Physical model for the width distribution of axons

The role of mechanics in axonal stability and development

Much of the focus of neuronal cell biology has been devoted to growth cone guidance, synaptogenesis, synaptic activity, plasticity, etc. The axonal shaft too has received much attention, mainly for its astounding ability to transmit action potentials and the transport of material over long distances. For these functions, the axonal cytoskeleton and membrane have been often assumed to play static structural roles. Recent experiments have changed this view by revealing an ultrastructure much richer in features than previously perceived and one that seems to be maintained at a dynamic steady state. The role of mechanics in this is only beginning to be broadly appreciated and appears to involve passive and active modes of coupling different biopolymer filaments, filament turnover dynamics and membrane biophysics. Axons, being unique cellular processes in terms of high aspect ratios and often extreme lengths, also exhibit unique passive mechanical properties that might have evolved to stabilize them under mechanical stress. In this review, we summarize the experiments that have exposed some of these features. It is our view that axonal mechanics deserves much more attention not only due to its significance in the development and maintenance of the nervous system but also due to the susceptibility of axons to injury and neurodegeneration.

Talin promotes integrin activation accompanied by generation of tension in talin and an increase in osmotic pressure in neurite outgrowth

Neuronal polarization depends on the interaction of intracellular chemical and mechanical activities in which the cytoplasmic protein, talin, plays a pivotal role during neurite growth. To better understand the mechanism underlying talin function in neuronal polarization, we overexpressed several truncated forms of talin and found that the presence of the rod domain within the overexpressed talin is required for its positive effect on neurite elongation because the neurite number only increased when the talin head region was overexpressed. The tension in the talin rod was recognized using a Förster resonance energy transfer-based tension probe. Nerve growth factor treatment resulted in inward tension of talin elicited by microfilament force and outward osmotic pressure. By contrast, the glial scar-inhibitor aggrecan weakened these forces, suggesting that interactions between inward pull forces in the talin rod and outward osmotic pressure participate in neuronal polarization. Integrin activation is also involved in up-regulation of talin tension and osmotic pressure. Aggrecan stimuli resulted in up-regulation of docking protein 1 (DOK1), leading to the down-regulation of integrin activity and attenuation of the intracellular mechanical force. Our study suggests interactions between the intracellular inward tension in talin and the outward osmotic pressure as the effective channel for promoting neurite outgrowth, which can be up-regulated by integrin activation and down-regulated by DOK1.-Wang, Y., Zhang, X., Tian, J., Shan, J., Hu, Y., Zhai, Y., Guo, J. Talin promotes integrin activation accompanied by generation of tension in talin and an increase in osmotic pressure in neurite outgrowth.

Analysis of subcellular structural tension in axonal growth of neurons

The growth and regeneration of axons are the core processes of nervous system development and functional recovery. They are also related to certain physiological and pathological conditions. For decades, it has been the consensus that a new axon is formed by adding new material at the growth cone. However, using the existing technology, we have studied the structural tension of the nerve cell, which led us to hypothesize that some subcellular structural tensions contribute synergistically to axonal growth and regeneration. In this review, we classified the subcellular structural tension, osmotic pressure, microfilament and microtubule-dependent tension involved controllably in promoting axonal growth. A squeezing model was built to analyze the mechanical mechanism underlying axonal elongation, which may provide a new view of axonal growth and inspire further research.

Parametric Probability Distribution Functions for Axon Diameters of Corpus Callosum

Axon diameter is an important neuroanatomical characteristic of the nervous system that alters in the course of neurological disorders such as multiple sclerosis. Axon diameters vary, even within a fiber bundle, and are not normally distributed. An accurate distribution function is therefore beneficial, either to describe axon diameters that are obtained from a direct measurement technique (e.g., microscopy), or to infer them indirectly (e.g., using diffusion-weighted MRI). The gamma distribution is a common choice for this purpose (particularly for the inferential approach) because it resembles the distribution profile of measured axon diameters which has been consistently shown to be non-negative and right-skewed. In this study we compared a wide range of parametric probability distribution functions against empirical data obtained from electron microscopy images. We observed that the gamma distribution fails to accurately describe the main characteristics of the axon diameter distribution, such as location and scale of the mode and the profile of distribution tails. We also found that the generalized extreme value distribution consistently fitted the measured distribution better than other distribution functions. This suggests that there may be distinct subpopulations of axons in the corpus callosum, each with their own distribution profiles. In addition, we observed that several other distributions outperformed the gamma distribution, yet had the same number of unknown parameters; these were the inverse Gaussian, log normal, log logistic and Birnbaum-Saunders distributions.

White matter microstructure from nonparametric axon diameter distribution mapping

We report the development of a double diffusion encoding (DDE) MRI method to estimate and map the axon diameter distribution (ADD) within an imaging volume. A variety of biological processes, ranging from development to disease and trauma, may lead to changes in the ADD in the central and peripheral nervous systems. Unlike previously proposed methods, this ADD experimental design and estimation framework employs a more general, nonparametric approach, without a priori assumptions about the underlying form of the ADD, making it suitable to analyze abnormal tissue. In the current study, this framework was used on an ex vivo ferret spinal cord, while emphasizing the way in which the ADD can be weighted by either the number or the volume of the axons. The different weightings, which result in different spatial contrasts, were considered throughout this work. DDE data were analyzed to derive spatially resolved maps of average axon diameter, ADD variance, and extra-axonal volume fraction, along with a novel sub-micron restricted structures map. The morphological information contained in these maps was then used to segment white matter into distinct domains by using a proposed k-means clustering algorithm with spatial contiguity and left-right symmetry constraints, resulting in identifiable white matter tracks. The method was validated by comparing histological measures to the estimated ADDs using a quantitative similarity metric, resulting in good agreement. With further acquisition acceleration and experimental parameters adjustments, this ADD estimation framework could be first used preclinically, and eventually clinically, enabling a wide range of neuroimaging applications for improved understanding of neurodegenerative pathologies and assessing microstructural changes resulting from trauma.

An optimum principle predicts the distribution of axon diameters in normal white matter

Many important functional properties affecting nerve conduction are influenced by axon diameter. It is also known that the axon diameter distribution (ADD) in normal nerve fascicles is heterogeneous and skewed. A recent attempt to model and explain the parametric form of these distributions was based on biomechanical principles. Here we explore a neurophysiologically-based hypothesis that the observed ADD can be obtained by optimizing the information flow through a fascicle subject to reasonable anatomical and metabolic constraints. Specifically, we use a variational framework to find an optimal distribution based on the fascicle's channel capacity and informative upper bound (IUB), subject to constraints of fixed available fascicle cross-sectional area and fixed number of axons, to derive two novel probability density functions, which we then compare to other previously used distributions. We show, using experimental histological data, that the distributions based on this optimum principle outperform other distributions. Moreover, the new distribution that optimizes the IUB is extremely robust in fitting ADD data obtained histologically, making it well-suited for use in MRI techniques to measure ADDs in vivo, e.g., AxCaliber MRI.

Size of cell-surface Kv2.1 domains is governed by growth fluctuations

The Kv2.1 voltage-gated potassium channel forms stable clusters on the surface of different mammalian cells. Even though these cell-surface structures have been observed for almost a decade, little is known about the mechanism by which cells maintain them. We measure the distribution of domain sizes to study the kinetics of their growth. Using a Fokker-Planck formalism, we find no evidence for a feedback mechanism present to maintain specific domain radii. Instead, the size of Kv2.1 clusters is consistent with a model where domain size is established by fluctuations in the trafficking machinery. These results are further validated using likelihood and Akaike weights to select the best model for the kinetics of domain growth consistent with our experimental data.