Growth cone chemotaxis

filoVision - using deep learning and tip markers to automate filopodia analysis

Filopodia are slender, actin-filled membrane projections used by various cell types for environment exploration. Analyzing filopodia often involves visualizing them using actin, filopodia tip or membrane markers. Due to the diversity of cell types that extend filopodia, from amoeboid to mammalian, it can be challenging for some to find a reliable filopodia analysis workflow suited for their cell type and preferred visualization method. The lack of an automated workflow capable of analyzing amoeboid filopodia with only a filopodia tip label prompted the development of filoVision. filoVision is an adaptable deep learning platform featuring the tools filoTips and filoSkeleton. filoTips labels filopodia tips and the cytosol using a single tip marker, allowing information extraction without actin or membrane markers. In contrast, filoSkeleton combines tip marker signals with actin labeling for a more comprehensive analysis of filopodia shafts in addition to tip protein analysis. The ZeroCostDL4Mic deep learning framework facilitates accessibility and customization for different datasets and cell types, making filoVision a flexible tool for automated analysis of tip-marked filopodia across various cell types and user data.

Clutching at Guidance Cues: The Integrin-FAK Axis Steers Axon Outgrowth

Integrin receptors are essential contributors to neurite outgrowth and axon elongation. Activated integrins engage components of the extracellular matrix, enabling the growth cone to form point contacts, which connect the extracellular substrate to dynamic intracellular protein complexes. These adhesion complexes facilitate efficient growth cone migration and neurite extension. Major signalling pathways mediated by the adhesion complex are instigated by focal adhesion kinase (FAK), whilst axonal guidance molecules present in vivo promote growth cone turning or retraction by local modulation of FAK activity. Activation of FAK is marked by phosphorylation following integrin engagement, and this activity is tightly regulated during neurite outgrowth. FAK inhibition slows neurite outgrowth by reducing point contact turnover; however, mutant FAK constructs with enhanced activity stimulate aberrant outgrowth. Importantly, FAK is a major structural component of maturing adhesion sites, which provide the platform for actin polymerisation to drive leading edge advance. In this review, we discuss the coordinated signalling of integrin receptors and FAK, as well as their role in regulating neurite outgrowth and axon elongation. We also discuss the importance of the integrin-FAK axis in vivo, as integrin expression and activation are key determinants of successful axon regeneration following injury.

Mechanics of axon growth and damage: A systematic review of computational models

Normal axon development depends on the action of mechanical forces both generated within the cytoskeleton and outside the cell, but forces of large magnitude or rate cause damage instead. Computational models aid scientists in studying the role of mechanical forces in axon growth and damage. These studies use simulations to evaluate how different sources of force generation within the cytoskeleton interact with each other to regulate axon elongation and retraction. Furthermore, mathematical models can help optimize externally applied tension to promote axon growth without causing damage. Finally, scientists also use simulations of axon damage to investigate how forces are distributed among different components of the axon and how the tissue surrounding an axon influences its susceptibility to injury. In this review, we discuss how computational studies complement experimental studies in the areas of axon growth, regeneration, and damage.

Mathematical models of neuronal growth

The establishment of a functioning neuronal network is a crucial step in neural development. During this process, neurons extend neurites-axons and dendrites-to meet other neurons and interconnect. Therefore, these neurites need to migrate, grow, branch and find the correct path to their target by processing sensory cues from their environment. These processes rely on many coupled biophysical effects including elasticity, viscosity, growth, active forces, chemical signaling, adhesion and cellular transport. Mathematical models offer a direct way to test hypotheses and understand the underlying mechanisms responsible for neuron development. Here, we critically review the main models of neurite growth and morphogenesis from a mathematical viewpoint. We present different models for growth, guidance and morphogenesis, with a particular emphasis on mechanics and mechanisms, and on simple mathematical models that can be partially treated analytically.

Mechanosensitive axon outgrowth mediated by L1-laminin clutch interface

Mechanical properties of the extracellular environment modulate axon outgrowth. Growth cones at the tip of extending axons generate traction force for axon outgrowth by transmitting the force of actin filament retrograde flow, produced by actomyosin contraction and F-actin polymerization, to adhesive substrates through clutch and cell adhesion molecules. A molecular clutch between the actin filament flow and substrate is proposed to contribute to cellular mechanosensing. However, the molecular identity of the clutch interface responsible for mechanosensitive growth cone advance is unknown. We previously reported that mechanical coupling between actin filament retrograde flow and adhesive substrates through the clutch molecule shootin1a and the cell adhesion molecule L1 generates traction force for axon outgrowth and guidance. Here, we show that cultured mouse hippocampal neurons extend longer axons on stiffer substrates under elastic conditions that correspond to the soft brain environments. We demonstrate that this stiffness-dependent axon outgrowth requires actin-adhesion coupling mediated by shootin1a, L1, and laminin on the substrate. Speckle imaging analyses showed that L1 at the growth cone membrane switches between two adhesive states: L1 that is immobilized and that undergoes retrograde movement on the substrate. The duration of the immobilized phase was longer on stiffer substrates; this was accompanied by increases in actin-adhesion coupling and in the traction force exerted on the substrate. These data suggest that the interaction between L1 and laminin is enhanced on stiffer substrates, thereby promoting force generation for axon outgrowth.

A novel stochastic simulation approach enables exploration of mechanisms for regulating polarity site movement

Cells polarize their movement or growth toward external directional cues in many different contexts. For example, budding yeast cells grow toward potential mating partners in response to pheromone gradients. Directed growth is controlled by polarity factors that assemble into clusters at the cell membrane. The clusters assemble, disassemble, and move between different regions of the membrane before eventually forming a stable polarity site directed toward the pheromone source. Pathways that regulate clustering have been identified but the molecular mechanisms that regulate cluster mobility are not well understood. To gain insight into the contribution of chemical noise to cluster behavior we simulated clustering using the reaction-diffusion master equation (RDME) framework to account for molecular-level fluctuations. RDME simulations are a computationally efficient approximation, but their results can diverge from the underlying microscopic dynamics. We implemented novel concentration-dependent rate constants that improved the accuracy of RDME-based simulations, allowing us to efficiently investigate how cluster dynamics might be regulated. Molecular noise was effective in relocating clusters when the clusters contained low numbers of limiting polarity factors, and when Cdc42, the central polarity regulator, exhibited short dwell times at the polarity site. Cluster stabilization occurred when abundances or binding rates were altered to either lengthen dwell times or increase the number of polarity molecules in the cluster. We validated key results using full 3D particle-based simulations. Understanding the mechanisms cells use to regulate the dynamics of polarity clusters should provide insights into how cells dynamically track external directional cues.

Cells localize polarity molecules in a small region of the plasma membrane forming a polarity cluster that directs functions such as migration, reproduction, and growth. Guided by external signals, these clusters move across the membrane allowing cells to reorient growth or motion. The polarity molecules continuously and randomly shuttle between the cluster and the cell cytosol and, as a result, the number and distribution of molecules at the cluster constantly changes. Here we present an improved stochastic simulation algorithm to investigate how such molecular-scale fluctuations induce cluster movement across the cell membrane. Unexpectedly, cluster mobility does not correlate with variations in total molecule abundance within the cluster, but rather with changes in the spatial distribution of molecules that form the cluster. Cluster motion is faster when polarity molecules are scarce and when they shuttle rapidly between the cluster and the cytosol. Our results suggest that cells control cluster mobility by regulating the abundance of polarity molecules and biochemical reactions that affect the time molecules spend at the cluster. We provide insights into how cells harness random molecular behavior to perform functions important for survival, such as detecting the direction of external signals.

Theory for Durotactic Axon Guidance

During the development of the nervous system, neurons extend bundles of axons that grow and meet other neurons to form the neuronal network. Robust guidance mechanisms are needed for these bundles to migrate and reach their functional target. Directional information depends on external cues such as chemical or mechanical gradients. Unlike chemotaxis that has been extensively studied, the role and mechanism of durotaxis, the directed response to variations in substrate rigidity, remain unclear. We model bundle migration and guidance by rigidity gradients by using the theory of morphoelastic rods. We show that, at a rigidity interface, the motion of axon bundles follows a simple behavior analogous to optic ray theory and obeys Snell's law for refraction and reflection. We use this powerful analogy to demonstrate that axons can be guided by the equivalent of optical lenses and fibers created by regions of different stiffnesses.

Phosphoregulation of the cytokinetic protein Fic1 contributes to fission yeast growth polarity establishment

Cellular polarization underlies many facets of cell behavior, including cell growth. The rod-shaped fission yeast Schizosaccharomyces pombe is a well-established, genetically tractable system for studying growth polarity regulation. S. pombe cells elongate at their two cell tips in a cell cycle-controlled manner, transitioning from monopolar to bipolar growth in interphase when new ends established by the most recent cell division begin to extend. We previously identified cytokinesis as a critical regulator of new end growth and demonstrated that Fic1, a cytokinetic factor, is required for normal polarized growth at new ends. Here, we report that Fic1 is phosphorylated on two C-terminal residues, which are each targeted by multiple protein kinases. Endogenously expressed Fic1 phosphomutants cannot support proper bipolar growth, and the resultant defects facilitate the switch into an invasive pseudohyphal state. Thus, phosphoregulation of Fic1 links the completion of cytokinesis to the re-establishment of polarized growth in the next cell cycle. These findings broaden the scope of signaling events that contribute to regulating S. pombe growth polarity, underscoring that cytokinetic factors constitute relevant targets of kinases affecting new end growth.This article has an associated First Person interview with Anthony M. Rossi, joint first author of the paper.

Local CPG Self Growing Network Model with Multiple Physical Properties

Compared with traditional control methods, the advantage of CPG (Central Pattern Generator) network control is that it can significantly reduce the size of the control variable without losing the complexity of its motion mode output. Therefore, it has been widely used in the motion control of robots. To date, the research into CPG network has been polarized: one direction has focused on the function of CPG control rather than biological rationality, which leads to the poor functional adaptability of the control network and means that the control network can only be used under fixed conditions and cannot adapt to new control requirements. This is because, when there are new control requirements, it is difficult to develop a control network with poor biological rationality into a new, qualified network based on previous research; instead, it must be explored again from the basic link. The other direction has focused on the rationality of biology instead of the function of CPG control, which means that the form of the control network is only similar to a real neural network, without practical use. In this paper, we propose some physical characteristics (including axon resistance, capacitance, length and diameter, etc.) that can determine the corresponding parameters of the control model to combine the growth process and the function of the CPG control network. Universal gravitation is used to achieve the targeted guidance of axon growth, Brownian random motion is used to simulate the random turning of axon self-growth, and the signal of a single neuron is established by the Rall Cable Model that simplifies the axon membrane potential distribution. The transfer model, which makes the key parameters of the CPG control network—the delay time constant and the connection weight between the synapses—correspond to the axon length and axon diameter in the growth model and the growth and development of the neuron processes and control functions are combined. By coordinating the growth and development process and control function of neurons, we aim to realize the control function of the CPG network as much as possible under the conditions of biological reality. In this way, the complexity of the control model we develop will be close to that of a biological neural network, and the control network will have more control functions. Finally, the effectiveness of the established CPG self-growth control network is verified through the experiments of the simulation prototype and experimental prototype.

ConFiG: Contextual Fibre Growth to generate realistic axonal packing for diffusion MRI simulation

This paper presents Contextual Fibre Growth (ConFiG), an approach to generate white matter numerical phantoms by mimicking natural fibre genesis. ConFiG grows fibres one-by-one, following simple rules motivated by real axonal guidance mechanisms. These simple rules enable ConFiG to generate phantoms with tuneable microstructural features by growing fibres while attempting to meet morphological targets such as user-specified density and orientation distribution. We compare ConFiG to the state-of-the-art approach based on packing fibres together by generating phantoms in a range of fibre configurations including crossing fibre bundles and orientation dispersion. Results demonstrate that ConFiG produces phantoms with up to 20% higher densities than the state-of-the-art, particularly in complex configurations with crossing fibres. We additionally show that the microstructural morphology of ConFiG phantoms is comparable to real tissue, producing diameter and orientation distributions close to electron microscopy estimates from real tissue as well as capturing complex fibre cross sections. Signals simulated from ConFiG phantoms match real diffusion MRI data well, showing that ConFiG phantoms can be used to generate realistic diffusion MRI data. This demonstrates the feasibility of ConFiG to generate realistic synthetic diffusion MRI data for developing and validating microstructure modelling approaches.

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We present ConFiG, a biologically motivated numerical phantom generator for white matter.

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ConFiG produces phantoms with state-of-the-art density and realistic microstructure.

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Diffusion MRI simulations in ConFiG phantoms are comparable to real dMRI signals.

Neuro-taxis: Neuronal movement in gradients of chemical and physical environments

Environmental chemical and physical cues dynamically interact with migrating neurons and sprouting axons, and in particular, the gradients of environmental cues are regarded as one of the factors intimately involved in the neuronal movement. Since a growth cone was first described by Cajal, more than one century ago, chemical gradients have been suggested as one of the mechanisms by which the neurons determine proper paths and destinations. However, the gradients of physical cues, such as stiffness and topography, which also interact constantly with the neurons and their axons as a component of the extracellular environments, have rarely been noted regarding the guidance of neurons, despite their gradually increasingly reported influences in the case of nonneuronal-cell migration. In this review, we discuss chemical (i.e., chemo- and hapto-) and physical (i.e., duro-) taxis phenomena on the movement of neurons including axonal elongation. In addition, we suggest topotaxis, the most recently proposed physical-taxis phenomenon, as another potential mechanism in the neuronal movement, based on the reports of neuronal recognition of and responses to nanotopography.

A generative growth model for thalamocortical axonal branching in primary visual cortex

Axonal morphology displays large variability and complexity, yet the canonical regularities of the cortex suggest that such wiring is based on the repeated initiation of a small set of genetically encoded rules. Extracting underlying developmental principles can hence shed light on what genetically encoded instructions must be available during cortical development. Within a generative model, we investigate growth rules for axonal branching patterns in cat area 17, originating from the lateral geniculate nucleus of the thalamus. This target area of synaptic connections is characterized by extensive ramifications and a high bouton density, characteristics thought to preserve the spatial resolution of receptive fields and to enable connections for the ocular dominance columns. We compare individual and global statistics, such as a newly introduced length-weighted asymmetry index and the global segment-length distribution, of generated and biological branching patterns as the benchmark for growth rules. We show that the proposed model surpasses the statistical accuracy of the Galton-Watson model, which is the most commonly employed model for biological growth processes. In contrast to the Galton-Watson model, our model can recreate the log-normal segment-length distribution of the experimental dataset and is considerably more accurate in recreating individual axonal morphologies. To provide a biophysical interpretation for statistical quantifications of the axonal branching patterns, the generative model is ported into the physically accurate simulation framework of Cx3D. In this 3D simulation environment we demonstrate how the proposed growth process can be formulated as an interactive process between genetic growth rules and chemical cues in the local environment.

Recent Progress and Perspectives of Thermally Drawn Multimaterial Fiber Electronics

Fibers are the building blocks of a broad spectrum of products from textiles to composites, and waveguides to wound dressings. While ubiquitous, the capabilities of fibers have not rapidly increased compared to semiconductor chip technology, for example. Recognizing that fibers lack the composition, geometry, and feature sizes for more functions, exploration of the boundaries of fiber functionality began some years ago. The approach focuses on a particular form of fiber production, thermal-drawing from a preform. This process has been used for producing single material fibers, but by combining metals, insulators, and semiconductors all within a single strand of fiber, an entire world of functionality in fibers has emerged. Fibers with optical, electrical, acoustic, or optoelectronic functionalities can be produced at scale from relatively easy-to-assemble macroscopic preforms. Two significant opportunities now present themselves. First, can one expect that fiber functions escalate in a predictable manner, creating the context for a "Moore's Law" analog in fibers? Second, as fabrics occupy an enormous surface around the body, could fabrics offer a valuable service to augment the human body? Toward answering these questions, the materials, performance, and limitations of thermally drawn fibers in different electronic applications are detailed and their potential in new fields is envisioned.

Modern Trends for Peripheral Nerve Repair and Regeneration: Beyond the Hollow Nerve Guidance Conduit

Peripheral nerve repair and regeneration remains among the greatest challenges in tissue engineering and regenerative medicine. Even though peripheral nerve injuries (PNIs) are capable of some degree of regeneration, frail recovery is seen even when the best microsurgical technique is applied. PNIs are known to be very incapacitating for the patient, due to the deprivation of motor and sensory abilities. Since there is no optimal solution for tackling this problem up to this day, the evolution in the field is constant, with innovative designs of advanced nerve guidance conduits (NGCs) being reported every day. As a basic concept, a NGC should act as a physical barrier from the external environment, concomitantly acting as physical guidance for the regenerative axons across the gap lesion. NGCs should also be able to retain the naturally released nerve growth factors secreted by the damaged nerve stumps, as well as reducing the invasion of scar tissue-forming fibroblasts to the injury site. Based on the neurobiological knowledge related to the events that succeed after a nerve injury, neuronal subsistence is subjected to the existence of an ideal environment of growth factors, hormones, cytokines, and extracellular matrix (ECM) factors. Therefore, it is known that multifunctional NGCs fabricated through combinatorial approaches are needed to improve the functional and clinical outcomes after PNIs. The present work overviews the current reports dealing with the several features that can be used to improve peripheral nerve regeneration (PNR), ranging from the simple use of hollow NGCs to tissue engineered intraluminal fillers, or to even more advanced strategies, comprising the molecular and gene therapies as well as cell-based therapies.

Mechanical stress alters protein O-GlcNAc in human periodontal ligament cells

Protein O-linked N-acetylglucosamine (O-GlcNAc) is a post-translational modification of intracellular proteins that regulates several physiological and pathophysiological process, including response to various stressors. However, O-GlcNAc's response to mechanical stress has not been investigated yet. As human periodontal ligament (PDL) cells are stimulated by compression force during orthodontic tooth movement that results in structural remodelling, in this study we investigated whether mechanical stress induces any alteration in protein O-GlcNAc in PDL cells. In this study, PDL cells isolated from premolars extracted for orthodontic indications were exposed to 0, 1.5, 3, 7 and 14 g/cm² compression forces for 12 hours. Cell viability was measured by flow cytometry, and protein O-GlcNAc was analysed by Western blot. Cellular structure and intracellular distribution of O-GlcNAc was studied by immunofluorescence microscopy. We found that between 1.5 and 3 g/cm² mechanical compression, O-GlcNAc significantly elevated; however, at higher forces O-GlcNAc level was not increased. We also found that intracellular localization of O-GlcNAc proteins became more centralized under 2 g/cm² compression force. Our results suggest that structural changes stimulated by compression forces have a significant effect on the regulation of O-GlcNAc; thus, it might play a role in the mechanical stress adaptation of PDL cells.

Axon growth regulation by a bistable molecular switch

For the brain to function properly, its neurons must make the right connections during neural development. A key aspect of this process is the tight regulation of axon growth as axons navigate towards their targets. Neuronal growth cones at the tips of developing axons switch between growth and paused states during axonal pathfinding, and this switching behaviour determines the heterogeneous axon growth rates observed during brain development. The mechanisms controlling this switching behaviour, however, remain largely unknown. Here, using mathematical modelling, we predict that the molecular interaction network involved in axon growth can exhibit bistability, with one state representing a fast-growing growth cone state and the other a paused growth cone state. Owing to stochastic effects, even in an unchanging environment, model growth cones reversibly switch between growth and paused states. Our model further predicts that environmental signals could regulate axon growth rate by controlling the rates of switching between the two states. Our study presents a new conceptual understanding of growth cone switching behaviour, and suggests that axon guidance may be controlled by both cell-extrinsic factors and cell-intrinsic growth regulatory mechanisms.

Molecular basis of the functions of the mammalian neuronal growth cone revealed using new methods

The neuronal growth cone is a highly motile, specialized structure for extending neuronal processes. This structure is essential for nerve growth, axon pathfinding, and accurate synaptogenesis. Growth cones are important not only during development but also for plasticity-dependent synaptogenesis and neuronal circuit rearrangement following neural injury in the mature brain. However, the molecular details of mammalian growth cone function are poorly understood. This review examines molecular findings on the function of the growth cone as a result of the introduction of novel methods such superresolution microscopy and (phospho)proteomics. These results increase the scope of our understating of the molecular mechanisms of growth cone behavior in the mammalian brain.

A perspective on SOAL, a stochastic model of neuronal outgrowth

A functional nervous system requires neuronal connections to be made in a highly detailed and stereotypic manner. During development, neurons extend processes that can branch, travel in different directions, and form elaborate patterns. These patterns are essential for forming proper connections. Patterns of outgrowth are produced by complex molecular events that cause a fluid membrane to move. The collective impact of dynamic fluctuating events at the microscale cause the patterns of outgrowth observed at the macroscale. Patterning is genetically controlled, but the effects genes have on membrane movement and patterning are not well understood. To better understand how genes control outgrowth patterns, I propose a statistically-oriented asymmetric localization (SOAL) model. This model is based on the theory that receptor-mediated outgrowth activity is stochastically oriented and when the system is at equilibrium there is an equal probability of outgrowth being oriented in any direction. This concept allows a statistical mechanics approach that can correlate the microscale events of outgrowth to the observed macroscale patterns. Proof-of-concept experiments suggest this approach can be used to study the effect genes have on outgrowth patterns. The SOAL model also provides a new theoretical framework for conceptualizing guidance. According to the model, outgrowth activity becomes asymmetrically localized to the neuron's surface in a statistically dependent manner. Extracellular cues regulate the probability of outgrowth along the surface and the orientation of outgrowth fluctuates across the surface over time. This creates a directional bias that allows the growth cone to navigate in reference to the composition of extracellular cues.

Theoretical Models of Neural Development

Constructing a functioning nervous system requires the precise orchestration of a vast array of mechanical, molecular, and neural-activity-dependent cues. Theoretical models can play a vital role in helping to frame quantitative issues, reveal mathematical commonalities between apparently diverse systems, identify what is and what is not possible in principle, and test the abilities of specific mechanisms to explain the data. This review focuses on the progress that has been made over the last decade in our theoretical understanding of neural development.

Regulation of axon repulsion by MAX-1 SUMOylation and AP-3

During neural development, growing axons navigate over long distances to reach their targets. A critical step in this process is the regulation of its surface receptors on the axon’s growth cone in response to environmental cues. We focus on how the UNC-5 receptor in Caenorhabditis elegans motor axons is regulated during axon repulsion. By combining C. elegans genetics, biochemistry, and imaging, we found that MAX-1 SUMOylation and AP-3 complex have significant roles in UNC-5–mediated axon repulsion. Our findings reveal how SUMOylation and AP-3–mediated trafficking and degradation interact to help the growing axon find its final target.

During neural development, growing axons express specific surface receptors in response to various environmental guidance cues. These axon guidance receptors are regulated through intracellular trafficking and degradation to enable navigating axons to reach their targets. In Caenorhabditis elegans, the UNC-5 receptor is necessary for dorsal migration of developing motor axons. We previously found that MAX-1 is required for UNC-5–mediated axon repulsion, but its mechanism of action remained unclear. Here, we demonstrate that UNC-5–mediated axon repulsion in C. elegans motor axons requires both max-1 SUMOylation and the AP-3 complex β subunit gene, apb-3. Genetic interaction studies show that max-1 is SUMOylated by gei-17/PIAS1 and acts upstream of apb-3. Biochemical analysis suggests that constitutive interaction of MAX-1 and UNC-5 receptor is weakened by MAX-1 SUMOylation and by the presence of APB-3, a competitive interactor with UNC-5. Overexpression of APB-3 reroutes the trafficking of UNC-5 receptor into the lysosome for protein degradation. In vivo fluorescence recovery after photobleaching experiments shows that MAX-1 SUMOylation and APB-3 are required for proper trafficking of UNC-5 receptor in the axon. Our results demonstrate that SUMOylation of MAX-1 plays an important role in regulating AP-3–mediated trafficking and degradation of UNC-5 receptors during axon guidance.

Gradient-reading and mechano-effector machinery for netrin-1-induced axon guidance

Growth cones navigate axonal projection in response to guidance cues. However, it is unclear how they can decide the migratory direction by transducing the local spatial cues into protrusive forces. Here we show that knockout mice of Shootin1 display abnormal projection of the forebrain commissural axons, a phenotype similar to that of the axon guidance molecule netrin-1. Shallow gradients of netrin-1 elicited highly polarized Pak1-mediated phosphorylation of shootin1 within growth cones. We demonstrate that netrin-1–elicited shootin1 phosphorylation increases shootin1 interaction with the cell adhesion molecule L1-CAM; this, in turn, promotes F-actin–adhesion coupling and concomitant generation of forces for growth cone migration. Moreover, the spatially regulated shootin1 phosphorylation within growth cones is required for axon turning induced by netrin-1 gradients. Our study defines a mechano-effector for netrin-1 signaling and demonstrates that shootin1 phosphorylation is a critical readout for netrin-1 gradients that results in a directional mechanoresponse for axon guidance.

Neurons communicate with each other by forming intricate webs that link cells together according to a precise pattern. A neuron can connect to another by growing a branch-like structure known as the axon. To contact the correct neuron, the axon must develop and thread its way to exactly the right place in the brain. Scientists know that the tip of the axon is extraordinarily sensitive to gradients of certain molecules in its surroundings, which guide the budding structure towards its final destination.

In particular, two molecules seem to play an important part in this process: netrin-1, which is a protein found outside cells that attracts a growing axon, and shootin1a, which is present inside neurons. Previous studies have shown that netrin-1 can trigger a cascade of reactions that activates shootin1a. In turn, activated shootin1a molecules join the internal skeleton of the cell with L1-CAM, a molecule that attaches the neuron to its surroundings. If the internal skeleton is the engine of the axon, L1-CAMs are the wheels, and shootin1a the clutch. However, it is not clear whether shootin1a is involved in guiding growing axons, and how it could help neurons ‘understand’ and react to gradients of netrin-1.

Here, Baba et al. discover that when shootin1a is absent in mice, the axons do not develop properly. Further experiments in rat neurons show that if there is a little more netrin-1 on one side of the tip of an axon, this switches on the shootin1a molecules on that edge. Activated shootin1a promote interactions between the internal skeleton and L1-CAM, helping the axon curve towards the area that has more netrin-1. In fact, if the activated shootin1a is present everywhere on the axon, and not just on one side, the structure can develop, but not turn. Taken together, the results suggest that shootin1a can read the gradients of netrin-1 and then coordinate the turning of a growing axon in response.

Wound healing, immune responses or formation of organs are just a few examples of processes that rely on cells moving in an orderly manner through the body. Dissecting how axons are guided through their development may shed light on the migration of cells in general. Ultimately, this could help scientists to understand disorders such as birth abnormalities or neurological disabilities, which arise when this process goes awry.

Control of Growth Cone Polarity, Microtubule Accumulation, and Protrusion by UNC-6/Netrin and Its Receptors in Caenorhabditis elegans

UNC-6/Netrin has a conserved role in dorsal-ventral axon guidance, but the cellular events in the growth cone regulated by UNC-6/Netrin signaling during outgrowth are incompletely understood. Previous studies showed that, in growth cones migrating away from UNC-6/Netrin, the receptor UNC-5 regulates growth cone polarity, as observed by polarized F-actin, and limits the extent of growth cone protrusion. It is unclear how UNC-5 inhibits protrusion, and how UNC-40 acts in concert with UNC-5 to regulate polarity and protrusion. New results reported here indicate that UNC-5 normally restricts microtubule (MT) + end accumulation in the growth cone. Tubulin mutant analysis and colchicine treatment suggest that stable MTs are necessary for robust growth cone protrusion. Thus, UNC-5 might inhibit protrusion in part by restricting growth cone MT accumulation. Previous studies showed that the UNC-73/Trio Rac GEF and UNC-33/CRMP act downstream of UNC-5 in protrusion. Here, we show that UNC-33/CRMP regulates both growth cone dorsal asymmetric F-actin accumulation and MT accumulation, whereas UNC-73/Trio Rac GEF activity only affects F-actin accumulation. This suggests an MT-independent mechanism used by UNC-5 to inhibit protrusion, possibly by regulating lamellipodial and filopodial actin. Furthermore, we show that UNC-6/Netrin and the receptor UNC-40/DCC are required for excess protrusion in unc-5 mutants, but not for loss of F-actin asymmetry or MT + end accumulation, indicating that UNC-6/Netrin and UNC-40/DCC are required for protrusion downstream of, or in parallel to, F-actin asymmetry and MT + end entry. F-actin accumulation might represent a polarity mark in the growth cone where protrusion will occur, and not protrusive lamellipodial and filopodial actin per se Our data suggest a model in which UNC-6/Netrin first polarizes the growth cone via UNC-5, and then regulates protrusion based upon this polarity (the polarity/protrusion model). UNC-6/Netrin inhibits protrusion ventrally via UNC-5, and stimulates protrusion dorsally via UNC-40, resulting in dorsally-directed migration. The polarity/protrusion model represents a novel conceptual paradigm in which to understand axon guidance and growth cone migration away from UNC-6/Netrin.

Alpha 7 nicotinic receptors attenuate neurite development through calcium activation of calpain at the growth cone

The α7 nicotinic acetylcholine receptor (nAChR) is a ligand-gated ion channel that plays an important role in cellular calcium signaling contributing to synaptic development and plasticity, and is a key drug target for the treatment of neurodegenerative conditions such as Alzheimer's disease. Here we show that α7 nAChR mediated calcium signals in differentiating PC12 cells activate the proteolytic enzyme calpain leading to spectrin breakdown, microtubule retraction, and attenuation in neurite growth. Imaging in growth cones confirms that α7 activation decreases EB3 comet motility in a calcium dependent manner as demonstrated by the ability of α7 nAChR, ryanodine, or IP3 receptor antagonists to block the effect of α7 nAChR on growth. α7 nAChR mediated EB3 comet motility, spectrin breakdown, and neurite growth was also inhibited by the addition of the selective calpain blocker calpeptin and attenuated by the expression of an α7 subunit unable to bind Gαq and activate calcium store release. The findings indicate that α7 nAChRs regulate cytoskeletal dynamics through local calcium signals for calpain protease activity.

Beyond the Channel: Metabotropic Signaling by Nicotinic Receptors

The α7 nicotinic acetylcholine receptor (nAChR) is a ligand-gated ion channel (LGIC) that plays an important role in cellular calcium signaling and contributes to several neurological diseases. Agonist binding to the α7 nAChR induces fast channel activation followed by inactivation and prolonged desensitization while triggering long-lasting calcium signaling. These activities foster neurotransmitter release, synaptic plasticity, and somatodendritic regulation in the brain. We discuss here the ability of α7 nAChRs to operate in ionotropic (α7ⁱ) and metabotropic (α7^m) modes, leading to calcium-induced calcium release (CICR) and G protein-associated inositol trisphosphate (IP₃)-induced calcium release (IICR), respectively. Metabotropic activity extends the spatial and temporal aspects of calcium signaling by the α7 channel beyond its ionotropic limits, persisting into the desensitized state. Delineation of the ionotropic and metabotropic properties of the α7 nAChR will provide definitive indicators of moment-to-moment receptor functional status that will, in turn, spearhead new drug development.

A Statistically-Oriented Asymmetric Localization (SOAL) Model for Neuronal Outgrowth Patterning by Caenorhabditis elegans UNC-5 (UNC5) and UNC-40 (DCC) Netrin Receptors

Neurons extend processes that vary in number, length, and direction of "outgrowth". Extracellular cues help determine outgrowth patterns. In Caenorhabditis elegans, neurons respond to the extracellular UNC-6 (netrin) cue via UNC-40 (DCC) and UNC-5 (UNC5) receptors. Previously, we presented evidence that UNC-40 asymmetric localization at the plasma membrane is self-organizing, and that UNC-40 can localize and mediate outgrowth at randomly selected sites. Here, we provide further evidence for a statistically-oriented asymmetric localization (SOAL) model in which UNC-5 receptor activity affects patterns of axon outgrowth by regulating UNC-40 asymmetric localization. According to the SOAL model, the direction of outgrowth activity fluctuates across the membrane over time. Random walk modeling predicts that increasing the degree to which the direction of outgrowth fluctuates will decrease the outward displacement of the membrane. By differentially affecting the degree to which the direction of outgrowth activity fluctuates over time, extracellular cues can produce different rates of outgrowth along the surface and create patterns of "extension". Consistent with the SOAL model, we show that unc-5 mutations alter UNC-40 asymmetric localization, increase the degree to which the direction of outgrowth fluctuates, and reduce the extent of outgrowth in multiple directions relative to the source of UNC-6 These results are inconsistent with current models, which predict that UNC-5 mediates a "repulsive" response to UNC-6 Genetic interactions suggest that UNC-5 acts through the UNC-53 (NAV2) cytoplasmic protein to regulate UNC-40 asymmetric localization in response to both the UNC-6 and EGL-20 (Wnt) extracellular cues.

Sevoflurane Impairs Growth Cone Motility in Dissociated Murine Neurons

BACKGROUND

Early postnatal exposure to general anesthetic agents causes a lasting impairment in learning and memory in animal models. One hypothesis to explain this finding is that exposure to anesthetic agents during critical points in neural development disrupts the formation of brain circuitry. Here, we explore the effects of sevoflurane on the neuronal growth cone, a specialization at the growing end of axons and dendrites that is responsible for the targeted growth that underlies connectivity between neurons.

METHODS

Dissociated neuronal cultures were prepared from embryonic mouse neocortex. Time-lapse images of live growth cones exposed to anesthetics were taken using differential interference contrast microscopy, and the rate of change of the area of the lamellipodia and the speed of the filopodial tip were quantified as measures of motility. The involvement of the p75 neurotropin receptor (p75NTR) was tested using inhibitors applied to the media and by a coimmunoprecipitation assay.

RESULTS

The rate of lamellipodial area change and filopodial tip velocity in both axonal and dendritic growth cones was significantly reduced with sevoflurane exposure between 2% and 6%. Motility could be substantially restored by treatment with Y27632 and TAT-peptide 5, which are inhibitors of Rho Kinase and p75NTR, respectively. Sevoflurane results in reduced coimmunoprecipitation of Rho-Guanosine-5'-diphosphate dissociation inhibitor after pulldown with p75NTR.

CONCLUSIONS

Sevoflurane interferes with growth cone motility, which is a critical process in brain circuitry formation. Our data suggest that this may occur through an action on the p75NTR, which promotes growth inhibitory signaling by the Rho pathway.

Flavin monooxygenases regulate Caenorhabditis elegans axon guidance and growth cone protrusion with UNC-6/Netrin signaling and Rac GTPases

The guidance cue UNC-6/Netrin regulates both attractive and repulsive axon guidance. Our previous work showed that in C. elegans, the attractive UNC-6/Netrin receptor UNC-40/DCC stimulates growth cone protrusion, and that the repulsive receptor, an UNC-5:UNC-40 heterodimer, inhibits growth cone protrusion. We have also shown that inhibition of growth cone protrusion downstream of the UNC-5:UNC-40 repulsive receptor involves Rac GTPases, the Rac GTP exchange factor UNC-73/Trio, and the cytoskeletal regulator UNC-33/CRMP, which mediates Semaphorin-induced growth cone collapse in other systems. The multidomain flavoprotein monooxygenase (FMO) MICAL (Molecule Interacting with CasL) also mediates growth cone collapse in response to Semaphorin by directly oxidizing F-actin, resulting in depolymerization. The C. elegans genome does not encode a multidomain MICAL-like molecule, but does encode five flavin monooxygenases (FMO-1, -2, -3, -4, and 5) and another molecule, EHBP-1, similar to the non-FMO portion of MICAL. Here we show that FMO-1, FMO-4, FMO-5, and EHBP-1 may play a role in UNC-6/Netrin directed repulsive guidance mediated through UNC-40 and UNC-5 receptors. Mutations in fmo-1, fmo-4, fmo-5, and ehbp-1 showed VD/DD axon guidance and branching defects, and variably enhanced unc-40 and unc-5 VD/DD axon guidance defects. Developing growth cones in vivo of fmo-1, fmo-4, fmo-5, and ehbp-1 mutants displayed excessive filopodial protrusion, and transgenic expression of FMO-5 inhibited growth cone protrusion. Mutations suppressed growth cone inhibition caused by activated UNC-40 and UNC-5 signaling, and activated Rac GTPase CED-10 and MIG-2, suggesting that these molecules are required downstream of UNC-6/Netrin receptors and Rac GTPases. From these studies we conclude that FMO-1, FMO-4, FMO-5, and EHBP-1 represent new players downstream of UNC-6/Netrin receptors and Rac GTPases that inhibit growth cone filopodial protrusion in repulsive axon guidance.

Mechanisms that guide axons to their targets in the developing nervous system have been elucidated, but how these pathways affect behavior of the growth cone of the axon during outgrowth remains poorly understood. We previously showed that the guidance cue UNC-6/Netrin and its receptors UNC-40/DCC and UNC-5 inhibit lamellipodial and filopodial growth cone protrusion to mediate repulsion from UNC-6/Netrin in C. elegans. Here we report a new mechanism downstream of UNC-6/Netrin involving flavin monooxygenase redox enzymes (FMOs). We show that FMOs are normally required for axon guidance and to inhibit growth cone protrusion. Furthermore, we show that they are required for the anti-protrusive effects of activated UNC-40 and UNC-5 receptors, and that they can partially compensate for loss of molecules in the pathway, indicating that they act downstream of UNC-6/Netrin signaling. Based on the function of the FMO-containing MICAL molecules in Drosophila and vertebrates, we speculate that the FMOs might directly oxidize actin, leading to filament disassembly and collapse, and/or lead to the phosphorylation of UNC-33/CRMP, which we show also genetically interacts with the FMOs downstream of UNC-6/Netrin. In conclusion, this is the first evidence that FMOs might act downstream of UNC-6/Netrin signaling in growth cone protrusion and axon repulsion.

Revisiting chemoaffinity theory: Chemotactic implementation of topographic axonal projection

Neural circuits are wired by chemotactic migration of growth cones guided by extracellular guidance cue gradients. How growth cone chemotaxis builds the macroscopic structure of the neural circuit is a fundamental question in neuroscience. I addressed this issue in the case of the ordered axonal projections called topographic maps in the retinotectal system. In the retina and tectum, the erythropoietin-producing hepatocellular (Eph) receptors and their ligands, the ephrins, are expressed in gradients. According to Sperry's chemoaffinity theory, gradients in both the source and target areas enable projecting axons to recognize their proper terminals, but how axons chemotactically decode their destinations is largely unknown. To identify the chemotactic mechanism of topographic mapping, I developed a mathematical model of intracellular signaling in the growth cone that focuses on the growth cone's unique chemotactic property of being attracted or repelled by the same guidance cues in different biological situations. The model presented mechanism by which the retinal growth cone reaches the correct terminal zone in the tectum through alternating chemotactic response between attraction and repulsion around a preferred concentration. The model also provided a unified understanding of the contrasting relationships between receptor expression levels and preferred ligand concentrations in EphA/ephrinA- and EphB/ephrinB-encoded topographic mappings. Thus, this study redefines the chemoaffinity theory in chemotactic terms.

The neurochemistry of peripheral nerve regeneration

Peripheral nerve injuries (PNIs) can be most disabling, resulting in the loss of sensitivity, motor function and autonomic control in the involved anatomical segment. Although injured peripheral nerves are capable of regeneration, sub-optimal recovery of function is seen even with the best reconstruction. Distal axonal degeneration is an unavoidable consequence of PNI. There are currently few strategies aimed to maintain the distal pathway and/or target fidelity during regeneration across the zone of injury. The current state of the art approaches have been focussed on the site of nerve injury and not on their distal muscular targets or representative proximal cell bodies or central cortical regions. This is a comprehensive literature review of the neurochemistry of peripheral nerve regeneration and a state of the art analysis of experimental compounds (inorganic and organic agents) with demonstrated neurotherapeutic efficacy in improving cell body and neuron survival, reducing scar formation and maximising overall nerve regeneration.

MyTH4-FERM myosins have an ancient and conserved role in filopod formation

The formation of filopodia in Metazoa and Amoebozoa requires the activity of myosin 10 (Myo10) in mammalian cells and of Dictyostelium unconventional myosin 7 (DdMyo7) in the social amoeba Dictyostelium However, the exact roles of these MyTH4-FERM myosins (myosin tail homology 4-band 4.1, ezrin, radixin, moesin; MF) in the initiation and elongation of filopodia are not well defined and may reflect conserved functions among phylogenetically diverse MF myosins. Phylogenetic analysis of MF myosin domains suggests that a single ancestral MF myosin existed with a structure similar to DdMyo7, which has two MF domains, and that subsequent duplications in the metazoan lineage produced its functional homolog Myo10. The essential functional features of the DdMyo7 myosin were identified using quantitative live-cell imaging to characterize the ability of various mutants to rescue filopod formation in myo7-null cells. The two MF domains were found to function redundantly in filopod formation with the C-terminal FERM domain regulating both the number of filopodia and their elongation velocity. DdMyo7 mutants consisting solely of the motor plus a single MyTH4 domain were found to be capable of rescuing the formation of filopodia, establishing the minimal elements necessary for the function of this myosin. Interestingly, a chimeric myosin with the Myo10 MF domain fused to the DdMyo7 motor also was capable of rescuing filopod formation in the myo7-null mutant, supporting fundamental functional conservation between these two distant myosins. Together, these findings reveal that MF myosins have an ancient and conserved role in filopod formation.

Multi-phasic bi-directional chemotactic responses of the growth cone

The nerve growth cone is bi-directionally attracted and repelled by the same cue molecules depending on the situations, while other non-neural chemotactic cells usually show uni-directional attraction or repulsion toward their specific cue molecules. However, how the growth cone differs from other non-neural cells remains unclear. Toward this question, we developed a theory for describing chemotactic response based on a mathematical model of intracellular signaling of activator and inhibitor. Our theory was first able to clarify the conditions of attraction and repulsion, which are determined by balance between activator and inhibitor, and the conditions of uni- and bi-directional responses, which are determined by dose-response profiles of activator and inhibitor to the guidance cue. With biologically realistic sigmoidal dose-responses, our model predicted tri-phasic turning response depending on intracellular Ca²⁺ level, which was then experimentally confirmed by growth cone turning assays and Ca²⁺ imaging. Furthermore, we took a reverse-engineering analysis to identify balanced regulation between CaMKII (activator) and PP1 (inhibitor) and then the model performance was validated by reproducing turning assays with inhibitions of CaMKII and PP1. Thus, our study implies that the balance between activator and inhibitor underlies the multi-phasic bi-directional turning response of the growth cone.

Natural search algorithms as a bridge between organisms, evolution, and ecology

The ability to navigate is a hallmark of living systems, from single cells to higher animals. Searching for targets, such as food or mates in particular, is one of the fundamental navigational tasks many organisms must execute to survive and reproduce. Here, we argue that a recent surge of studies of the proximate mechanisms that underlie search behavior offers a new opportunity to integrate the biophysics and neuroscience of sensory systems with ecological and evolutionary processes, closing a feedback loop that promises exciting new avenues of scientific exploration at the frontier of systems biology.

Reverse Migration of Neutrophils: Where, When, How, and Why?

Neutrophil migration to injured and pathogen-infected tissues is a fundamental component of innate immunity. An array of cellular and molecular events mediate this response to collectively guide neutrophils out of the vasculature and towards the core of the ensuing inflammatory reaction where they exert effector functions. Advances in imaging modalities have revealed that neutrophils can also exhibit motility away from sites of inflammation and injury, although it is unclear under what circumstances this reverse migration is a physiological protective response, and when it has pathophysiological relevance. Here we review different types of neutrophil reverse migration and discuss the current understanding of the associated mechanisms. In this context we propose clarifications to the existing terminology used to describe the many facets of neutrophil reverse migration.

A mathematical model explains saturating axon guidance responses to molecular gradients

Correct wiring is crucial for the proper functioning of the nervous system. Molecular gradients provide critical signals to guide growth cones, which are the motile tips of developing axons, to their targets. However, in vitro, growth cones trace highly stochastic trajectories, and exactly how molecular gradients bias their movement is unclear. Here, we introduce a mathematical model based on persistence, bias, and noise to describe this behaviour, constrained directly by measurements of the detailed statistics of growth cone movements in both attractive and repulsive gradients in a microfluidic device. This model provides a mathematical explanation for why average axon turning angles in gradients in vitro saturate very rapidly with time at relatively small values. This work introduces the most accurate predictive model of growth cone trajectories to date, and deepens our understanding of axon guidance events both in vitro and in vivo.

Nerve growth factor stimulates axon outgrowth through negative regulation of growth cone actomyosin restraint of microtubule advance

Nerve growth factor (NGF) promotes growth, differentiation, and survival of sensory neurons in the mammalian nervous system. Little is known about how NGF elicits faster axon outgrowth or how growth cones integrate and transform signal input to motor output. Using cultured mouse dorsal root ganglion neurons, we found that myosin II (MII) is required for NGF to stimulate faster axon outgrowth. From experiments inducing loss or gain of function of MII, specific MII isoforms, and vinculin-dependent adhesion-cytoskeletal coupling, we determined that NGF causes decreased vinculin-dependent actomyosin restraint of microtubule advance. Inhibition of MII blocked NGF stimulation, indicating the central role of restraint in directed outgrowth. The restraint consists of myosin IIB- and IIA-dependent processes: retrograde actin network flow and transverse actin bundling, respectively. The processes differentially contribute on laminin-1 and fibronectin due to selective actin tethering to adhesions. On laminin-1, NGF induced greater vinculin-dependent adhesion-cytoskeletal coupling, which slowed retrograde actin network flow (i.e., it regulated the molecular clutch). On fibronectin, NGF caused inactivation of myosin IIA, which negatively regulated actin bundling. On both substrates, the result was the same: NGF-induced weakening of MII-dependent restraint led to dynamic microtubules entering the actin-rich periphery more frequently, giving rise to faster elongation.

Optogenetic control of nerve growth

Due to the limited regenerative ability of neural tissue, a diverse set of biochemical and biophysical cues for increasing nerve growth has been investigated, including neurotrophic factors, topography, and electrical stimulation. In this report, we explore optogenetic control of neurite growth as a cell-specific alternative to electrical stimulation. By investigating a broad range of optical stimulation parameters on dorsal root ganglia (DRGs) expressing channelrhodopsin 2 (ChR2), we identified conditions that enhance neurite outgrowth by three-fold as compared to unstimulated or wild-type (WT) controls. Furthermore, optogenetic stimulation of ChR2 expressing DRGs induces directional outgrowth in WT DRGs co-cultured within a 10 mm vicinity of the optically sensitive ganglia. This observed enhancement and polarization of neurite growth was accompanied by an increased expression of neural growth and brain derived neurotrophic factors (NGF, BDNF). This work highlights the potential for implementing optogenetics to drive nerve growth in specific cell populations.

How receptor diffusion influences gradient sensing

Chemotaxis, or directed motion in chemical gradients, is critical for various biological processes. Many eukaryotic cells perform spatial sensing, i.e. they detect gradients by comparing spatial differences in binding occupancy of chemosensory receptors across their membrane. In many theoretical models of spatial sensing, it is assumed, for the sake of simplicity, that the receptors concerned do not move. However, in reality, receptors undergo diverse modes of diffusion, and can traverse considerable distances in the time it takes such cells to turn in an external gradient. This sets a physical limit on the accuracy of spatial sensing, which we explore using a model in which receptors diffuse freely over the membrane. We find that the Fisher information carried in binding and unbinding events decreases monotonically with the diffusion constant of the receptors.

Living scaffolds for neuroregeneration

Neural tissue engineers are exploiting key mechanisms responsible for neural cell migration and axonal path finding during embryonic development to create living scaffolds for neuroregeneration following injury and disease. These mechanisms involve the combined use of haptotactic, chemotactic, and mechanical cues to direct cell movement and re-growth. Living scaffolds provide these cues through the use of cells engineered in a predefined architecture, generally in combination with biomaterial strategies. Although several hurdles exist in the implementation of living regenerative scaffolds, there are considerable therapeutic advantages to using living cells in conjunction with biomaterials. The leading contemporary living scaffolds for neurorepair are utilizing aligned glial cells and neuronal/axonal tracts to direct regenerating axons across damaged tissue to appropriate targets, and in some cases to directly replace the function of lost cells. Future advances in technology, including the use of exogenous stimulation and genetically engineered stem cells, will further the potential of living scaffolds and drive a new era of personalized medicine for neuroregeneration.

Quantifying biased response of axon to chemical gradient steepness in a microfluidic device

Axons are very sensitive to molecular gradients and can discriminate extremely small differences in gradient steepness. Microfluidic devices capable of generating chemical gradients and adjusting their steepness could be used to quantify the sensitivity of axonal response. Here, we present a versatile and robust microfluidic device that can generate substrate-bound molecular gradients with evenly varying steepness on a single chip to precisely quantify axonal response. In this device, two solutions are perfused into a central channel via two inlets while partially flowing into two peripheral channels through interconnecting grooves, which gradually decrease the fluid velocity along the central channel. Molecular gradients with evenly and gradually decreased steepness can therefore be generated with a high resolution that is less than 0.05%/mm. In addition, the overall distribution range and resolution of the gradient steepness can be highly and flexibly controlled by adjusting various parameters of the device. Using this device, we quantified the hippocampal axonal response to substrate-bound laminin and ephrin-A5 gradients with varying steepnesses. Our results provided more detailed information on how and to what extent different steepnesses guide hippocampal neuron development during the initial outgrowth. Furthermore, our results show that axons can sensitively respond to very shallow laminin and ephrin-A5 gradients, which could effectively initiate biased differentiation of hippocampal neurons in the steepness range investigated in this study.

Context-aware modeling of neuronal morphologies

Neuronal morphologies are pivotal for brain functioning: physical overlap between dendrites and axons constrain the circuit topology, and the precise shape and composition of dendrites determine the integration of inputs to produce an output signal. At the same time, morphologies are highly diverse and variant. The variance, presumably, originates from neurons developing in a densely packed brain substrate where they interact (e.g., repulsion or attraction) with other actors in this substrate. However, when studying neurons their context is never part of the analysis and they are treated as if they existed in isolation. Here we argue that to fully understand neuronal morphology and its variance it is important to consider neurons in relation to each other and to other actors in the surrounding brain substrate, i.e., their context. We propose a context-aware computational framework, NeuroMaC, in which large numbers of neurons can be grown simultaneously according to growth rules expressed in terms of interactions between the developing neuron and the surrounding brain substrate. As a proof of principle, we demonstrate that by using NeuroMaC we can generate accurate virtual morphologies of distinct classes both in isolation and as part of neuronal forests. Accuracy is validated against population statistics of experimentally reconstructed morphologies. We show that context-aware generation of neurons can explain characteristics of variation. Indeed, plausible variation is an inherent property of the morphologies generated by context-aware rules. We speculate about the applicability of this framework to investigate morphologies and circuits, to classify healthy and pathological morphologies, and to generate large quantities of morphologies for large-scale modeling.

Computational and mathematical methods for morphogenetic gradient analysis, boundary formation and axonal targeting

Morphogenesis and axonal targeting are key processes during development that depend on complex interactions at molecular, cellular and tissue level. Mathematical modeling is essential to bridge this multi-scale gap in order to understand how the emergence of large structures is controlled at molecular level by interactions between various signaling pathways. We summarize mathematical modeling and computational methods for time evolution and precision of morphogenetic gradient formation. We discuss tissue patterning and the formation of borders between regions labeled by different morphogens. Finally, we review models and algorithms that reveal the interplay between morphogenetic gradients and patterned activity for axonal pathfinding and the generation of the retinotopic map in the visual system.