A mechanism for the polarity formation of chemoreceptors at the growth cone membrane for gradient amplification during directional sensing

Region and layer-specific expression of GABAA receptor isoforms and KCC2 in developing cortex

Introduction

γ-Aminobutyric acid (GABA) type A receptors (GABAARs) are ligand-gated Cl-channels that mediate the bulk of inhibitory neurotransmission in the mature CNS and are targets of many drugs. During cortical development, GABAAR-mediated signals are significantly modulated by changing subunit composition and expression of Cl-transporters as part of developmental processes and early network activity. To date, this developmental evolution has remained understudied, particularly at the level of cortical layer-specific changes. In this study, we characterized the expression of nine major GABAAR subunits and K-Cl transporter 2 (KCC2) in mouse somatosensory cortex from embryonic development to postweaning maturity.

Methods

We evaluated expression of α1-5, β2-3, γ2, and δ GABAAR subunits using immunohistochemistry and Western blot techniques, and expression of KCC2 using immunohistochemistry in cortices from E13.5 to P25 mice.

Results

We found that embryonic cortex expresses mainly α3, α5, β3, and γ2, while expression of α1, α2, α4, β2, δ, and KCC2 begins at later points in development; however, many patterns of nuanced expression can be found in specific lamina, cortical regions, and cells and structures.

Discussion

While the general pattern of expression of each subunit and KCC2 is similar to previous studies, we found a number of unique temporal, regional, and laminar patterns that were previously unknown. These findings provide much needed knowledge of the intricate developmental evolution in GABAAR composition and KCC2 expression to accommodate developmental signals that transition to mature neurotransmission.

Computational methods and diffusion theory in triangulation sensing to model neuronal navigation

Computational methods are now recognized as powerful and complementary approaches in various applied sciences such as biology. These computing methods are used to explore the gap between scales such as the one between molecular and cellular. Here we present recent progress in the development of computational approaches involving diffusion modeling, asymptotic analysis of the model partial differential equations, hybrid methods and simulations in the generic context of cell sensing and guidance via external gradients. Specifically, we highlight the reconstruction of the location of a point source in two and three dimensions from the steady-state diffusion fluxes arriving to narrow windows located on the cell. We discuss cases in which these windows are located on the boundary of a two-dimensional plane or three-dimensional half-space, on a disk in free space or inside a two-dimensional corridor, or a ball in three dimensions. The basis of this computational approach is explicit solutions of the Neumann-Green's function for the mentioned geometry. This analysis can be used to design hybrid simulations where Brownian paths are generated only in small regions in which the local spatial organization is relevant. Particle trajectories outside of this region are only implicitly treated by generating exit points at the boundary of this domain of interest. This greatly accelerates the simulation time by avoiding the explicit computation of Brownian paths in an infinite domain and serves to generate statistics, without following all trajectories at the same time, a process that can become numerically expensive quickly. Moreover, these computational approaches are used to reconstruct a point source and estimating the uncertainty in the source reconstruction due to an additive noise perturbation present in the fluxes. We also discuss the influence of various window configurations (cluster vs uniform distributions) on recovering the source position. Finally, the applications in developmental biology are formulated into computational principles that could underly neuronal navigation in the brain.

Triangulation Sensing to Determine the Gradient Source from Diffusing Particles to Small Cell Receptors

How does a cell locate the source of molecular guidance cues from within a concentration gradient? We present a computational approach to recover the source from the absorbed fluxes at narrow receptor windows located on the surface of the cell. In the limit of fast binding, we solve the steady-state diffusion equation using an asymptotic approach and hybrid stochastic-analytical simulations. We show that the sensitivity to the gradient direction decays too rapidly to enable long-distance sensing. We illustrate how this constraint can be alleviated when triangulating the source with an increasing number of receptor windows and quantify the susceptibility of this process to flux perturbations.

Receptor Organization Determines the Limits of Single-Cell Source Location Detection

Many types of cells require the ability to pinpoint the location of an external stimulus from the arrival of diffusing signaling molecules at cell-surface receptors. How does the organization (number and spatial configuration) of these receptors shape the limit of a cell's ability to infer the source location? In the idealized scenario of a spherical cell, we apply asymptotic analysis to compute splitting probabilities between individual receptors and formulate an information-theoretic framework to quantify the role of receptor organization. Clustered configurations of receptors provide an advantage in detecting sources aligned with the clusters, suggesting a possible multiscale mechanism for single-cell source inference.

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.

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.

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.

Mixed analytical-stochastic simulation method for the recovery of a Brownian gradient source from probability fluxes to small windows

Is it possible to recover the position of a source from the steady-state fluxes of Brownian particles to small absorbing windows located on the boundary of a domain? To address this question, we develop a numerical procedure to avoid tracking Brownian trajectories in the entire infinite space. Instead, we generate particles near the absorbing windows, computed from the analytical expression of the exit probability. When the Brownian particles are generated by a steady-state gradient at a single point, we compute asymptotically the fluxes to small absorbing holes distributed on the boundary of half-space and on a disk in two dimensions, which agree with stochastic simulations. We also derive an expression for the splitting probability between small windows using the matched asymptotic method. Finally, when there are more than two small absorbing windows, we show how to reconstruct the position of the source from the diffusion fluxes. The present approach provides a computational first principle for the mechanism of sensing a gradient of diffusing particles, a ubiquitous problem in cell biology.

Neuronal polarization: From spatiotemporal signaling to cytoskeletal dynamics

Neuronal polarization establishes distinct molecular structures to generate a single axon and multiple dendrites. Studies over the past years indicate that this efficient separation is brought about by a network of feedback loops. Axonal growth seems to play a major role in fueling those feedback loops and thereby stabilizing neuronal polarity. Indeed, various effectors involved in feedback loops are pivotal for axonal growth by ultimately acting on the actin and microtubule cytoskeleton. These effectors have key roles in interconnecting actin and microtubule dynamics - a mechanism crucial to commanding the growth of axons. We propose a model connecting signaling with cytoskeletal dynamics and neurite growth to better describe the underlying processes involved in neuronal polarization. We will discuss the current views on feedback loops and highlight the current limits of our understanding.

A hybrid computational model to predict chemotactic guidance of growth cones

The overall strategy used by growing axons to find their correct paths during the nervous system development is not yet completely understood. Indeed, some emergent and counterintuitive phenomena were recently described during axon pathfinding in presence of chemical gradients. Here, a novel computational model is presented together with its ability to reproduce both regular and counterintuitive axonal behaviours. In this model, the key role of intracellular calcium was phenomenologically modelled through a non standard Gierer-Meinhardt system, as a crucial factor influencing the growth cone behaviour both in regular and complex conditions. This model was able to explicitly reproduce neuritic paths accounting for the complex interplay between extracellular and intracellular environments, through the sensing capability of the growth cone. The reliability of this approach was proven by using quantitative metrics, numerically supporting the similarity between in silico and biological results in regular conditions (control and attraction). Finally, the model was able to qualitatively predict emergent and counterintuitive phenomena resulting from complex boundary conditions.

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.

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.

The interdependence of membrane shape and cellular signal processing

Cellular membranes are constantly reshaped by vesicular fission and fusion as well as by interactions with the dynamic cytoskeleton. Signaling activity at membranes depends on their geometric parameters, such as surface area and curvature; these affect local concentration and thereby regulate the potency of molecular reactions. A membrane's shape is thus inextricably tied to information processing. Here, we review how a trinity of signaling, cytoskeletal dynamics, and membrane shape interact within a closed-loop causality that gives rise to an energy-consuming, self-organized system that changes shape to sense the extracellular environment.

Experimental evidence for UNC-6 (netrin) axon guidance by stochastic fluctuations of intracellular UNC-40 (DCC) outgrowth activity

How the direction of axon guidance is determined is not understood. In Caenorhabditis elegans the UNC-40 (DCC) receptor mediates a response to the UNC-6 (netrin) guidance cue that directs HSN axon development. UNC-40 becomes asymmetrically localized within the HSN neuron to the site of axon outgrowth. Here we provide experimental evidence that the direction of guidance can be explained by the stochastic fluctuations of UNC-40 asymmetric outgrowth activity. We find that the UNC-5 (UNC5) receptor and the cytoskeletal binding protein UNC-53 (NAV2) regulate the induction of UNC-40 localization by UNC-6. If UNC-40 localization is induced without UNC-6 by using an unc-53 mutation, the direction of UNC-40 localization undergoes random fluctuations. Random walk models describe the path made by a succession of randomly directed movement. This model was experimentally tested using mutations that affect Wnt/PCP signaling. These mutations inhibit UNC-40 localization in the anterior and posterior directions. As the axon forms in Wnt/PCP mutants, the direction of UNC-40 localization randomly fluctuates; it can localize in either the anterior, posterior, or ventral direction. Consistent with a biased random walk, over time the axon will develop ventrally in response to UNC-6, even though at a discrete time UNC-40 localization and outgrowth can be observed anterior or posterior. Also, axon formation is slower in the mutants than in wild-type animals. This is also consistent with a random walk since this model predicts that the mean square displacement (msd) will increase only linearly with time, whereas the msd increases quadratically with time for straight-line motion.

Spatial and temporal sensing limits of microtubule polarization in neuronal growth cones by intracellular gradients and forces

Neuronal growth cones are the most sensitive among eukaryotic cells in responding to directional chemical cues. Although a dynamic microtubule cytoskeleton has been shown to be essential for growth-cone turning, the precise nature of coupling of the spatial cue with microtubule polarization is less understood. Here we present a computational model of microtubule polarization in a turning neuronal growth cone. We explore the limits of directional cues in modifying the spatial polarization of microtubules by testing the role of microtubule dynamics, gradients of regulators, and retrograde forces along filopodia. We analyze the steady state and transition behavior of microtubules on being presented with a directional stimulus. Our model makes novel, to our knowledge, predictions about the minimal angular spread of the chemical signal at the growth cone and the fastest polarization times. A regulatory reaction-diffusion network based on the cyclic phosphorylation-dephosphorylation of a regulator predicts that the receptor-signal magnitude can generate the maximal polarization of microtubules and not feedback loops or amplifications in the network. Using both the phenomenological and network models, we have demonstrated some of the physical limits within which the microtubule polarization system works in turning the neuron.

Amplification and temporal filtering during gradient sensing by nerve growth cones probed with a microfluidic assay

Nerve growth cones (GCs) are chemical sensors that convert graded extracellular cues into oriented axonal motion. To ensure a sensitive and robust response to directional signals in complex and dynamic chemical landscapes, GCs are presumably able to amplify and filter external information. How these processing tasks are performed remains however poorly known. Here, we probe the signal-processing capabilities of single GCs during γ-Aminobutyric acid (GABA) directional sensing with a shear-free microfluidic assay that enables systematic measurements of the GC output response to variable input gradients. By measuring at the single molecule level the polarization of GABA(A) chemoreceptors at the GC membrane, as a function of the external GABA gradient, we find that GCs act as i), signal amplifiers over a narrow range of concentrations, and ii), low-pass temporal filters with a cutoff frequency independent of stimuli conditions. With computational modeling, we determine that these systems-level properties arise at a molecular level from the saturable occupancy response and the lateral dynamics of GABA(A) receptors.

Calcium and cAMP levels interact to determine attraction versus repulsion in axon guidance

Correct guidance of axons to their targets depends on an intricate network of signaling molecules in the growth cone. Calcium and cAMP are two key regulators of whether axons are attracted or repelled by molecular gradients, but how these molecules interact to determine guidance responses remains unclear. Here, we constructed a mathematical model for the relevant signaling network, which explained a large range of previous biological data and made predictions for when axons will be attracted or repelled. We then confirmed these predictions experimentally, in particular showing that while small increases in cAMP levels promote attraction large increases do not, and that under some circumstances reducing cAMP levels promotes attraction. Together, these results show that a relatively simple mathematical model can quantitatively predict guidance decisions across a wide range of conditions, and that calcium and cAMP levels play a more complex role in these decisions than previously determined.

Whence directionality: guidance mechanisms in solitary and collective cell migration

As individual cells or groups of cells move through the complex environment of the body, their migration is affected by multiple external cues. Some cues are diffusible signaling molecules, and some are solid biophysical features. How do cells respond appropriately? This perspective discusses the relationship between guidance input and the cellular output, considering effects from classical chemotaxis to contact-dependent guidance. The influences of membrane trafficking and of imposed constraints on directional movement are also considered. New insights regarding guidance and dynamic cell polarity have emerged from examining new cell migration models and from re-examining well known ones with new approaches and new tools.

Cellular responses to extracellular guidance cues

Extracellular guidance cues have a key role in orchestrating cell behaviour. They can take many forms, including soluble and cell-bound ligands (proteins, lipids, peptides or small molecules) and insoluble matrix substrates, but to act as guidance cues, they must be presented to the cell in a spatially restricted manner. Cells that recognize such cues respond by activating intracellular signal transduction pathways in a spatially restricted manner and convert the extracellular information into intracellular polarity. Although extracellular cues influence a broad range of cell polarity decisions, such as mitotic spindle orientation during asymmetric cell division, or the establishment of apical-basal polarity in epithelia, this review will focus specifically on guidance cues that promote cell migration (chemotaxis), or localized cell shape changes (chemotropism).