydrodynamic memory. We investigate the transport of a particle within a rough potential under external forces in a subdiffusive media with fractional hydrodynamic memory. The results demonstrate that roughness induces current reversal and a transition from no transport to transport. These phenomena are analyzed through the subdiffusion, Peclet number, useful work, input power, and thermodynamic efficiency. The analysis reveals that transport results from energy conversion, wherein time-dependent periodic force is partially converted into mechanical energy to drive transport against load, and partially dissipated through environmental absorption. In addition, the findings indicate that the size and shape of ratchet tune the occurrence and disappearance of the current reversal, and control the number of times of the current reversal occurring. Furthermore, we find that temperature, friction, and load tune transport, resonant-like activity, and enhanced stability of the system, as evidenced by thermodynamic efficiency. These findings may have implications for understanding dynamics in biological systems and may be relevant for applications involving molecular devices for particle separation at the mesoscopic scale.

Optimal Control of the F1-ATPase Molecular Motor

F₁-ATPase is a rotary molecular motor that in vivo is subject to strong nonequilibrium driving forces. There is great interest in understanding the operational principles governing its high efficiency of free-energy transduction. Here we use a near-equilibrium framework to design a nontrivial control protocol to minimize dissipation in rotating F₁ to synthesize adenosine triphosphate. We find that the designed protocol requires much less work than a naive (constant-velocity) protocol across a wide range of protocol durations. Our analysis points to a possible mechanism for energetically efficient driving of F₁ in vivo and provides insight into free-energy transduction for a broader class of biomolecular and synthetic machines.

Insights into the Mechanism of the Cardiac Drug Omecamtiv Mecarbil─A Computational Study

Omecamtiv mecarbil (OM) is a positive inotrope that is thought to bind directly to an allosteric site of the β-cardiac myosin. The drug is under investigation for the treatment of systolic heart failure. The drug is classified as a cardiac myosin modulator and has been observed to affect multiple vital steps of the cross-bridge cycle including the recovery stroke and the chemical step. We explored the free-energy surface of the recovery stroke of the human cardiac β-myosin in the presence of OM to determine its influence on this process. We also investigated the effects of OM on the recovery stroke in the presence of genetic cardiomyopathic mutations R712L, F764L, and P710R using metadynamics. We also utilized the method of transition path sampling to generate an unbiased ensemble of reactive trajectories for the ATP hydrolysis step in the presence of OM that were able to provide insight into the differences observed due to OM in the dynamics and mechanism of the decomposition of ATP to ADP and HPO₄^2-, a central part of the power generation in cardiac muscle. We studied chemistry in the presence of the same three mutations to further elucidate the effect of OM, and its use in the treatment of cardiac disease.

Virial-like thermodynamic uncertainty relation in the tight-binding regime

We presented a methodology to approximate the entropy production for Brownian motion in a tilted periodic potential. The approximation stems from the well known thermodynamic uncertainty relation. By applying a virial-like expansion, we provided a tighter lower limit solely in terms of the drift velocity and diffusion. The approach presented is systematically analyzed in the tight-binding regime. We also provide a relative simple rule to validate using the tight-binding approach based on drift and diffusion relations rather than energy barriers and forces. We also discuss the implications of our results outside the tight-binding regime.

A model of minimal entropy generation for cytoskeletal transport systems with multiple interacting motors

We study the steady-state rate of entropy generation for multiple interacting particles. The description used is based on the partially asymmetric exclusion process in a lattice with periodic boundary conditions. Our methodology shows that in the steady-state, the rate of entropy generation is directly proportional to the bulk drift and the applied driving force. Since in many cases the driving force is unknown or hard to determine. We circumvent this by deriving a lower bound for the entropy, resulting in an extended thermodynamic uncertainty relation for the asymmetric simple exclusion process. We systematically compared this bound with the actual entropy generation. Thus, we identify the force regimes, and particles' density conditions where the entropy bound derived from this extended thermodynamic uncertainty relation is meaningful.

Perspective: a stirring role for metabolism in cells

Based on recent findings indicating that metabolism might be governed by a limit on the rate at which cells can dissipate Gibbs energy, in this Perspective, we propose a new mechanism of how metabolic activity could globally regulate biomolecular processes in a cell. Specifically, we postulate that Gibbs energy released in metabolic reactions is used to perform work, allowing enzymes to self-propel or to break free from supramolecular structures. This catalysis-induced enzyme movement will result in increased intracellular motion, which in turn can compromise biomolecular functions. Once the increased intracellular motion has a detrimental effect on regulatory mechanisms, this will establish a feedback mechanism on metabolic activity, and result in the observed thermodynamic limit. While this proposed explanation for the identified upper rate limit on cellular Gibbs energy dissipation rate awaits experimental validation, it offers an intriguing perspective of how metabolic activity can globally affect biomolecular functions and will hopefully spark new research.

Oscillating external force as a tool to tune motility characteristics of molecular motors

Molecular motors move in a dynamic environment of the cytoskeleton which generates fluctuations exceeding the thermal agitation. Their efficient motility and force generation are generally achieved via complex gating and coupling mechanisms between chemical steps, conformational changes, and mechanical steps in the working cycle. However, the motors display various force-velocity relations seemingly related (also) to the asymmetry of their unbinding from the track depending on the direction of the applied force. Here we study theoretically how the motility of molecular motors changes when they operate under an oscillating external force. We explore the roles of the shape of the force-velocity relation and the asymmetry of the force-induced unbinding. We find that a motor speeds up under force oscillations if its unbinding has a strong load dependence and a moderate asymmetry with respect to the direction of load. Motors whose unbinding is slowed down under hindering forces withstand average loads higher than the usual stall force. The relation between the function, unbinding properties, and predicted responses to the oscillating force supports the idea that the asymmetry of the load induced unbinding could serve as an adaptation of motors to their different physiological functions.

Spectroscopic glimpses of the transition state of ATP hydrolysis trapped in a bacterial DnaB helicase

The ATP hydrolysis transition state of motor proteins is a weakly populated protein state that can be stabilized and investigated by replacing ATP with chemical mimics. We present atomic-level structural and dynamic insights on a state created by ADP aluminum fluoride binding to the bacterial DnaB helicase from Helicobacter pylori. We determined the positioning of the metal ion cofactor within the active site using electron paramagnetic resonance, and identified the protein protons coordinating to the phosphate groups of ADP and DNA using proton-detected 31P,1H solid-state nuclear magnetic resonance spectroscopy at fast magic-angle spinning > 100 kHz, as well as temperature-dependent proton chemical-shift values to prove their engagements in hydrogen bonds. 19F and 27Al MAS NMR spectra reveal a highly mobile, fast-rotating aluminum fluoride unit pointing to the capture of a late ATP hydrolysis transition state in which the phosphoryl unit is already detached from the arginine and lysine fingers.

Cytoskeletal Arrest: An Anoxia Tolerance Mechanism

Polymerization of actin filaments and microtubules constitutes a ubiquitous demand for cellular adenosine-5′-triphosphate (ATP) and guanosine-5′-triphosphate (GTP). In anoxia-tolerant animals, ATP consumption is minimized during overwintering conditions, but little is known about the role of cell structure in anoxia tolerance. Studies of overwintering mammals have revealed that microtubule stability in neurites is reduced at low temperature, resulting in withdrawal of neurites and reduced abundance of excitatory synapses. Literature for turtles is consistent with a similar downregulation of peripheral cytoskeletal activity in brain and liver during anoxic overwintering. Downregulation of actin dynamics, as well as modification to microtubule organization, may play vital roles in facilitating anoxia tolerance. Mitochondrial calcium release occurs during anoxia in turtle neurons, and subsequent activation of calcium-binding proteins likely regulates cytoskeletal stability. Production of reactive oxygen species (ROS) formation can lead to catastrophic cytoskeletal damage during overwintering and ROS production can be regulated by the dynamics of mitochondrial interconnectivity. Therefore, suppression of ROS formation is likely an important aspect of cytoskeletal arrest. Furthermore, gasotransmitters can regulate ROS levels, as well as cytoskeletal contractility and rearrangement. In this review we will explore the energetic costs of cytoskeletal activity, the cellular mechanisms regulating it, and the potential for cytoskeletal arrest being an important mechanism permitting long-term anoxia survival in anoxia-tolerant species, such as the western painted turtle and goldfish.

Emergence of directional bias in tau deposition from axonal transport dynamics

Defects in axonal transport may partly underpin the differences between the observed pathophysiology of Alzheimer's disease (AD) and that of other non-amyloidogenic tauopathies. Particularly, pathological tau variants may have molecular properties that dysregulate motor proteins responsible for the anterograde-directed transport of tau in a disease-specific fashion. Here we develop the first computational model of tau-modified axonal transport that produces directional biases in the spread of tau pathology. We simulated the spatiotemporal profiles of soluble and insoluble tau species in a multicompartment, two-neuron system using biologically plausible parameters and time scales. Changes in the balance of tau transport feedback parameters can elicit anterograde and retrograde biases in the distributions of soluble and insoluble tau between compartments in the system. Aggregation and fragmentation parameters can also perturb this balance, suggesting a complex interplay between these distinct molecular processes. Critically, we show that the model faithfully recreates the characteristic network spread biases in both AD-like and non-AD-like mouse tauopathy models. Tau transport feedback may therefore help link microscopic differences in tau conformational states and the resulting variety in clinical presentations.

Electroactive macromolecular motors as model materials of ectotherm muscles

The electrochemical reaction in liquid electrolytes of conducting polymers, carbon nanotubes, graphenes, among other materials, replicates the active components (macromolecular electro-chemical motors, ions and solvent) and volume variation of the sarcomere in any natural muscles during actuation, allowing the development of electro-chemo-mechanical artificial muscles. Materials, reactions and artificial muscles have been used as model materials, model reactions and model devices of the muscles from ectotherm animals. We present in this perspective the experimental results and a quantitative description of the thermal influence on the reaction extension and energetic achievements of those muscular models using different experimental methodologies. By raising the temperature for 40 °C keeping the extension of the muscular movement the cooperative actuation of the macromolecular motors harvest, saving chemical energy, up to 60% of the reaction energy from the thermal environment. The synergic thermal influence on either, the reaction rate (Arrhenius), the conformational movement rates of the motors (ESCR model) and the diffusion coefficients of ions across polymer matrix (WLF equation) can support the physical chemical foundations for the selection by nature of ectotherm muscles. Macromolecular motors act, simultaneously, as electro-chemo-mechanical and thermo-mechanical transducers. Technological and biological perspectives are presented.

Investigation of the Recovery Stroke and ATP Hydrolysis and Changes Caused Due to the Cardiomyopathic Point Mutations in Human Cardiac β Myosin

Human cardiac β myosin undergoes the cross-bridge cycle as part of the force-generating mechanism of cardiac muscle. The recovery stroke is considered one of the key steps of the kinetic cycle as it is the conformational rearrangement required to position the active site residues for hydrolysis of ATP and interaction with actin. We explored the free-energy surface of the transition and investigated the effect of the genetic cardiomyopathy causing mutations R453C, I457T, and I467T on this step using metadynamics. This work extends previous studies on Dictyostelium myosin II with engineered mutations. Here, like previously, we generated an unbiased thermodynamic ensemble of reactive trajectories for the chemical step using transition path sampling. Our methodologies were able to predict the changes to the dynamics of the recovery stroke as well as predict the pathway of breakdown of ATP to ADP and HPO₄^2- with the stabilization of the metaphosphate intermediate. We also observed clear differences between the Dictyostelium myosin II and human cardiac β myosin for ATP hydrolysis as well as predict the effect of the mutation I467T on the chemical step.

Mechanistic analysis of light-driven overcrowded alkene-based molecular motors by multiscale molecular simulations

We analyze light-driven overcrowded alkene-based molecular motors, an intriguing class of small molecules that have the potential to generate MHz-scale rotation rates. The full rotation process is simulated at multiple scales by combining quantum surface-hopping molecular dynamics (MD) simulations for the photoisomerization step with classical MD simulations for the thermal helix inversion step. A Markov state analysis resolves conformational substates, their interconversion kinetics, and their roles in the motor's rotation process. Furthermore, motor performance metrics, including rotation rate and maximal power output, are computed to validate computations against experimental measurements and to inform future designs. Lastly, we find that to correctly model these motors, the force field must be optimized by fitting selected parameters to reference quantum mechanical energy surfaces. Overall, our simulations yield encouraging agreement with experimental observables such as rotation rates, and provide mechanistic insights that may help future designs.

Enzymatic trans-bilayer lipid transport: Mechanisms, efficiencies, slippage, and membrane curvature

The eukaryotic plasma membrane's lipid composition is found to be ubiquitously asymmetric comparing inner and outer leaflets. This membrane lipid asymmetry plays a crucial role in diverse cellular processes critical for cell survival. A specialized set of transmembrane proteins called translocases, or flippases, have evolved to maintain this membrane lipid asymmetry in an energy-dependent manner. One potential consequence of local variations in membrane lipid asymmetry is membrane remodeling, which is essential for cellular processes such as intracellular trafficking. Recently, there has been a surge in the identification and characterization of flippases, which has significantly advanced the understanding of their functional mechanisms. Furthermore, there are intriguing possibilities for a coupling between membrane curvature and flippase activity. In this review we highlight studies that link membrane shape and remodeling to differential stresses generated by the activity of lipid flippases with an emphasis on data obtained through model membrane systems. We review the common mechanistic models of flippase-mediated lipid flipping and discuss common techniques used to test lipid flippase activity. We then compare the existing data on lipid translocation rates by flippases and conclude with potential future directions for this field.

Heat diffusion-related damping process in a highly precise coarse-grained model for nonlinear motion of SWCNT

Second sound and heat diffusion in single-walled carbon nanotubes (SWCNT) are well-known phenomena which is related to the high thermal conductivity of this material. In this paper, we have shown that the heat diffusion along the tube axis affects the macroscopic motion of SWCNT and adapting this phenomena to coarse-grained (CG) model can improve the precision of the coarse-grained molecular dynamics (CGMD) exceptionally. The nonlinear macroscopic motion of SWCNT in the free thermal vibration condition in adiabatic environment is demonstrated in the most simplified version of CG modeling as maintaining finite temperature and total energy with suggested dissipation process derived from internal heat diffusion. The internal heat diffusion related to the cross correlated momentum from different potential energy functions is considered, and it can reproduce the nonlinear dynamic nature of SWCNTs without external thermostatting in CG model. Memory effect and thermostat with random noise distribution are not included, and the effect of heat diffusion on memory effect is quantified through Mori-Zwanzig formalism. This diffusion shows perfect syncronization of the motion between that of CGMD and MD simulation, which is started with initial conditions from the molecular dynamics (MD) simulation. The heat diffusion related to this process has shown the same dispersive characteristics to second wave in SWCNT. This replication with good precision indicates that the internal heat diffusion process is the essential cause of the nonlinearity of the tube. The nonlinear dynamic characteristics from the various scale of simple beads systems are examined with expanding its time step and node length.

Mechanochemical Function of Myosin II: Investigation into the Recovery Stroke and ATP Hydrolysis

Myosin regulates muscle function through a complex cycle of conformational rearrangements coupled with the hydrolysis of adenosine triphosphate (ATP). The recovery stroke reorganizes the myosin active site to hydrolyze ATP and cross bridge with the thin filament to produce muscle contraction. Engineered mutations K84M and R704E in Dictyostelium myosin have been designed to specifically inhibit the recovery stroke and have been shown to indirectly affect the ATPase activity of myosin. We investigated these mutagenic perturbations to the recovery stroke and generated thermodynamically correct and unbiased trajectories for native ATP hydrolysis with computationally enhanced sampling methods. Our methodology was able to resolve experimentally observed changes to kinetic and equilibrium dynamics for the recovery stroke with the correct prediction in the severity of these changes. For ATP hydrolysis, the sequential nature along with the stabilization of a metaphosphate intermediate was observed in agreement with previous studies. However, we observed glutamate 459 being utilized as a proton abstractor to prime the attacking water instead of a lytic water, a phenomenon not well categorized in myosin but has in other ATPases. Both rare event methodologies can be extended to human myosin to investigate isoformic differences from Dictyostelium and scan cardiomyopathic mutations to see differential perturbations to kinetics of other conformational changes in myosin such as the power stroke.

Regeneration of Burnt Bridges on a DNA Catenane Walker

DNA walkers are molecular machines that can move with high precision onthe nanoscale due to their structural and functional programmability. Despite recent advances in the field that allow exploring different energy sources, stimuli, and mechanisms of action for these nanomachines, the continuous operation and reusability of DNA walkers remains challenging because in most cases the steps, once taken by the walker, cannot be taken again. Herein we report the path regeneration of a burnt-bridges DNA catenane walker using RNase A. This walker uses a T7RNA polymerase that produces long RNA transcripts to hybridize to the path and move forward while the RNA remains hybridized to the path and blocks it for an additional walking cycle. We show that RNA degradation triggered by RNase A restores the path and returns the walker to the initial position. RNase inhibition restarts the function of the walker.

C-terminal Tail of β-Tubulin and its Role in the Alterations of Dynein Binding Mode

Dynein is a cytoskeletal molecular motor protein that moves along the microtubule (MT) and transports various cellular cargos during its movement. Using standard Molecular Dynamics (MD) simulation, Principle Component Analysis (PCA), and Normal Mode Analysis (NMA) methods, this investigation studied large-scale movements and local interactions of dynein's Microtubule Binding Domain (MTBD) when bound to tubulin heterodimer subunits. Examination of the interactions between the MTBD segments, and their adjustments in terms of intra- and intermolecular distances at the interfacial area with tubulin heterodimer, particularly at α-H16, β-H18, and β-tubulin C-terminal tail (CTT), was the main focus of this study. The specific intramolecular interactions, electrostatic forces, and the salt bridge residue pairs were shown to be the dominating factors in orchestrating movements of the MTBD and MT interfacial segments in the dynein's low-high-affinity binding modes. Important interactions included β-Glu447 and β-Glu449 (CTT) with Arg3469 (MTBD-H6), Lys3472 (MTBD-H6-H7 loop) and Lys3479 (MTBD-H7); β-Glu449 with Lys3384 (MTBD-H8), Lys3386 and His3387 (MTBD-H1). The structural and precise position, orientation, and functional effects of the CTTs on the MT-MTBD, within reasonable cut-off distance for non-bonding interactions and under physiological conditions, are unavailable from previous studies. The absence of the residues in the highly flexible MT-CTTs in the experimentally solved structures is perhaps in some cases due to insufficient data from density maps, but these segments are crucial in protein binding. The presented work contributes to the information useful for the MT-MTBD structure refinement.

Pinned or moving: States of a single shock in a ring

Totally asymmetric exclusion processes (TASEPs) with open boundaries are known to exhibit moving shocks or delocalized domain walls (DDWs) for sufficiently small equal injection and extraction rates. In contrast, TASEPs in a ring with a single inhomogeneity display pinned shocks or localized domain walls (LDWs) under equivalent conditions [see, e.g., H. Hinsch and E. Frey, Phys. Rev. Lett. 97, 095701 (2006)PRLTAO0031-900710.1103/PhysRevLett.97.095701]. By studying periodic exclusion processes composed of a driven (TASEP) and a diffusive segment, we discuss gradual fluctuation-induced depinning of the LDW, leading to its delocalization and formation of a DDW-like domain wall, similar to the DDWs in open TASEPs in some limiting cases under long-time averaging. This smooth crossover is controlled essentially by the fluctuations in the diffusive segment. Our studies provide an explicit route to control the quantitative extent of domain-wall fluctuations in driven periodic inhomogeneous systems, and should be relevant in any quasi-one-dimensional transport processes where the availability of carriers is the rate-limiting constraint.

Single-file transport in periodic potentials: The Brownian asymmetric simple exclusion process

Single-file Brownian motion in periodic structures is an important process in nature and technology, which becomes increasingly amenable for experimental investigation under controlled conditions. To explore and understand generic features of this motion, the Brownian asymmetric simple exclusion process (BASEP) was recently introduced. The BASEP refers to diffusion models where hard spheres are driven by a constant drag force through a periodic potential. Here we derive general properties of the rich collective dynamics in the BASEP. Average currents in the steady state change dramatically with the particle size and density. For an open system coupled to particle reservoirs, extremal current principles predict various nonequilibrium phases, which we verify by Brownian dynamics simulations. For general pair interactions we discuss connections to single-file transport by traveling-wave potentials and prove the impossibility of current reversals in systems driven by a constant drag and by traveling waves.

Single-molecule localization to study cytoskeletal structures, membrane complexes, and mechanosensors

In the last decades, a promising breakthrough in fluorescence imaging was represented by the advent of super-resolution microscopy (SRM). Super-resolution techniques recently became a popular method to study sub-cellular structures, providing a successful approach to observe cytoskeletal and focal adhesion proteins. Among the SR techniques, single-molecule localization microscopy plays a significant role due to its ability to unveil structures and molecular organizations in biological systems. Furthermore, since they provide information at the molecular level, these techniques are increasingly being used to study the stoichiometry and interaction between several membrane channel proteins and their accessory subunits. The aim of this review is to describe the single-molecule localization-based techniques and their applications relevant to cytoskeletal structures and membrane complexes in order to provide as future prospective an overall picture of their correlation with the mechanosensor channel expression and activity.

Theory of Nonequilibrium Free Energy Transduction by Molecular Machines

Biomolecular machines are protein complexes that convert between different forms of free energy. They are utilized in nature to accomplish many cellular tasks. As isothermal nonequilibrium stochastic objects at low Reynolds number, they face a distinct set of challenges compared with more familiar human-engineered macroscopic machines. Here we review central questions in their performance as free energy transducers, outline theoretical and modeling approaches to understand these questions, identify both physical limits on their operational characteristics and design principles for improving performance, and discuss emerging areas of research.

Active cargo positioning in antiparallel transport networks

Cytoskeletal filaments assemble into dense parallel, antiparallel, or disordered networks, providing a complex environment for active cargo transport and positioning by molecular motors. The interplay between the network architecture and intrinsic motor properties clearly affects transport properties but remains poorly understood. Here, by using surface micropatterns of actin polymerization, we investigate stochastic transport properties of colloidal beads in antiparallel networks of overlapping actin filaments. We found that 200-nm beads coated with myosin Va motors displayed directed movements toward positions where the net polarity of the actin network vanished, accumulating there. The bead distribution was dictated by the spatial profiles of local bead velocity and diffusion coefficient, indicating that a diffusion-drift process was at work. Remarkably, beads coated with heavy-mero-myosin II motors showed a similar behavior. However, although velocity gradients were steeper with myosin II, the much larger bead diffusion observed with this motor resulted in less precise positioning. Our observations are well described by a 3-state model, in which active beads locally sense the net polarity of the network by frequently detaching from and reattaching to the filaments. A stochastic sequence of processive runs and diffusive searches results in a biased random walk. The precision of bead positioning is set by the gradient of net actin polarity in the network and by the run length of the cargo in an attached state. Our results unveiled physical rules for cargo transport and positioning in networks of mixed polarity.

Molecular Assembly of Rotary and Linear Motor Proteins

Molecular machines are an important and emerging frontier in research encompassing interdisciplinary subjects of chemistry, physics, biology, and nanotechnology. Although there has been major interest in creating synthetic molecular machines, research on natural molecular machines is also crucial. Biomolecular motors are natural molecular machines existing in nearly every living systems. They play a vital role in almost every essential process ranging from intracellular transport to cell division, muscle contraction and the biosynthesis of ATP that fuels life processes. The construction of biomolecular motor-based biomimetic systems can help not only to deeply understand the mechanisms of motor proteins in the biological process but also to push forward the development of bionics and biomolecular motor-based devices or nanomachines. From combination of natural biomolecular motors with supramolecular chemistry, great opportunities could emerge toward the development of intelligent molecular machines and biodevices. In this Account, we describe our efforts to design and reconstitute biomolecular motor-based active biomimetic systems, in particular, the combination of motor proteins with layer-by-layer (LbL) assembled cellular structures. They are divided into two parts: (i) reconstitution of rotary molecular motor F_OF₁-ATPase, which is coated on the surface of LbL assembled microcapsules or multilayers and synthesizes adenosine triphosphate (ATP) through creating a proton gradient; (ii) molecular assembly of linear molecular motors, the kinesin-based active biomimetic systems, which are coated on a planar surface or LbL assembled tubular structure and drive the movement of microtubules. LbL assembled structures offer motor proteins with an environment that resembles the natural cell. This enables high activity and optimized function of the motor proteins. The assembled biomolecular motors can mimic their functionalities from the natural system. In addition, LbL assembly provides facile integration of functional components into motor protein-based active biomimetic systems and achieves the manipulation of F_OF₁-ATPase and kinesin. For F_OF₁-ATPase, the light-driven proton gradient and controlled ATP synthesis are highlighted. For kinesin, the strategies used for the direction and velocity control of kinesin-based molecular shuttles are discussed. We hope this research can inspire new ideas and propel the actual applications of biomolecular motor-based devices in the future.

First passage of molecular motors on networks of cytoskeletal filaments

Molecular motors facilitate intracellular transport through a combination of passive motion in the cytoplasm and active transport along cytoskeletal filaments. Although the motion of motors on individual filaments is often well characterized, it remains a challenge to understand their transport on networks of filaments. Here we use computer simulations of a stochastic jump process to determine first-passage times (FPTs) of a molecular motor traversing an interval containing randomly distributed filaments of fixed length. We characterize the mean first-passage time (MFPT) as a function of the number and length of filaments. Intervals containing moderate numbers of long filaments lead to the largest MFPTs with the largest relative standard deviation; in this regime, some filament configurations lead to anomalously large FPTs due to spatial regions where motors become trapped for long times. For specific filament configurations, we systematically reverse the directionality of single filaments and determine the MFPT of the perturbed configuration. Surprisingly, altering a single filament can dramatically impact the MFPT, and filaments leading to the largest changes are commonly found in different regions than the traps. We conclude by analyzing the mean square displacement of motors in unconfined systems with a large density of filaments and show that they behave diffusively at times substantially less than the MFPT to traverse the interval. However, the effective diffusion coefficient underestimates the MFPT across the bounded interval, emphasizing the importance of local configurations of filaments on first-passage properties.

Optimal control of rotary motors

Single-molecule experiments have found near-perfect thermodynamic efficiency in the rotary motor F_{1}-ATP synthase. To help elucidate the principles underlying nonequilibrium energetic efficiency in such stochastic machines, we investigate driving protocols that minimize dissipation near equilibrium in a simple model rotary mechanochemical motor, as determined by a generalized friction coefficient. Our simple model has a periodic friction coefficient that peaks near system energy barriers. This implies a minimum-dissipation protocol that proceeds rapidly when the system is overwhelmingly in a single macrostate but slows significantly near energy barriers, thereby harnessing thermal fluctuations to kick the system over energy barriers with minimal work input. This model also manifests a phenomenon not seen in otherwise similar nonperiodic systems: Sufficiently fast protocols can effectively lap the system. While this leads to a trade-off between accuracy of driving and energetic cost, we find that our designed protocols outperform naive protocols.

Brownian Asymmetric Simple Exclusion Process

We study the driven Brownian motion of hard rods in a one-dimensional cosine potential with a large amplitude compared to the thermal energy. In a closed system, we find surprising features of the steady-state current in dependence of the particle density. The form of the current-density relation changes greatly with the particle size and can exhibit both a local maximum and minimum. The changes are caused by an interplay of a barrier reduction, blocking, and exchange symmetry effect. The latter leads to a current equal to that of noninteracting particles for a particle size commensurate with the period length of the cosine potential. For an open system coupled to particle reservoirs, we predict five different phases of nonequilibrium steady states to occur. Our results show that the particle size can be of crucial importance for nonequilibrium phase transitions in driven systems. Possible experiments for demonstrating our findings are pointed out.

Tight-binding derivation of a discrete-continuous description of mechanochemical coupling in a molecular motor

We present a tight-binding derivation of a discrete-continuous description of mechanochemical coupling in a molecular motor. Our derivation is based on the continuous diffusion equation for overdamped Brownian motion on a time-independent tilted periodic potential in two dimensions. The free-energy potential is nonseparable to allow coupling between the chemical and mechanical degrees of freedom. We formally discretize the chemical coordinate by expanding in Wannier states that are localized along the chemical coordinate and parametrized along the mechanical coordinate. A discrete-continuous equation is derived that is valid for anisotropic systems with weak mechanochemical coupling and deep potential wells along the chemical coordinate. The discrete-continuous description is consistent with established theoretical models of molecular motors with discrete chemical states but is constrained by the underlying continuous two-dimensional potential. In particular, we derive analytic expressions for the effective potential along the mechanical coordinate and for the rate of thermal hopping between chemical states. We determine the thermodynamic efficiency of energy conversion and find that, for a molecular motor with one chemical state per cycle, the derived discrete-continuous equation can accurately describe mechanochemical coupling but cannot describe energy conversion.

Motion of kinesin in a viscoelastic medium

Kinesin is a molecular motor that transports cargo along microtubules. The results of many in vitro experiments on kinesin-1 are described by kinetic models in which one transition corresponds to the forward motion and subsequent binding of the tethered motor head. We argue that in a viscoelastic medium like the cytosol of a cell this step is not Markov and has to be described by a nonexponential waiting time distribution. We introduce a semi-Markov kinetic model for kinesin that takes this effect into account. We calculate, for arbitrary waiting time distributions, the moment generating function of the number of steps made, and determine from this the average velocity and the diffusion constant of the motor. We illustrate our results for the case of a waiting time distribution that is Weibull. We find that for realistic parameter values, viscoelasticity decreases the velocity and the diffusion constant, but increases the randomness (or Fano factor).

Nanoparticles engineered to bind cellular motors for efficient delivery

Background

Dynein is a cytoskeletal molecular motor protein that transports cellular cargoes along microtubules. Biomimetic synthetic peptides designed to bind dynein have been shown to acquire dynamic properties such as cell accumulation and active intra- and inter-cellular motion through cell-to-cell contacts and projections to distant cells. On the basis of these properties dynein-binding peptides could be used to functionalize nanoparticles for drug delivery applications.

Results

Here, we show that gold nanoparticles modified with dynein-binding delivery sequences become mobile, powered by molecular motor proteins. Modified nanoparticles showed dynamic properties, such as travelling the cytosol, crossing intracellular barriers and shuttling the nuclear membrane. Furthermore, nanoparticles were transported from one cell to another through cell-to-cell contacts and quickly spread to distant cells through cell projections.

Conclusions

The capacity of these motor-bound nanoparticles to spread to many cells and increasing cellular retention, thus avoiding losses and allowing lower dosage, could make them candidate carriers for drug delivery.

Electronic supplementary material

The online version of this article (10.1186/s12951-018-0354-1) contains supplementary material, which is available to authorized users.

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.

Dynamics of microtubules: highlights of recent computational and experimental investigations

Microtubules are found in most eukaryotic cells, with homologs in eubacteria and archea, and they have functional roles in mitosis, cell motility, intracellular transport, and the maintenance of cell shape. Numerous efforts have been expended over the last two decades to characterize the interactions between microtubules and the wide variety of microtubule associated proteins that control their dynamic behavior in cells resulting in microtubules being assembled and disassembled where and when they are required by the cell. We present the main findings regarding microtubule polymerization and depolymerization and review recent work about the molecular motors that modulate microtubule dynamics by inducing either microtubule depolymerization or severing. We also discuss the main experimental and computational approaches used to quantify the thermodynamics and mechanics of microtubule filaments.

Minimum requirements for motility of a processive motor protein

Motor proteins generally have a two-way coupling between the ATP hydrolysis site, the lever movement and the binding affinity for their track, which allows them to perform efficient stepping. Here we explore the minimal requirements for directed motility based on simpler schemes in which the binding/unbinding from the track is decoupled from the ATPase cycle. We show that a directed power stroke alone is not sufficient for motility, but combined with an asymmetry in force-induced unbinding rates it can generate stepping. The energetic efficiency of such stepping is limited to approximately 20%. We conclude that the allosteric coupling between the ATP hydrolysis and the track binding is not strictly necessary for motility, but it greatly improves its efficiency.

Allocating dissipation across a molecular machine cycle to maximize flux

Biomolecular machines consume free energy to break symmetry and make directed progress. Nonequilibrium ATP concentrations are the typical free energy source, with one cycle of a molecular machine consuming a certain number of ATP, providing a fixed free energy budget. Since evolution is expected to favor rapid-turnover machines that operate efficiently, we investigate how this free energy budget can be allocated to maximize flux. Unconstrained optimization eliminates intermediate metastable states, indicating that flux is enhanced in molecular machines with fewer states. When maintaining a set number of states, we show that-in contrast to previous findings-the flux-maximizing allocation of dissipation is not even. This result is consistent with the coexistence of both "irreversible" and reversible transitions in molecular machine models that successfully describe experimental data, which suggests that, in evolved machines, different transitions differ significantly in their dissipation.

A deterministic model for one-dimensional excluded flow with local interactions

Natural phenomena frequently involve a very large number of interacting molecules moving in confined regions of space. Cellular transport by motor proteins is an example of such collective behavior. We derive a deterministic compartmental model for the unidirectional flow of particles along a one-dimensional lattice of sites with nearest-neighbor interactions between the particles. The flow between consecutive sites is governed by a “soft” simple exclusion principle and by attracting or repelling forces between neighboring particles. Using tools from contraction theory, we prove that the model admits a unique steady-state and that every trajectory converges to this steady-state. Analysis and simulations of the effect of the attracting and repelling forces on this steady-state highlight the crucial role that these forces may play in increasing the steady-state flow, and reveal that this increase stems from the alleviation of traffic jams along the lattice. Our theoretical analysis clarifies microscopic aspects of complex multi-particle dynamic processes.

Sufficient conditions for the additivity of stall forces generated by multiple filaments or motors

Molecular motors and cytoskeletal filaments work collectively most of the time under opposing forces. This opposing force may be due to cargo carried by motors or resistance coming from the cell membrane pressing against the cytoskeletal filaments. Some recent studies have shown that the collective maximum force (stall force) generated by multiple cytoskeletal filaments or molecular motors may not always be just a simple sum of the stall forces of the individual filaments or motors. To understand this excess or deficit in the collective force, we study a broad class of models of both cytoskeletal filaments and molecular motors. We argue that the stall force generated by a group of filaments or motors is additive, that is, the stall force of N number of filaments (motors) is N times the stall force of one filament (motor), when the system is reversible at stall. Conversely, we show that this additive property typically does not hold true when the system is irreversible at stall. We thus present a novel and unified understanding of the existing models exhibiting such non-addivity, and generalise our arguments by developing new models that demonstrate this phenomena. We also propose a quantity similar to thermodynamic efficiency to easily predict this deviation from stall-force additivity for filament and motor collectives.

Intrinsic irreversibility limits the efficiency of multidimensional molecular motors

We consider the efficiency limits of Brownian motors able to extract work from the temperature difference between reservoirs or from external thermodynamic forces. These systems can operate in a variety of modes, including as isothermal engines, heat engines, refrigerators, and heat pumps. We derive analytical results showing that certain classes of multidimensional Brownian motor, including the Smoluchowski-Feynman ratchet, are unable to attain perfect efficiency (Carnot efficiency for heat engines). This demonstrates the presence of intrinsic irreversibilities in their operating mechanism. We present numerical simulations showing that in some cases the loss process that limits efficiency is associated with vortices in the probability current.

A catalytic oligomeric motor that walks along a filament track

Most biological motors in the cell execute chemically powered conformational changes as they walk on biopolymer filaments in order to carry out directed transport functions. Synthetic motors that operate in a similar manner are being studied since they have the potential to perform similar tasks in a variety of applications. In this paper, a synthetic nanomotor that moves along a filament track, without invoking motor conformational changes, is constructed and its properties are studied in detail. The motor is an oligomer comprising three linked beads with specific binding properties. The filament track is a stiff polymer chain, also described by a linear chain of linked coarse-grained molecular groups modeled as beads. Reactions on the filament that are catalyzed by a motor bead and use fuel in the environment, in conjunction within the binding affinities of the motor beads to the filament beads, lead to directed motion. The system operates out of equilibrium due to the state of the filament and supply of fuel. The motor, filament, and surrounding medium are all described at microscopic level that permits a full analysis of the motor motion. A stochastic model that captures the main trends seen in the simulations is also presented. The results of this study point to some of the key features that could be used to construct nanomotors that undergo biased walks powered by chemical reactions on filaments.

Collective dynamics of processive cytoskeletal motors

Major cellular processes are supported by various biomolecular motors that usually operate together as teams. We present an overview of the collective dynamics of processive cytokeletal motor proteins based on recent experimental and theoretical investigations. Experimental studies show that multiple motors function with different degrees of cooperativity, ranging from negative to positive. This effect depends on the mechanical properties of individual motors, the geometry of their connections, and the surrounding cellular environment. Theoretical models based on stochastic approaches underline the importance of intermolecular interactions, the properties of single motors, and couplings with cellular medium in predicting the collective dynamics. We discuss several features that specify the cooperativity in motor proteins. Based on this approach a general picture of collective dynamics of motor proteins is formulated, and the future directions and challenges are discussed.

Cytoskeletal Network Morphology Regulates Intracellular Transport Dynamics

Intracellular transport is essential for maintaining proper cellular function in most eukaryotic cells, with perturbations in active transport resulting in several types of disease. Efficient delivery of critical cargos to specific locations is accomplished through a combination of passive diffusion and active transport by molecular motors that ballistically move along a network of cytoskeletal filaments. Although motor-based transport is known to be necessary to overcome cytoplasmic crowding and the limited range of diffusion within reasonable timescales, the topological features of the cytoskeletal network that regulate transport efficiency and robustness have not been established. Using a continuum diffusion model, we observed that the time required for cellular transport was minimized when the network was localized near the nucleus. In simulations that explicitly incorporated network spatial architectures, total filament mass was the primary driver of network transit times. However, filament traps that redirect cargo back to the nucleus caused large variations in network transport. Filament polarity was more important than filament orientation in reducing average transit times, and transport properties were optimized in networks with intermediate motor on and off rates. Our results provide important insights into the functional constraints on intracellular transport under which cells have evolved cytoskeletal structures, and have potential applications for enhancing reactions in biomimetic systems through rational transport network design.

Formation of helical membrane tubes around microtubules by single-headed kinesin KIF1A

The kinesin-3 motor KIF1A is in charge of vesicular transport in neuronal axons. Its single-headed form is known to be very inefficient due to the presence of a diffusive state in the mechanochemical cycle. However, recent theoretical studies have suggested that these motors could largely enhance force generation by working in teams. Here we test this prediction by challenging single-headed KIF1A to extract membrane tubes from giant vesicles along microtubule filaments in a minimal in vitro system. Remarkably, not only KIF1A motors are able to extract tubes but they feature a novel phenomenon: tubes are wound around microtubules forming tubular helices. This finding reveals an unforeseen combination of cooperative force generation and self-organized manoeuvreing capability, suggesting that the diffusive state may be a key ingredient for collective motor performance under demanding traffic conditions. Hence, we conclude that KIF1A is a genuinely cooperative motor, possibly explaining its specificity to axonal trafficking.

Molecular machines - a new dimension of biological sciences

Biological systems are characterized by directional and precisely controlled flow of matter and information along with the maintenance of their structural patterns. This is possible thanks to sequential transformations of information, energy and structure carried out by molecular machines. The new perception of biological systems, including their mechanical aspects, requires the implementation of tools and approaches previously developed for engineering sciences. In this review paper, a biological system is presented in a new perspective as an ensemble of coordinated molecular devices functioning in the limited space confined by the biological membrane. The working of a molecular machine is presented using the example of F0F1 ATPase, and the general conditions necessary for the coordination of a large number of functional units are described.