Protein fluxes along the filopodium as a framework for understanding the growth-retraction dynamics: The interplay between diffusion and active transport

We present a picture of filopodial growth and retraction from physics perspective, where we emphasize the significance of the role played by protein fluxes due to spatially extended nature of the filopodium. We review a series of works, which used stochastic simulations and mean field analytical modeling to find the concentration profile of G-actin inside a filopodium, which, in turn, determines the stationary filopodial length. In addition to extensively reviewing the prior works, we also report some new results on the role of active transport in regulating the length of filopodia. We model a filopodium where delivery of actin monomers toward the tip can occur both through passive diffusion and active transport by myosin motors. We found that the concentration profile of G-actin along the filopodium is rather non-trivial, containing a narrow minimum near the base followed by a broad maximum. For efficient enough actin transport, this non-monotonous shape is expected to occur under a broad set of conditions. We also raise the issue of slow approach to the stationary length and the possibility of multiple steady-state solutions.Key words: filopodia, active transport, molecular motors, stochastic process, mean-field theory     

Protein fluxes along the filopodium as a framework for understanding the growth-retraction dynamics

We present a picture of filopodial growth and retraction from physics perspective, where we emphasize the significance of the role played by protein fluxes due to spatially extended nature of the filopodium. We review a series of works, which used stochastic simulations and mean field analytical modeling to find the concentration profile of G-actin inside a filopodium, which, in turn, determines the stationary filopodial length. In addition to extensively reviewing the prior works, we also report some new results on the role of active transport in regulating the length of filopodia. We model a filopodium where delivery of actin monomers towards the tip can occur both through passive diffusion and active transport by myosin motors. We found that the concentration profile of G-actin along the filopodium is rather non-trivial, containing a narrow minimum near the base followed by a broad maximum. For efficient enough actin transport, this non-monotonous shape is expected to occur under a broad set of conditions. We also raise the issue of slow approach to the stationary length and the possibility of multiple steady state solutions.     

The physics of filopodial protrusion

Filopodium, a spike-like actin protrusion at the leading edge of migrating cells, functions as a sensor of the local environment and has a mechanical role in protrusion. We use modeling to examine mechanics and spatial-temporal dynamics of filopodia. We find that >10 actin filaments have to be bundled to overcome the membrane resistance and that the filopodial length is limited by buckling for 10-30 filaments and by G-actin diffusion for >30 filaments. There is an optimal number of bundled filaments, approximately 30, at which the filopodial length can reach a few microns. The model explains characteristic interfilopodial distance of a few microns as a balance of initiation, lateral drift, and merging of the filopodia. The theory suggests that F-actin barbed ends have to be focused and protected from capping (the capping rate has to decrease one order of magnitude) once every hundred seconds per micron of the leading edge to initiate the observed number of filopodia. The model generates testable predictions about how filopodial length, rate of growth, and interfilopodial distance should depend on the number of bundled filaments, membrane resistance, lamellipodial protrusion rate, and G-actin diffusion coefficient.     

Stimulation-induced changes in filopodial dynamics determine the action radius of growth cones in the snail Helisoma trivolvis

Filopodia on neuronal growth cones constantly extend and retract, thereby functioning as both sensory probes and structural devices during neuronal pathfinding. To better understand filopodial dynamics and their regulation by encounters with molecules in the environment, we investigated filopodial dynamics of identified B5 neurons from the buccal ganglion of the snail Helisoma trivolvis before and after treatment with nitric oxide (NO). We have previously demonstrated that treatment with several NO-donors caused a transient, cGMP-mediated elevation in [Ca(2+)](i), which was causally related to an increase in filopodial length and a reduction in the number of filopodia on growth cones. We demonstrate here that these effects were the result of distinct changes in filopodial dynamics. The NO-donor SIN-1 induced a general increase in filopodial motility. Filopodial elongation after treatment with SIN-1 resulted from a significant increase in the rate at which filopodia extended, as well as a significant increase in the time filopodia spent elongating. The reduction in filopodial number was caused by a significant decrease in the frequency with which new filopodia were inserted into the growth cone. With the exception of the back where filopodia appeared less motile, filopodial dynamics appeared to be mostly independent of the location on the growth cone. These results suggest that NO can regulate filopodial dynamics on migrating growth cones and might function as a messenger to adjust the action radius of a growth cone during pathfinding.     

Engineered Tug‐of‐War Between Kinesin and Dynein Controls Direction of Microtubule Based Transport In Vivo

Bidirectional transport of membrane organelles along microtubules (MTs) is driven by plus‐end directed kinesins and minus‐end directed dynein bound to the same cargo. Activities of opposing MT motors produce bidirectional movement of membrane organelles and cytoplasmic particles along MT transport tracks. Directionality of MT‐based transport might be controlled by a protein complex that determines which motor type is active at any given moment of time, or determined by the outcome of a tug‐of‐war between MT motors dragging cargo organelles in opposite directions. However, evidence in support of each mechanisms of regulation is based mostly on the results of theoretical analyses or indirect experimental data. Here, we test whether the direction of movement of membrane organelles in vivo can be controlled by the tug‐of‐war between opposing MT motors alone, by attaching a large number of kinesin‐1 motors to organelles transported by dynein to minus‐ends of MTs. We find that recruitment of kinesin significantly reduces the length and velocity of minus‐end‐directed dynein‐dependent MT runs, leading to a reversal of the overall direction of dynein‐driven organelles in vivo. Therefore, in the absence of external regulators tug‐of‐war between opposing MT motors alone is sufficient to determine the directionality of MT transport in vivo.      

Posttranslational Modifications of Tubulin and the Polarized Transport of Kinesin-1 in Neurons

Polarized transport by microtubule-based motors is critical for neuronal development and function. Selective translocation of the Kinesin-1 motor domain is the earliest known marker of axonal identity, occurring before morphological differentiation. Thus, Kinesin-1–mediated transport may contribute to axonal specification. We tested whether posttranslational modifications of tubulin influence the ability of Kinesin-1 motors to distinguish microtubule tracks during neuronal development. We detected no difference in microtubule stability between axons and minor neurites in polarized stage 3 hippocampal neurons. In contrast, microtubule modifications were enriched in a subset of neurites in unpolarized stage 2 cells and the developing axon in polarized stage 3 cells. This enrichment correlated with the selective accumulation of constitutively active Kinesin-1 motors. Increasing tubulin acetylation, without altering the levels of other tubulin modifications, did not alter the selectivity of Kinesin-1 accumulation in polarized cells. However, globally enhancing tubulin acetylation, detyrosination, and polyglutamylation by Taxol treatment or inhibition of glycogen synthase kinase 3β decreased the selectivity of Kinesin-1 translocation and led to the formation of multiple axons. Although microtubule acetylation enhances the motility of Kinesin-1, the preferential translocation of Kinesin-1 on axonal microtubules in polarized neuronal cells is not determined by acetylation alone but is probably specified by a combination of tubulin modifications.     

Nitric oxide release from a single cell affects filopodial motility on growth cones of neighboring neurons

Nitric oxide (NO), a gaseous messenger, has been reported to be involved in a variety of functions in the nervous system, ranging from neuronal pathfinding to learning and memory. We have shown previously that the application of NO via NO donors to growth cones of identified Helisoma buccal neurons B5 in vitro induces an increase in filopodial length, a decrease in filopodial number, and a slowing in neurite advance. It is unclear, however, whether NO released from a physiological source would affect growth cone dynamics. Here we used cell bodies of identified neurons known to express the NO synthesizing enzyme nitric oxide synthase (NOS) as a source of constitutive NO production and tested their effect on growth cones of other cells in a sender-receiver paradigm. We showed that B5 cell bodies induced a rapid increase in filopodial length in NO-responsive growth cones, and that this effect was blocked by the NOS inhibitor 7-NI, suggesting that the effect was mediated by NO. Inhibition of soluble guanylyl cyclase (sGC) with ODQ blocked filopodial elongation induced by B5 somata, confirming that NO acted via sGC. We also demonstrate that the effect of NO was reversible and that a cell releasing NO can affect growth cones over a distance of at least 100 microm. Our results suggest that NO released from a physiological source can affect the motility of nearby growth cones and thus should be considered a signaling molecule with the potential to affect the outcome of neuronal pathfinding in vivo.     

Cdc42 participates in the regulation of ADF/cofilin and retinal growth cone filopodia by brain derived neurotrophic factor

Rho family GTPases have important roles in mediating the effects of guidance cues and growth factors on the motility of neuronal growth cones. We previously showed that the neurotrophin BDNF regulates filopodial dynamics on growth cones of retinal ganglion cell axons through activation of the actin regulatory proteins ADF and cofilin by inhibiting a RhoA-dependent pathway that phosphorylates (inactivates) ADF/cofilin. The GTPase Cdc42 has also been implicated in mediating the effects of positive guidance cues. In this article we investigated whether Cdc42 is involved in the effects of BDNF on filopodial dynamics. BDNF treatment increases Cdc42 activity in retinal neurons, and neuronal incorporation of constitutively active Cdc42 mimics the increases in filopodial number and length. Furthermore, constitutively active and dominant negative Cdc42 decreased and increased, respectively, the activity of RhoA in retinal growth cones, indicating crosstalk between these GTPases in retinal growth cones. Constitutively active Cdc42 mimicked the activation of ADF/cofilin that resulted from BDNF treatment, while dominant negative Cdc42 blocked the effects of BDNF on filopodia and ADF/cofilin. The inability of dominant negative Cdc42 to block ADF/cofilin activation and stimulation of filopodial dynamics by the ROCK inhibitor Y-27632 indicate interaction between Cdc42 and RhoA occurs upstream of ROCK. Our results demonstrate crosstalk occurs between GTPases in mediating the effects of BDNF on growth cone motility, and Cdc42 activity can promote actin dynamics via activation of ADF/cofilin.     

Transport Properties of Melanosomes along Microtubules Interpreted by a Tug-of-War Model with Loose Mechanical Coupling

In this work, we explored theoretically the transport of organelles driven along microtubules by molecular motors of opposed polarities using a stochastic model that considers a Langevin dynamics for the cargo, independent cargo-motor linkers and stepping motion for the motors. It has been recently proposed that the stiffness of the motor plays an important role when multiple motors collectively transport a cargo. Therefore, we considered in our model the recently reported values for the stiffness of the cargo-motor linker determined in living cells (～0.01 pN/nm, [1]) which is significantly lower than the motor stiffness obtained in in vitro assays and used in previous studies. Our model could reproduce the multimodal velocity distributions and typical trajectory characteristics including the properties of the reversions in the overall direction of motion observed during melanosome transport along microtubules in Xenopus laevis melanophores. Moreover, we explored the contribution of the different motility states of the cargo-motor system to the different modes of the velocity distributions and could identify the microscopic mechanisms of transport leading to trajectories compatible with those observed in living cells. Finally, by changing the attachment and detachment rates, the model could reproduce the different velocity distributions observed during melanosome transport along microtubules in Xenopus laevis melanophores stimulated for aggregation and dispersion. Our analysis suggests that active tug-of-war processes with loose mechanical coupling can account for several aspects of cargo transport along microtubules in living cells.     

Transport characteristics of molecular motors

Properties of transport of molecular motors are investigated. A simplified model based on the concept of Brownian ratchets is applied. We analyze a stochastic equation of motion by means of numerical methods. The transport is systematically studied with respect to its energetic efficiency and quality expressed by an effective diffusion coefficient. We demonstrate the role of friction and non-equilibrium driving on the transport quantifiers and identify regions of a parameter space where motors are optimally transported.     

HDAC6 Inhibitor Blocks Amyloid Beta-Induced Impairment of Mitochondrial Transport in Hippocampal Neurons

Even though the disruption of axonal transport is an important pathophysiological factor in neurodegenerative diseases including Alzheimer's disease (AD), the relationship between disruption of axonal transport and pathogenesis of AD is poorly understood. Considering that α-tubulin acetylation is an important factor in axonal transport and that Aβ impairs mitochondrial axonal transport, we manipulated the level of α-tubulin acetylation in hippocampal neurons with Aβ cultured in a microfluidic system and examined its effect on mitochondrial axonal transport. We found that inhibiting histone deacetylase 6 (HDAC6), which deacetylates α-tubulin, significantly restored the velocity and motility of the mitochondria in both anterograde and retrograde axonal transports, which would be otherwise compromised by Aβ. The inhibition of HDAC6 also recovered the length of the mitochondria that had been shortened by Aβ to a normal level. These results suggest that the inhibition of HDAC6 significantly rescues hippocampal neurons from Aβ-induced impairment of mitochondrial axonal transport as well as mitochondrial length. The results presented in this paper identify HDAC6 as an important regulator of mitochondrial transport as well as elongation and, thus, a potential target whose pharmacological inhibition contributes to improving mitochondrial dynamics in Aβ treated neurons.     

Improving the understanding of cytoneme-mediated morphogen gradients by in silico modeling

Morphogen gradients are crucial for the development of organisms. The biochemical properties of many morphogens prevent their extracellular free diffusion, indicating the need of an active mechanism for transport. The involvement of filopodial structures (cytonemes) has been proposed for morphogen signaling. Here, we describe an in silico model based on the main general features of cytoneme-meditated gradient formation and its implementation into Cytomorph, an open software tool. We have tested the spatial and temporal adaptability of our model quantifying Hedgehog (Hh) gradient formation in two Drosophila tissues. Cytomorph is able to reproduce the gradient and explain the different scaling between the two epithelia. After experimental validation, we studied the predicted impact of a range of features such as length, size, density, dynamics and contact behavior of cytonemes on Hh morphogen distribution. Our results illustrate Cytomorph as an adaptive tool to test different morphogen gradients and to generate hypotheses that are difficult to study experimentally.     

Providing Positional Information with Active Transport on Dynamic Microtubules

Microtubules (MTs) are dynamic protein polymers that change their length by switching between growing and shrinking states in a process termed dynamic instability. It has been suggested that the dynamic properties of MTs are central to the organization of the eukaryotic intracellular space, and that they are involved in the control of cell morphology, but the actual mechanisms are not well understood. Here, we present a theoretical analysis in which we explore the possibility that a system of dynamic MTs and MT end-tracking molecular motors is providing specific positional information inside cells. We compute the MT length distribution for the case of MT-length-dependent switching between growing and shrinking states, and analyze the accumulation of molecular motors at the tips of growing MTs. Using these results, we show that a transport system consisting of dynamic MTs and associated motor proteins can deliver cargo proteins preferentially to specific positions within the cell. Comparing our results with experimental data in the model organism fission yeast, we propose that the suggested mechanisms could play important roles in setting length scales during cellular morphogenesis.     

Bidirectional Transport by Molecular Motors: Enhanced Processivity and Response to External Forces

Intracellular transport along cytoskeletal filaments is often mediated by two teams of molecular motors that pull on the same cargo and move in opposite directions along the filaments. We have recently shown theoretically that this bidirectional transport can be understood as a stochastic tug-of-war between the two motor teams. Here, we further develop our theory to investigate the experimentally accessible dynamic behavior of cargos transported by strong motors such as kinesin-1 or cytoplasmic dynein. By studying the run and binding times of such a cargo, we show that the properties of biological motors, such as the large ratio of stall/detachment force and the small ratio of superstall backward/forward velocity, are favorable for bidirectional cargo transport, leading to fast motion and enhanced diffusion. In addition, cargo processivity is shown to be strongly enhanced by transport via several molecular motors even if these motors are engaged in a tug-of-war. Finally, we study the motility of a bidirectional cargo under force. Frictional forces arising, e.g., from the viscous cytoplasm, lead to peaks in the velocity distribution, while external forces as exerted, e.g., by an optical trap, lead to hysteresis effects. Our results, in particular our explicit expressions for the cargo binding time and the distance of the peaks in the velocity relation under friction, are directly accessible to in vitro as well as in vivo experiments.     

Exchange of Microtubule Molecular Motors During Melanosome Transport in <Emphasis Type="Italic">Xenopus laevis</Emphasis> Melanophores is Triggered by Collisions with Intracellular Obstacles

The observation that several cargoes move bidirectionally along microtubules in vivo raised the question regarding how molecular motors with opposed polarity coordinate during transport. In this work, we analyzed the switch of microtubule motors during the transport of melanosomes in Xenopus melanophores by registering trajectories of these organelles moving along microtubules using a fast and precise tracking method. We analyzed in detail the intervals of trajectories showing reversions in the original direction of transport and processive motion in the opposite direction for at least 250 nm. In most of the cases, the speed of the melanosome before the reversion slowly decreases with time approaching zero then, the organelle returns over the same path moving initially at a very high speed and slowing down with time. These results could be explained according to a model in which reversions are triggered by an elastic collision of the cargo with obstacles in the cytosol. This interaction generates a force opposed to the movement of the motor-driven organelle increasing the probability of detaching the active motors from the track. The model can explain reversions in melanosome trajectories as well as other characteristics of in vivo transport along microtubules observed by other authors. Our results suggest that the crowded cytoplasm plays a key role in regulating the coordination of microtubules-dependent motors. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Critical role of collapsin response mediator protein-associated molecule CRAM for filopodia and growth cone development in neurons

Collapsin response mediator proteins (CRMPs) have been implicated in signaling of axonal guidance, including semaphorins. We have previously identified a unique member of this gene family, CRMP-associated molecule CRAM (CRMP-5), which is phylogenetically divergent from the other four CRMPs. In this study, we have examined the distribution and function of CRAM in developing neurons. Immunohistochemical analysis showed accumulation of CRAM in the filopodia of growth cones. Experiments using cytochalasin D indicated that filopodial localization of CRAM was independent of filamentous actin. Overexpression of CRAM in neuronal cells significantly promoted filopodial growth and led to the formation of supernumerary growth cones, which acquired resistance to semaphorin-3A stimulation. Finally, knockdown of CRAM by using RNA interference blocked filopodial formation and revealed an aberrant morphology of growth cones. We propose that CRAM regulates filopodial dynamics and growth cone development, thereby restricting the response of growth cone to repulsive guidance cues.