Stochastic modeling reveals how motor protein and filament properties affect intermediate filament transport

Steady state distributions of moving particles in one dimension: with an eye towards axonal transport

Axonal transport, propelled by motor proteins, plays a crucial role in maintaining the homeostasis of functional and structural components over time. To establish a steady-state distribution of moving particles, what conditions are necessary for axonal transport? This question is pertinent, for instance, to both neurofilaments and mitochondria, which are structural and functional cargoes of axonal transport. In this paper we prove four theorems regarding steady state distributions of moving particles in one dimension on a finite domain. Three of the theorems consider cases where particles approach a uniform distribution at large time. Two consider periodic boundary conditions and one considers reflecting boundary conditions. The other theorem considers reflecting boundary conditions where the velocity is space dependent. If the theoretical results hold in the complex setting of the cell, they would imply that the uniform distribution of neurofilaments observed under healthy conditions appears to require a continuous distribution of neurofilament velocities. Similarly, the spatial distribution of axonal mitochondria may be linked to spatially dependent transport velocities that remain invariant over time.

Cytoskeletal crosstalk: A focus on intermediate filaments

The cytoskeleton, comprising actin microfilaments, microtubules, and intermediate filaments, is crucial for cell motility and tissue integrity. While prior studies largely focused on individual cytoskeletal networks, recent research underscores the interconnected nature of these systems in fundamental cellular functions like adhesion, migration, and division. Understanding the coordination of these distinct networks in both time and space is essential. This review synthesizes current findings on the intricate interplay between these networks, emphasizing the pivotal role of intermediate filaments. Notably, these filaments engage in extensive crosstalk with microfilaments and microtubules through direct molecular interactions, cytoskeletal linkers, and molecular motors that form molecular bridges, as well as via more complex regulation of intracellular signaling.

Computational Studies Reveal How Passive Cross-Linkers Regulate Anaphase Spindle Elongation

In eukaryotic cell division, a series of events are organized to produce two daughter cells. The spindle elongation in anaphase B is essential for providing enough space to maintain cell size and distribute sister chromatids properly, which is associated with microtubules and microtubule-associated proteins such as kinesin-5 Eg5 and the Ase1-related protein, PRC1. The available experimental data indicated that after the start of anaphase B more PRC1 proteins can bind to the antiparallel microtubule pairs in the spindle but the excess amount of PRC1 proteins can lead to the failure of cell division, indicating that PRC1 proteins can regulate the spindle elongation in a concentration-dependent manner. However, the underlying mechanism of the PRC1 proteins regulating the spindle elongation has not been explained up to now. Here, we use a simplified model, where only the two important participants (kinesin-5 Eg5 motors and PRC1 proteins) are considered, to study the spindle elongation during anaphase B. We first show that only in the appropriate range of the PRC1 concentration can the spindle elongation complete properly. Furthermore, we explore the underlying mechanism of PRC1 as a regulator for spindle elongation.

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.

Simulations suggest robust microtubule attachment of kinesin and dynein in antagonistic pairs

Intracellular transport is propelled by kinesin and cytoplasmic dynein motors that carry membrane-bound vesicles and organelles bidirectionally along microtubule tracks. Much is known about these motors at the molecular scale, but many questions remain regarding how kinesin and dynein cooperate and compete during bidirectional cargo transport at the cellular level. The goal of the present study was to use a stochastic stepping model constructed by using published load-dependent properties of kinesin-1 and dynein-dynactin-BicD2 (DDB) to identify specific motor properties that determine the speed, directionality, and transport dynamics of a cargo carried by one kinesin and one dynein motor. Model performance was evaluated by comparing simulations to recently published experiments of kinesin-DDB pairs connected by complementary oligonucleotide linkers. Plotting the instantaneous velocity distributions from kinesin-DDB experiments revealed a single peak centered around zero velocity. In contrast, velocity distributions from simulations displayed a central peak around 100 nm/s, along with two side peaks corresponding to the unloaded kinesin and DDB velocities. We hypothesized that frequent motor detachment events and relatively slow motor reattachment rates resulted in periods in which only one motor is attached. To investigate this hypothesis, we varied specific model parameters and compared the resulting instantaneous velocity distributions, and we confirmed this systematic investigation using a machine-learning approach that minimized the residual sum of squares between the experimental and simulation velocity distributions. The experimental data were best recapitulated by a model in which the kinesin and dynein stall forces are matched, the motor detachment rates are independent of load, and the kinesin-1 reattachment rate is 50 s-1. These results provide new insights into motor dynamics during bidirectional transport and put forth hypotheses that can be tested by future experiments.

Regulation of neurofilament length and transport by a dynamic cycle of phospho-dependent polymer severing and annealing

Neurofilaments are cargoes of axonal transport which are unique among known intracellular cargoes in that they are long, flexible protein polymers. These polymers are transported into axons, where they accumulate in large numbers to drive the expansion of axon caliber, which is an important determinant of axonal conduction velocity. We reported previously that neurofilaments can be lengthened by joining ends, called end-to-end annealing, and that they can be shortened by severing. Here, we show that neurofilament annealing and severing are robust and quantifiable phenomena in cultured neurons that act antagonistically to regulate neurofilament length. We show that this in turn regulates neurofilament transport and that severing is regulated by N-terminal phosphorylation of the neurofilament subunit proteins. We propose that focal destabilization of intermediate filaments by site-directed phosphorylation may be a general enzymatic mechanism for severing these cytoskeletal polymers, providing a mechanism to regulate the transport and accumulation of neurofilaments in axons.

Using Fluorescence Recovery After Photobleaching data to uncover filament dynamics

Fluorescence Recovery After Photobleaching (FRAP) has been extensively used to understand molecular dynamics in cells. This technique when applied to soluble, globular molecules driven by diffusion is easily interpreted and well understood. However, the classical methods of analysis cannot be applied to anisotropic structures subjected to directed transport, such as cytoskeletal filaments or elongated organelles transported along microtubule tracks. A new mathematical approach is needed to analyze FRAP data in this context and determine what information can be obtain from such experiments. To address these questions, we analyze fluorescence intensity profile curves after photobleaching of fluorescently labelled intermediate filaments anterogradely transported along microtubules. We apply the analysis to intermediate filament data to determine information about the filament motion. Our analysis consists of deriving equations for fluorescence intensity profiles and developing a mathematical model for the motion of filaments and simulating the model. Two closed forms for profile curves were derived, one for filaments of constant length and one for filaments with constant velocity, and three types of simulation were carried out. In the first type of simulation, the filaments have random velocities which are constant for the duration of the simulation. In the second type, filaments have random velocities which instantaneously change at random times. In the third type, filaments have random velocities and exhibit pausing between velocity changes. Our analysis shows: the most important distribution governing the shape of the intensity profile curves obtained from filaments is the distribution of the filament velocity. Furthermore, filament length which is constant during the experiment, had little impact on intensity profile curves. Finally, gamma distributions for the filament velocity with pauses give the best fit to asymmetric fluorescence intensity profiles of intermediate filaments observed in FRAP experiments performed in polarized migrating astrocytes. Our analysis also shows that the majority of filaments are stationary. Overall, our data give new insight into the regulation of intermediate filament dynamics during cell migration.

Fluorescence Recovery After Photobleaching (FRAP) is a commonly-used technique to analyze the dynamics of fluorescently-tagged proteins or structures in biology. After photochemical altering the fluorophor in a specific region, fluorescent material from the surrounding region moves into the photobleached region. Usually applied to the diffusion of soluble or membrane associate proteins, the existing models of analysis are not suitable for the elucidation of directional transport of elongated structures. Different modes of motions for the elongated structures with distributed lengths and velocities in cells are considered. First, we observe that filament lengths can be inferred from the level of noisiness. We further show the characteristics of fluorescence profile curves mainly depend on the occurrence of changes in velocities and distributions of velocities; whereas length distributions have negligible impact. Analysis of experimental data using this new framework indicates intermediate filaments transported by kinesins along microtubules in polarized migrating cells have gamma distributed velocities changing over time between pausing. Most filaments are found to be very slow or stationary with a few moving fast. This new computational approach should permit the interpretation of FRAP experimental data obtained with any directionally moving elongated structures of various lengths.

Impact of noise on the regulation of intracellular transport of intermediate filaments

Noise affects all biological processes from molecules to cells, organisms and populations. Although the effect of noise on these processes is highly variable, evidence is accumulating which shows natural stochastic fluctuations (noise) can facilitate biological functions. Herein, we investigate the effect of noise on the transport of intermediate filaments in cells by comparing the stochastic and deterministic formalizations of the bidirectional transport of intermediate filaments, long elastic polymers transported along microtubules by antagonistic motor proteins Dallon et al., 2019; Portet et al., 2019. By numerically exploring discrepancies in timescales and attractors between both formalizations, we characterize the impact of stochastic fluctuations on the individual and ensemble transport. Biologically, we find that noise promotes the collective movement of intermediate filaments and increases the efficiency of its regulation by the biochemical properties of motor-cargo interactions. While stochastic fluctuations reduce the impact of the initial distributions of motor proteins in cells, the number of binding sites and the affinity of motor-cargo interactions are the key parameters controlling transport efficiency and efficacy.

Quantitative mapping of keratin networks in 3D

Mechanobiology requires precise quantitative information on processes taking place in specific 3D microenvironments. Connecting the abundance of microscopical, molecular, biochemical, and cell mechanical data with defined topologies has turned out to be extremely difficult. Establishing such structural and functional 3D maps needed for biophysical modeling is a particular challenge for the cytoskeleton, which consists of long and interwoven filamentous polymers coordinating subcellular processes and interactions of cells with their environment. To date, useful tools are available for the segmentation and modeling of actin filaments and microtubules but comprehensive tools for the mapping of intermediate filament organization are still lacking. In this work, we describe a workflow to model and examine the complete 3D arrangement of the keratin intermediate filament cytoskeleton in canine, murine, and human epithelial cells both, in vitro and in vivo. Numerical models are derived from confocal airyscan high-resolution 3D imaging of fluorescence-tagged keratin filaments. They are interrogated and annotated at different length scales using different modes of visualization including immersive virtual reality. In this way, information is provided on network organization at the subcellular level including mesh arrangement, density and isotropic configuration as well as details on filament morphology such as bundling, curvature, and orientation. We show that the comparison of these parameters helps to identify, in quantitative terms, similarities and differences of keratin network organization in epithelial cell types defining subcellular domains, notably basal, apical, lateral, and perinuclear systems. The described approach and the presented data are pivotal for generating mechanobiological models that can be experimentally tested.

Motor Protein Transport Along Inhomogeneous Microtubules

Many cellular processes rely on the cell's ability to transport material to and from the nucleus. Networks consisting of many microtubules and actin filaments are key to this transport. Recently, the inhibition of intracellular transport has been implicated in neurodegenerative diseases such as Alzheimer's disease and Amyotrophic Lateral Sclerosis. Furthermore, microtubules may contain so-called defective regions where motor protein velocity is reduced due to accumulation of other motors and microtubule-associated proteins. In this work, we propose a new mathematical model describing the motion of motor proteins on microtubules which incorporate a defective region. We take a mean-field approach derived from a first principle lattice model to study motor protein dynamics and density profiles. In particular, given a set of model parameters we obtain a closed-form expression for the equilibrium density profile along a given microtubule. We then verify the analytic results using mathematical analysis on the discrete model and Monte Carlo simulations. This work will contribute to the fundamental understanding of inhomogeneous microtubules providing insight into microscopic interactions that may result in the onset of neurodegenerative diseases. Our results for inhomogeneous microtubules are consistent with prior work studying the homogeneous case.

Dynamics of Vesicles Driven Into Closed Constrictions by Molecular Motors

We study the dynamics of a model of membrane vesicle transport into dendritic spines, which are bulbous intracellular compartments in neurons driven by molecular motors. We reduce the lubrication model proposed in Fai et al. (Phys Rev Fluids 2:113601, 2017) to a fast-slow system, yielding an analytically and numerically tractable equation equivalent to the original model in the overdamped limit. The model's key parameters include: (1) the ratio of motors that prefer to push toward the head of the dendritic spine to the motors that prefer to push in the opposite direction, and (2) the viscous drag exerted on the vesicle by the spine constriction. We perform a numerical bifurcation analysis in these parameters and find that steady-state vesicle velocities appear and disappear through several saddle-node bifurcations. This process allows us to identify the region of parameter space in which multiple stable velocities exist. We show by direct calculations that there can only be unidirectional motion for sufficiently close vesicle-to-spine diameter ratios. Our analysis predicts the critical vesicle-to-spine diameter ratio, at which there is a transition from unidirectional to bidirectional motion, consistent with experimental observations of vesicle trajectories in the literature.

Theoretical Analysis of Dynamics of Kinesin Molecular Motors

Kinesin is a typical molecular motor that can step processively on microtubules powered by hydrolysis of adenosine triphosphate (ATP) molecules, playing a critical role in intracellular transports. Its dynamical properties such as its velocity, stepping ratio, run length, dissociation rate, etc. as well as the load dependencies of these quantities have been well documented through single-molecule experimental methods. In particular, the run length shows a dramatic asymmetry with respect to the direction of the load, and the dissociation rate exhibits a slip-catch-slip bond behavior under the backward load. Here, an analytic theory was provided for the dynamics of kinesin motors under both forward and backward loads, explaining consistently and quantitatively the diverse available experimental results.

Force dependence of unbinding rate of kinesin motor during its processive movement on microtubule

Kinesin is a biological molecular motor that can move continuously on microtubule until it unbinds. Here, we studied computationally the force dependence of the unbinding rate of the motor. Our results showed that while the unbinding rate under the forward load has the expected characteristic of "slip bond", with the unbinding rate increasing monotonically with the increase of the forward load, the unbinding rate under the backward load shows counterintuitive characteristic of "slip-catch-slip bond": as the backward load increases, the unbinding rate increases exponentially firstly, then drops rapidly and then increases again. Our calculated data are in agreement with the available single-molecule data from different research groups. The mechanism of the slip-catch-slip bond was revealed.

Deciphering the transport of elastic filaments by antagonistic motor proteins

Intermediate filaments are long elastic fibers that are transported by the microtubule-associated motor proteins kinesin and dynein inside the cell. How elastic filaments are efficiently transported by antagonistic motors is not well understood and is difficult to measure with current experimental techniques. Adapting the tug-of-war paradigm for vesiclelike cargos, we develop a mathematical model to describe the motion of an elastic filament punctually bound to antagonistic motors. As observed in cells, up to three modes of transport are obtained; dynein-driven retrograde, kinesin-driven anterograde fast motions, and a slow motion. Motor properties and initial conditions that depend on intracellular context regulate the transport of filaments. Filament elasticity is found to affect both the mode and the efficiency of transport. We further show that the coordination of motors along the filament emerges from the interplay between intracellular context and elastic properties of filaments.