Modelling intracellular transport in crowded environments: effects of motor association to cargos.

In intracellular transports, motor proteins transport macromolecules as cargos to desired locations by moving on biopolymers such as microtubules. Recent experiments suggest that, while moving in crowded environments, cargos that can associate motor proteins during their translocation have larger run-length and association time compared to free motors. Here, we model the dynamics of a cargo that can associate at the most m free motors present on the microtubule track as obstacles to its motion. The proposed models display competing effects of association and crowding, leading to a peak in the run-length with the free-motor density. For m = 2 and 3, we show that this feature is governed by the largest eigenvalue of the transition matrix describing the cargo dynamics. In all the above cases, free motors are assumed to be present on the microtubule as stalled obstacles. We finally compare simulation results for the run-length for general scenarios where the free motors undergo processive motion in addition to binding and unbinding to or from the microtubule.

Kinesin-1-transported liposomes prefer to go straight in 3D microtubule intersections by a mechanism shared by other molecular motors.

Kinesin-1 ensembles maneuver vesicular cargoes through the three-dimensional (3D) intracellular microtubule (MT) network. To define how such cargoes navigate MT intersections, we first determined how many kinesins from an ensemble on a lipid-based cargo simultaneously engage a MT, and then determined the directional outcomes (straight, turn, terminate) for liposome cargoes at perpendicular MT intersections. Run lengths of 350-nm diameter liposomes decorated with up to 20, constitutively active, truncated kinesin-1 KIF5B (K543) were longer than single motor transported cargo, suggesting multiple motor engagement. However, detachment forces of lipid-coated beads with ~20 kinesins, measured using an optical trap, showed no more than three simultaneously engaged motors, with a single engaged kinesin predominating, indicating anticooperative MT binding. At two-dimensional (2D) and 3D in vitro MT intersections, liposomes frequently paused (~2 s), suggesting kinesins simultaneously bind both MTs and engage in a tug-of-war. Liposomes showed no directional outcome bias in 2D (1.1 straight:turn ratio) but preferentially went straight (1.8 straight:turn ratio) in 3D intersections. To explain these data, we developed a mathematical model of liposome transport incorporating the known mechanochemistry of kinesins, which diffuse on the liposome surface, and have stiff tails in both compression and extension that impact how motors engage the intersecting MTs. Our model predicts the ~3 engaged motor limit observed in the optical trap and the bias toward going straight in 3D intersections. The striking similarity of these results to our previous study of liposome transport by myosin Va suggests a "universal" mechanism by which cargoes navigate 3D intersections.

Magnetic motors in interphases: Motion control and integration in soft robots.

Magnetic motors are a class of out-of-equilibrium particles that exhibit controlled and fast motion overcoming Brownian fluctuations by harnessing external magnetic fields. The advances in this field resulted in motors that have been used for different applications, such as biomedicine or environmental remediation. In this Perspective, an overview of the recent advancements of magnetic motors is provided, with a special focus on controlled motion. This aspect extends from trapping, steering, and guidance to organized motor grouping and degrouping, which is known as swarm control. Further, the integration of magnetic motors in soft robots to actuate their motion is also discussed. Finally, some remarks and perspectives of the field are outlined.

Motorized chain models of the ideal chromosome.

An array of motor proteins consumes chemical energy in setting up the architectures of chromosomes. Here, we explore how the structure of ideal polymer chains is influenced by two classes of motors. The first class which we call "swimming motors" acts to propel the chromatin fiber through three-dimensional space. They represent a caricature of motors such as RNA polymerases. Previously, they have often been described by adding a persistent flow onto Brownian diffusion of the chain. The second class of motors, which we call "grappling motors" caricatures the loop extrusion processes in which segments of chromatin fibers some distance apart are brought together. We analyze these models using a self-consistent variational phonon approximation to a many-body Master equation incorporating motor activities. We show that whether the swimming motors lead to contraction or expansion depends on the susceptibility of the motors, that is, how their activity depends on the forces they must exert. Grappling motors in contrast to swimming motors lead to long-ranged correlations that resemble those first suggested for fractal globules and that are consistent with the effective interactions inferred by energy landscape analyses of Hi-C data on the interphase chromosome.

Coordination, cooperation, competition, crowding and congestion of molecular motors: Theoretical models and computer simulations.

Cytoskeletal motor proteins are biological nanomachines that convert chemical energy into mechanical work to carry out various functions such as cell division, cell motility, cargo transport, muscle contraction, beating of cilia and flagella, and ciliogenesis. Most of these processes are driven by the collective operation of several motors in the crowded viscous intracellular environment. Imaging and manipulation of the motors with powerful experimental probes have been complemented by mathematical analysis and computer simulations of the corresponding theoretical models. In this article, we illustrate some of the key theoretical approaches used to understand how coordination, cooperation and competition of multiple motors in the crowded intra-cellular environment drive the processes that are essential for biological function of a cell. In spite of the focus on theory, experimentalists will also find this article as an useful summary of the progress made so far in understanding multiple motor systems.

Towards the understanding of molecular motors and its relationship with local unfolding.

Molecular motors are machines essential for life since they convert chemical energy into mechanical work. However, the precise mechanism by which nucleotide binding, catalysis, or release of products is coupled to the work performed by the molecular motor is still not entirely clear. This is due, in part, to a lack of understanding of the role of force in the mechanical-structural processes involved in enzyme catalysis. From a mechanical perspective, one promising hypothesis is the Haldane-Pauling hypothesis which considers the idea that part of the enzymatic catalysis is strain-induced. It suggests that enzymes cannot be efficient catalysts if they are fully complementary to the substrates. Instead, they must exert strain on the substrate upon binding, using enzyme-substrate energy interaction (binding energy) to accelerate the reaction rate. A novel idea suggests that during catalysis, significant strain energy is built up, which is then released by a local unfolding/refolding event known as 'cracking'. Recent evidence has also shown that in catalytic reactions involving conformational changes, part of the heat released results in a center-of-mass acceleration of the enzyme, raising the possibility that the heat released by the reaction itself could affect the enzyme's integrity. Thus, it has been suggested that this released heat could promote or be linked to the cracking seen in proteins such as adenylate kinase (AK). We propose that the energy released as a consequence of ligand binding/catalysis is associated with the local unfolding/refolding events (cracking), and that this energy is capable of driving the mechanical work.

Helical motion and torque generation by microtubule motors.

Microtubule motors play key roles in cellular functions, such as transport, mitosis and cell motility. Fueled by ATP hydrolysis, they convert chemical energy into mechanical work, which enables their movement on microtubules. While their motion along the long axis of microtubules has been studied extensively, some motors display an off-axis component, which results in helical motion around microtubules and the generation of torque in addition to linear forces. Understanding these nuanced movements expands our comprehension of motor protein dynamics and their impact on cellular processes.

Autonomous assembly and disassembly of gliding molecular robots regulated by a DNA-based molecular controller.

In recent years, there has been a growing interest in engineering dynamic and autonomous systems with robotic functionalities using biomolecules. Specifically, the ability of molecular motors to convert chemical energy to mechanical forces and the programmability of DNA are regarded as promising components for these systems. However, current systems rely on the manual addition of external stimuli, limiting the potential for autonomous molecular systems. Here, we show that DNA-based cascade reactions can act as a molecular controller that drives the autonomous assembly and disassembly of DNA-functionalized microtubules propelled by kinesins. The DNA controller is designed to produce two different DNA strands that program the interaction between the microtubules. The gliding microtubules integrated with the controller autonomously assemble to bundle-like structures and disassemble into discrete filaments without external stimuli, which is observable by fluorescence microscopy. We believe this approach to be a starting point toward more autonomous behavior of motor protein-based multicomponent systems with robotic functionalities.

Design of artificial molecular motor inheriting directionality and scalability.

Realizing artificial molecular motors with autonomous functionality and high performance is a major challenge in biophysics. Such motors not only provide new perspectives in biotechnology but also offer a novel approach for the bottom-up elucidation of biological molecular motors. Directionality and scalability are critical factors for practical applications. However, the simultaneous realization of both remains challenging. In this study, we propose a novel design for a rotary motor that can be fabricated using a currently available technology, DNA origami, and validate its functionality through simulations with practical parameters. We demonstrate that the motor rotates unidirectionally and processively in the direction defined by structural asymmetry, which induces kinetic asymmetry in motor motion. The motor also exhibits scalability, such that increasing the number of connections between the motor and stator allows for a larger speed, run length, and stall force.

Motor crosslinking augments elasticity in active nematics.

In active materials, uncoordinated internal stresses lead to emergent long-range flows. An understanding of how the behavior of active materials depends on mesoscopic (hydrodynamic) parameters is developing, but there remains a gap in knowledge concerning how hydrodynamic parameters depend on the properties of microscopic elements. In this work, we combine experiments and multiscale modeling to relate the structure and dynamics of active nematics composed of biopolymer filaments and molecular motors to their microscopic properties, in particular motor processivity, speed, and valency. We show that crosslinking of filaments by both motors and passive crosslinkers not only augments the contributions to nematic elasticity from excluded volume effects but dominates them. By altering motor kinetics we show that a competition between motor speed and crosslinking results in a nonmonotonic dependence of nematic flow on motor speed. By modulating passive filament crosslinking we show that energy transfer into nematic flow is in large part dictated by crosslinking. Thus motor proteins both generate activity and contribute to nematic elasticity. Our results provide new insights for rationally engineering active materials.

Motility of an autonomous protein-based artificial motor that operates via a burnt-bridge principle.

Inspired by biology, great progress has been made in creating artificial molecular motors. However, the dream of harnessing proteins - the building blocks selected by nature - to design autonomous motors has so far remained elusive. Here we report the synthesis and characterization of the Lawnmower, an autonomous, protein-based artificial molecular motor comprised of a spherical hub decorated with proteases. Its "burnt-bridge" motion is directed by cleavage of a peptide lawn, promoting motion towards unvisited substrate. We find that Lawnmowers exhibit directional motion with average speeds of up to 80 nm/s, comparable to biological motors. By selectively patterning the peptide lawn on microfabricated tracks, we furthermore show that the Lawnmower is capable of track-guided motion. Our work opens an avenue towards nanotechnology applications of artificial protein motors.

Roles of linker region flanked by transmembrane and peptidoglycan binding region of PomB in energy conversion of the Vibrio flagellar motor.

The flagellar components of Vibrio spp., PomA and PomB, form a complex that transduces sodium ion and contributes to rotate flagella. The transmembrane protein PomB is attached to the basal body T-ring by its periplasmic region and has a plug segment following the transmembrane helix to prevent ion flux. Previously we showed that PomB deleted from E41 to R120 (Δ41-120) was functionally comparable to the full-length PomB. In this study, three deletions after the plug region, PomB (Δ61-120), PomB (Δ61-140), and PomB (Δ71-150), were generated. PomB (Δ61-120) conferred motility, whereas the other two mutants showed almost no motility in soft agar plate; however, we observed some swimming cells with speed comparable for the wild-type cells. When the two PomB mutants were introduced into a wild-type strain, the swimming ability was not affected by the mutant PomBs. Then, we purified the mutant PomAB complexes to confirm the stator formation. When plug mutations were introduced into the PomB mutants, the reduced motility by the deletion was rescued, suggesting that the stator was activated. Our results indicate that the deletions prevent the stator activation and the linker and plug regions, from E41 to S150, are not essential for the motor function of PomB but are important for its regulation.

Structure and Assembly of the Proteus mirabilis Flagellar Motor by Cryo-Electron Tomography.

Proteus mirabilis is a Gram-negative Gammaproteobacterium and a major causative agent of urinary tract infections in humans. It is characterized by its ability to switch between swimming motility in liquid media and swarming on solid surfaces. Here, we used cryo-electron tomography and subtomogram averaging to reveal the structure of the flagellar motor of P. mirabilis at nanometer resolution in intact cells. We found that P. mirabilis has a motor that is structurally similar to those of Escherichia coli and Salmonella enterica, lacking the periplasmic elaborations that characterize other more specialized gammaproteobacterial motors. In addition, no density corresponding to stators was present in the subtomogram average suggesting that the stators are dynamic. Finally, several assembly intermediates of the motor were seen that support the inside-out assembly pathway.

Purification of Na+-Driven MotPS Stator Complexes and Single-Molecule Imaging by High-Speed Atomic Force Microscopy.

The stator unit of the bacterial flagellar motor coordinates the number of active stators in the motor by sensing changes in external load and ion motive force across the cytoplasmic membrane. The structural dynamics of the stator unit at the single-molecule level is key to understanding the sensing mechanism and motor assembly. High-speed atomic force microscopy (HS-AFM) is a powerful tool for directly observing dynamically acting biological molecules with high spatiotemporal resolution without interfering with their function. Here, we describe protocols for single-molecule imaging of the Na+-driven MotPS stator complex by HS-AFM.

Intrinsically unidirectional chemically fuelled rotary molecular motors.

Biological systems mainly utilize chemical energy to fuel autonomous molecular motors, enabling the system to be driven out of equilibrium1. Taking inspiration from rotary motors such as the bacterial flagellar motor2 and adenosine triphosphate synthase3, and building on the success of light-powered unidirectional rotary molecular motors4-6, scientists have pursued the design of synthetic molecular motors solely driven by chemical energy7-13. However, designing artificial rotary molecular motors operating autonomously using a chemical fuel and simultaneously featuring the intrinsic structural design elements to allow full 360° unidirectional rotary motion like adenosine triphosphate synthase remains challenging. Here we show that a homochiral biaryl Motor-3, with three distinct stereochemical elements, is a rotary motor that undergoes repetitive and unidirectional 360° rotation of the two aryl groups around a single-bond axle driven by a chemical fuel. It undergoes sequential ester cyclization, helix inversion and ring opening, and up to 99% unidirectionality is realized over the autonomous rotary cycle. The molecular rotary motor can be operated in two modes: synchronized motion with pulses of a chemical fuel and acid-base oscillations; and autonomous motion in the presence of a chemical fuel under slightly basic aqueous conditions. This rotary motor design with intrinsic control over the direction of rotation, simple chemical fuelling for autonomous motion and near-perfect unidirectionality illustrates the potential for future generations of multicomponent machines to perform mechanical functions.

A DNA origami rotary ratchet motor.

To impart directionality to the motions of a molecular mechanism, one must overcome the random thermal forces that are ubiquitous on such small scales and in liquid solution at ambient temperature. In equilibrium without energy supply, directional motion cannot be sustained without violating the laws of thermodynamics. Under conditions away from thermodynamic equilibrium, directional motion may be achieved within the framework of Brownian ratchets, which are diffusive mechanisms that have broken inversion symmetry1-5. Ratcheting is thought to underpin the function of many natural biological motors, such as the F1F0-ATPase6-8, and it has been demonstrated experimentally in synthetic microscale systems (for example, to our knowledge, first in ref. 3) and also in artificial molecular motors created by organic chemical synthesis9-12. DNA nanotechnology13 has yielded a variety of nanoscale mechanisms, including pivots, hinges, crank sliders and rotary systems14-17, which can adopt different configurations, for example, triggered by strand-displacement reactions18,19 or by changing environmental parameters such as pH, ionic strength, temperature, external fields and by coupling their motions to those of natural motor proteins20-26. This previous work and considering low-Reynolds-number dynamics and inherent stochasticity27,28 led us to develop a nanoscale rotary motor built from DNA origami that is driven by ratcheting and whose mechanical capabilities approach those of biological motors such as F1F0-ATPase.

Direct Measurement of the Stall Torque of the Flagellar Motor in Escherichia coli with Magnetic Tweezers.

The flagellar motor drives the rotation of flagellar filaments, propelling the swimming of flagellated bacteria. The maximum torque the motor generates, the stall torque, is a key characteristic of the motor function. Direct measurements of the stall torque carried out 3 decades ago suffered from large experimental uncertainties, and subsequently there were only indirect measurements. Here, we applied magnetic tweezers to directly measure the stall torque in E. coli. We precisely calibrated the torsional stiffness of the magnetic tweezers and performed motor resurrection experiments at stall, accomplishing a precise determination of the stall torque per torque-generating unit (stator unit). From our measurements, each stator passes 2 protons per step, indicating a tight coupling between motor rotation and proton flux. IMPORTANCE The maximum torque the bacterial flagellar motor generates, the stall torque, is a critical parameter that describes the motor energetics. As the motor operates in equilibrium near stall, from the stall torque one can determine how many protons each torque-generating unit (stator) of the motor passes per revolution and then test whether motor rotation and proton flux are tightly or loosely coupled, which has been controversial in recent years. Direct measurements performed 3 decades ago suffered from large uncertainties, and subsequently, only indirect measurements were attempted, obtaining a range of values inconsistent with the previous direct measurements. Here, we developed a method that used magnetic tweezers to perform motor resurrection experiments at stall, resulting in a direct precise measurement of the stall torque per stator. Our study resolved the previous inconsistencies and provided direct experimental support for the tight coupling mechanism between motor rotation and proton flux.

Human HELB is a processive motor protein that catalyzes RPA clearance from single-stranded DNA.

Human DNA helicase B (HELB) is a poorly characterized helicase suggested to play both positive and negative regulatory roles in DNA replication and recombination. In this work, we used bulk and single-molecule approaches to characterize the biochemical activities of HELB protein with a particular focus on its interactions with Replication Protein A (RPA) and RPA­single-stranded DNA (ssDNA) filaments. HELB is a monomeric protein that binds tightly to ssDNA with a site size of ∼20 nucleotides. It couples ATP hydrolysis to translocation along ssDNA in the 5' to 3' direction accompanied by the formation of DNA loops. HELB also displays classical helicase activity, but this is very weak in the absence of an assisting force. HELB binds specifically to human RPA, which enhances its ATPase and ssDNA translocase activities but inhibits DNA unwinding. Direct observation of HELB on RPA nucleoprotein filaments shows that translocating HELB concomitantly clears RPA from ssDNA. This activity, which can allow other proteins access to ssDNA intermediates despite their shielding by RPA, may underpin the diverse roles of HELB in cellular DNA transactions.

A chemical thermodynamic model of motor enzymes unifies chemical-Fx and powerstroke models.

Molecular motors play a central role in many biological processes, ranging from pumping blood and breathing to growth and wound healing. Through motor-catalyzed chemical reactions, these nanomachines convert the chemical free energy from ATP hydrolysis into two different forms of mechanical work. Motor enzymes perform reversible work, wrev, through an intermediate step in their catalyzed reaction cycle referred to as a working step, and they perform Fx work when they move a distance, x, against a force, F. In a powerstroke model, wrev is performed when the working step stretches a spring within a given motor enzyme. In a chemical-Fx model, wrev is performed in generating a conserved Fx potential defined external to the motor enzyme. It is difficult to find any common ground between these models even though both have been shown to account for mechanochemical measurements of motor enzymes with reasonable accuracy. Here, I show that, by changing one simple assumption in each model, the powerstroke and chemical-Fx model can be reconciled through a chemical thermodynamic model. The formal and experimental justifications for changing these assumptions are presented. The result is a unifying model for mechanochemical coupling in motor enzymes first presented by A.V. Hill in 1938 that is consistent with single-molecule structural and mechanical data.

Nucleosome recognition and DNA distortion by the Chd1 remodeler in a nucleotide-free state.

Chromatin remodelers are ATP-dependent enzymes that reorganize nucleosomes within all eukaryotic genomes. Here we report a complex of the Chd1 remodeler bound to a nucleosome in a nucleotide-free state, determined by cryo-EM to 2.3 Å resolution. The remodeler stimulates the nucleosome to absorb an additional nucleotide on each strand at two different locations: on the tracking strand within the ATPase binding site and on the guide strand one helical turn from the ATPase motor. Remarkably, the additional nucleotide on the tracking strand is associated with a local transformation toward an A-form geometry, explaining how sequential ratcheting of each DNA strand occurs. The structure also reveals a histone-binding motif, ChEx, which can block opposing remodelers on the nucleosome and may allow Chd1 to participate in histone reorganization during transcription.