CTW: Axonal Transport and Neuronal Mechanics

(November 3,2014 - November 7,2014 )

Organizers


Paul Bressloff
Department of Mathematics, University of Utah
Kristian Franze
Department of Physiology, Development and Neuroscience, University of Cambridge
Kyle Miller
Dept. of Zoology, Michigan State University
Jay Newby
Mathematical Biosciences Institute, The Ohio State University
Daniel Suter
Biological Sciences, Purdue University

A fundamental question in neurobiology is how do axons, the thin cellular cables that transmit information in the nervous system, grow? Since ~95% of total protein found in the axon is made in the cell body, it is widely recognized that axonal transport is essential for this process. In parallel, there is a deep interest in developing a better understanding of how growth cone mechanics, at the tip of the axon, modulate the rate and control the direction of axonal elongation. While these topics lend themselves well to mathematical modeling there has been limited direct interaction between experimentalists and theoreticians. Answering these questions is important for understanding the development of the nervous system, the pathological progression of neurodegenerative diseases such as Alzheimer's, and for designing novel approaches to promote neuronal regeneration following disease, stroke, or trauma. Recent progress in the field, facilitated by the development of novel experimental and theoretical approaches, has led to new insights and interest in interdisciplinary studies of axonal transport and neuromechanics. The goal of this workshop is to bring together leading cell biologists, engineers, physicists, and mathematicians to openly discuss exciting new findings, long-standing questions, and the future of our field. The timeliness of this meeting and its relevance to the mission of the MBI is most evident from three recent reviews by the organizers (Bressloff and Newby, 2013; Franze et al., 2013; Suter and Miller, 2011). In brief these reviews discuss the emerging role of forces in axonal elongation, mathematical models that have been developed to study the contribution of axonal transport to elongation, and the importance of developing mathematical models to study neuromechanics.

Accepted Speakers

Ahmad Athamneh
Biological Sciences, Purdue University
Roberto Bernal
Physics Department, Universidad de Santiago de Chile (USACH)
Anthony Brown
Neuroscience, The Ohio State University
Catherine Collins
Molecular, Cellular, and Developmental Biology, University of Michigan
Corina Drapaca
Engineering Science and Mechanics, Pennsylvania State University
Bonnie Firestein
Cell Biology and Neuroscience, Rutgers University
Gianluca Gallo
Anatomy and Cell Biology, Temple University
Fernanda Garate
Physics, universidad de santiago de chile
Julian Garcia Grajales
Mathematical Institute, Mathematical Institute
Timothy Gomez
Neuroscience, University of Wisconsin
Alain Goriely
Mathematical Institute, University of Oxford
Bruce Graham
Computing Science and Mathematics, University of Stirling
Stephanie Gupton
Cell Biology & Physiology, University of North Carolina, Chapel Hill
Mary Halloran
Zoology, University of Wisconsin
David Holcman
Applied mathematics and Computational Biology, Ecole Normale Superieure
Paul Janmey
Physiology, University of Pennsylvania
Christopher Johnson
Physics & Astronomy, Ohio University
Peter Jung
Quantitative Biology Institute, Ohio University
Ellen Kuhl
Mechanical Engineering and Bioengineering, Stanford University
Michelle LaPlaca
Biomedical Engineering, Georgia Institute of Technology / Emory University
Scott McKinley
Mathematics, University of Florida
Jay Newby
Mathematical Biosciences Institute, The Ohio State University
Matthew O'Toole
Mathematics, Kettering University
Bryan Pfister
Biomedical Engineering, New Jersey Institute of Technology
Sathya Puthanveettil
Neuroscience, The Scripps Research Institute
Jürgen Reingruber
Biology, Ecole Normale Superieure
Taher Saif
Mechanical Science and Engineering, University of Illinois at Urbana-Champaign
Esther Stoeckli
Institute of Molecular Life Sciences, University of Zurich
Joy Thompson
Physiology, Development and Neuroscience, University of Cambridge
Jeff Urbach
Physics, Georgetown University
Chuan Xue
Department of Mathematics, The Ohio State University
Monday, November 3, 2014
Time Session
08:00 AM

Shuttle to MBI

08:15 AM
09:00 AM

Breakfast

09:00 AM
09:15 AM

Greetings and info from MBI - Marty Golubitsky

09:15 AM
09:30 AM

Welcome By Organizers

09:30 AM
10:10 AM
Anthony Brown - Axonal transport of neurofilaments

Neurofilaments are space-filling protein polymers in axons that function to maximize axonal cross-sectional area, which is an important determinant of axonal conduction velocity. In large axons they are the single most abundant structure, occupying most of the axonal volume. Remarkably, these polymers are also cargoes of axonal transport, moving anterogradely and retrogradely along microtubule tracks in rapid bursts of movement interrupted by prolonged pauses. This stop-and-go behavior results in a slow average rate of movement, termed slow axonal transport. A central hypothesis of our laboratory is that neurofilament transport is a principal determinant of the neurofilament content and distribution along axons, and thus a principal determinant of axonal morphology. Thus it is important to understand the mechanisms that regulate neurofilament transport. We have shown recently that axonal neurofilaments can lengthen by joining end-to-end, called end-to-end annealing, and that they can also be shortened by a severing mechanism, which is a novel phenomenon for intermediate filaments. These mechanisms give rise to a broad range of neurofilament lengths in axons ranging from <1 m to >180 m. This raises intriguing questions about the mechanism of movement. Intriguingly, we find that short neurofilaments move rapidly and continuously in one direction, rarely reversing, whereas long filaments exhibit long pauses and frequent reversals, resulting in much less net movement. Long-term imaging of neurofilaments using a multi-field tracking technique has revealed that severing and annealing are robust phenomena and that short filaments anneal more frequently than long filaments, whereas long filaments sever more frequently than short filaments. These observations suggest that there is a dynamic cycle of neurofilament severing and annealing in axons that regulates the length and axonal transport of these cytoskeletal polymers. I will present evidence to support this model.

10:10 AM
10:50 AM
Peter Jung - Slow Axonal Transport and Axon Morphology

Shapes and calibers of neuronal axons are largely determined by the local abundance of neurofilaments. Neurofilaments are intermediate filaments, which are assembled in the cell body and transported along the axon towards the nerve terminal. It is evident from experiments that the neurofilaments axoskeleton is not at rest but exhibits a net downstream velocity. Our fundamental hypothesis is that the overall flux of neurofilaments, as determined by the rate of assembly, determines the overall caliber of the axon while local changes in caliber are determined by local modulation of neurofilament transport velocity. A suitable model to study this hypothesized relation between axon caliber and neurofilament velocity are the nodes of Ranvier, which separate two myelinated sections of myelinated axons. At the nodes of Ranvier, axons exhibit constrictions, which reduce the local caliber of the axon to a fraction of what it is at the internodes. According our hypothesis, such a local reduction of caliber should go along with a proportionate increase in neurofilament transport rate. We first describe our working model for neurofilament transport and how the associated rate constants are extracted from fluorescent imaging experiments at the myelinated segments and the nodes of Ranvier. We then discuss how the predicted change of caliber (based on the differential transport rates) matches up with experimentally determined abundances of neurofilaments at the nodes and internodes.

The nodes of Ranvier are also the locations of the vast majority of ion channels necessary for neuronal conduction. This begs the question what if any is the role of nodal constrictions for conduction velocity. Using the neuron programming-environment we set up a computational model of a myelinated axon, which incorporates detailed morphology of the axon including nodal constrictions. We found that nodal constrictions modulate conduction velocities and allow for a significant reduction of the fiber diameters for targeted conduction speeds in comparison to an unconstricted axon.

10:50 AM
11:20 AM

Break

11:20 AM
12:00 PM
Chuan Xue - A stochastic multiscale model that explains the segregation of axonal microtubules and neurofilaments in diseases

The axonal cytoskeleton is a dynamic system of protein polymers that is responsible for the fast and slow axonal transports and for the structural integrity and morphology of axons. The normal organization of the axonal cytoskeleton is disrupted in many neurodegenerative diseases. A fundamental question is to understand how the normal organization of the axonal cytoskeleton is developed and maintained in health, and how it is perturbed in diseases. Under normal conditions, the axonal microtubules and neurofilaments form a mixture in cross-section and the caliber of an axon is roughly constant over long distances. However, if treated with IDPN, a compound that causes similar symptoms as amyotrophic lateral sclerosis (ALS), microtubules and neurofilaments segregate into different regions on a time scale of hours, and the axon swells locally on a time scale of days. Although these phenomena have been reported for over 40 years now, the underlying mechanisms are still poorly understood. In this talk, I will present our new insights into this problem using a stochastic model. This is joint work with Anthony Brown from the Department of Neurosciences at the Ohio State University.

12:00 PM
02:00 PM

Lunch Break

02:00 PM
02:40 PM
Sathya Puthanveettil - Axonal Transport and Long-Term Memory Storage

Little is known regarding the identity of the population of proteins and RNAs that are transported to and localized to synapses and how this transport is regulated in neurons. To address this, using the sea slug Aplysia californica and mice, we have begun to study the molecular composition of transport complexes and how the transport is regulated during long-term memory storage. We find that several hundreds of proteins and RNAs are transported by kinesins, the molecular motor that mediate anterograde transport to synapses from the cell body. We further find that axonal transport is regulated in specific neurons for long-term memory storage. These studies bring important insights into the function of axonal transport in synapse formation and memory storage.

02:40 PM
03:20 PM
Scott McKinley - Multi-Motor Transport in Neurons: Moving Beyond Tug-of-War

Transport in neurons is intrinsically bidirectional, with each movement modality carried out by molecular motors in either the kinesin (anterograde) or the dynein (retrograde) families. Because all motors are present at a given time there must be competition and/or cooperation among motors that simultaneously bind a single vesicle to nearby microtubules. It has been assumed for much of the last decade that the competition must resolve itself though some kind of tug-of-war; but recent evidence shows conclusively that this is often not the case in vivo. In this talk, we will see a few biological mechanisms (and associated mathematical models) that may lead to resolving theory with experimental observations. Joint work with Will Hancock (Penn State), John Fricks (Penn State), and Pete Kramer (RPI).

03:20 PM
03:50 PM

Break

03:50 PM
04:30 PM
Jay Newby - Microtubule transport of mRNA in dendrites

A key component in the cellular mechanisms underlying learning and memory involves the distribution and delivery of mRNA to synaptic sites in dendrites. A minimal three-state random intermittent search model of motor-driven mRNA transport is developed to explore the question of why motor-driven mRNA are observed moving bidirectionally. The model is analyzed by computing the probability an mRNA is delivered to a synaptic target and the average delivery time (MFPT). It is found that if the branched geometry of the dendrite is ignored, a purely unidirectional transport strategy will result in the smallest MFPT at any given delivery probability. The branched geometry of the dendrite is then incorporated into the model, and it is shown that a phase transition exists for a critical delivery probability where bidirectional strategies improve the corresponding MFPT. To further explore the impact of motor-driven transport behavior on mRNAdelivery, the three-state model is extended to include a detailed, biophysical model of a multimotor complex coordinated through a tug-of-war. The model is analyzed to explore how various measurable, physical quantities, such as adenosine triphosphate, can be tuned to optimize cargo delivery.

04:30 PM
05:00 PM

General Discussion

05:00 PM
07:00 PM

Reception and Poster Session

07:00 PM

Shuttle pick-up from MBI

Tuesday, November 4, 2014
Time Session
08:00 AM

Shuttle to MBI

08:15 AM
09:00 AM

Breakfast

09:00 AM
09:40 AM
Mary Halloran - The kinesin adaptor Calsyntenin-1 regulates axon branching, axonal transport and microtubule dynamics

Precise regulation of axon growth and branching is crucial for neuronal circuit formation. Moreover, the highly complex morphology of neurons makes them highly dependent on protein/membrane trafficking and transport systems. Both axon growth and axonal transport require tight regulation of microtubule (MT) polarity and dynamics. We identified a kinesin adaptor, Calsyntenin-1 (Clstn-1), as an essential regulator of axon branching and neuronal compartmentalization. We found that Clstn-1 is required for formation of peripheral but not central sensory axons, and for peripheral axon branching in zebrafish. We use live imaging of endosomal trafficking in vivo to show that Clstn-1 regulates transport of Rab5 containing endosomes from the cell body to specific locations of developing axons. Our results suggest a model in which Clstn-1 patterns separate axonal compartments and defines their ability to branch by directing trafficking of specific endosomes. Furthermore, we used live imaging with EB3-GFP to characterize MT dynamics during axon development in vivo. We find that Clstn-1 knockdown causes aberrant retrograde EB3 comets in axons, indicating defects in MT polarity. Furthermore, loss of Clstn-1 slows anterograde MT comets. These results suggest that in addition to regulating trafficking of cargo along MTs, Clstn-1 also functions to organize MT polarity and regulate MT dynamics.

09:40 AM
10:20 AM
Esther Stoeckli - Trafficking of specific guidance receptors regulates axonal behavior at choice points

During neural circuit formation, axons have to find their target cells to make appropriate synaptic contacts. Along their trajectory, axons contact one or several intermediate targets. At each of them, axons need to switch their behavior from attraction to repulsion in order to move on. Axon guidance at intermediate targets, or choice points, depends on the precise regulation of guidance receptors on the growth cone surface. Dorsal commissural (dI1) axons crossing the ventral midline of the spinal cord in the floor plate represent a convenient model for the analysis of the molecular mechanism underlying the switch in axonal behavior.

We identified a role of Calsyntenin1 in the regulation of vesicular trafficking of guidance receptors in dI1 axons. In cooperation with RabGDI, Calsyntenin1 shuttles Rab11-positive vesicles containing Robo1 to the growth cone surface. In contrast, Calsyntenin1-mediated trafficking of Frizzled3, a guidance receptor in the Wnt pathway is independent of RabGDI. Thus, tightly regulated insertion of guidance receptors, which is required for midline crossing and the subsequent turn into the longitudinal axis, is achieved by their specific trafficking along axons.

10:20 AM
10:50 AM

Break

10:50 AM
11:30 AM
David Holcman - Modeling neurite outgrowth based on vesicular trafficking and microtubule dynamics

Neurite growth is a fundamental process of neuronal development, which requires both membrane expansions by exocytosis and cytoskeletal dynamics. However the specific contribution of these processes has not been yet assessed quantitatively. In this talk, I will present a biophysical model in which we relate the overall neurite outgrowth rate to the vesicle dynamics. We considered the complex motion of vesicles in the cell soma and demonstrated from biophysical consideration, that the main step of finding the neurite initiation site relies mainly on a two dimensional diffusion/sequestration/fusion at the cell surface and we obtain a novel formula for the flux of vesicles at the neurite base. In the absence of microtubules, a nascent neurite initiated by vesicular delivery can only reach a small length. By adding the microtubules dynamics to the secretory pathway and using stochastic analysis and simulations, we showed that the complex dynamics of neurite growth depends on the coupling parameter between the microtubules and the neurite.To validate one aspect of our model, we demonstrated that the experimental flux of TI-VAMP but not Synaptobrevin 2 vesicles contributes to the neurite growth. We conclude that although vesicles can be generated randomly in the cell body, the search for the neurite position using the microtubule network and diffusion is quite fast. Finally our study demonstrates that cytoskeletal dynamics is necessary to generate long protrusion, while vesicular delivery alone can only generate small neurite.

11:30 AM
12:10 PM
Matthew O'Toole - Measurement of subcellular force generation in neurons

Forces are important for neuronal outgrowth during the initial wiring of the nervous system and following trauma, yet sub-cellular force generation over the microtubule rich region at the rear of the growth cone and along the axon has never been directly measured. Because previous studies have indicated microtubule polymerization and the microtubule associated proteins Kinesin-1 and dynein all generate forces that push microtubules forward, a major question is if the net forces in these regions are contractile or expansive. A challenge in addressing this is that measuring local sub-cellular force generation is difficult. Here we develop the first analytical mathematical model for viscous fluids that describes the relationship between unequal sub-cellular forces arranged in series within the neuron and the net overall tension measured externally. Using force-calibrated towing needles to measure and apply forces, in combination with docked mitochondria to monitor sub-cellular strain, we then directly measure force generation over the rear of the growth cone and along the axon of chick sensory neurons. We find the rear of the growth cone generates 1.99 nN of contractile force, the axon generates 0.64 nN of contractile force and that the net traction force generated by the neuron is 1.27 nN. Together this work suggests that the forward bulk flow of the cytoskeletal framework that occurs during axonal elongation and growth cone pauses occurs because strong contractile forces in the rear of the growth cone pull material forward.

12:10 PM
02:00 PM

Lunch Break

02:00 PM
02:40 PM
Stephanie Gupton - TRIM9 Coordinates Cytoskeletal Dynamics and Vesicle Trafficking During Netrin-Dependent Axon Guidance and Branching

Cytoskeletal remodeling and insertion of membrane components into the expanding plasma membrane are required during developmental axon guidance and branching. Although the axon guidance cue Netrin stimulates axon turning and branching, the molecular mechanisms mediating these cell morphological changes are not well defined. We recently identified a direct interaction between the Netrin receptor DCC and the E3 ubiquitin ligase TRIM9. Genetic deletion of TRIM9 results in exuberant cortical axon branching in vitro and in vivo, and a failure in axon turning and branching in response to Netrin, suggesting that TRIM9 restrains constitutive axonal branching and regulates axonal response to Netrin. Exuberant branching in vitro can be rescued by reintroduction of TRIM9 or TRIM9 mutants lacking ubiquitin ligase activity, however Netrin response requires intact TRIM9 ligase activity. In addition to DCC, we have found that TRIM9 directly interacts with the Ena/VASP family of actin regulatory proteins and the exocytic tSNARE SNAP25. Based on biochemical studies performed in heterologous cells and cortical lysates, TRIM9 binds SNAP25 and Ena/VASP proteins in the absence of Netrin, which we suggest sequesters their function. In response to Netrin stimulation, TRIM9 releases SNAP25 and Ena/VASP proteins. Using TIRF microscopy-based assay in wildtype and TRIM9-/- embryonic cortical neurons, we conclude that TRIM9 release of Ena/VASP and SNAP25 following Netrin stimulation promotes SNARE complex formation, vesicle fusion, and filopodia formation. Thus, TRIM9 spatially and temporally coordinates filopodia formation and membrane expansion in response to Netrin in cortical neurons. We are currently using a recently developed a PDMS-based microfluidic device to determine how deletion of TRIM9 affects turning of individual axons in a local Netrin concentration gradient. These assays are corroborated by analysis of axonal projection defects in vivo.

02:40 PM
03:20 PM
Gianluca Gallo - Cytoskeletal basis of axon collateral branching: Insights from Monte Carlo simulations

The formation of a functional nervous system requires the establishment of proper patterns of synaptic connectivity between neurons. Each neuron generates a single axon, but often makes synapses on 100s-1000s of other neurons in disparate parts of the nervous system. The ability of a single axon to generate such complex patterns of connectivity is due to the branching of the axon. Neuronal morphogenesis is dependent on the interactions between the two major components of the cytoskeleton; actin filaments and microtubules. Branches are initiated as actin filament based filopodial protrusions from the main axon shaft, which subsequently mature into branches containing actin filaments and microtubules. This presentation will detail a Monte Carlo simulation of the basic cytoskeletal events underlying the formation of axon branches. The simulation receives empirically derived input values related to aspects of the dynamics of the actin and microtubule cytoskeleton, and returns outputs in the same metric as empirically determined measurement of branch formation. The simulation thus allows direct analysis between empirically derived variables and the final output of the system (i.e., branch formation). The simulation faithfully reproduces the effects of branch inducing factors (e.g., NGF) and suggests new venues of empirical investigation.

03:20 PM
03:50 PM

Break

03:50 PM
04:30 PM
Bruce Graham - Mathematical models of intracellular transport-limited neurite elongation and branching

Neurite outgrowth (dendrites and axons) should be a stable, but easily regulated process to enable a neuron to make its appropriate network connections during development. We explore the dynamics of outgrowth in a mathematical continuum model of neurite elongation (McLean & Graham, Proc. R. Soc. Lond. A, 460:2437-2456, 2004; Graham et al, J. Comput. Neurosci., 20:43-60, 2006). The model describes the construction of the internal microtubule cytoskeleton, which results from the production and transport of tubulin dimers and their assembly into microtubules at the growing neurite tip. Tubulin is assumed to be largely synthesised in the cell body from where it is transported by active mechanisms and by diffusion along the neurite. It is argued that this construction process is a fundamental limiting factor in neurite elongation. In the model, elongation is highly stable when tubulin transport is dominated by either active transport or diffusion, but oscillations in length may occur when both active transport and diffusion contribute. Autoregulation of tubulin production can eliminate these oscillations. In all cases a stable steady-state length is reached, provided there is intrinsic decay of tubulin. Small changes in growth parameters, such as the tubulin production rate, can lead to large changes in length. Thus cytoskeleton construction can be both stable and easily regulated, as seems necessary for neurite outgrowth during nervous system development.

In a model variant, we demonstrate competitive growth between two neurite branches being supplied by the same source of tubulin (van Ooyen et al, Neurocomputing, 38-40:73-78, 2001). The faster growing neurite can completely inhibit elongation in the other neurite. Such apparent competition has been observed in real neuron outgrowth.

In a different model formulation, the propensity of neurite branching is assumed to depend on the amount of tubulin reaching the growth cone (Graham & van Ooyen, J. Theor. Biol., 230:421-432, 2004). This transport-limited branching yields matches to the characteristic dendritic morphologies from different neuronal types.

04:30 PM
05:00 PM

General Discussion

05:00 PM

Shuttle pick-up from MBI

Wednesday, November 5, 2014
Time Session
08:00 AM

Shuttle to MBI

08:15 AM
09:00 AM

Breakfast

09:00 AM
09:40 AM
Jeff Urbach - Biomechanics and Dynamics of Growth Cones in Engineered Environments

In the developing nervous system, axons respond to a diverse array of cues to generate the intricate connection network required for proper function. The growth cone integrates information about the local environment and modulates outgrowth and guidance, but relatively little is known about effects of external mechanical or structural cues and internal mechanical forces on growth cone behavior. We have investigated axon outgrowth and force generation on soft elastic substrates for dorsal root ganglion (DRG) neurons (from the peripheral nervous system) and hippocampal neurons (from the central) to see how the mechanics of the microenvironment affect different populations. We find that force generation and stiffness-dependent outgrowth are strongly dependent on cell type. I will discuss recent analyses of the dynamic aspects of growth cone force generation that show surprising regularity underlying the dynamic pattern of traction forces. I will also describe experiments showing that micron-scale confinement affects growth cone shape but, surprisingly, not neurite growth rates. Changes in confinement, by contrast, produce dramatic changes in extension rates. These results suggest a range of opportunities and challenges for developing a quantitative understanding of the influence on engineered environments on axon growth and guidance.

09:40 AM
10:20 AM
Roberto Bernal - TBD

Abstract Not Submitted

10:20 AM
10:50 AM

Break

10:50 AM
11:30 AM
Taher Saif - Axonal transport is modulated by axonal tension

A large majority of neurons have a long axon that forms junctions (synapse) with muscle tissue or another neuron. They carry neurotransmitters enclosed within vesicles that are about 50nm in size. Clustering of vesicles at the synapse is essential for neurotransmission and hence memory and learning. We showed earlier, using embryonic Drosophila (fruit fly), that axons actively maintain a rest tension of about 1 nN. Without this tension, clustering disappears, but reappears with the application of tension. Increase of tension results in increased clustering. Here we explore the role of tension or stretch on vesicle transport along the axon. We use of Aplysia as a model system in this study. We analyze the dynamics of an ensemble of vesicles using the framework of statistical mechanics. We find that the vesicles move along the axon in two modes: (1) random walk (passive motion), and (2) directed motion (active), transported by molecular motors. With increased tension or stretch, vesicles spend more time in active mode compared to that of random walk. Furthermore, increased stretch results in an increased flux of vesicles along the axon. It thus appears that the axonal transport is modulated by the net tension in the axons. In search of the origin of tension in axons, we employed a series of drugs. We find, tension is most likely generated by myosin II motors acting on cortical actin. This corticle actin-myosin complex is distributed along the entire length of the axon, and participates in tension generation. Microtubules play a relatively minor role. Thus, disruption of myosin II, or the filamentous actin, or depletion of ATP results in a loss of tension in axon. Disruption of microtubules shows little effect. It thus appears that the corticle actin, together with myosin II, provide a taut peripheral structure for aligned microtubule tracks for vesicle transport along the axon, and hence clustering at the synapse.

11:30 AM
02:00 PM

Lunch Break

02:00 PM
02:40 PM
Laura Anne Lowery - TACC3 is a microtubule plus-end tracking protein that promotes axon elongation and microtubule polymerization in growth cones

Abstract not submitted.

02:40 PM
03:20 PM
Timothy Gomez - Mechanochemical signals that guide axon development.

Growth cones interact with the extracellular matrix (ECM) through integrin receptors at adhesion sites termed point contacts. Point contact adhesions link ECM proteins to the actin cytoskeleton through numerous adaptor and signaling proteins. One presumed function of growth cone point contacts is to restrain or “clutch” myosin II-based F-actin retrograde flow (RF) to promote leading edge membrane protrusion. In motile non-neuronal cells, myosin II binds and exerts force upon actin filaments at the leading edge where clutching forces occur. However, in growth cones it is unclear whether similar F-actin clutching forces affect axon outgrowth and guidance. I will show that RF is reduced in rapidly migrating growth cones on laminin (LN) compared to non-integrin binding poly-d-lysine (PDL). Moreover, acute stimulation with LN leads to accelerated axon outgrowth over a time course that correlates with point contact formation and reduced RF. These results suggest that actin RF is restricted by the assembly of point contacts, which we show directly by two color imaging of actin RF and paxillin. Further, using micro-patterns of PDL and LN, we demonstrate that individual growth cones have differential actin RF rates while interacting with two distinct substrata. Opposing effects on actin RF rates were also observed in growth cones treated with chemoattractive and chemorepulsive axon guidance cues known to influence point contact adhesions. Finally, using GFP-actin, we show that actin RF within growth cones in the spinal cord is slow, suggesting RF is being restrained by molecular clutching forces in vivo.

03:20 PM
03:50 PM

Break

03:50 PM
04:30 PM
Alain Goriely - Some brain mechanics: tissue swelling and damage propagation

Tissue swelling, or edema, is a dangerous consequence of traumatic brain injury and stroke. Local edema can exacerbate the original injury and increase intracranial pressure in surrounding tissue. This can result in damage spreading beyond the original injury. In particular, a locally swollen region can cause the injury to propagate further through the brain, due to mechanical compression of the blood supply in surrounding tissue. Here, we first present a quadriphasic model that includes both the mechanical and electrochemical responses of a tissue and use it to revisit the role of the Donnan effect in edema. Second, we investigate how a local change in blood brain barrier permeability, a known cause of edema, can lead to abnormal stresses and strains in the tissue. Third, we couple the tissue mechanics with oxygen delivery, to investigate the propagation of swelling and damage.

This is joint work with Georgina Lang, Sarah Waters, and Dominic Vella

04:30 PM
05:00 PM

General Discussion

05:00 PM

Shuttle pick-up from MBI

Thursday, November 6, 2014
Time Session
08:00 AM

Shuttle to MBI

08:15 AM
09:00 AM

Breakfast

09:00 AM
09:20 AM
Dan Fenn - Short Talk: Is the axonal transport of neurofilaments a 'tug-of-war' Part I

Neurofilaments are the intermediate filament of neurons and are the most abundant structure in the cytoplasm of large axons. They serve as space filling structures that help regulate axon diameter, which in turn regulates conduction velocity. In addition to their structural roles, neurofilaments are also cargoes of axonal transport. They are synthesized within the cell body and then transported out along the axon on microtubules tracks. This movement is characterized by long pauses interrupted by infrequent bouts of rapid movement driven by the molecular motors kinesin and dynein. To further investigate neurofilament motility, we acquired movies of the movement of GFP-tagged neurofilaments with 30 ms temporal resolution in cultured neurons from neonatal rat brain cortex and used kymograph analysis to obtain trajectories of the leading and trailing ends of the moving filaments. Using a newly developed and unbiased noise-filtering algorithm, we extracted bouts of movement and pauses from these trajectories for statistical analysis. Our findings show that although a net anterograde directionality exists overall, individual filaments frequently alternate, sporadically, between anterograde and retrograde directions. Unexpectedly, we find no correlation between neurofilament length and any characteristic feature analyzed including average net velocity, average run velocity, average pause-time, average run length and average run time. The intermittent and bidirectional motions of the filaments led us to investigate, computationally, whether the observed trajectories could be generated by a tug-of-war model. In such a model, the movements are a result of the independent and antagonistic forces generated by kinesin and dynein motors attached to each neurofilament cargo. By systematically varying the number of bound kinesin and dynein motors in the model, we can identify combinations of motors that correlate with the above-mentioned motile characteristics found in each kymograph trace. So far we have found no inconsistencies between the tug-of-war model and the experimental data, but distinct kinetic phases within individual traces suggest that the number of motors bound to the neurofilament cargo is not fixed and may change over time. The model predicts that the total number of active motors on each neurofilament is relatively small and relatively independent of polymer length. Thus the motors may not be distributed uniformly along the filaments.

09:20 AM
09:40 AM
Christopher Johnson - Short Talk: Is the axonal transport of neurofilaments a 'tug-of-war' Part II

Neurofilaments are the intermediate filament of neurons and are the most abundant structure in the cytoplasm of large axons. They serve as space filling structures that help regulate axon diameter, which in turn regulates conduction velocity. In addition to their structural roles, neurofilaments are also cargoes of axonal transport. They are synthesized within the cell body and then transported out along the axon on microtubules tracks. This movement is characterized by long pauses interrupted by infrequent bouts of rapid movement driven by the molecular motors kinesin and dynein. To further investigate neurofilament motility, we acquired movies of the movement of GFP-tagged neurofilaments with 30 ms temporal resolution in cultured neurons from neonatal rat brain cortex and used kymograph analysis to obtain trajectories of the leading and trailing ends of the moving filaments. Using a newly developed and unbiased noise-filtering algorithm, we extracted bouts of movement and pauses from these trajectories for statistical analysis. Our findings show that although a net anterograde directionality exists overall, individual filaments frequently alternate, sporadically, between anterograde and retrograde directions. Unexpectedly, we find no correlation between neurofilament length and any characteristic feature analyzed including average net velocity, average run velocity, average pause-time, average run length and average run time. The intermittent and bidirectional motions of the filaments led us to investigate, computationally, whether the observed trajectories could be generated by a tug-of-war model. In such a model, the movements are a result of the independent and antagonistic forces generated by kinesin and dynein motors attached to each neurofilament cargo. By systematically varying the number of bound kinesin and dynein motors in the model, we can identify combinations of motors that correlate with the above-mentioned motile characteristics found in each kymograph trace. So far we have found no inconsistencies between the tug-of-war model and the experimental data, but distinct kinetic phases within individual traces suggest that the number of motors bound to the neurofilament cargo is not fixed and may change over time. The model predicts that the total number of active motors on each neurofilament is relatively small and relatively independent of polymer length. Thus the motors may not be distributed uniformly along the filaments.

09:40 AM
10:00 AM
Ahmad Athamneh - Short Talk: The level of substrate deformation regulates adhesion-mediated neuronal growth cone advance

Although pulling forces have been observed in axonal growth for several decades, their exact roles are not fully understood. Here, we quantified retrograde traction forces in neuronal growth cones as they develop over time in response to an adhesion substrate using two different experimental approaches. In the first approach, we used force-calibrated glass microneedles coated with ligands for the Aplysia cell adhesion molecule apCAM to guide the advance of Aplysia Californica growth cones. The traction force exerted by the growth cone was measured by monitoring the microneedle deflection using an optical microscope. In the second approach, we developed a new method for measuring traction forces using an atomic force microscope (AFM) with a static cantilever that contained a ligand-coated microbead. Both approaches showed that Aplysia growth cones can develop maximum traction forces up to 100 nN, which is an order of magnitude higher than previously reported for other experimental methods or growth cones. Moreover, our results suggest that the traction force is directly correlated to the stiffness of the microneedle, which is consistent with a reinforcement mechanism supported by other research. Over a range of substrate stiffness, the absolute level of force did not predict well whether the growth cone would advance towards the adhesion site or not, but the level of microneedle deflection did. In cases of adhesion-mediated growth cone advance, the mean deflection was 1.08 0.08 mm. By contrast, the mean deflection was significantly lower (0.49 0.04 mm) when the growth cones did not advance in response to the adhesion substrate. In summary, our results provide novel insights into significance of the level of substrate deformation as opposed to the level of traction force for the regulation of adhesion-mediated directional growth cone advance.

10:00 AM
10:20 AM
Jürgen Reingruber - Short Talk: Modeling axonal targeting with synergetic interactions

Axonal transport and growth cone dynamics play a fundamental role for pathfinding and the formation of neuronal networks in the brain. During neuronal development, migrating axons wire the brain by generating long range connections between different brain regions. In the visual system, the retinotopic map connects the retina to the visual centers in the midbrain. When axons from retinal ganglion cells reach the optic tectum (superior colliculus in mammals) they form ordered connections with tectal neurons thereby establishing a topographic map. The map precision is important to correctly transmit the visual information projected onto the retina. Families of ephrin guidance molecule distributed in gradients in the retina and tectum play a crucial role in the map formation process. In addition, engrailed homeoprotein transcription factors are important for axonal guidance. Engrailed displays a graded expression in the chick optic tectum and participates in axonal guidance. Moreover, engrailed regulates the expression of ephrinA5 and increases the sensitivity of growth cones to ephrinA5 repellent activity. The molecular pathway for the engrailed-ephrinA5 interaction involves the internalization of engrailed into the growth cone, which stimulates the production and secretion of ATP, followed by hydrolysis of extracellular ATP into adenosine and the activation of membrane bound
adenosine A1 receptor that are present in higher concentrations in temporal than nasal GCs. Based on these findings, we propose a computational model that shows how the synergetic interaction between engrailed and ephrinA5 increases the precision of the map formation.

10:20 AM
10:50 AM

Break

10:50 AM
11:10 AM
Joy Thompson - Short Talk: Role of tissue stiffness in embryonic axon guidance.

Neuronal growth is essential for nervous system development and is also required for regeneration after nervous tissue injury. As axons and dendrites grow towards their targets, they are guided by environmental cues, including a well-characterised set of biochemical signals. Recent in vitro studies suggest that neuronal growth can also be regulated by mechanical properties of the substrate. However, the role of mechanical cues in axon pathfinding in vivo, and the spatiotemporal dynamics of tissue mechanics during early nervous system development, are still largely unknown. Here we investigate the role of tissue stiffness in axon guidance within the early embryo, using the Xenopus laevis optic tract as a model system. Retinal ganglion cell (RGC) axons form the optic tract by growing from the embryonic retina, along a stereotypical path on the brain surface, and terminating at their target, the tectum. We have developed in vivo atomic force microscopy (AFM) to map tissue stiffness along the optic tract at different developmental stages. We find that the embryonic brain is overall mechanically inhomogeneous, and that brain stiffness changes over time. Specifically, we find that the elastic stiffness of the tectum is consistently lower than the rest of the path taken by RGCs. Our results indicate that the path of RGCs is correlated with stiffness gradients in vivo, before axon growth stalls after reaching the softer region. These findings are consistent with a role for substrate mechanics in axon pathfinding, which might not only be crucial during development but also during regenerative processes in the nervous system.

11:10 AM
11:30 AM
Julian Garcia Grajales - Short Talk: Mechanical modeling of neurites

Computational Neuron Mechanics appears as a new multidisciplinary _eld potentially able to study medical challenges such as Alzheimer's disease, tumor growth/migration or traumatic brain injury at cell level. Although computational modeling has been widely used in di_erent Neuroscience applications, the tremendous importance of the interactions between the neuron and its surrounding media/stimulus have been rarely explored. Aimed at analyzing these inter- actions, this work proposes a new multiscale computational framework particularized for two representative scenarios: axonal growth and electrophysiological-mechanical coupling of neu- rites. In the former, the intertwined relation between a biochemical stimulus and the mechanical properties of axons is studied, whereas in the latter, the functional impairments of neurites as a consequence of mechanical constraints are explored. To accomplish these objectives, we de- vise a large scale parallel _nite di_erence program, called Neurite, with the necessary exibility and versatility to implement biological models. In the case of the axonal growth, the program was adapted to simulate microtubule polymerization providing axon mechanical properties as a function of its microtubule occupancy. For the electrophysiological-mechanical coupling case, Neurite was used to relate macroscopic mechanical loading to microscopic strains and strain rates, and to simulate electrical signal propagation along neurites under mechanical loading. For both cases, the models were calibrated against experimental results available in the litera- ture. The growth model showed dramatic variations in the mechanical properties at the tip of the axon, whereas the electrophysiological-mechanical model represents a novelty for predicting the alteration of neuronal electrophysiological function under mechanical loading, thus linking mechanical traumas to subsequent acute functional de_cits.

11:30 AM
11:50 AM
Fernanda Garate - Short Talk: Mechanical Properties of a quasi one-dimensional biological system

In recent years, thermal fluctuations in combination with noninvasive technique, weak Optical tweezers, is a powerful tool to obtain mechanical information. In this work, we get PC12 neurites mechanical properties by fluctuations amplitudes measurements combined with a model system of neurons, developed here.

11:50 AM
12:10 PM

General Discussion

12:10 PM
02:00 PM

Lunch Break

02:00 PM
02:40 PM
Bonnie Firestein - Assessing Effects on Dendritic Arborization: Novel Sholl Analyses and Imaging of Microtubule Dynamics.

The precise patterning of dendrites is important for determining how information is processed by a neuron. The neuron cannot receive appropriate information when there is an abnormal decrease in dendrite branching. Thus, disruption of proper signaling networks results. We and others have made significant progress on characterizing extracellular and intrinsic factors that regulate dendrite number or branching by altering cytoskeletal dynamics. Generally, changes to the dendritic arbor are assessed by Sholl analysis or simple dendrite counting. However, we have found that this general method often overlooks local changes to the arbor. We have developed a program (titled "Bonfire") to facilitate digitization of neurite morphology and subsequent Sholl analysis and to assess changes to root, intermediate, and terminal neurites. More recently, we have studied how microtubule dynamics are altered when changes occur to the dendritic arbor. Our future goal is to combine Sholl analysis and microtubule dynamic studies to understand how dendrites assume specific morphologies.

02:40 PM
03:20 PM
Ellen Kuhl - On The Role Of Neuromechanics In Human Brain Development

Convolutions are a classical hallmark of most mammalian brains. Brain surface morphology is often associated with intelligence and closely correlated to neurological dysfunction. Yet, we know surprisingly little about the underlying mechanisms that drive cortical folding. To explore the evolution of brain surface morphology, we establish a neuromechanical model using the nonlinear field theories of mechanics supplemented by the continuum theory of finite growth. Continuum modeling allows us to seamlessly integrate information across the scales and correlate organ-level phenomena such as cortical folding to molecular-level processes such as axonal elongation. We show that our model can predict the formation of complex surface morphologies including symmetry breaking and secondary folding. Computational modeling naturally explains why larger mammalian brains tend to be more convoluted than smaller brains and provides a mechanistic interpretation of pathological malformations of lissencephaly and polymicrogyria. Understanding the role of physical forces during the development of the nervous system may have direct implications on the diagnostics and treatment of neurological disorders including severe retardation, epilepsy, schizophrenia, and autism.

03:20 PM
03:50 PM

Break

03:50 PM
04:30 PM
Paul Janmey - How soft is the brain? Compression stiffening and mechanosensing by glial cells

A common feature of many solid tumors and is that they are stiffer than the normal tissue in which they arise and have increased interstitial fluid pressures and solid tissue stress. These physical changes, which often involve increased synthesis and cross-linking of extracellular matrix protein, can lead to deleterious changes in mechanosensitive cells.Brain and other CNS tissues lack the filamentous protein-based extracellular matrix characteristic of most mesenchymal and epithelial environments, and isolated glioma samples have the same shear storage moduli as normal brain when measured ex vivo at low strains. However, the shear moduli of both normal and malignant brain tissue increase to the kPa range that activates glioma cells and normal glial cells in vitro when the tissue is uniaxially compressed. We suggest that compression stiffening, which might occur with the increased vascularization and interstitial pressure gradients that are characteristic of glioma and other tumors, effectively stiffens the environment of glioma cells and that in situ, the elastic resistance these cells sense might be sufficient to trigger the same responses that are activated in vitro by increased substrate stiffness.

04:30 PM
05:00 PM

General Discussion

05:00 PM

Shuttle pick-up from MBI

06:00 PM
07:00 PM

Cash Bar at Crowne Plaza

07:00 PM
09:00 PM

Banquet Dinner in Fusion Room at the Crowne Plaza

Friday, November 7, 2014
Time Session
08:00 AM

Shuttle to MBI

08:15 AM
09:00 AM

Breakfast

09:00 AM
09:40 AM
Corina Drapaca - Mathematical Modeling of Brain Neuro-Mechanics

It is well known that mechanical loading and biochemical imbalances can alter brain’s functions and/or structure and lead to neurological diseases. Mathematical models of brain neuro-mechanics can play an important role in highlighting the mechanisms that govern healthy and diseased processes and thus help develop better diagnostic and therapeutic tools. We propose to model the brain as a triphasic composite made of solid, fluid and ionic phases and show some numerical simulations that suggest that normal pressure hydrocephalus could be caused by an imbalance in the salt concentration in the absence of an elevated intracranial pressure. We will also show some numerical simulations of the coupling between the proposed triphasic model and the Hodgkin-Huxley model that permit the investigation of possible linkages between brain’s functionality and mechanical behavior.

09:40 AM
10:20 AM
Bryan Pfister - Extreme Axon Stretch Growth

Axons span the body over great distances; up to a meter in humans and much longer in large mammals. The study of axon growth has mainly focused on the extension and migration of growth cones during development. Once axons integrate with their targets, however, axonal fibers continue to grow in synchrony with body growth. The likely regulatory mechanism that accommodates for such symbiotic interaction is the biomechanical stretching of axons, a formidable stimulus of neuronal growth. Our lab has engineered bioreactors to uniaxially stretch grow axons in culture that can be microscopically visualized in real time. Nerves can quickly adapt to increasing rates of stretch-growth. Below 25% applied strain axons grow in absence of occlusion of axon transport and long-term disconnection. Neurons from stretch grown axons do not show evidence of chromatolysis and can produce normal electrical activity. Under these conditions, persistent axon stretch upregulates developmental and regenerative associated genes. Bioinformatics analysis using Ingenuity pathway analysis software revealed significant changes in lipid metabolism, molecular transport, and small molecule biochemistry. Further, stress-response and regenerative associated genes such as SPRR1a and ATF3 were found to be upregulated, implicating a novel role in development in addition to their transient expression following injury. These results suggest that axon stretch growth is a process whereby neuronal expansion is regulated by developmental stress, which leads to a unique transcriptional profile that accommodates axon growth.

10:20 AM
10:50 AM

Break

10:50 AM
11:30 AM
Michelle LaPlaca - Neural mechanobiology and neuronal vulnerability to traumatic loading

Traumatic brain injury (TBI) is a leading cause of death and disability in the United States and in the world. Physical insults to the brain, by nature, are heterogeneous, as is the underlying physiology of an individual, rendering the study of TBI mechanisms very difficult. Furthermore, the complexity of brain tissue cytoarchitecture (e.g., neuron morphology, neuron-glial interactions, synapses) adds to the challenge of determining tissue-level tolerances. There is a critical need to understand the mechano-chemo-electrical transduction from macroscopic loading to the cells that may contribute to cumulative damage and degeneration. In an effort to tackle these challenges, we and others have used isolated systems to study cellular response to traumatic loading conditions. From these studies it is evident that there is strain and/or strain rate dependent membrane damage, ion imbalance, channel dysfunction, compromised energetics, inflammation, electrophysiological disruptions, and other cascades that may contribute to cell death. Questions remain regarding if the membrane transduces forces to the cell primarily through matrix-cytoskeleton loading or if plasma membrane stretch directly causes lipid rearrangement and damage. We will discuss traumatic loading to neurons at the cellular level, the relationships between mechanical trauma and secondary responses, as well as present issues related to cell to tissue scale up. Understanding TBI at the human level requires an appreciation of complexity across scales and severities as it pertains to cellular and mathematical modeling and this discussion is expected to spur ideas that will ultimately accelerate the path to translational discovery in neurotrauma and other acute brain insults.

11:30 AM
12:10 PM
Catherine Collins - Cellular Mechanism(s) for Detection of Axonal Injury

Because axons make connections over great distances, they are vulnerable components of neuronal circuits. While neurons in the peripheral nervous system (PNS) can initiate new axonal growth after damage, neurons in the central nervous system (CNS) seldom regrow, and instead often die. Work over the past several years has identified a conserved dileucine zipper kinase, DLK, as a critical regulator of both regenerative responses to axonal damage in the PNS, and degenerative responses to damage in the CNS. DLK protein is transported in axons and regulates an axon-to-nucleus retrograde signal in response to injury, however the mechanism by which this kinase detects axonal damage is not yet clear. Several recent findings suggest that the DLK becomes activated when axonal cytoskeleton is disrupted. I will discuss current models along with our recent findings that the kinesin-3 family member, unc-104, functions as a negative regulator of DLK signaling.

12:10 PM
01:00 PM

General Discussion and Closing Remarks

01:00 PM

Shuttle pick-up from MBI (One back to hotel and one to airport)

Name Email Affiliation
Athamneh, Ahmad aathamne@purdue.edu Biological Sciences, Purdue University
Bates, Dan bates@math.colostate.edu Department of Mathematics, Colorado State University
Bernal, Roberto roberto.bernal@usach.cl Physics Department, Universidad de Santiago de Chile (USACH)
Bray, Dennis db10009@cam.ac.uk Physiology, Develoment, Neuroscience, University of Cambridge
Bressloff, Paul bressloff@math.utah.edu Department of Mathematics, University of Utah
Brown, Anthony brown.2302@osu.edu Neuroscience, The Ohio State University
Cebulla, Colleen colleen.cebulla@osumc.edu Ophthalmology and Visual Science, The Ohio State University
Collins, Catherine collinca@umich.edu Molecular, Cellular, and Developmental Biology, University of Michigan
Drapaca, Corina csd12@psu.edu Engineering Science and Mechanics, Pennsylvania State University
Firestein, Bonnie firestein@biology.rutgers.edu Cell Biology and Neuroscience, Rutgers University
Franze, Kristian kf284@cam.ac.uk Department of Physiology, Development and Neuroscience, University of Cambridge
Gallo, Gianluca gianluca.gallo@temple.edu Anatomy and Cell Biology, Temple University
Garate, Fernanda fernanda.garate@usach.cl Physics, universidad de santiago de chile
Garcia Grajales, Julian Julian.GarciaGrajales@maths.ox.ac.uk Mathematical Institute, Mathematical Institute
Gomez, Timothy tmgomez@wisc.edu Neuroscience, University of Wisconsin
Goriely, Alain Alain.Goriely@maths.ox.ac.uk Mathematical Institute, University of Oxford
Graham, Bruce b.graham@cs.stir.ac.uk Computing Science and Mathematics, University of Stirling
Gupton, Stephanie stephanie_gupton@med.unc.edu Cell Biology & Physiology, University of North Carolina, Chapel Hill
Halloran, Mary mchalloran@wisc.edu Zoology, University of Wisconsin
Heidemann, Steven heideman@msu.edu Physiology, Michigan State University
Holcman, David holcman@biologie.ens.fr Applied mathematics and Computational Biology, Ecole Normale Superieure
Janmey, Paul janmey@mail.med.upenn.edu Physiology, University of Pennsylvania
Johnson, Christopher cj791502@ohio.edu Physics & Astronomy, Ohio University
Jung, Peter jung@phy.ohiou.edu Quantitative Biology Institute, Ohio University
Karamched, Bhargav bkaramched@gmail.com Mathematics, University of Utah
Kuhl, Ellen ekuhl@stanford.edu Mechanical Engineering and Bioengineering, Stanford University
LaPlaca, Michelle michelle.laplaca@bme.gatech.edu Biomedical Engineering, Georgia Institute of Technology / Emory University
Lowery, Laura Anne laura.lowery@bc.edu Biology, Boston College
Maia, Pedro pedro.doria.maia@gmail.com Applied Mathematics, University of Washington
McKinley, Scott scott.mckinley@ufl.edu Mathematics, University of Florida
Miller, Kyle kmiller@msu.edu Dept. of Zoology, Michigan State University
Mussel, Matan matanmus@gmail.com Department of Biomedical Engineering, Tel Aviv University
Newby, Jay newby.23@mbi.osu.edu Mathematical Biosciences Institute, The Ohio State University
O'Neill, Kate km.fitzgerald@rutgers.edu Biomedical Engineering, Rutgers University
O'Toole, Matthew motoole@kettering.edu Mathematics, Kettering University
Osan, Remus rosan@gsu.edu Mathematics and Statistics, Georgia State University
Pfister, Bryan bryan.j.pfister@njit.edu Biomedical Engineering, New Jersey Institute of Technology
Puthanveettil, Sathya sputhanv@scripps.edu Neuroscience, The Scripps Research Institute
Reingruber, Juergen reingrub@biologie.ens.fr Biology, Ecole Normale Superieure
Saif, Taher saif@illinois.edu Mechanical Science and Engineering, University of Illinois at Urbana-Champaign
Stoeckli, Esther esther.stoeckli@imls.uzh.ch Institute of Molecular Life Sciences, University of Zurich
Suter, Daniel dsuter@purdue.edu Biological Sciences, Purdue University
Thompson, Amelia ajt88@cam.ac.uk Physiology, Development and Neuroscience, University of Cambridge
Urbach, Jeffrey urbach@physics.georgetown.edu Physics, Georgetown University
Xue, Chuan cxue@math.osu.edu Department of Mathematics, The Ohio State University
Zemel, Assaf assaf.zemel@ekmd.huji.ac.il Institute of Dental Sciences, Hebrew University of Jerusalem
Short Talk: The level of substrate deformation regulates adhesion-mediated neuronal growth cone advance

Although pulling forces have been observed in axonal growth for several decades, their exact roles are not fully understood. Here, we quantified retrograde traction forces in neuronal growth cones as they develop over time in response to an adhesion substrate using two different experimental approaches. In the first approach, we used force-calibrated glass microneedles coated with ligands for the Aplysia cell adhesion molecule apCAM to guide the advance of Aplysia Californica growth cones. The traction force exerted by the growth cone was measured by monitoring the microneedle deflection using an optical microscope. In the second approach, we developed a new method for measuring traction forces using an atomic force microscope (AFM) with a static cantilever that contained a ligand-coated microbead. Both approaches showed that Aplysia growth cones can develop maximum traction forces up to 100 nN, which is an order of magnitude higher than previously reported for other experimental methods or growth cones. Moreover, our results suggest that the traction force is directly correlated to the stiffness of the microneedle, which is consistent with a reinforcement mechanism supported by other research. Over a range of substrate stiffness, the absolute level of force did not predict well whether the growth cone would advance towards the adhesion site or not, but the level of microneedle deflection did. In cases of adhesion-mediated growth cone advance, the mean deflection was 1.08 ± 0.08 mm. By contrast, the mean deflection was significantly lower (0.49 ± 0.04 mm) when the growth cones did not advance in response to the adhesion substrate. In summary, our results provide novel insights into significance of the level of substrate deformation as opposed to the level of traction force for the regulation of adhesion-mediated directional growth cone advance.

TBD

Abstract Not Submitted

Axonal transport of neurofilaments

Neurofilaments are space-filling protein polymers in axons that function to maximize axonal cross-sectional area, which is an important determinant of axonal conduction velocity. In large axons they are the single most abundant structure, occupying most of the axonal volume. Remarkably, these polymers are also cargoes of axonal transport, moving anterogradely and retrogradely along microtubule tracks in rapid bursts of movement interrupted by prolonged pauses. This stop-and-go behavior results in a slow average rate of movement, termed slow axonal transport. A central hypothesis of our laboratory is that neurofilament transport is a principal determinant of the neurofilament content and distribution along axons, and thus a principal determinant of axonal morphology. Thus it is important to understand the mechanisms that regulate neurofilament transport. We have shown recently that axonal neurofilaments can lengthen by joining end-to-end, called end-to-end annealing, and that they can also be shortened by a severing mechanism, which is a novel phenomenon for intermediate filaments. These mechanisms give rise to a broad range of neurofilament lengths in axons ranging from <1 µm to >180 µm. This raises intriguing questions about the mechanism of movement. Intriguingly, we find that short neurofilaments move rapidly and continuously in one direction, rarely reversing, whereas long filaments exhibit long pauses and frequent reversals, resulting in much less net movement. Long-term imaging of neurofilaments using a multi-field tracking technique has revealed that severing and annealing are robust phenomena and that short filaments anneal more frequently than long filaments, whereas long filaments sever more frequently than short filaments. These observations suggest that there is a dynamic cycle of neurofilament severing and annealing in axons that regulates the length and axonal transport of these cytoskeletal polymers. I will present evidence to support this model.

Cellular Mechanism(s) for Detection of Axonal Injury

Because axons make connections over great distances, they are vulnerable components of neuronal circuits. While neurons in the peripheral nervous system (PNS) can initiate new axonal growth after damage, neurons in the central nervous system (CNS) seldom regrow, and instead often die. Work over the past several years has identified a conserved dileucine zipper kinase, DLK, as a critical regulator of both regenerative responses to axonal damage in the PNS, and degenerative responses to damage in the CNS. DLK protein is transported in axons and regulates an axon-to-nucleus retrograde signal in response to injury, however the mechanism by which this kinase detects axonal damage is not yet clear. Several recent findings suggest that the DLK becomes activated when axonal cytoskeleton is disrupted. I will discuss current models along with our recent findings that the kinesin-3 family member, unc-104, functions as a negative regulator of DLK signaling.

Mathematical Modeling of Brain Neuro-Mechanics

It is well known that mechanical loading and biochemical imbalances can alter brain’s functions and/or structure and lead to neurological diseases. Mathematical models of brain neuro-mechanics can play an important role in highlighting the mechanisms that govern healthy and diseased processes and thus help develop better diagnostic and therapeutic tools. We propose to model the brain as a triphasic composite made of solid, fluid and ionic phases and show some numerical simulations that suggest that normal pressure hydrocephalus could be caused by an imbalance in the salt concentration in the absence of an elevated intracranial pressure. We will also show some numerical simulations of the coupling between the proposed triphasic model and the Hodgkin-Huxley model that permit the investigation of possible linkages between brain’s functionality and mechanical behavior.

Short Talk: Is the axonal transport of neurofilaments a 'tug-of-war' Part I

Neurofilaments are the intermediate filament of neurons and are the most abundant structure in the cytoplasm of large axons. They serve as space filling structures that help regulate axon diameter, which in turn regulates conduction velocity. In addition to their structural roles, neurofilaments are also cargoes of axonal transport. They are synthesized within the cell body and then transported out along the axon on microtubules tracks. This movement is characterized by long pauses interrupted by infrequent bouts of rapid movement driven by the molecular motors kinesin and dynein. To further investigate neurofilament motility, we acquired movies of the movement of GFP-tagged neurofilaments with 30 ms temporal resolution in cultured neurons from neonatal rat brain cortex and used kymograph analysis to obtain trajectories of the leading and trailing ends of the moving filaments. Using a newly developed and unbiased noise-filtering algorithm, we extracted bouts of movement and pauses from these trajectories for statistical analysis. Our findings show that although a net anterograde directionality exists overall, individual filaments frequently alternate, sporadically, between anterograde and retrograde directions. Unexpectedly, we find no correlation between neurofilament length and any characteristic feature analyzed including average net velocity, average run velocity, average pause-time, average run length and average run time. The intermittent and bidirectional motions of the filaments led us to investigate, computationally, whether the observed trajectories could be generated by a tug-of-war model. In such a model, the movements are a result of the independent and antagonistic forces generated by kinesin and dynein motors attached to each neurofilament cargo. By systematically varying the number of bound kinesin and dynein motors in the model, we can identify combinations of motors that correlate with the above-mentioned motile characteristics found in each kymograph trace. So far we have found no inconsistencies between the tug-of-war model and the experimental data, but distinct kinetic phases within individual traces suggest that the number of motors bound to the neurofilament cargo is not fixed and may change over time. The model predicts that the total number of active motors on each neurofilament is relatively small and relatively independent of polymer length. Thus the motors may not be distributed uniformly along the filaments.

Assessing Effects on Dendritic Arborization: Novel Sholl Analyses and Imaging of Microtubule Dynamics.

The precise patterning of dendrites is important for determining how information is processed by a neuron. The neuron cannot receive appropriate information when there is an abnormal decrease in dendrite branching. Thus, disruption of proper signaling networks results. We and others have made significant progress on characterizing extracellular and intrinsic factors that regulate dendrite number or branching by altering cytoskeletal dynamics. Generally, changes to the dendritic arbor are assessed by Sholl analysis or simple dendrite counting. However, we have found that this general method often overlooks local changes to the arbor. We have developed a program (titled "Bonfire") to facilitate digitization of neurite morphology and subsequent Sholl analysis and to assess changes to root, intermediate, and terminal neurites. More recently, we have studied how microtubule dynamics are altered when changes occur to the dendritic arbor. Our future goal is to combine Sholl analysis and microtubule dynamic studies to understand how dendrites assume specific morphologies.

Cytoskeletal basis of axon collateral branching: Insights from Monte Carlo simulations

The formation of a functional nervous system requires the establishment of proper patterns of synaptic connectivity between neurons. Each neuron generates a single axon, but often makes synapses on 100s-1000s of other neurons in disparate parts of the nervous system. The ability of a single axon to generate such complex patterns of connectivity is due to the branching of the axon. Neuronal morphogenesis is dependent on the interactions between the two major components of the cytoskeleton; actin filaments and microtubules. Branches are initiated as actin filament based filopodial protrusions from the main axon shaft, which subsequently mature into branches containing actin filaments and microtubules. This presentation will detail a Monte Carlo simulation of the basic cytoskeletal events underlying the formation of axon branches. The simulation receives empirically derived input values related to aspects of the dynamics of the actin and microtubule cytoskeleton, and returns outputs in the same metric as empirically determined measurement of branch formation. The simulation thus allows direct analysis between empirically derived variables and the final output of the system (i.e., branch formation). The simulation faithfully reproduces the effects of branch inducing factors (e.g., NGF) and suggests new venues of empirical investigation.

Short Talk: Mechanical Properties of a quasi one-dimensional biological system

In recent years, thermal fluctuations in combination with noninvasive technique, weak Optical tweezers, is a powerful tool to obtain mechanical information. In this work, we get PC12 neurites mechanical properties by fluctuations amplitudes measurements combined with a model system of neurons, developed here.

Short Talk: Mechanical modeling of neurites

Computational Neuron Mechanics appears as a new multidisciplinary _eld potentially able to study medical challenges such as Alzheimer's disease, tumor growth/migration or traumatic brain injury at cell level. Although computational modeling has been widely used in di_erent Neuroscience applications, the tremendous importance of the interactions between the neuron and its surrounding media/stimulus have been rarely explored. Aimed at analyzing these inter- actions, this work proposes a new multiscale computational framework particularized for two representative scenarios: axonal growth and electrophysiological-mechanical coupling of neu- rites. In the former, the intertwined relation between a biochemical stimulus and the mechanical properties of axons is studied, whereas in the latter, the functional impairments of neurites as a consequence of mechanical constraints are explored. To accomplish these objectives, we de- vise a large scale parallel _nite di_erence program, called Neurite, with the necessary exibility and versatility to implement biological models. In the case of the axonal growth, the program was adapted to simulate microtubule polymerization providing axon mechanical properties as a function of its microtubule occupancy. For the electrophysiological-mechanical coupling case, Neurite was used to relate macroscopic mechanical loading to microscopic strains and strain rates, and to simulate electrical signal propagation along neurites under mechanical loading. For both cases, the models were calibrated against experimental results available in the litera- ture. The growth model showed dramatic variations in the mechanical properties at the tip of the axon, whereas the electrophysiological-mechanical model represents a novelty for predicting the alteration of neuronal electrophysiological function under mechanical loading, thus linking mechanical traumas to subsequent acute functional de_cits.

Mechanochemical signals that guide axon development.

Growth cones interact with the extracellular matrix (ECM) through integrin receptors at adhesion sites termed point contacts. Point contact adhesions link ECM proteins to the actin cytoskeleton through numerous adaptor and signaling proteins. One presumed function of growth cone point contacts is to restrain or “clutch” myosin II-based F-actin retrograde flow (RF) to promote leading edge membrane protrusion. In motile non-neuronal cells, myosin II binds and exerts force upon actin filaments at the leading edge where clutching forces occur. However, in growth cones it is unclear whether similar F-actin clutching forces affect axon outgrowth and guidance. I will show that RF is reduced in rapidly migrating growth cones on laminin (LN) compared to non-integrin binding poly-d-lysine (PDL). Moreover, acute stimulation with LN leads to accelerated axon outgrowth over a time course that correlates with point contact formation and reduced RF. These results suggest that actin RF is restricted by the assembly of point contacts, which we show directly by two color imaging of actin RF and paxillin. Further, using micro-patterns of PDL and LN, we demonstrate that individual growth cones have differential actin RF rates while interacting with two distinct substrata. Opposing effects on actin RF rates were also observed in growth cones treated with chemoattractive and chemorepulsive axon guidance cues known to influence point contact adhesions. Finally, using GFP-actin, we show that actin RF within growth cones in the spinal cord is slow, suggesting RF is being restrained by molecular clutching forces in vivo.

Some brain mechanics: tissue swelling and damage propagation

Tissue swelling, or edema, is a dangerous consequence of traumatic brain injury and stroke. Local edema can exacerbate the original injury and increase intracranial pressure in surrounding tissue. This can result in damage spreading beyond the original injury. In particular, a locally swollen region can cause the injury to propagate further through the brain, due to mechanical compression of the blood supply in surrounding tissue. Here, we first present a quadriphasic model that includes both the mechanical and electrochemical responses of a tissue and use it to revisit the role of the Donnan effect in edema. Second, we investigate how a local change in blood brain barrier permeability, a known cause of edema, can lead to abnormal stresses and strains in the tissue. Third, we couple the tissue mechanics with oxygen delivery, to investigate the propagation of swelling and damage.

This is joint work with Georgina Lang, Sarah Waters, and Dominic Vella

Mathematical models of intracellular transport-limited neurite elongation and branching

Neurite outgrowth (dendrites and axons) should be a stable, but easily regulated process to enable a neuron to make its appropriate network connections during development. We explore the dynamics of outgrowth in a mathematical continuum model of neurite elongation (McLean & Graham, Proc. R. Soc. Lond. A, 460:2437-2456, 2004; Graham et al, J. Comput. Neurosci., 20:43-60, 2006). The model describes the construction of the internal microtubule cytoskeleton, which results from the production and transport of tubulin dimers and their assembly into microtubules at the growing neurite tip. Tubulin is assumed to be largely synthesised in the cell body from where it is transported by active mechanisms and by diffusion along the neurite. It is argued that this construction process is a fundamental limiting factor in neurite elongation. In the model, elongation is highly stable when tubulin transport is dominated by either active transport or diffusion, but oscillations in length may occur when both active transport and diffusion contribute. Autoregulation of tubulin production can eliminate these oscillations. In all cases a stable steady-state length is reached, provided there is intrinsic decay of tubulin. Small changes in growth parameters, such as the tubulin production rate, can lead to large changes in length. Thus cytoskeleton construction can be both stable and easily regulated, as seems necessary for neurite outgrowth during nervous system development.

In a model variant, we demonstrate competitive growth between two neurite branches being supplied by the same source of tubulin (van Ooyen et al, Neurocomputing, 38-40:73-78, 2001). The faster growing neurite can completely inhibit elongation in the other neurite. Such apparent competition has been observed in real neuron outgrowth.

In a different model formulation, the propensity of neurite branching is assumed to depend on the amount of tubulin reaching the growth cone (Graham & van Ooyen, J. Theor. Biol., 230:421-432, 2004). This transport-limited branching yields matches to the characteristic dendritic morphologies from different neuronal types.

TRIM9 Coordinates Cytoskeletal Dynamics and Vesicle Trafficking During Netrin-Dependent Axon Guidance and Branching

Cytoskeletal remodeling and insertion of membrane components into the expanding plasma membrane are required during developmental axon guidance and branching. Although the axon guidance cue Netrin stimulates axon turning and branching, the molecular mechanisms mediating these cell morphological changes are not well defined. We recently identified a direct interaction between the Netrin receptor DCC and the E3 ubiquitin ligase TRIM9. Genetic deletion of TRIM9 results in exuberant cortical axon branching in vitro and in vivo, and a failure in axon turning and branching in response to Netrin, suggesting that TRIM9 restrains constitutive axonal branching and regulates axonal response to Netrin. Exuberant branching in vitro can be rescued by reintroduction of TRIM9 or TRIM9 mutants lacking ubiquitin ligase activity, however Netrin response requires intact TRIM9 ligase activity. In addition to DCC, we have found that TRIM9 directly interacts with the Ena/VASP family of actin regulatory proteins and the exocytic tSNARE SNAP25. Based on biochemical studies performed in heterologous cells and cortical lysates, TRIM9 binds SNAP25 and Ena/VASP proteins in the absence of Netrin, which we suggest sequesters their function. In response to Netrin stimulation, TRIM9 releases SNAP25 and Ena/VASP proteins. Using TIRF microscopy-based assay in wildtype and TRIM9-/- embryonic cortical neurons, we conclude that TRIM9 release of Ena/VASP and SNAP25 following Netrin stimulation promotes SNARE complex formation, vesicle fusion, and filopodia formation. Thus, TRIM9 spatially and temporally coordinates filopodia formation and membrane expansion in response to Netrin in cortical neurons. We are currently using a recently developed a PDMS-based microfluidic device to determine how deletion of TRIM9 affects turning of individual axons in a local Netrin concentration gradient. These assays are corroborated by analysis of axonal projection defects in vivo.

The kinesin adaptor Calsyntenin-1 regulates axon branching, axonal transport and microtubule dynamics

Precise regulation of axon growth and branching is crucial for neuronal circuit formation. Moreover, the highly complex morphology of neurons makes them highly dependent on protein/membrane trafficking and transport systems. Both axon growth and axonal transport require tight regulation of microtubule (MT) polarity and dynamics. We identified a kinesin adaptor, Calsyntenin-1 (Clstn-1), as an essential regulator of axon branching and neuronal compartmentalization. We found that Clstn-1 is required for formation of peripheral but not central sensory axons, and for peripheral axon branching in zebrafish. We use live imaging of endosomal trafficking in vivo to show that Clstn-1 regulates transport of Rab5 containing endosomes from the cell body to specific locations of developing axons. Our results suggest a model in which Clstn-1 patterns separate axonal compartments and defines their ability to branch by directing trafficking of specific endosomes. Furthermore, we used live imaging with EB3-GFP to characterize MT dynamics during axon development in vivo. We find that Clstn-1 knockdown causes aberrant retrograde EB3 comets in axons, indicating defects in MT polarity. Furthermore, loss of Clstn-1 slows anterograde MT comets. These results suggest that in addition to regulating trafficking of cargo along MTs, Clstn-1 also functions to organize MT polarity and regulate MT dynamics.

Modeling neurite outgrowth based on vesicular trafficking and microtubule dynamics

Neurite growth is a fundamental process of neuronal development, which requires both membrane expansions by exocytosis and cytoskeletal dynamics. However the specific contribution of these processes has not been yet assessed quantitatively. In this talk, I will present a biophysical model in which we relate the overall neurite outgrowth rate to the vesicle dynamics. We considered the complex motion of vesicles in the cell soma and demonstrated from biophysical consideration, that the main step of finding the neurite initiation site relies mainly on a two dimensional diffusion/sequestration/fusion at the cell surface and we obtain a novel formula for the flux of vesicles at the neurite base. In the absence of microtubules, a nascent neurite initiated by vesicular delivery can only reach a small length. By adding the microtubules dynamics to the secretory pathway and using stochastic analysis and simulations, we showed that the complex dynamics of neurite growth depends on the coupling parameter between the microtubules and the neurite.To validate one aspect of our model, we demonstrated that the experimental flux of TI-VAMP but not Synaptobrevin 2 vesicles contributes to the neurite growth. We conclude that although vesicles can be generated randomly in the cell body, the search for the neurite position using the microtubule network and diffusion is quite fast. Finally our study demonstrates that cytoskeletal dynamics is necessary to generate long protrusion, while vesicular delivery alone can only generate small neurite.

How soft is the brain? Compression stiffening and mechanosensing by glial cells

A common feature of many solid tumors and is that they are stiffer than the normal tissue in which they arise and have increased interstitial fluid pressures and solid tissue stress. These physical changes, which often involve increased synthesis and cross-linking of extracellular matrix protein, can lead to deleterious changes in mechanosensitive cells.Brain and other CNS tissues lack the filamentous protein-based extracellular matrix characteristic of most mesenchymal and epithelial environments, and isolated glioma samples have the same shear storage moduli as normal brain when measured ex vivo at low strains. However, the shear moduli of both normal and malignant brain tissue increase to the kPa range that activates glioma cells and normal glial cells in vitro when the tissue is uniaxially compressed. We suggest that compression stiffening, which might occur with the increased vascularization and interstitial pressure gradients that are characteristic of glioma and other tumors, effectively stiffens the environment of glioma cells and that in situ, the elastic resistance these cells sense might be sufficient to trigger the same responses that are activated in vitro by increased substrate stiffness.

Short Talk: Is the axonal transport of neurofilaments a 'tug-of-war' Part II

Neurofilaments are the intermediate filament of neurons and are the most abundant structure in the cytoplasm of large axons. They serve as space filling structures that help regulate axon diameter, which in turn regulates conduction velocity. In addition to their structural roles, neurofilaments are also cargoes of axonal transport. They are synthesized within the cell body and then transported out along the axon on microtubules tracks. This movement is characterized by long pauses interrupted by infrequent bouts of rapid movement driven by the molecular motors kinesin and dynein. To further investigate neurofilament motility, we acquired movies of the movement of GFP-tagged neurofilaments with 30 ms temporal resolution in cultured neurons from neonatal rat brain cortex and used kymograph analysis to obtain trajectories of the leading and trailing ends of the moving filaments. Using a newly developed and unbiased noise-filtering algorithm, we extracted bouts of movement and pauses from these trajectories for statistical analysis. Our findings show that although a net anterograde directionality exists overall, individual filaments frequently alternate, sporadically, between anterograde and retrograde directions. Unexpectedly, we find no correlation between neurofilament length and any characteristic feature analyzed including average net velocity, average run velocity, average pause-time, average run length and average run time. The intermittent and bidirectional motions of the filaments led us to investigate, computationally, whether the observed trajectories could be generated by a tug-of-war model. In such a model, the movements are a result of the independent and antagonistic forces generated by kinesin and dynein motors attached to each neurofilament cargo. By systematically varying the number of bound kinesin and dynein motors in the model, we can identify combinations of motors that correlate with the above-mentioned motile characteristics found in each kymograph trace. So far we have found no inconsistencies between the tug-of-war model and the experimental data, but distinct kinetic phases within individual traces suggest that the number of motors bound to the neurofilament cargo is not fixed and may change over time. The model predicts that the total number of active motors on each neurofilament is relatively small and relatively independent of polymer length. Thus the motors may not be distributed uniformly along the filaments.

Slow Axonal Transport and Axon Morphology

Shapes and calibers of neuronal axons are largely determined by the local abundance of neurofilaments. Neurofilaments are intermediate filaments, which are assembled in the cell body and transported along the axon towards the nerve terminal. It is evident from experiments that the neurofilaments axoskeleton is not at rest but exhibits a net downstream velocity. Our fundamental hypothesis is that the overall flux of neurofilaments, as determined by the rate of assembly, determines the overall caliber of the axon while local changes in caliber are determined by local modulation of neurofilament transport velocity. A suitable model to study this hypothesized relation between axon caliber and neurofilament velocity are the nodes of Ranvier, which separate two myelinated sections of myelinated axons. At the nodes of Ranvier, axons exhibit constrictions, which reduce the local caliber of the axon to a fraction of what it is at the internodes. According our hypothesis, such a local reduction of caliber should go along with a proportionate increase in neurofilament transport rate. We first describe our working model for neurofilament transport and how the associated rate constants are extracted from fluorescent imaging experiments at the myelinated segments and the nodes of Ranvier. We then discuss how the predicted change of caliber (based on the differential transport rates) matches up with experimentally determined abundances of neurofilaments at the nodes and internodes.

The nodes of Ranvier are also the locations of the vast majority of ion channels necessary for neuronal conduction. This begs the question what if any is the role of nodal constrictions for conduction velocity. Using the neuron programming-environment we set up a computational model of a myelinated axon, which incorporates detailed morphology of the axon including nodal constrictions. We found that nodal constrictions modulate conduction velocities and allow for a significant reduction of the fiber diameters for targeted conduction speeds in comparison to an unconstricted axon.

On The Role Of Neuromechanics In Human Brain Development

Convolutions are a classical hallmark of most mammalian brains. Brain surface morphology is often associated with intelligence and closely correlated to neurological dysfunction. Yet, we know surprisingly little about the underlying mechanisms that drive cortical folding. To explore the evolution of brain surface morphology, we establish a neuromechanical model using the nonlinear field theories of mechanics supplemented by the continuum theory of finite growth. Continuum modeling allows us to seamlessly integrate information across the scales and correlate organ-level phenomena such as cortical folding to molecular-level processes such as axonal elongation. We show that our model can predict the formation of complex surface morphologies including symmetry breaking and secondary folding. Computational modeling naturally explains why larger mammalian brains tend to be more convoluted than smaller brains and provides a mechanistic interpretation of pathological malformations of lissencephaly and polymicrogyria. Understanding the role of physical forces during the development of the nervous system may have direct implications on the diagnostics and treatment of neurological disorders including severe retardation, epilepsy, schizophrenia, and autism.

Neural mechanobiology and neuronal vulnerability to traumatic loading

Traumatic brain injury (TBI) is a leading cause of death and disability in the United States and in the world. Physical insults to the brain, by nature, are heterogeneous, as is the underlying physiology of an individual, rendering the study of TBI mechanisms very difficult. Furthermore, the complexity of brain tissue cytoarchitecture (e.g., neuron morphology, neuron-glial interactions, synapses) adds to the challenge of determining tissue-level tolerances. There is a critical need to understand the mechano-chemo-electrical transduction from macroscopic loading to the cells that may contribute to cumulative damage and degeneration. In an effort to tackle these challenges, we and others have used isolated systems to study cellular response to traumatic loading conditions. From these studies it is evident that there is strain and/or strain rate dependent membrane damage, ion imbalance, channel dysfunction, compromised energetics, inflammation, electrophysiological disruptions, and other cascades that may contribute to cell death. Questions remain regarding if the membrane transduces forces to the cell primarily through matrix-cytoskeleton loading or if plasma membrane stretch directly causes lipid rearrangement and damage. We will discuss traumatic loading to neurons at the cellular level, the relationships between mechanical trauma and secondary responses, as well as present issues related to cell to tissue scale up. Understanding TBI at the human level requires an appreciation of complexity across scales and severities as it pertains to cellular and mathematical modeling and this discussion is expected to spur ideas that will ultimately accelerate the path to translational discovery in neurotrauma and other acute brain insults.

TACC3 is a microtubule plus-end tracking protein that promotes axon elongation and microtubule polymerization in growth cones

Abstract not submitted.

Multi-Motor Transport in Neurons: Moving Beyond Tug-of-War

Transport in neurons is intrinsically bidirectional, with each movement modality carried out by molecular motors in either the kinesin (anterograde) or the dynein (retrograde) families. Because all motors are present at a given time there must be competition and/or cooperation among motors that simultaneously bind a single vesicle to nearby microtubules. It has been assumed for much of the last decade that the competition must resolve itself though some kind of tug-of-war; but recent evidence shows conclusively that this is often not the case in vivo. In this talk, we will see a few biological mechanisms (and associated mathematical models) that may lead to resolving theory with experimental observations. Joint work with Will Hancock (Penn State), John Fricks (Penn State), and Pete Kramer (RPI).

Microtubule transport of mRNA in dendrites

A key component in the cellular mechanisms underlying learning and memory involves the distribution and delivery of mRNA to synaptic sites in dendrites. A minimal three-state random intermittent search model of motor-driven mRNA transport is developed to explore the question of why motor-driven mRNA are observed moving bidirectionally. The model is analyzed by computing the probability an mRNA is delivered to a synaptic target and the average delivery time (MFPT). It is found that if the branched geometry of the dendrite is ignored, a purely unidirectional transport strategy will result in the smallest MFPT at any given delivery probability. The branched geometry of the dendrite is then incorporated into the model, and it is shown that a phase transition exists for a critical delivery probability where bidirectional strategies improve the corresponding MFPT. To further explore the impact of motor-driven transport behavior on mRNAdelivery, the three-state model is extended to include a detailed, biophysical model of a multimotor complex coordinated through a tug-of-war. The model is analyzed to explore how various measurable, physical quantities, such as adenosine triphosphate, can be tuned to optimize cargo delivery.

Measurement of subcellular force generation in neurons

Forces are important for neuronal outgrowth during the initial wiring of the nervous system and following trauma, yet sub-cellular force generation over the microtubule rich region at the rear of the growth cone and along the axon has never been directly measured. Because previous studies have indicated microtubule polymerization and the microtubule associated proteins Kinesin-1 and dynein all generate forces that push microtubules forward, a major question is if the net forces in these regions are contractile or expansive. A challenge in addressing this is that measuring local sub-cellular force generation is difficult. Here we develop the first analytical mathematical model for viscous fluids that describes the relationship between unequal sub-cellular forces arranged in series within the neuron and the net overall tension measured externally. Using force-calibrated towing needles to measure and apply forces, in combination with docked mitochondria to monitor sub-cellular strain, we then directly measure force generation over the rear of the growth cone and along the axon of chick sensory neurons. We find the rear of the growth cone generates 1.99 nN of contractile force, the axon generates 0.64 nN of contractile force and that the net traction force generated by the neuron is 1.27 nN. Together this work suggests that the forward bulk flow of the cytoskeletal framework that occurs during axonal elongation and growth cone pauses occurs because strong contractile forces in the rear of the growth cone pull material forward.

Extreme Axon Stretch Growth

Axons span the body over great distances; up to a meter in humans and much longer in large mammals. The study of axon growth has mainly focused on the extension and migration of growth cones during development. Once axons integrate with their targets, however, axonal fibers continue to grow in synchrony with body growth. The likely regulatory mechanism that accommodates for such symbiotic interaction is the biomechanical stretching of axons, a formidable stimulus of neuronal growth. Our lab has engineered bioreactors to uniaxially stretch grow axons in culture that can be microscopically visualized in real time. Nerves can quickly adapt to increasing rates of stretch-growth. Below 25% applied strain axons grow in absence of occlusion of axon transport and long-term disconnection. Neurons from stretch grown axons do not show evidence of chromatolysis and can produce normal electrical activity. Under these conditions, persistent axon stretch upregulates developmental and regenerative associated genes. Bioinformatics analysis using Ingenuity® pathway analysis software revealed significant changes in lipid metabolism, molecular transport, and small molecule biochemistry. Further, stress-response and regenerative associated genes such as SPRR1a and ATF3 were found to be upregulated, implicating a novel role in development in addition to their transient expression following injury. These results suggest that axon stretch growth is a process whereby neuronal expansion is regulated by developmental stress, which leads to a unique transcriptional profile that accommodates axon growth.

Axonal Transport and Long-Term Memory Storage

Little is known regarding the identity of the population of proteins and RNAs that are transported to and localized to synapses and how this transport is regulated in neurons. To address this, using the sea slug Aplysia californica and mice, we have begun to study the molecular composition of transport complexes and how the transport is regulated during long-term memory storage. We find that several hundreds of proteins and RNAs are transported by kinesins, the molecular motor that mediate anterograde transport to synapses from the cell body. We further find that axonal transport is regulated in specific neurons for long-term memory storage. These studies bring important insights into the function of axonal transport in synapse formation and memory storage.

Short Talk: Modeling axonal targeting with synergetic interactions

Axonal transport and growth cone dynamics play a fundamental role for pathfinding and the formation of neuronal networks in the brain. During neuronal development, migrating axons wire the brain by generating long range connections between different brain regions. In the visual system, the retinotopic map connects the retina to the visual centers in the midbrain. When axons from retinal ganglion cells reach the optic tectum (superior colliculus in mammals) they form ordered connections with tectal neurons thereby establishing a topographic map. The map precision is important to correctly transmit the visual information projected onto the retina. Families of ephrin guidance molecule distributed in gradients in the retina and tectum play a crucial role in the map formation process. In addition, engrailed homeoprotein transcription factors are important for axonal guidance. Engrailed displays a graded expression in the chick optic tectum and participates in axonal guidance. Moreover, engrailed regulates the expression of ephrinA5 and increases the sensitivity of growth cones to ephrinA5 repellent activity. The molecular pathway for the engrailed-ephrinA5 interaction involves the internalization of engrailed into the growth cone, which stimulates the production and secretion of ATP, followed by hydrolysis of extracellular ATP into adenosine and the activation of membrane bound
adenosine A1 receptor that are present in higher concentrations in temporal than nasal GCs. Based on these findings, we propose a computational model that shows how the synergetic interaction between engrailed and ephrinA5 increases the precision of the map formation.

Axonal transport is modulated by axonal tension

A large majority of neurons have a long axon that forms junctions (synapse) with muscle tissue or another neuron. They carry neurotransmitters enclosed within vesicles that are about 50nm in size. Clustering of vesicles at the synapse is essential for neurotransmission and hence memory and learning. We showed earlier, using embryonic Drosophila (fruit fly), that axons actively maintain a rest tension of about 1 nN. Without this tension, clustering disappears, but reappears with the application of tension. Increase of tension results in increased clustering. Here we explore the role of tension or stretch on vesicle transport along the axon. We use of Aplysia as a model system in this study. We analyze the dynamics of an ensemble of vesicles using the framework of statistical mechanics. We find that the vesicles move along the axon in two modes: (1) random walk (passive motion), and (2) directed motion (active), transported by molecular motors. With increased tension or stretch, vesicles spend more time in active mode compared to that of random walk. Furthermore, increased stretch results in an increased flux of vesicles along the axon. It thus appears that the axonal transport is modulated by the net tension in the axons. In search of the origin of tension in axons, we employed a series of drugs. We find, tension is most likely generated by myosin II motors acting on cortical actin. This corticle actin-myosin complex is distributed along the entire length of the axon, and participates in tension generation. Microtubules play a relatively minor role. Thus, disruption of myosin II, or the filamentous actin, or depletion of ATP results in a loss of tension in axon. Disruption of microtubules shows little effect. It thus appears that the corticle actin, together with myosin II, provide a taut peripheral structure for aligned microtubule tracks for vesicle transport along the axon, and hence clustering at the synapse.

Trafficking of specific guidance receptors regulates axonal behavior at choice points

During neural circuit formation, axons have to find their target cells to make appropriate synaptic contacts. Along their trajectory, axons contact one or several intermediate targets. At each of them, axons need to switch their behavior from attraction to repulsion in order to move on. Axon guidance at intermediate targets, or choice points, depends on the precise regulation of guidance receptors on the growth cone surface. Dorsal commissural (dI1) axons crossing the ventral midline of the spinal cord in the floor plate represent a convenient model for the analysis of the molecular mechanism underlying the switch in axonal behavior.

We identified a role of Calsyntenin1 in the regulation of vesicular trafficking of guidance receptors in dI1 axons. In cooperation with RabGDI, Calsyntenin1 shuttles Rab11-positive vesicles containing Robo1 to the growth cone surface. In contrast, Calsyntenin1-mediated trafficking of Frizzled3, a guidance receptor in the Wnt pathway is independent of RabGDI. Thus, tightly regulated insertion of guidance receptors, which is required for midline crossing and the subsequent turn into the longitudinal axis, is achieved by their specific trafficking along axons.

E3 Ubiquitin Ligase TRIM9, a Novel Regulatory Component of the Filopodia Tip Complex in Neurons

Abstract not submitted.

Short Talk: Role of tissue stiffness in embryonic axon guidance.

Neuronal growth is essential for nervous system development and is also required for regeneration after nervous tissue injury. As axons and dendrites grow towards their targets, they are guided by environmental cues, including a well-characterised set of biochemical signals. Recent in vitro studies suggest that neuronal growth can also be regulated by mechanical properties of the substrate. However, the role of mechanical cues in axon pathfinding in vivo, and the spatiotemporal dynamics of tissue mechanics during early nervous system development, are still largely unknown. Here we investigate the role of tissue stiffness in axon guidance within the early embryo, using the Xenopus laevis optic tract as a model system. Retinal ganglion cell (RGC) axons form the optic tract by growing from the embryonic retina, along a stereotypical path on the brain surface, and terminating at their target, the tectum. We have developed in vivo atomic force microscopy (AFM) to map tissue stiffness along the optic tract at different developmental stages. We find that the embryonic brain is overall mechanically inhomogeneous, and that brain stiffness changes over time. Specifically, we find that the elastic stiffness of the tectum is consistently lower than the rest of the path taken by RGCs. Our results indicate that the path of RGCs is correlated with stiffness gradients in vivo, before axon growth stalls after reaching the softer region. These findings are consistent with a role for substrate mechanics in axon pathfinding, which might not only be crucial during development but also during regenerative processes in the nervous system.

Biomechanics and Dynamics of Growth Cones in Engineered Environments

In the developing nervous system, axons respond to a diverse array of cues to generate the intricate connection network required for proper function. The growth cone integrates information about the local environment and modulates outgrowth and guidance, but relatively little is known about effects of external mechanical or structural cues and internal mechanical forces on growth cone behavior. We have investigated axon outgrowth and force generation on soft elastic substrates for dorsal root ganglion (DRG) neurons (from the peripheral nervous system) and hippocampal neurons (from the central) to see how the mechanics of the microenvironment affect different populations. We find that force generation and stiffness-dependent outgrowth are strongly dependent on cell type. I will discuss recent analyses of the dynamic aspects of growth cone force generation that show surprising regularity underlying the dynamic pattern of traction forces. I will also describe experiments showing that micron-scale confinement affects growth cone shape but, surprisingly, not neurite growth rates. Changes in confinement, by contrast, produce dramatic changes in extension rates. These results suggest a range of opportunities and challenges for developing a quantitative understanding of the influence on engineered environments on axon growth and guidance.

A stochastic multiscale model that explains the segregation of axonal microtubules and neurofilaments in diseases

The axonal cytoskeleton is a dynamic system of protein polymers that is responsible for the fast and slow axonal transports and for the structural integrity and morphology of axons. The normal organization of the axonal cytoskeleton is disrupted in many neurodegenerative diseases. A fundamental question is to understand how the normal organization of the axonal cytoskeleton is developed and maintained in health, and how it is perturbed in diseases. Under normal conditions, the axonal microtubules and neurofilaments form a mixture in cross-section and the caliber of an axon is roughly constant over long distances. However, if treated with IDPN, a compound that causes similar symptoms as amyotrophic lateral sclerosis (ALS), microtubules and neurofilaments segregate into different regions on a time scale of hours, and the axon swells locally on a time scale of days. Although these phenomena have been reported for over 40 years now, the underlying mechanisms are still poorly understood. In this talk, I will present our new insights into this problem using a stochastic model. This is joint work with Anthony Brown from the Department of Neurosciences at the Ohio State University.

Posters

Delayed Feedback Model of Axonal Length Control

A fundamental question in cell biology is how the sizes of cellular and subcellular structures are determined in order to scale with physiological requirements. Here, we develop a mathematical model of a recently hypothesized bidirectional motor transport mechanism for cellular length control in axons, which is distinct from standard proposed mechanisms for cellular size regulation. An anterograde signal is transported by kinesin motors from the cell body to the tip of the growing axon, where it activates the dynein-mediated transport of a retrograde signal back to the cell body. The retrograde signal then represses the anterograde signal via negative feedback, resulting in an oscillation whose frequency decreases with axonal length. If this frequency is correlated with axonal length, then frequency-dependent activation of transcription factors could regulate axonal growth. The proposed mechanism predicts that reducing either of the signals should increase axonal length. We describe this model mathematically using a system of delay differential equations. We then mathematically examine how these delay equations arise naturally as a result of molecular motor dynamics according to advection-diffusion equations.

Compromised axonal functionality after neurodegeneration, concussion and/or traumatic brain injury

Axonal swellings are almost universal in neurodegenerative diseases of the central nervous system, including Alzheimer’s and Parkinson’s disease. Concussions and traumatic brain injuries can also produce cognitive and behavioral deficits by compromising neuronal morphology. Using a spike metric analysis, we characterize computationally the effects of such axonal varicosities on spike train propagation by comparing Poisson spike train classes before and after propagation through a prototypical axonal enlargement, or focused axonal swelling. Misclassification of spike train classes and low-pass filtering of firing rate activity increases with more pronounced axonal injury. We show that confusion matrices and a calculation of the loss of transmitted information provide a very practical way to characterize how injured neurons compromise the signal processing and faithful conductance of spike trains. The method demonstrates that (i) neural codes encoded with low firing rates are more robust to injury than those encoded with high firing rates, (ii) classification depends upon the length of the spike train used to encode information, and (iii) axonal injuries reduce the variance of spike trains within a given stimulus class. The work introduces a novel theoretical and computational framework to quantify the interplay between electrophysiological dynamics with focused axonal swellings generated by injury or other neurodegenerative processes. It further suggests how pharmacology and plasticity may play a role in recovery of neural computation. Ultimately, the work bridges vast experimental observations ofin vitromorphological pathologies with post-traumatic cognitive and behavioral dysfunction.

Drag of the cytosol as a transport mechanism in neurons

Axonal transport is typically divided into two components, distinguished by their mean velocity The fast component includes steady trafficking of different organelles and vesicles, actively transported by motor proteins. The slow component comprises non-membranous materials, undergoing infrequent bidirectional motion. The underlying mechanism of the slow axonal transport has been under debate during the past three decades. We propose a simple displacement mechanism that may be central for the distribution of soluble molecules not carried by vesicles. It relies on the cytoplasmic drag induced by organelle movement and readily accounts for the key experimental observations pertaining to the slow component transport. The induced cytoplasmic drag is predicted to depend mainly on the distribution of microtubules in the axon, the organelle transport rate, and the physical properties of the axon's external layer.

Matan Mussel1*, Keren Zeevy1*, Haim Diamant2and Uri Nevo1

1Department of Biomedical Engineering,

2School of Chemistry, Tel Aviv University

*These authors contributed equally to the work