Small Crowders Slow Down Kinesin-1 Stepping by Hindering Motor Domain Diffusion

Impact of physiological ionic strength and crowding on kinesin-1 motility

The motility of biological molecular motors has typically been analyzed by in vitro reconstitution systems using motors isolated and purified from organs or expressed in cultured cells. The behavior of biomolecular motors within cells has frequently been reported to be inconsistent with that observed in reconstituted systems in vitro. Although this discrepancy has been attributed to differences in ionic strength and intracellular crowding, understanding how such parameters affect the motility of motors remains challenging. In this report, we investigated the impact of intracellular crowding in vitro on the mechanical properties of kinesin under a high ionic strength that is comparable to the cytoplasm. Initially, we characterized viscosity in a cell by using a kinesin motor lacking the cargo-binding domain. We then used polyethylene glycol to create a viscous environment in vitro comparable to the intracellular environment. Our results showed that kinesin frequently dissociated from microtubules under high ionic strength conditions. However, under conditions of both high ionic strength and crowding with polymers, the processive movement of kinesin persisted and increased in frequency. This setting reproduces the significant variations in the mechanical properties of motors measured in the intracellular environment and suggests a mechanism whereby kinesin maintains motility under the high ionic strengths found in cells.Key words: kinesin motility, molecular crowding, ionic strength, intracellular transport, processivity of molecular motors.

Multiple kinesins speed up cargo transport in crowded environments by sharing load

Kinesin motors transport cargoes along microtubules inside of cells. Although it is well known that the cargoes are typically carried by multiple kinesins and that the more motors used, the further the cargoes travel, it has been challenging to determine the number of motors moving a cargo and any instant. Further, there is no unified statement on the relationship between cargo velocity and motor number, especially in the presence of a very crowded cytoplasmic environment. Here, we use a non-invasive method to quantify instantaneous motor number, and use it to investigate the effects of crowded environments on cargo motion when it is carried by multiple kinesins. Our experiments reveal that the velocity of the cargo depends on the number of motors on the cargo and the size of the crowders in crowded environments. Our finding suggests that kinesin tension plays a role in collective motion, which has been confirmed through stochastic kinesin simulations. Overall, our study demonstrates the broad applicability of the non-invasive method to determine engaged motor numbers and sheds light on the intriguing interplay between macromolecular crowding, kinesin tension, and kinesin-mediated cargo transport.

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.

Microtubule-associated protein MAP7 promotes tubulin posttranslational modifications and cargo transport to enable osmotic adaptation

Cells remodel their cytoskeletal networks to adapt to their environment. Here, we analyze the mechanisms utilized by the cell to tailor its microtubule landscape in response to changes in osmolarity that alter macromolecular crowding. By integrating live-cell imaging, ex vivo enzymatic assays, and in vitro reconstitution, we probe the impact of cytoplasmic density on microtubule-associated proteins (MAPs) and tubulin posttranslational modifications (PTMs). We find that human epithelial cells respond to fluctuations in cytoplasmic density by modulating microtubule acetylation, detyrosination, or MAP7 association without differentially affecting polyglutamylation, tyrosination, or MAP4 association. These MAP-PTM combinations alter intracellular cargo transport, enabling the cell to respond to osmotic challenges. We further dissect the molecular mechanisms governing tubulin PTM specification and find that MAP7 promotes acetylation and inhibits detyrosination. Our data identify MAP7 in modulating the tubulin code, resulting in microtubule cytoskeleton remodeling and alteration of intracellular transport as an integrated mechanism of cellular adaptation.

Molecular Ratchets and Kinetic Asymmetry: Giving Chemistry Direction

Over the last two decades ratchet mechanisms have transformed the understanding and design of stochastic molecular systems-biological, chemical and physical-in a move away from the mechanical macroscopic analogies that dominated thinking regarding molecular dynamics in the 1990s and early 2000s (e.g. pistons, springs, etc), to the more scale-relevant concepts that underpin out-of-equilibrium research in the molecular sciences today. Ratcheting has established molecular nanotechnology as a research frontier for energy transduction and metabolism, and has enabled the reverse engineering of biomolecular machinery, delivering insights into how molecules 'walk' and track-based synthesisers operate, how the acceleration of chemical reactions enables energy to be transduced by catalysts (both motor proteins and synthetic catalysts), and how dynamic systems can be driven away from equilibrium through catalysis. The recognition of molecular ratchet mechanisms in biology, and their invention in synthetic systems, is proving significant in areas as diverse as supramolecular chemistry, systems chemistry, dynamic covalent chemistry, DNA nanotechnology, polymer and materials science, molecular biology, heterogeneous catalysis, endergonic synthesis, the origin of life, and many other branches of chemical science. Put simply, ratchet mechanisms give chemistry direction. Kinetic asymmetry, the key feature of ratcheting, is the dynamic counterpart of structural asymmetry (i.e. chirality). Given the ubiquity of ratchet mechanisms in endergonic chemical processes in biology, and their significance for behaviour and function from systems to synthesis, it is surely just as fundamentally important. This Review charts the recognition, invention and development of molecular ratchets, focussing particularly on the role for which they were originally envisaged in chemistry, as design elements for molecular machinery. Different kinetically asymmetric systems are compared, and the consequences of their dynamic behaviour discussed. These archetypal examples demonstrate how chemical systems can be driven inexorably away from equilibrium, rather than relax towards it.

Living Cell as a Self-Synchronized Chemical Reactor

Thermal fluctuations power all processes inside living cells. Therefore, these processes are inherently random. However, myriad multistep chemical reactions act in concerto inside a cell, finally leading to this chemical reactor's self-replication. We speculate that an underlying mechanism in nature must exist that allows all of these reactions to synchronize at multiple time and length scales, overcoming in this way the random nature of any single process in a cell. This Perspective discusses what type of research is needed to understand this undiscovered synchronization law.

Effect of small molecular crowders on dynamics of kinesin molecular motors

Kinesin is a motor protein that can convert chemical energy of ATP hydrolysis into mechanical energy of moving processively on microtubules. Apart from the load and ATP concentration affecting the dynamics of the motor such as velocity, run length, dissociation rate, etc., the increase of solution viscosity by supplementing crowding agents of low molecular weight into the buffer can also affect the dynamics. Here, based on our proposed model for the chemomechanical coupling of the kinesin motor, a systematically theoretical study of the motor dynamics under the variation of the viscosity and load is presented. Both the load on the motor's stalk and that on one of the two heads are considered. The theoretical results provide a consistent explanation of the available contradictory experimental results, with some showing that increasing viscosity decreases sensitively the velocity whereas others showing that increasing viscosity has little effect on the velocity. The theoretical results reproduce quantitatively the puzzling experimental data showing that under different directions of the load on the stalk, increasing viscosity has very different effects on the change of run length or dissociation rate. The theoretical results predict that in both the pure and crowded buffers the dependence of the run length on the load acting one of the two heads has very different feature from that on the load acting on the stalk.

Non-specific cargo-filament interactions slow down motor-driven transport

Active, motor-based cargo transport is important for many cellular functions and cellular development. However, the cell interior is complex and crowded and could have many weak, non-specific interactions with the cargo being transported. To understand how cargo-environment interactions will affect single motor cargo transport and multi-motor cargo transport, we use an artificial quantum dot cargo bound with few (~ 1) to many (~ 5-10) motors allowed to move in a dense microtubule network. We find that kinesin-driven quantum dot cargo is slower than single kinesin-1 motors. Excitingly, there is some recovery of the speed when multiple motors are attached to the cargo. To determine the possible mechanisms of both the slow down and recovery of speed, we have developed a computational model that explicitly incorporates multi-motor cargos interacting non-specifically with nearby microtubules, including, and predominantly with the microtubule on which the cargo is being transported. Our model has recovered the experimentally measured average cargo speed distribution for cargo-motor configurations with few and many motors, implying that numerous, weak, non-specific interactions can slow down cargo transport and multiple motors can reduce these interactions thereby increasing velocity.

Macromolecular Crowding and DNA: Bridging the Gap between In Vitro and In Vivo

The cellular environment is highly crowded, with up to 40% of the volume fraction of the cell occupied by various macromolecules. Most laboratory experiments take place in dilute buffer solutions; by adding various synthetic or organic macromolecules, researchers have begun to bridge the gap between in vitro and in vivo measurements. This is a review of the reported effects of macromolecular crowding on the compaction and extension of DNA, the effect of macromolecular crowding on DNA kinetics, and protein-DNA interactions. Theoretical models related to macromolecular crowding and DNA are briefly reviewed. Gaps in the literature, including the use of biologically relevant crowders, simultaneous use of multi-sized crowders, empirical connections between macromolecular crowding and liquid-liquid phase separation of nucleic materials are discussed.

Long-term cargo tracking reveals intricate trafficking through active cytoskeletal networks in the crowded cellular environment

A eukaryotic cell is a microscopic world within which efficient material transport is essential. Yet, how a cell manages to deliver cellular cargos efficiently in a crowded environment remains poorly understood. Here, we used interferometric scattering microscopy to track unlabeled cargos in directional motion in a massively parallel fashion. Our label-free, cargo-tracing method revealed not only the dynamics of cargo transportation but also the fine architecture of the actively used cytoskeletal highways and the long-term evolution of the associated traffic at sub-diffraction resolution. Cargos frequently run into a blocked road or experience a traffic jam. Still, they have effective strategies to circumvent those problems: opting for an alternative mode of transport and moving together in tandem or migrating collectively. All taken together, a cell is an incredibly complex and busy space where the principle and practice of transportation intriguingly parallel those of our macroscopic world.

Macromolecular Crowding Tailors the Microtubule Cytoskeleton Through Tubulin Modifications and Microtubule-Associated Proteins

Cells remodel their cytoskeletal networks to adapt to their environment. Here, we analyze the mechanisms utilized by the cell to tailor its microtubule landscape in response to changes in osmolarity that alter macromolecular crowding. By integrating live cell imaging, ex vivo enzymatic assays, and in vitro reconstitution, we probe the impact of acute perturbations in cytoplasmic density on microtubule-associated proteins (MAPs) and tubulin posttranslational modifications (PTMs), unraveling the molecular underpinnings of cellular adaptation via the microtubule cytoskeleton. We find that cells respond to fluctuations in cytoplasmic density by modulating microtubule acetylation, detyrosination, or MAP7 association, without differentially affecting polyglutamylation, tyrosination, or MAP4 association. These MAP-PTM combinations alter intracellular cargo transport, enabling the cell to respond to osmotic challenges. We further dissect the molecular mechanisms governing tubulin PTM specification, and find that MAP7 promotes acetylation by biasing the conformation of the microtubule lattice, and directly inhibits detyrosination. Acetylation and detyrosination can therefore be decoupled and utilized for distinct cellular purposes. Our data reveal that the MAP code dictates the tubulin code, resulting in remodeling of the microtubule cytoskeleton and alteration of intracellular transport as an integrated mechanism of cellular adaptation.

Physical properties of the cytoplasm modulate the rates of microtubule polymerization and depolymerization

The cytoplasm is a crowded, visco-elastic environment whose physical properties change according to physiological or developmental states. How the physical properties of the cytoplasm impact cellular functions in vivo remains poorly understood. Here, we probe the effects of cytoplasmic concentration on microtubules by applying osmotic shifts to fission yeast, moss, and mammalian cells. We show that the rates of both microtubule polymerization and depolymerization scale linearly and inversely with cytoplasmic concentration; an increase in cytoplasmic concentration decreases the rates of microtubule polymerization and depolymerization proportionally, whereas a decrease in cytoplasmic concentration leads to the opposite. Numerous lines of evidence indicate that these effects are due to changes in cytoplasmic viscosity rather than cellular stress responses or macromolecular crowding per se. We reconstituted these effects on microtubules in vitro by tuning viscosity. Our findings indicate that, even in normal conditions, the viscosity of the cytoplasm modulates the reactions that underlie microtubule dynamic behaviors.

Ion Complexation Explains Orders of Magnitude Changes in the Equilibrium Constant of Biochemical Reactions in Buffers Crowded by Nonionic Compounds

The equilibrium constant (K) of biochemical complex formation in aqueous buffers with high concentration (>20 wt %) of nonionic compounds can vary by orders of magnitude in comparison with the K in a pure buffer. The precise molecular mechanisms of these profound changes are not known. Herein, we show up to a 1000-fold decrease of the K value of DNA hybridization (at nM concentration) in standard molecular crowder systems such as PEG, dextrans, Ficoll, and glycerol. The effect responsible for the decrease of K is the complexation of positively charged ions from a buffer by nonionic polymers/small molecules. We determined the average equilibrium constant for the complexation of ions per monomer (∼0.49 M^-1). We retrieve K's original value for a pure buffer if we properly increase the ionic strength of the buffer crowded by the polymers, compensating for the loss of complexed ions.

Noise-Induced Acceleration of Single Molecule Kinesin-1

The movement of single kinesin molecules was observed while applying noisy external forces that mimic intracellular active fluctuations. We found kinesin accelerates under noise, especially when a large hindering load is added. The behavior quantitatively conformed to a theoretical model that describes the kinesin movement with simple two-state reactions. The universality of the kinetic theory suggests that intracellular enzymes share a similar noise-induced acceleration mechanism, i.e., active fluctuations in cells are not just noise but are utilized to promote various physiological processes.

Modeling spatiotemporally varying protein-protein interactions in CyLaKS, the Cytoskeleton Lattice-based Kinetic Simulator

Interaction of cytoskeletal filaments, motor proteins, and crosslinking proteins drives important cellular processes such as cell division and cell movement. Cytoskeletal networks also exhibit nonequilibrium self-assembly in reconstituted systems. An emerging problem in cytoskeletal modeling and simulation is spatiotemporal alteration of the dynamics of filaments, motors, and associated proteins. This can occur due to motor crowding, obstacles along the filament, motor interactions and direction switching, and changes, defects, or heterogeneity in the filament binding lattice. How such spatiotemporally varying cytoskeletal filaments and motor interactions affect their collective properties is not fully understood. We developed the Cytoskeleton Lattice-based Kinetic Simulator (CyLaKS) to investigate such problems. The simulation model builds on previous work by incorporating motor mechanochemistry into a simulation with many interacting motors and/or associated proteins on a discretized lattice. CyLaKS also includes detailed balance in binding kinetics, movement, and lattice heterogeneity. The simulation framework is flexible and extensible for future modeling work and is available on GitHub for others to freely use or build upon. Here we illustrate the use of CyLaKS to study long-range motor interactions, microtubule lattice heterogeneity, motion of a heterodimeric motor, and how changing crosslinker number affects filament separation.

Quantifying Nanoscale Viscosity and Structures of Living Cells Nucleus from Mobility Measurements

Understanding the mobility of nano-objects in the eukaryotic cell nucleus, at multiple length-scales, is essential for dissecting nuclear structure-function relationships both in space and in time. Here, we demonstrate, using single-molecule fluorescent correlation spectroscopies, that motion of inert probes (proteins, polymers, or nanoparticles) with diameters ranging from 2.6 to 150 nm is mostly unobstructed in a nucleus. Supported by the analysis of electron tomography images, these results advocate the ∼150 nm-wide interchromosomal channels filled with the aqueous diluted protein solution. The nucleus is percolated by these channels to allow various cargos to migrate freely at the nanoscale. We determined the volume of interchromosomal channels in the HeLa cell nucleus to 237 ± 61 fL, which constitutes 34% of the cell nucleus volume. The volume fraction of mobile proteins in channels equals 16% ± 4%, and the concentration is 1 mM.

The effects of osmolytes on in vitro kinesin-microtubule motility assays

The gliding motility of microtubule filaments has been used to study the biophysical properties of kinesin motors, as well as being used in a variety of nanotechnological applications. While microtubules are generally stabilized in vitro with paclitaxel (Taxol®), osmolytes such as polyethylene glycol (PEG) and trimethylamine N-oxide (TMAO) are also able to inhibit depolymerization over extended periods of time. High concentrations of TMAO have also been reported to reversibly inhibit kinesin motility of paclitaxel-stabilized microtubules. Here, we examined the effects of the osmolytes PEG, TMAO, and glycerol on stabilizing microtubules during gliding motility on kinesin-coated substrates. As previously observed, microtubule depolymerization was inhibited in a concentration dependent manner by the addition of the different osmolytes. Kinesin-driven motility also exhibited concentration dependent effects with the addition of the osmolytes, specifically reducing the velocity, increasing rates of pinning, and altering trajectories of the microtubules. These data suggest that there is a delicate balance between the ability of osmolytes to stabilize microtubules without inhibiting motility. Overall, these findings provide a more comprehensive understanding of how osmolytes affect the dynamics of microtubules and kinesin motors, and their interactions in crowded environments.

Investigation of the Electrical Properties of Microtubule Ensembles under Cell-Like Conditions

Microtubules are hollow cylindrical polymers composed of the highly negatively-charged (~23e), high dipole moment (1750 D) protein α, β- tubulin. While the roles of microtubules in chromosomal segregation, macromolecular transport, and cell migration are relatively well-understood, studies on the electrical properties of microtubules have only recently gained strong interest. Here, we show that while microtubules at physiological concentrations increase solution capacitance, free tubulin has no appreciable effect. Further, we observed a decrease in electrical resistance of solution, with charge transport peaking between 20-60 Hz in the presence of microtubules, consistent with recent findings that microtubules exhibit electric oscillations at such low frequencies. We were able to quantify the capacitance and resistance of the microtubules (MT) network at physiological tubulin concentrations to be 1.27 × 10^-5 F and 9.74 × 10⁴ Ω. Our results show that in addition to macromolecular transport, microtubules also act as charge storage devices through counterionic condensation across a broad frequency spectrum. We conclude with a hypothesis of an electrically tunable cytoskeleton where the dielectric properties of tubulin are polymerisation-state dependent.

Stability of cytoplasmic nanoviscosity during cell cycle of HeLa cells synchronized with Aphidicolin

Nanoviscosity of the cytoplasm is a key factor affecting diffusion of biomolecules and – as a consequence – rates of biochemical reactions in a cell. Nanoviscosity is an outcome of variable chemical and structural factors, which can temporarily change with cell-cycle associated changes of intracellular architecture. Thus, the question arises, whether rates of biochemical reactions depend on the point of cell cycle. In this paper we address this topic by constant observation of nanoviscosity of HeLa cells cytoplasm during S, G2 and G1 phases after Aphidicolin synchronization. For this purpose we measured diffusion rates of EGFP molecules using fluorescence correlation spectroscopy (FCS). To our surprise, a counter-intuitive stability of cytoplasmic viscosity was observed during the cell cycle. Our results hint at possible existence of robust mechanism maintaining stable physiological viscosity of the cytoplasm, despite huge structural changes during cell cycle.

Transport of microtubules according to the number and spacing of kinesin motors on gold nano-pillars

Motor proteins function in in vivo ensembles to achieve cargo transport, flagellum motion, and mitotic cell division. Although the cooperativity of multiple motors is indispensable for physiological function, reconstituting the arrangement of motors in vitro is challenging, so detailed analysis of the functions of motor ensembles has not yet been achieved. Here, we developed an assay platform to study the motility of microtubules driven by a defined number of kinesin motors spaced in a definite manner. Gold (Au) nano-pillar arrays were fabricated on a silicon/silicon dioxide (Si/SiO₂) substrate with spacings of 100 nm to 500 nm. The thiol-polyethylene glycol (PEG)-biotin self-assembled monolayer (SAM) and silane-PEG-CH₃ SAM were then selectively formed on the pillars and SiO₂ surface, respectively. This allowed for both immobilization of kinesin molecules on Au nano-pillars in a precise manner and repulsion of kinesins from the SiO₂ surface. Using arrayed kinesin motors, we report that motor number and spacing do not influence the motility of microtubules driven by kinesin-1 motors. This assay platform is applicable to all kinds of biotinylated motors, allows the study of the effects of motor number and spacing, and is expected to reveal novel behaviors of motor proteins.

Determination of oligomerization state of Drp1 protein in living cells at nanomolar concentrations

Biochemistry in living cells is an emerging field of science. Current quantitative bioassays are performed ex vivo, thus equilibrium constants and reaction rates of reactions occurring in human cells are still unknown. To address this issue, we present a non-invasive method to quantitatively characterize interactions (equilibrium constants, K_D) directly within the cytosol of living cells. We reveal that cytosolic hydrodynamic drag depends exponentially on a probe's size, and provide a model for its determination for different protein sizes (1-70 nm). We analysed oligomerization of dynamin-related protein 1 (Drp1, wild type and mutants: K668E, G363D, C505A) in HeLa cells. We detected the coexistence of wt-Drp1 dimers and tetramers in cytosol, and determined that K_D for tetramers was 0.7 ± 0.5 μM. Drp1 kinetics was modelled by independent simulations, giving computational results which matched experimental data. This robust method can be applied to in vivo determination of K_D for other protein-protein complexes, or drug-target interactions.

Cargo diffusion shortens single-kinesin runs at low viscous drag

Molecular motors such as kinesin-1 drive active, long-range transport of cargos along microtubules in cells. Thermal diffusion of the cargo can impose a randomly directed, fluctuating mechanical load on the motor carrying the cargo. Recent experiments highlighted a strong asymmetry in the sensitivity of single-kinesin run length to load direction, raising the intriguing possibility that cargo diffusion may non-trivially influence motor run length. To test this possibility, here we employed Monte Carlo-based simulations to evaluate the transport of cargo by a single kinesin. Our simulations included physiologically relevant viscous drag on the cargo and interrogated a large parameter space of cytoplasmic viscosities, cargo sizes, and motor velocities that captures their respective ranges in living cells. We found that cargo diffusion significantly shortens single-kinesin runs. This diffusion-based shortening is countered by viscous drag, leading to an unexpected, non-monotonic variation in run length as viscous drag increases. To our knowledge, this is the first identification of a significant effect of cargo diffusion on motor-based transport. Our study highlights the importance of cargo diffusion and load-detachment kinetics on single-motor functions under physiologically relevant conditions.

Crowding and Pausing Strongly Affect Dynamics of Kinesin-1 Motors along Microtubules

Molecular motors of the kinesin-1 family move in a directed and processive fashion along microtubules. It is generally accepted that steric hindrance of motors leads to crowding effects; however, little is known about the specific interactions involved. We employ an agent-based lattice gas model to study the impact of interactions that enhance the detachment of motors from crowded filaments on their collective dynamics. The predictions of our model quantitatively agree with the experimentally observed concentration dependence of key motor characteristics including their run length, dwell time, velocity, and landing rate. From the anomalous stepping statistics of individual motors that exhibit relatively long pauses, we infer that kinesin-1 motors sometimes lapse into an inactive state. Hereby, the formation of traffic jams amplifies the impact of single inactive motors and leads to a crowding dependence of the frequencies and durations of the resulting periods of no or slow motion. We interpret these findings and conclude that kinesin-1 spends a significant fraction of its stepping cycle in a weakly bound state in which only one of its heads is bound to the microtubule.

Crowding Induces Entropically-Driven Changes to DNA Dynamics That Depend on Crowder Structure and Ionic Conditions

Macromolecular crowding plays a principal role in a wide range of biological processes including gene expression, chromosomal compaction, and viral infection. However, the impact that crowding has on the dynamics of nucleic acids remains a topic of debate. To address this problem, we use single-molecule fluorescence microscopy and custom particle-tracking algorithms to investigate the impact of varying macromolecular crowding conditions on the transport and conformational dynamics of large DNA molecules. Specifically, we measure the mean-squared center-of-mass displacements, as well as the conformational size, shape, and fluctuations, of individual 115 kbp DNA molecules diffusing through various in vitro solutions of crowding polymers. We determine the role of crowder structure and concentration, as well as ionic conditions, on the diffusion and configurational dynamics of DNA. We find that branched, compact crowders (10 kDa PEG, 420 kDa Ficoll) drive DNA to compact, whereas linear, flexible crowders (10, 500 kDa dextran) cause DNA to elongate. Interestingly, the extent to which DNA mobility is reduced by increasing crowder concentrations appears largely insensitive to crowder structure (branched vs. linear), despite the highly different configurations DNA assumes in each case. We also characterize the role of ionic conditions on crowding-induced DNA dynamics. We show that both DNA diffusion and conformational size exhibit an emergent non-monotonic dependence on salt concentration that is not seen in the absence of crowders.

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).

Dynamics of dimeric kinesins: Limping, effect of longitudinal force, effects of neck linker extension and mutation, and comparison between kinesin-1 and kinesin-2

Conventional kinesin (kinesin-1) can walk on microtubule filaments in an asymmetric hand-over-hand manner, exhibiting a marked alternation in the mean dwell time in successive steps. Here, we study computationally the asymmetric stepping dynamics of the kinesin-1 homodimer, revealing its origin and providing quantitative explanations of the available experimental data. The alternation in the mean dwell time in successive steps arises from the alternation in the mechanochemical coupling ratio, which is in turn caused by the alternation in the slight variation of the stretched neck linker length. Both the vertical and backward longitudinal forces can enhance the asymmetric ratio. Additionally, other aspects of the stepping dynamics of the dimer such as the velocity versus longitudinal force, extended neck linker, etc., are also studied. In particular, the conflicting experimental data, with some showing that the velocity does not change with the forward longitudinal load while others showing that the velocity increases largely with the forward longitudinal load, are explained quantitatively and consistently. The intriguing experimental data showing that cysteine-light Drosophila and human kinesin-1 mutants have different load-dependent velocity from the wild-type cases as well as that kinesin-2 dimers have different load-dependent velocity from the kinesin-1 are also explained consistently and quantitatively.

Macromolecular Crowding Modulates Actomyosin Kinetics

Actomyosin kinetics is usually studied in dilute solutions, which do not reflect conditions in the cytoplasm. In cells, myosin and actin work in a dense macromolecular environment. High concentrations of macromolecules dramatically reduce the amount of free space available for all solutes, which results in an effective increase of the solutes' chemical potential and protein stabilization. Moreover, in a crowded solution, the chemical potential depends on the size of the solute, with larger molecules experiencing a larger excluded volume than smaller ones. Therefore, since myosin interacts with two ligands of different sizes (actin and ATP), macromolecular crowding can modulate the kinetics of individual steps of the actomyosin ATPase cycle. To emulate the effect of crowding in cells, we studied actomyosin cycle reactions in the presence of a high-molecular-weight polymer, Ficoll70. We observed an increase in the maximum velocity of the actomyosin ATPase cycle, and our transient-kinetics experiments showed that virtually all individual steps of the actomyosin cycle were affected by the addition of Ficoll70. The observed effects of macromolecular crowding on the myosin-ligand interaction cannot be explained by the increase of a solute's chemical potential. A time-resolved Förster resonance energy transfer experiment confirmed that the myosin head assumes a more compact conformation in the presence of Ficoll70 than in a dilute solution. We conclude that the crowding-induced myosin conformational change plays a major role in the changed kinetics of actomyosin ATPase.

Phase behavior of colloid-polymer depletion mixtures with unary or binary depletants

Adding depletants to a colloidal suspension induces an attractive interparticle interaction that can be tuned to obtain desired structures or to probe phase behavior. When the depletant is not uniform in size, however, both the range and strength of the attraction become difficult to predict and hence control. We investigated the effects of depletant bidispersity on the non-equilibrium phase behavior of colloid-polymer mixtures. We added unary or binary mixtures of polystyrene as the depletant to suspensions of charged poly(methyl methacrylate) particles. The structure and dynamics of the particles were compared over three sets of samples with various mixtures of two different polystyrenes whose size varied by an order of magnitude. The structure and dynamics were nearly independent of depletant dispersity if the polymer concentration was represented as a sum of normalized concentrations of each species. Near the transition region between a fluid of clusters and an interconnected gel at intermediate volume fractions, partitioning of polymers in a binary mixture into colloid-rich and polymer-rich phase leads to a slightly different gelation pathway.

A model of processive movement of dimeric kinesin

Dimeric kinesin can move processively on microtubule filaments by hydrolyzing ATP. Diverse aspects of its movement dynamics have been studied extensively by using various experimental methods. However, the detailed molecular mechanism of the processive movement is still undetermined and a model that can provide a consistent and quantitative explanation of the diverse experimental data is still lacking. Here, we present such a model, with which we study the movement dynamics of the dimer under variations of solution viscosity, external load, ATP concentration, neck linker length, effect of neck linker docking, effect of a large-size particle attached to one kinesin head, etc., providing consistent and quantitative explanations of the available diverse experimental data. Moreover, predicted results are also provided.

Structural fluctuations and thermal stability of proteins in crowded environments: effects of the excluded volume

We perform molecular dynamics simulations for a simple coarse-grained model of a protein placed inside of a softly repulsive sphere of radius R. The protein is surrounded either by a number of same molecules or a number of spherical crowding particles that immitate other biomolecules such as the osmolytes. The two descriptions are shown to lead to distinct results when testing thermal stability as assessed by studying the unfolding times as a function of temperature. We consider three examples of proteins and show that crowding increases the thermal stability provided the inter-protein or protein-crowder interactions are repulsive. On the other hand, an introduction of attraction between the proteins is found to destabilize the proteins. Crowding by repulsive crowder particles is seen to enhance the RMSF in certain exposed regions. The effect grows on decreasing the size of the crowding particles. In the absence of crowding the RMSF anticorrelates with the coordination number related to the residue-residue interaction.