How the optic nerve allocates space, energy capacity, and information

Along-axon diameter variation and axonal orientation dispersion revealed with 3D electron microscopy: implications for quantifying brain white matter microstructure with histology and diffusion MRI

Tissue microstructure modeling of diffusion MRI signal is an active research area striving to bridge the gap between macroscopic MRI resolution and cellular-level tissue architecture. Such modeling in neuronal tissue relies on a number of assumptions about the microstructural features of axonal fiber bundles, such as the axonal shape (e.g., perfect cylinders) and the fiber orientation dispersion. However, these assumptions have not yet been validated by sufficiently high-resolution 3-dimensional histology. Here, we reconstructed sequential scanning electron microscopy images in mouse brain corpus callosum, and introduced a random-walker (RaW)-based algorithm to rapidly segment individual intra-axonal spaces and myelin sheaths of myelinated axons. Confirmed by a segmentation based on human annotations initiated with conventional machine-learning-based carving, our semi-automatic algorithm is reliable and less time-consuming. Based on the segmentation, we calculated MRI-relevant estimates of size-related parameters (inner axonal diameter, its distribution, along-axon variation, and myelin g-ratio), and orientation-related parameters (fiber orientation distribution and its rotational invariants; dispersion angle). The reported dispersion angle is consistent with previous 2-dimensional histology studies and diffusion MRI measurements, while the reported diameter exceeds those in other mouse brain studies. Furthermore, we calculated how these quantities would evolve in actual diffusion MRI experiments as a function of diffusion time, thereby providing a coarse-graining window on the microstructure, and showed that the orientation-related metrics have negligible diffusion time-dependence over clinical and pre-clinical diffusion time ranges. However, the MRI-measured inner axonal diameters, dominated by the widest cross sections, effectively decrease with diffusion time by ~ 17% due to the coarse-graining over axonal caliber variations. Furthermore, our 3d measurement showed that there is significant variation of the diameter along the axon. Hence, fiber orientation dispersion estimated from MRI should be relatively stable, while the "apparent" inner axonal diameters are sensitive to experimental settings, and cannot be modeled by perfectly cylindrical axons.

Higher Reliance on Glycolysis Limits Glycolytic Responsiveness in Degenerating Glaucomatous Optic Nerve

Metabolic dysfunction accompanies neurodegenerative disease and aging. An important step for therapeutic development is a more sophisticated understanding of the source of metabolic dysfunction, as well as to distinguish disease-associated changes from aging effects. We examined mitochondrial function in ex vivo aging and glaucomatous optic nerve using a novel approach, the Seahorse Analyzer. Optic nerves (ON) from the DBA/2J mouse model of glaucoma and the DBA/2-Gpnmb⁺ control strain were isolated, and oxygen consumption rate (OCR) and extracellular acidification rate (ECAR), the discharge of protons from lactate release or byproducts of substrate oxidation, were measured. The glial-specific aconitase inhibitor fluorocitrate was used to limit the contribution of glial mitochondria to OCR and ECAR. We observed significant decreases in maximal respiration, ATP production, and spare capacity with aging. In the presence of fluorocitrate, OCR was higher, with more ATP produced, in glaucoma compared to aged ON. However, glaucoma ON showed lower maximal respiration. In the presence of fluorocitrate and challenged with ATPase inhibition, glaucoma ON was incapable of further upregulation of glycolysis to compensate for the loss of oxidative phosphorylation. Inclusion of 2-deoxyglucose as a substrate during ATPase inhibition indicated a significantly higher proportion of ECAR was derived from TCA cycle substrate oxidation than glycolysis in glaucoma ON. These data indicate that glaucoma axons have limited ability to respond to increased energy demand given their lower maximal respiration and inability to upregulate glycolysis when challenged. The higher ATP output from axonal mitochondria in glaucoma optic nerve compensates for this lack of resiliency but is ultimately inadequate for continued function.

Imaging brain microstructure with diffusion MRI: practicality and applications

This article gives an overview of microstructure imaging of the brain with diffusion MRI and reviews the state of the art. The microstructure-imaging paradigm aims to estimate and map microscopic properties of tissue using a model that links these properties to the voxel scale MR signal. Imaging techniques of this type are just starting to make the transition from the technical research domain to wide application in biomedical studies. We focus here on the practicalities of both implementing such techniques and using them in applications. Specifically, the article summarizes the relevant aspects of brain microanatomy and the range of diffusion-weighted MR measurements that provide sensitivity to them. It then reviews the evolution of mathematical and computational models that relate the diffusion MR signal to brain tissue microstructure, as well as the expanding areas of application. Next we focus on practicalities of designing a working microstructure imaging technique: model selection, experiment design, parameter estimation, validation, and the pipeline of development of this class of technique. The article concludes with some future perspectives on opportunities in this topic and expectations on how the field will evolve in the short-to-medium term.

Modeling conduction delays in the corpus callosum using MRI-measured g-ratio

Conduction of action potentials along myelinated axons is affected by their structural features, such as the axonal g-ratio, the ratio between the inner and outer diameters of the myelin sheath surrounding the axon. The effect of g-ratio variance on conduction properties has been quantitatively evaluated using single-axon models. It has recently become possible to estimate a g-ratio weighted measurement in vivo using quantitative MRI. Nevertheless, it is still unclear whether the variance in the g-ratio in the healthy human brain leads to significant differences in conduction velocity. In this work we tested whether the g-ratio MRI measurement can be used to predict conduction delays in the corpus callosum. We present a comprehensive framework in which the structural properties of fibers (i.e. length and g-ratio, measured using MRI), are incorporated in a biophysical model of axon conduction, to model conduction delays of long-range white matter fibers. We applied this framework to the corpus callosum, and found conduction delay estimates that are compatible with previously estimated values of conduction delays. We account for the variance in the velocity given the axon diameter distribution in the splenium, mid-body and genu, to further compare the fibers within the corpus callosum. Conduction delays have been suggested to increase with age. Therefore, we investigated whether there are differences in the g-ratio and the fiber length between young and old adults, and whether this leads to a difference in conduction speed and delays. We found very small differences between the predicted delays of the two groups in the motor fibers of the corpus callosum. We also found that the motor fibers of the corpus callosum have the fastest conduction estimates. Using the axon diameter distributions, we found that the occipital fibers have the slowest estimations, while the frontal and motor fiber tracts have similar estimates. Our study provides a framework for predicting conduction latencies in vivo. The framework could have major implications for future studies of white matter diseases and large range network computations. Our results highlight the need for improving additional in vivo measurements of white matter microstructure.

Mitochondrial Dynamics in Physiology and Pathology of Myelinated Axons

Mitochondria play essential roles in neurons and abnormal functions of mitochondria have been implicated in neurological disorders including myelin diseases. Since mitochondrial functions are regulated and maintained by their dynamic behavior involving localization, transport, and fusion/fission, modulation of mitochondrial dynamics would be involved in physiology and pathology of myelinated axons. In fact, the integration of multimodal imaging in vivo and in vitro revealed that mitochondrial localization and transport are differentially regulated in nodal and internodal regions in response to the changes of metabolic demand in myelinated axons. In addition, the mitochondrial behavior in axons is modulated as adaptive responses to demyelination irrespective of the cause of myelin loss, and the behavioral modulation is partly through interactions with cytoskeletons and closely associated with the pathophysiology of demyelinating diseases. Furthermore, the behavior and functions of axonal mitochondria are modulated in congenital myelin disorders involving impaired interactions between axons and myelin-forming cells, and, together with the inflammatory environment, implicated in axonal degeneration and disease phenotypes. Further studies on the regulatory mechanisms of the mitochondrial dynamics in myelinated axons would provide deeper insights into axo-glial interactions mediated through myelin ensheathment, and effective manipulations of the dynamics may lead to novel therapeutic strategies protecting axonal and neuronal functions and survival in primary diseases of myelin.

Spatial control of neuronal metabolism through glucose-mediated mitochondrial transport regulation

Eukaryotic cells modulate their metabolism by organizing metabolic components in response to varying nutrient availability and energy demands. In rat axons, mitochondria respond to glucose levels by halting active transport in high glucose regions. We employ quantitative modeling to explore physical limits on spatial organization of mitochondria and localized metabolic enhancement through regulated stopping of processive motion. We delineate the role of key parameters, including cellular glucose uptake and consumption rates, that are expected to modulate mitochondrial distribution and metabolic response in spatially varying glucose conditions. Our estimates indicate that physiological brain glucose levels fall within the limited range necessary for metabolic enhancement. Hence mitochondrial localization is shown to be a plausible regulatory mechanism for neuronal metabolic flexibility in the presence of spatially heterogeneous glucose, as may occur in long processes of projection neurons. These findings provide a framework for the control of cellular bioenergetics through organelle trafficking.

Cells are equipped with power factories called mitochondria that turn nutrients into chemical energy to fuel processes in the cell. Hundreds of mitochondria move throughout the cell, shifting their positions in response to energy demands. This happens via molecular motors that pick the mitochondria up and carry them to new locations. Such movements enable the mitochondria to accumulate in parts of the cell with the greatest energy needs.

Mitochondria of nerve cells or neurons have a particular challenging job, as neurons can be very long and different parts within the cells can have different energy needs. It has been shown that mitochondria stop in regions where nutrients such as sugar are most concentrated. So far, it has been unclear whether this regulated stopping helps control energy balance in neurons.

Here, Agrawal et al. used a computational model of rat neurons to find out whether sugar levels are sufficient in guiding mitochondria. The results showed that the mitochondria only accumulated in high-nutrient regions when the sugar concentrations were moderate – not too low and not too high. A specific range of sugar levels was necessary to make this mechanism useful for increasing the efficiency of energy production. Such concentrations match the ones observed in healthy rat brains.

When neurons are unable to meet their energy demands, they stop working and sometimes even die. This is the case in many diseases, including diabetes, dementia, and Alzheimer’s disease. Computer models allow us to explore the complex energy regulation in detail. A better understanding of how neurons regulate their energy production and demand may help us discover how they become faulty in these diseases.

Antioxidants prevent inflammation and preserve the optic projection and visual function in experimental neurotrauma

We investigated the role of oxidative stress and the inflammasome in trauma-induced axon degeneration and vision loss using a mouse model. The left eyes of male mice were exposed to over-pressure air waves. Wild-type C57Bl/6 mice were fed normal, high-vitamin-E (VitE), ketogenic or ketogenic-control diets. Mice lacking the ability to produce vitamin C (VitC) were maintained on a low-VitC diet. Visual evoked potentials (VEPs) and retinal superoxide levels were measured in vivo. Tissue was collected for biochemical and histological analysis. Injury increased retinal superoxide, decreased SOD2, and increased cleaved caspase-1, IL-1α, IL-1β, and IL-18 levels. Low-VitC exacerbated the changes and the high-VitE diet mitigated them, suggesting that oxidative stress led to the increase in IL-1α and activation of the inflammasome. The injury caused loss of nearly 50% of optic nerve axons at 2 weeks and astrocyte hypertrophy in mice on normal diet, both of which were prevented by the high-VitE diet. The VEP amplitude was decreased after injury in both control-diet and low-VitC mice, but not in the high-VitE-diet mice. The ketogenic diet also prevented the increase in superoxide levels and IL-1α, but had no effect on IL-1β. Despite this, the ketogenic diet preserved optic nerve axons, prevented astrocyte hypertrophy, and preserved the VEP amplitude. These data suggest that oxidative stress induces priming and activation of the inflammasome pathway after neurotrauma of the visual system. Further, blocking the activation of the inflammasome pathway may be an effective post-injury intervention.

Axons morphometry in the human spinal cord

Due to the technical challenges of large-scale microscopy and analysis, to date only limited knowledge has been made available about axon morphometry (diameter, shape, myelin thickness, volume fraction), thereby limiting our understanding of neuronal microstructure and slowing down research on neurodegenerative pathologies. This study addresses this knowledge gap by establishing a state-of-the-art acquisition and analysis framework for mapping axon morphometry, and providing the first comprehensive mapping of axon morphometry in the human spinal cord. We dissected, fixed and stained a human spinal cord with osmium tetroxide, and used a scanning electron microscope to image the entirety of 23 axial slices, covering C1 to L5 spinal levels. An automatic method based on deep learning was then used to segment each axon and myelin sheath to produce maps of axon morphometry. These maps were then registered to a standard spinal cord magnetic resonance imaging (MRI) template. Between 500,000 (lumbar) and 1 million (cervical) myelinated axons were segmented at each level of this human spinal cord. Morphometric features show a large disparity between tracts, but high right-left symmetry. Our results suggest a modality-based organization of the dorsal column in the human, as it has been observed in the rat. The generated axon morphometry template is publicly available at https://osf.io/8k7jr/ and could be used as a reference for quantitative MRI studies. The proposed framework for axon morphometry mapping could be extended to other parts of the central or peripheral nervous system that exhibit coherently-oriented axons.

The Axon-Myelin Unit in Development and Degenerative Disease

Axons are electrically excitable, cable-like neuronal processes that relay information between neurons within the nervous system and between neurons and peripheral target tissues. In the central and peripheral nervous systems, most axons over a critical diameter are enwrapped by myelin, which reduces internodal membrane capacitance and facilitates rapid conduction of electrical impulses. The spirally wrapped myelin sheath, which is an evolutionary specialisation of vertebrates, is produced by oligodendrocytes and Schwann cells; in most mammals myelination occurs during postnatal development and after axons have established connection with their targets. Myelin covers the vast majority of the axonal surface, influencing the axon's physical shape, the localisation of molecules on its membrane and the composition of the extracellular fluid (in the periaxonal space) that immerses it. Moreover, myelinating cells play a fundamental role in axonal support, at least in part by providing metabolic substrates to the underlying axon to fuel its energy requirements. The unique architecture of the myelinated axon, which is crucial to its function as a conduit over long distances, renders it particularly susceptible to injury and confers specific survival and maintenance requirements. In this review we will describe the normal morphology, ultrastructure and function of myelinated axons, and discuss how these change following disease, injury or experimental perturbation, with a particular focus on the role the myelinating cell plays in shaping and supporting the axon.

Structural and Functional Rescue of Chronic Metabolically Stressed Optic Nerves through Respiration

Axon degeneration can arise from metabolic stress, potentially a result of mitochondrial dysfunction or lack of appropriate substrate input. In this study, we investigated whether the metabolic vulnerability observed during optic neuropathy in the DBA/2J (D2) model of glaucoma is due to dysfunctional mitochondria or impaired substrate delivery to axons, the latter based on our observation of significantly decreased glucose and monocarboxylate transporters in D2 optic nerve (ON), human ON, and mice subjected to acute glaucoma injury. We placed both sexes of D2 mice destined to develop glaucoma and mice of a control strain, the DBA/2J-Gpnmb⁺, on a ketogenic diet to encourage mitochondrial function. Eight weeks of the diet generated mitochondria, improved energy availability by reversing monocarboxylate transporter decline, reduced glial hypertrophy, protected retinal ganglion cells and their axons from degeneration, and maintained physiological signaling to the brain. A robust antioxidant response also accompanied the response to the diet. These results suggest that energy compromise and subsequent axon degeneration in the D2 is due to low substrate availability secondary to transporter downregulation.SIGNIFICANCE STATEMENT We show axons in glaucomatous optic nerve are energy depleted and exhibit chronic metabolic stress. Underlying the metabolic stress are low levels of glucose and monocarboxylate transporters that compromise axon metabolism by limiting substrate availability. Axonal metabolic decline was reversed by upregulating monocarboxylate transporters as a result of placing the animals on a ketogenic diet. Optic nerve mitochondria responded capably to the oxidative phosphorylation necessitated by the diet and showed increased number. These findings indicate that the source of metabolic challenge can occur upstream of mitochondrial dysfunction. Importantly, the intervention was successful despite the animals being on the cusp of significant glaucoma progression.

Design and validation of diffusion MRI models of white matter

Diffusion MRI is arguably the method of choice for characterizing white matter microstructure in vivo. Over the typical duration of diffusion encoding, the displacement of water molecules is conveniently on a length scale similar to that of the underlying cellular structures. Moreover, water molecules in white matter are largely compartmentalized which enables biologically-inspired compartmental diffusion models to characterize and quantify the true biological microstructure. A plethora of white matter models have been proposed. However, overparameterization and mathematical fitting complications encourage the introduction of simplifying assumptions that vary between different approaches. These choices impact the quantitative estimation of model parameters with potential detriments to their biological accuracy and promised specificity. First, we review biophysical white matter models in use and recapitulate their underlying assumptions and realms of applicability. Second, we present up-to-date efforts to validate parameters estimated from biophysical models. Simulations and dedicated phantoms are useful in assessing the performance of models when the ground truth is known. However, the biggest challenge remains the validation of the "biological accuracy" of estimated parameters. Complementary techniques such as microscopy of fixed tissue specimens have facilitated direct comparisons of estimates of white matter fiber orientation and densities. However, validation of compartmental diffusivities remains challenging, and complementary MRI-based techniques such as alternative diffusion encodings, compartment-specific contrast agents and metabolites have been used to validate diffusion models. Finally, white matter injury and disease pose additional challenges to modeling, which are also discussed. This review aims to provide an overview of the current state of models and their validation and to stimulate further research in the field to solve the remaining open questions and converge towards consensus.

What is the optimal distribution of myelin along a single axon?

The myelin sheath that insulates some axons in the central nervous system allows for faster signal conduction. Previously, axons were thought to be either unmyelinated or fully myelinated. Recent experimental work has discovered a new pattern of myelination (intermittent myelination) along axons in the mouse brain, in which long unmyelinated axon segments are followed by myelinated segments of comparable length. We use a computational model to explore how myelin distribution (in particular intermittent myelination) affects conduction velocity. We find that although fully myelinated axons minimize conduction velocity, varying the spatial distribution of a fixed amount of myelin along a partially myelinated axon leads to considerable variation in the conduction velocity for action potentials. Whether sodium ion channel number or sodium ion channel density is held constant as the area of the unmyelinated segments increases has a strong influence on the optimal pattern of myelin and the conduction velocity.

Energy-efficient neural information processing in individual neurons and neuronal networks

Brains are composed of networks of an enormous number of neurons interconnected with synapses. Neural information is carried by the electrical signals within neurons and the chemical signals among neurons. Generating these electrical and chemical signals is metabolically expensive. The fundamental issue raised here is whether brains have evolved efficient ways of developing an energy-efficient neural code from the molecular level to the circuit level. Here, we summarize the factors and biophysical mechanisms that could contribute to the energy-efficient neural code for processing input signals. The factors range from ion channel kinetics, body temperature, axonal propagation of action potentials, low-probability release of synaptic neurotransmitters, optimal input and noise, the size of neurons and neuronal clusters, excitation/inhibition balance, coding strategy, cortical wiring, and the organization of functional connectivity. Both experimental and computational evidence suggests that neural systems may use these factors to maximize the efficiency of energy consumption in processing neural signals. Studies indicate that efficient energy utilization may be universal in neuronal systems as an evolutionary consequence of the pressure of limited energy. As a result, neuronal connections may be wired in a highly economical manner to lower energy costs and space. Individual neurons within a network may encode independent stimulus components to allow a minimal number of neurons to represent whole stimulus characteristics efficiently. This basic principle may fundamentally change our view of how billions of neurons organize themselves into complex circuits to operate and generate the most powerful intelligent cognition in nature. © 2017 Wiley Periodicals, Inc.

Sound-Evoked Activity Influences Myelination of Brainstem Axons in the Trapezoid Body

Plasticity of myelination represents a mechanism to tune the flow of information by balancing functional requirements with metabolic and spatial constraints. The auditory system is heavily myelinated and operates at the upper limits of action potential generation frequency and speed observed in the mammalian CNS. This study aimed to characterize the development of myelin within the trapezoid body, a central auditory fiber tract, and determine the influence sensory experience has on this process in mice of both sexes. We find that in vitro conduction speed doubles following hearing onset and the ability to support high-frequency firing increases concurrently. Also in this time, the diameter of trapezoid body axons and the thickness of myelin double, reaching mature-like thickness between 25 and 35 d of age. Earplugs were used to induce ∼50 dB elevation in auditory thresholds. If introduced at hearing onset, trapezoid body fibers developed thinner axons and myelin than age-matched controls. If plugged during adulthood, the thickest trapezoid body fibers also showed a decrease in myelin. These data demonstrate the need for sensory activity in both development and maintenance of myelin and have important implications in the study of myelin plasticity and how this could relate to sensorineural hearing loss following peripheral impairment.SIGNIFICANCE STATEMENT The auditory system has many mechanisms to maximize the dynamic range of its afferent fibers, which operate at the physiological limit of action potential generation, precision, and speed. In this study we demonstrate for the first time that changes in peripheral activity modifies the thickness of myelin in sensory neurons, not only in development but also in mature animals. The current study suggests that changes in CNS myelination occur as a downstream mechanism following peripheral deficit. Given the required submillisecond temporal precision for binaural auditory processing, reduced myelination might augment sensorineural hearing impairment.

Reduced axonal diameter of peripheral nerve fibers in a mouse model of Rett syndrome

Rett syndrome (RTT) is a neurological disorder characterized by motor and cognitive impairment, autonomic dysfunction and a loss of purposeful hand skills. In the majority of cases, typical RTT is caused by de novo mutations in the X-linked gene, MECP2. Alterations in the structure and function of neurons within the central nervous system of RTT patients and Mecp2-null mouse models are well established. In contrast, few studies have investigated the effects of MeCP2-deficiency on peripheral nerves. In this study, we conducted detailed morphometric as well as functional analysis of the sciatic nerves of symptomatic adult female Mecp2^+/- mice. We observed a significant reduction in the mean diameter of myelinated nerve fibers in Mecp2^+/- mice. In myelinated fibers, mitochondrial densities per unit area of axoplasm were significantly altered in Mecp2^+/- mice. However, conduction properties of the sciatic nerve of Mecp2 knockout mice were not different from control. These subtle changes in myelinated peripheral nerve fibers in heterozygous Mecp2 knockout mice could potentially explain some RTT phenotypes.

Resolution limit of cylinder diameter estimation by diffusion MRI: The impact of gradient waveform and orientation dispersion

Diffusion MRI has been proposed as a non-invasive technique for axonal diameter mapping. However, accurate estimation of small diameters requires strong gradients, which is a challenge for the transition of the technique from preclinical to clinical MRI scanners, since these have weaker gradients. In this work, we develop a framework to estimate the lower bound for accurate diameter estimation, which we refer to as the resolution limit. We analyse only the contribution from the intra-axonal space and assume that axons can be represented by impermeable cylinders. To address the growing interest in using techniques for diffusion encoding that go beyond the conventional single diffusion encoding (SDE) sequence, we present a generalised analysis capable of predicting the resolution limit regardless of the gradient waveform. Using this framework, waveforms were optimised to minimise the resolution limit. The results show that, for parallel cylinders, the SDE experiment is optimal in terms of yielding the lowest possible resolution limit. In the presence of orientation dispersion, diffusion encoding sequences with square-wave oscillating gradients were optimal. The resolution limit for standard clinical MRI scanners (maximum gradient strength 60-80 mT/m) was found to be between 4 and 8 μm, depending on the noise levels and the level of orientation dispersion. For scanners with a maximum gradient strength of 300 mT/m, the limit was reduced to between 2 and 5 μm.

Evaluating g-ratio weighted changes in the corpus callosum as a function of age and sex

Recent years have seen a growing interest in relating MRI measurements to the structural-biophysical properties of white matter fibers. The fiber g-ratio, defined as the ratio between the inner and outer radii of the axon myelin sheath, is an important structural property of white matter, affecting signal conduction. Recently proposed modeling methods that use a combination of quantitative-MRI signals, enable a measurement of the fiber g-ratio in vivo. Here we use an MRI-based g-ratio estimation to observe the variance of the g-ratio within the corpus callosum, and evaluate sex and age related differences. To estimate the g-ratio we used a model (Stikov et al., 2011; Duval et al., 2017) based on two different WM microstructure parameters: the relative amounts of myelin (myelin volume fraction, MVF) and fibers (fiber volume fraction, FVF) in a voxel. We derived the FVF from the fractional anisotropy (FA), and estimated the MVF by using the lipid and macromolecular tissue volume (MTV), calculated from the proton density (Mezer et al., 2013). In comparison to other methods of estimating the MVF, MTV represents a stable parameter with a straightforward route of acquisition. To establish our model, we first compared histological MVF measurements (West et al., 2016) with the MRI derived MTV. We then implemented our model on a large database of 92 subjects (44 males), aged 7 to 81, in order to evaluate age and sex related changes within the corpus callosum. Our results show that the MTV provides a good estimation of MVF for calculating g-ratio, and produced values from the corpus callosum that correspond to those found in animals ex vivo and are close to the theoretical optimum, as well as to published in vivo data. Our results demonstrate that the MTV derived g-ratio provides a simple and reliable in vivo g-ratio-weighted (GR*) measurement in humans. In agreement with theoretical predictions, and unlike other tissue parameters measured with MRI, the g-ratio estimations were found to be relatively stable with age, and we found no support for a significant sexual dimorphism with age.

Decreased Axon Caliber Underlies Loss of Fiber Tract Integrity, Disproportional Reductions in White Matter Volume, and Microcephaly in Angelman Syndrome Model Mice

Angelman syndrome (AS) is a debilitating neurodevelopmental disorder caused by loss of function of the maternally inherited UBE3A allele. It is currently unclear how the consequences of this genetic insult unfold to impair neurodevelopment. We reasoned that by elucidating the basis of microcephaly in AS, a highly penetrant syndromic feature with early postnatal onset, we would gain new insights into the mechanisms by which maternal UBE3A loss derails neurotypical brain growth and function. Detailed anatomical analysis of both male and female maternal Ube3a-null mice reveals that microcephaly in the AS mouse model is primarily driven by deficits in the growth of white matter tracts, which by adulthood are characterized by densely packed axons of disproportionately small caliber. Our results implicate impaired axon growth in the pathogenesis of AS and identify noninvasive structural neuroimaging as a potentially valuable tool for gauging therapeutic efficacy in the disorder.SIGNIFICANCE STATEMENT People who maternally inherit a deletion or nonfunctional copy of the UBE3A gene develop Angelman syndrome (AS), a severe neurodevelopmental disorder. To better understand how loss of maternal UBE3A function derails brain development, we analyzed brain structure in a maternal Ube3a knock-out mouse model of AS. We report that the volume of white matter (WM) is disproportionately reduced in AS mice, indicating that deficits in WM development are a major factor underlying impaired brain growth and microcephaly in the disorder. Notably, we find that axons within the WM pathways of AS model mice are abnormally small in caliber. This defect is associated with slowed nerve conduction, which could contribute to behavioral deficits in AS, including motor dysfunction.

Metabolic Vulnerability in the Neurodegenerative Disease Glaucoma

Axons can be several orders of magnitude longer than neural somas, presenting logistical difficulties in cargo trafficking and structural maintenance. Keeping the axon compartment well supplied with energy also presents a considerable challenge; even seemingly subtle modifications of metabolism can result in functional deficits and degeneration. Axons require a great deal of energy, up to 70% of all energy used by a neuron, just to maintain the resting membrane potential. Axonal energy, in the form of ATP, is generated primarily through oxidative phosphorylation in the mitochondria. In addition, glial cells contribute metabolic intermediates to axons at moments of high activity or according to need. Recent evidence suggests energy disruption is an early contributor to pathology in a wide variety of neurodegenerative disorders characterized by axonopathy. However, the degree to which the energy disruption is intrinsic to the axon vs. associated glia is not clear. This paper will review the role of energy availability and utilization in axon degeneration in glaucoma, a chronic axonopathy of the retinal projection.

Modeling white matter microstructure

Quantitative magnetic resonance imaging can be combined with advanced biophysical models to measure microstructural features of white matter. Non-invasive microstructural imaging has the potential to revolutionize neuroscience, and acquiring these measures in clinically feasible times would greatly improve patient monitoring and clinical studies of drug efficacy. However, a good understanding of microstructural imaging techniques is essential to set realistic expectations and to prevent over-interpretation of results. This review explains the methodology behind microstructural modeling and imaging, and gives an overview of the breakthroughs and challenges associated with it.

Mechanisms creating transient and sustained photoresponses in mammalian retinal ganglion cells

Visual stimuli of different frequencies are encoded in the retina using transient and sustained responses. Zhao et al. describe the different strategies that are used by four types of retinal ganglion cells to shape photoresponse kinetics.

Retinal neurons use sustained and transient light responses to encode visual stimuli of different frequency ranges, but the underlying mechanisms remain poorly understood. In particular, although earlier studies in retinal ganglion cells (RGCs) proposed seven potential mechanisms, all seven have since been disputed, and it remains unknown whether different RGC types use different mechanisms or how many mechanisms are used by each type. Here, we conduct a comprehensive survey in mice and rats of 12 candidate mechanisms that could conceivably produce tonic rod/cone-driven ON responses in intrinsically photosensitive RGCs (ipRGCs) and transient ON responses in three types of direction-selective RGCs (TRHR+, Hoxd10+ ON, and Hoxd10+ ON-OFF cells). We find that the tonic kinetics of ipRGCs arises from their substantially above-threshold resting potentials, input from sustained ON bipolar cells, absence of amacrine cell inhibition of presynaptic ON bipolar cells, and mGluR7-mediated maintenance of light-evoked glutamatergic input. All three types of direction-selective RGCs receive input from transient ON bipolar cells, and each type uses additional strategies to promote photoresponse transience: presynaptic inhibition and dopaminergic modulation for TRHR+ cells, center/surround antagonism and relatively negative resting potentials for Hoxd10+ ON cells, and presynaptic inhibition for Hoxd10+ ON-OFF cells. We find that the sustained nature of ipRGCs’ rod/cone-driven responses depends neither on melanopsin nor on N-methyl-d-aspartate (NMDA) receptors, whereas the transience of the direction-selective cells’ responses is influenced neither by α-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid (AMPA)/kainate receptor desensitization nor by glutamate uptake. For all cells, we further rule out spike frequency adaptation and intracellular Ca²⁺ as determinants of photoresponse kinetics. In conclusion, different RGC types use diverse mechanisms to produce sustained or transient light responses. Parenthetically, we find evidence in both mice and rats that the kinetics of light-induced mGluR6 deactivation determines whether an ON bipolar cell responds tonically or transiently to light.

AxonPacking: An Open-Source Software to Simulate Arrangements of Axons in White Matter

HIGHLIGHTS

AxonPacking: Open-source software for simulating white matter microstructure.

Validation on a theoretical disk packing problem.

Reproducible and stable for various densities and diameter distributions.

Can be used to study interplay between myelin/fiber density and restricted fraction.

Quantitative Magnetic Resonance Imaging (MRI) can provide parameters that describe white matter microstructure, such as the fiber volume fraction (FVF), the myelin volume fraction (MVF) or the axon volume fraction (AVF) via the fraction of restricted water (fr). While already being used for clinical application, the complex interplay between these parameters requires thorough validation via simulations. These simulations required a realistic, controlled and adaptable model of the white matter axons with the surrounding myelin sheath. While there already exist useful algorithms to perform this task, none of them combine optimisation of axon packing, presence of myelin sheath and availability as free and open source software. Here, we introduce a novel disk packing algorithm that addresses these issues. The performance of the algorithm is tested in term of reproducibility over 50 runs, resulting density, and stability over iterations. This tool was then used to derive multiple values of FVF and to study the impact of this parameter on fr and MVF in light of the known microstructure based on histology sample. The standard deviation of the axon density over runs was lower than 10⁻³ and the expected hexagonal packing for monodisperse disks was obtained with a density close to the optimal density (obtained: 0.892, theoretical: 0.907). Using an FVF ranging within [0.58, 0.82] and a mean inter-axon gap ranging within [0.1, 1.1] μm, MVF ranged within [0.32, 0.44] and fr ranged within [0.39, 0.71], which is consistent with the histology. The proposed algorithm is implemented in the open-source software AxonPacking (https://github.com/neuropoly/axonpacking) and can be useful for validating diffusion models as well as for enabling researchers to study the interplay between microstructure parameters when evaluating qMRI methods.

g-Ratio weighted imaging of the human spinal cord in vivo

The fiber g-ratio is defined as the ratio of the inner to the outer diameter of the myelin sheath. This ratio provides a measure of the myelin thickness that complements axon morphology (diameter and density) for assessment of demyelination in diseases such as multiple sclerosis. Previous work has shown that an aggregate g-ratio map can be computed using a formula that combines axon and myelin density measured with quantitative MRI. In this work, we computed g-ratio weighted maps in the cervical spinal cord of nine healthy subjects. We utilized the 300mT/m gradients from the CONNECTOM scanner to estimate the fraction of restricted water (fr) with high accuracy, using the CHARMED model. Myelin density was estimated using the lipid and macromolecular tissue volume (MTV) method, derived from normalized proton density (PD) mapping. The variability across spinal level, laterality and subject were assessed using a three-way ANOVA. The average g-ratio value obtained in the white matter was 0.76+/-0.03, consistent with previous histology work. Coefficients of variation of fr and MTV were respectively 4.3% and 13.7%. fr and myelin density were significantly different across spinal tracts (p=3×10-7 and 0.004 respectively) and were positively correlated in the white matter (r=0.42), suggesting shared microstructural information. The aggregate g-ratio did not show significant differences across tracts (p=0.6). This study suggests that fr and myelin density can be measured in vivo with high precision and that they can be combined to produce a g-ratio-weighted map robust to free water pool contamination from cerebrospinal fluid or veins. Potential applications include the study of early demyelination in multiple sclerosis, and the quantitative assessment of remyelination drugs.

In vivo observation and biophysical interpretation of time-dependent diffusion in human white matter

The presence of micrometer-level restrictions leads to a decrease of diffusion coefficient with diffusion time. Here we investigate this effect in human white matter in vivo. We focus on a broad range of diffusion times, up to 600 ms, covering diffusion length scales up to about 30 μm. We perform stimulated echo diffusion tensor imaging on 5 healthy volunteers and observe a relatively weak time-dependence in diffusion transverse to major fiber tracts. Remarkably, we also find notable time-dependence in the longitudinal direction. Comparing models of diffusion in ordered, confined and disordered media, we argue that the time-dependence in both directions can arise due to structural disorder, such as axonal beads in the longitudinal direction, and the random packing geometry of fibers within a bundle in the transverse direction. These time-dependent effects extend beyond a simple picture of Gaussian compartments, and may lead to novel markers that are specific to neuronal fiber geometry at the micrometer scale.

Energy-Efficient Information Transfer by Visual Pathway Synapses

The architecture of computational devices is shaped by their energy consumption. Energetic constraints are used to design silicon-based computers but are poorly understood for neural computation. In the brain, most energy is used to reverse ion influxes generating excitatory postsynaptic currents (EPSCs) and action potentials. Thus, EPSCs should be small to minimize energy use, but not so small as to impair information transmission. We quantified information flow through the retinothalamic synapse in the visual pathway in brain slices, with cortical and inhibitory input to the postsynaptic cell blocked. Altering EPSC size with dynamic clamp, we found that a larger-than-normal EPSC increased information flow through the synapse. Thus, the evolutionarily selected EPSC size does not maximize retinal information flow to the cortex. By assessing the energy used on postsynaptic ion pumping and action potentials, we show that, instead, the EPSC size optimizes the ratio of retinal information transmitted to energy consumed. These data suggest maximization of information transmission per energy used as a synaptic design principle.

Early astrocyte redistribution in the optic nerve precedes axonopathy in the DBA/2J mouse model of glaucoma

Glaucoma challenges the survival of retinal ganglion cell axons in the optic nerve through processes dependent on both aging and ocular pressure. Relevant stressors likely include complex interplay between axons and astrocytes, both in the retina and optic nerve. In the DBA/2J mouse model of pigmentary glaucoma, early progression involves axonopathy characterized by loss of functional transport prior to outright degeneration. Here we describe novel features of early pathogenesis in the DBA/2J nerve. With age the cross-sectional area of the nerve increases; this is associated generally with diminished axon packing density and survival and increased glial coverage of the nerve. However, for nerves with the highest axon density, as the nerve expands mean cross-sectional axon area enlarges as well. This early expansion was marked by disorganized axoplasm and accumulation of hyperphosphorylated neurofilamants indicative of axonopathy. Axon expansion occurs without loss up to a critical threshold for size (about 0.45-0.50 μm(2)), above which additional expansion tightly correlates with frank loss of axons. As well, early axon expansion prior to degeneration is concurrent with decreased astrocyte ramification with redistribution of processes towards the nerve edge. As axons expand beyond the critical threshold for loss, glial area resumes an even distribution from the center to edge of the nerve. We also found that early axon expansion is accompanied by reduced numbers of mitochondria per unit area in the nerve. Finally, our data indicate that both IOP and nerve expansion are associated with axon enlargement and reduced axon density for aged nerves. Collectively, our data support the hypothesis that diminished bioenergetic resources in conjunction with early nerve and glial remodeling could be a primary inducer of progression of axon pathology in glaucoma.

Decreased Energy Capacity and Increased Autophagic Activity in Optic Nerve Axons With Defective Anterograde Transport

PURPOSE

Autophagy is a critical process, compromised in neurodegenerative disease, by which terminally differentiated cells like neurons manage cytoskeletal and organelle turnover. How autophagy relates to associated neurodegenerative pathologies remain unclear. We examined autophagy in optic neuropathy by investigating cytoskeletal degradation, mitochondria, and autophagic vesicles in the DBA2/J mouse model of glaucoma exhibiting differing levels of axon transport functionality.

METHODS

DBA/2J and DBA/2J(wt-gpnmb) control mice 11 to 14 months of age were injected with cholera toxin-B (CTB) to assay anterograde axonal transport. Axonal mitochondria and autophagic vesicles were analyzed with respect to transport integrity in proximal and distal optic nerve using serial block face scanning electron microscopy (3D EM).

RESULTS

Several indices varied significantly between the DBA/2J and DBA/2J(wt-gpnmb) mice, including mitochondrial volume, average number of autophagic vesicles per axon, and mitochondrial cristae. However, there were no differences in mitochondrial cristae for axons with functional versus dysfunctional CTB transport, suggesting that mitochondrial dysfunction precedes overt transport blockade. Anterograde transport failure was accompanied by a dissociation of the relationship between mitochondrial and axon volumes. Autophagic vesicle profiles were significantly increased in optic nerve with transport deficit, consistent with greater autophagic activity. Mitochondria within autophagosomes, indicative of mitophagy, were observed in both proximal and distal axons.

CONCLUSIONS

Loss of anterograde transport in DBA/2J optic nerve is concomitant with diminished mitochondrial volume, increased cytoskeletal breakdown and autophagic activity, and accumulation of autophagic profiles, including signs of mitophagy, in proximal optic nerve. Axons with transport deficit are metabolically underserved, though not necessarily from mitophagy.

Ribbon Synapses and Visual Processing in the Retina

The first synapses transmitting visual information contain an unusual organelle, the ribbon, which is involved in the transport and priming of vesicles to be released at the active zone. The ribbon is one of many design features that allow efficient refilling of the active zone, which in turn enables graded changes in membrane potential to be transmitted using a continuous mode of neurotransmitter release. The ribbon also plays a key role in supplying vesicles for rapid and transient bursts of release that signal fast changes, such as the onset of light. We increasingly understand how the physiological properties of ribbon synapses determine basic transformations of the visual signal and, in particular, how the process of refilling the active zone regulates the gain and adaptive properties of the retinal circuit. The molecular basis of ribbon function is, however, far from clear.

Ischemic tolerance in pre-myelinated white matter: the role of astrocyte glycogen in brain pathology

In isolated white matter, ischemic tolerance changes dramatically in the period immediately before the onset of myelination. In the absence of an extrinsic energy source, postnatal day 0 to 2 (P0 to P2) white matter axons are here shown to maintain excitability for over twice as long as axons >P2, a differential that was dependent on glycogen metabolism. Prolonged withdrawal of extrinsic energy supply tended to spare axons in zones around astrocytes, which are shown to be the sole repository for glycogen particles in developing white matter. Analysis of mitochondrial volume fraction revealed that neither axons nor astrocytes had a low metabolic rate in neonatal white matter, while oligodendroglia at older ages had an elevated metabolism. The astrocyte population is established early in neural development, and exhibits reduced cell density as maturation progresses and white matter expands. The findings show that this event establishes the necessary conditions for ischemia sensitivity in white matter and indicates that astrocyte proximity may be significant for the survival of neuronal elements in conditions associated with compromised energy supply.

Evolution of bow-tie architectures in biology

Bow-tie or hourglass structure is a common architectural feature found in many biological systems. A bow-tie in a multi-layered structure occurs when intermediate layers have much fewer components than the input and output layers. Examples include metabolism where a handful of building blocks mediate between multiple input nutrients and multiple output biomass components, and signaling networks where information from numerous receptor types passes through a small set of signaling pathways to regulate multiple output genes. Little is known, however, about how bow-tie architectures evolve. Here, we address the evolution of bow-tie architectures using simulations of multi-layered systems evolving to fulfill a given input-output goal. We find that bow-ties spontaneously evolve when the information in the evolutionary goal can be compressed. Mathematically speaking, bow-ties evolve when the rank of the input-output matrix describing the evolutionary goal is deficient. The maximal compression possible (the rank of the goal) determines the size of the narrowest part of the network—that is the bow-tie. A further requirement is that a process is active to reduce the number of links in the network, such as product-rule mutations, otherwise a non-bow-tie solution is found in the evolutionary simulations. This offers a mechanism to understand a common architectural principle of biological systems, and a way to quantitate the effective rank of the goals under which they evolved.

Many biological systems show bow-tie (also called hourglass) architecture. A bow-tie means that a large number of inputs are converted to a small number of intermediates, which then fan out to generate a large number of outputs. For example, cells use a wide variety of nutrients; process them into 12 metabolic precursors, which are then used to make all of the cells biomass. Similar principles exist in biological signaling and in the information processing in the visual system. Despite the ubiquity of bow-tie structures in biology, there is no explanation of how they evolved. Here, we find that bow-ties spontaneously evolve when the information in the evolutionary goal they evolved to satisfy can be compressed. Mathematically, this means that the matrix representing the goal has deficient rank. The maximal compression possible determines the width of the bow-tie—the narrowest part in the network (equal to the rank of the goal matrix). This offers a mechanism to understand a common architectural principle of biological systems, and a way to quantitate the rank of the goals under which they evolved.

Mitochondrial morphology differences and mitophagy deficit in murine glaucomatous optic nerve

PURPOSE

Decreased ATP correlates with intraocular pressure exposure in the optic nerves of mice with glaucoma. To understand what underlies this energy deficit, we examined mitochondria in the myelinated optic nerve axons of the DBA/2J mouse, a model of glaucoma secondary to iris pigment disease, and the DBA/2(wt-gpnmb) control strain.

METHODS

Mitochondrial length, width, surface area, and health status were measured in 30 electron microscopic fields within the myelinated portion of optic nerves from DBA/2J and DBA/2(wt-gpnmb) mice at 3, 6, and 10 months of age. Protein was isolated from optic nerve for analysis of PINK1, Parkin, LC3-I and -II, and lysosome-associated membrane protein 1 (LAMP1) by Western blot.

RESULTS

The number of mitochondria in DBA/2J optic nerve was increased, and they had significantly smaller surface area. Mitochondria in DBA/2J were closer to the axolemma, more spatially isolated, and their cristae were more disrupted at every age group as compared to DBA/2(wt-gpnmb). Autophagosomes were significantly increased in DBA/2J optic nerve at all ages. Protein analysis showed higher LC3-II to LC3-I ratio in aged DBA/2J optic nerve than in DBA/2(wt-gpnmb). PINK1 and Parkin levels were not statistically different across age groups. LAMP1 was significantly decreased in the aged DBA/2J optic nerve.

CONCLUSIONS

Decreased surface area, combined with reduced oxidative capacity in mitochondria from the aged DBA/2J axon, indicate that mitochondrial pathology may contribute to the energy deficit in glaucomatous optic nerve. Though autophagosomes were increased in DBA/2J optic nerve, the increased mitochondria and decreased LAMP1 suggest deteriorating mitochondria are not being efficiently recycled by mitophagy.

Modelling extracellular electrical stimulation: part 4. Effect of the cellular composition of neural tissue on its spatio-temporal filtering properties

OBJECTIVE

The objective of this paper is to present a concrete application of the cellular composite model for calculating the membrane potential, described in an accompanying paper.

APPROACH

A composite model that is used to determine the membrane potential for both longitudinal and transverse modes of stimulation is demonstrated.

MAIN RESULTS

Two extreme limits of the model, near-field and far-field for an electrode close to or distant from a neuron, respectively, are derived in this paper. Results for typical neural tissue are compared using the composite, near-field and far-field models as well as the standard isotropic volume conductor model. The self-consistency of the composite model, its spatial profile response and the extracellular potential time behaviour are presented. The magnitudes of the longitudinal and transverse components for different values of electrode-neurite separations are compared.

SIGNIFICANCE

The unique features of the composite model and its simplified versions can be used to accurately estimate the spatio-temporal response of neural tissue to extracellular electrical stimulation.

The emerging functions of oligodendrocytes in regulating neuronal network behaviour

Myelin is required for efficient nerve conduction, but not all axons are myelinated to the same extent. Here we review recent studies that have revealed distinct myelination patterns of different axonal paths, suggesting that myelination is not an all or none phenomenon and that its presence is finely regulated in central nervous system networks. Whereas powerful reductionist biology has led to important knowledge of how oligodendrocytes function by themselves, little is known about their role in neuronal networks. We still do not understand how oligodendrocytes integrate information from neurons to adapt their function to the need of the system. An intricate cross talk between neurons and glia is likely to exist and to determine how neuronal circuits operate as a whole. Dissecting these mechanisms by using integrative systems biology approaches is one of the major challenges ahead.

A synaptic mechanism for temporal filtering of visual signals

The visual system transmits information about fast and slow changes in light intensity through separate neural pathways. We used in vivo imaging to investigate how bipolar cells transmit these signals to the inner retina. We found that the volume of the synaptic terminal is an intrinsic property that contributes to different temporal filters. Individual cells transmit through multiple terminals varying in size, but smaller terminals generate faster and larger calcium transients to trigger vesicle release with higher initial gain, followed by more profound adaptation. Smaller terminals transmitted higher stimulus frequencies more effectively. Modeling global calcium dynamics triggering vesicle release indicated that variations in the volume of presynaptic compartments contribute directly to all these differences in response dynamics. These results indicate how one neuron can transmit different temporal components in the visual signal through synaptic terminals of varying geometries with different adaptational properties.

Distribution of axon diameters in cortical white matter: an electron-microscopic study on three human brains and a macaque

The aim of this study was to obtain information on the axonal diameters of cortico-cortical fibres in the human brain, connecting distant regions of the same hemisphere via the white matter. Samples for electron microscopy were taken from the region of the superior longitudinal fascicle and from the transitional white matter between temporal and frontal lobe where the uncinate and inferior occipitofrontal fascicle merge. We measured the inner diameter of cross sections of myelinated axons. For comparison with data from the literature on the human corpus callosum, we also took samples from that region. For comparison with well-fixed material, we also included samples from corresponding regions of a monkey brain (Macaca mulatta). Fibre diameters in human brains ranged from 0.16 to 9 μm. Distributions of diameters were similar in the three systems of cortico-cortical fibres investigated, both in humans and the monkey, with most of the average values below 1 μm diameter and a small population of much thicker fibres. Within individual human brains, the averages were larger in the superior longitudinal fascicle than in the transitional zone between temporal and frontal lobe. An asymmetry between left and right could be found in one of the human brains, as well as in the monkey brain. A correlation was also found between the thickness of the myelin sheath and the inner axon diameter for axons whose calibre was greater than about 0.6 μm. The results are compared to white matter data in other mammals and are discussed with respect to conduction velocity, brain size, cognition, as well as diffusion weighted imaging studies.

Lifespan maturation and degeneration of human brain white matter

Properties of human brain tissue change across the lifespan. Here we model these changes in the living human brain by combining quantitative magnetic resonance imaging (MRI) measurements of R1 (1/T1) with diffusion MRI and tractography (N=102, ages 7-85). The amount of R1 change during development differs between white-matter fascicles, but in each fascicle the rate of development and decline are mirror-symmetric; the rate of R1 development as the brain approaches maturity predicts the rate of R1 degeneration in aging. Quantitative measurements of macromolecule tissue volume (MTV) confirm that R1 is an accurate index of the growth of new brain tissue. In contrast to R1, diffusion development follows an asymmetric time-course with rapid childhood changes but a slow rate of decline in old age. Together, the time-courses of R1 and diffusion changes demonstrate that multiple biological processes drive changes in white-matter tissue properties over the lifespan.

Structural and functional aspects relating to cost and benefit of rich club organization in the human cerebral cortex

Recent findings have demonstrated that a small set of highly connected brain regions may play a central role in enabling efficient communication between cortical regions, together forming a densely interconnected "rich club." However, the density and spatial layout of the rich club also suggest that it constitutes a costly feature of brain architecture. Here, combining anatomical T1, diffusion tensor imaging, magnetic transfer imaging, and functional MRI, several aspects of structural and functional connectivity of the brain's rich club were examined. Our findings suggest that rich club regions and rich club connections exhibit high levels of wiring volume, high levels of white matter organization, high levels of metabolic energy usage, long maturational trajectories, more variable regional time series, and more inter-regional functional couplings. Taken together, these structural and functional measures extend the notion that rich club organization represents a high-cost feature of brain architecture that puts a significant strain on brain resources. The high cost of the rich club may, however, be offset by significant functional benefits that the rich club confers to the brain network as a whole.

A simple model of optimal population coding for sensory systems

A fundamental task of a sensory system is to infer information about the environment. It has long been suggested that an important goal of the first stage of this process is to encode the raw sensory signal efficiently by reducing its redundancy in the neural representation. Some redundancy, however, would be expected because it can provide robustness to noise inherent in the system. Encoding the raw sensory signal itself is also problematic, because it contains distortion and noise. The optimal solution would be constrained further by limited biological resources. Here, we analyze a simple theoretical model that incorporates these key aspects of sensory coding, and apply it to conditions in the retina. The model specifies the optimal way to incorporate redundancy in a population of noisy neurons, while also optimally compensating for sensory distortion and noise. Importantly, it allows an arbitrary input-to-output cell ratio between sensory units (photoreceptors) and encoding units (retinal ganglion cells), providing predictions of retinal codes at different eccentricities. Compared to earlier models based on redundancy reduction, the proposed model conveys more information about the original signal. Interestingly, redundancy reduction can be near-optimal when the number of encoding units is limited, such as in the peripheral retina. We show that there exist multiple, equally-optimal solutions whose receptive field structure and organization vary significantly. Among these, the one which maximizes the spatial locality of the computation, but not the sparsity of either synaptic weights or neural responses, is consistent with known basic properties of retinal receptive fields. The model further predicts that receptive field structure changes less with light adaptation at higher input-to-output cell ratios, such as in the periphery.

Studies of the computational principles of sensory coding have largely focused on the redundancy reduction hypothesis, which posits that a neural population should encode the raw sensory signal efficiently by reducing its redundancy. Models based on this idea, however, have not taken into account some important aspects of sensory systems. First, neurons are noisy, and therefore, some redundancy in the code can be useful for transmitting information reliably. Second, the sensory signal itself is noisy, which should be counteracted as early as possible in the sensory pathway. Finally, neural resources such as the number of neurons are limited, which should strongly affect the form of the sensory code. Here we examine a simple model that takes all these factors into account. We find that the model conveys more information compared to redundancy reduction. When applied to the retina, the model provides a unified functional account for several known properties of retinal coding and makes novel predictions that have yet to be tested experimentally. The generality of the framework allows it to model a wide range of conditions and can be applied to predict optimal sensory coding in other systems.

The log-dynamic brain: how skewed distributions affect network operations

We often assume that the variables of functional and structural brain parameters - such as synaptic weights, the firing rates of individual neurons, the synchronous discharge of neural populations, the number of synaptic contacts between neurons and the size of dendritic boutons - have a bell-shaped distribution. However, at many physiological and anatomical levels in the brain, the distribution of numerous parameters is in fact strongly skewed with a heavy tail, suggesting that skewed (typically lognormal) distributions are fundamental to structural and functional brain organization. This insight not only has implications for how we should collect and analyse data, it may also help us to understand how the different levels of skewed distributions - from synapses to cognition - are related to each other.

Contactin-1 regulates myelination and nodal/paranodal domain organization in the central nervous system

Myelin, a multilayered membrane sheath formed by oligodendrocytes around axons in the CNS, enables rapid nerve impulse conduction and sustains neuronal health. The signals exchanged between axons and oligodendrocytes in myelin remain to be fully elucidated. Here we provide genetic evidence for multiple and critical functions of Contactin-1 in central myelin. We document dynamic Contactin-1 expression on oligodendrocytes in vivo, and progressive accumulation at nodes of Ranvier and paranodes during postnatal mouse development. Nodal and paranodal expression stabilized in mature myelin, but overall membranous expression diminished. Contactin-1-deficiency disrupted paranodal junction formation as evidenced by loss of Caspr, mislocalized potassium Kv1.2 channels, and abnormal myelin terminal loops. Reduced numbers and impaired maturation of sodium channel clusters accompanied this phenotype. Histological, electron microscopic, and biochemical analyses uncovered significant hypomyelination in Contactin-1-deficient central nerves, with up to 60% myelin loss. Oligodendrocytes were present in normal numbers, albeit a minor population of neuronal/glial antigen 2-positive (NG2(+)) progenitors lagged in maturation by postnatal day 18, when the mouse null mutation was lethal. Major contributing factors to hypomyelination were defects in the generation and organization of myelin membranes, as judged by electron microscopy and quantitative analysis of oligodendrocyte processes labeled by GFP transgenically expressed from the proteolipid protein promoter. These data reveal that Contactin-1 regulates both myelin formation and organization of nodal and paranodal domains in the CNS. These multiple roles distinguish central Contactin-1 functions from its specific role at paranodes in the periphery, and emphasize mechanistic differences in central and peripheral myelination.

Age-related changes in the visual pathways: blame it on the axon

The aging visual system is marked by a decline in some, but not all, key functions. Some of this decline is attributed to changes in the optics of the eye, but other aspects must have a neural basis. Across mammals, with aging there is remarkable persistence of central structures to which retinal ganglion cell (RGC) axons project with little or no loss of neurons. Similarly, RGC bodies in the retina are subject to variable age-related loss, with most mammals showing none over time. In contrast, the RGC axon itself is highly vulnerable. Across species, the rate of axon loss in the optic nerve is related inversely to the total number of axons at maturity and lifespan. The result of this scaling is approximately a 40% total decline in axon number. Evidence suggests that the consistent vulnerability of RGC axons to aging arises from their high metabolic demand combined with diminishing resources. Thus, therapeutic interventions that conserve bioenergetics may have potential to abate age-related decline in visual function.

Changes to mitochondrial ultrastructure in optic nerve vulnerable to secondary degeneration in vivo are limited by irradiation at 670 nm

Background

Traumatic injury to the central nervous system results in damage to tissue beyond the primary injury, termed secondary degeneration. Key events thought to be associated with secondary degeneration involve aspects of mitochondrial function which may be modulated by red/near-infrared irradiation therapy (R/NIR-IT), but precisely how mitochondria are affected in vivo has not been investigated. Secondary degeneration was modelled by transecting the dorsal aspect of the optic nerve in adult rats and mitochondrial ultrastructure in intact ventral optic nerve vulnerable to secondary degeneration investigated with transmission electron microscopy.

Results

Despite reported increases in fission following central nervous system injury, we saw no change in mitochondrial densities in optic nerve vulnerable to secondary degeneration in vivo. However, in axons, frequency distributions of mitochondrial profile areas showed higher cumulative probabilities of smaller mitochondrial profiles at day 1 after injury. Glial mitochondrial profiles did not exhibit changes in area, but a more elliptical mitochondrial shape was observed at both day 1 and 7 following injury. Importantly, mitochondrial autophagic profiles were observed at days 1 and 7 in optic nerve vulnerable to secondary degeneration in vivo. Citrate synthase activity was used as an additional measure of mitochondrial mass in ventral optic nerve and was decreased at day 7, whereas mitochondrial aconitase activity increased at day 1 and day 28 after injury in optic nerve vulnerable to secondary degeneration. R/NIR-IT has been used to treat the injured central nervous system, with reported improvements in oxidative metabolism suggesting mitochondrial involvement, but ultrastructural information is lacking. Here we show that R/NIR-IT of injured animals resulted in distributions of mitochondrial areas and shape not significantly different from control and significantly reduced mitochondrial autophagic profiles. R/NIR-IT also resulted in decreased citrate synthase activity (day 7) and increased aconitase activity (day 1) in optic nerve vulnerable to secondary degeneration.

Conclusions

These findings suggest that mitochondrial structure and activity of enzymes of the citric acid cycle are dynamically altered during secondary degeneration in vivo and R/NIR-IT may protect mitochondrial structure.

The effect of cell size and channel density on neuronal information encoding and energy efficiency

Identifying the determinants of neuronal energy consumption and their relationship to information coding is critical to understanding neuronal function and evolution. Three of the main determinants are cell size, ion channel density, and stimulus statistics. Here we investigate their impact on neuronal energy consumption and information coding by comparing single-compartment spiking neuron models of different sizes with different densities of stochastic voltage-gated Na(+) and K(+) channels and different statistics of synaptic inputs. The largest compartments have the highest information rates but the lowest energy efficiency for a given voltage-gated ion channel density, and the highest signaling efficiency (bits spike(-1)) for a given firing rate. For a given cell size, our models revealed that the ion channel density that maximizes energy efficiency is lower than that maximizing information rate. Low rates of small synaptic inputs improve energy efficiency but the highest information rates occur with higher rates and larger inputs. These relationships produce a Law of Diminishing Returns that penalizes costly excess information coding capacity, promoting the reduction of cell size, channel density, and input stimuli to the minimum possible, suggesting that the trade-off between energy and information has influenced all aspects of neuronal anatomy and physiology.

Neuroglobin involvement in visual pathways through the optic nerve

Neuroglobin is a member of the globin superfamily proposed to be only expressed in neurons and involved in neuronal protection from hypoxia or oxidative stress. A significant fraction of the protein localizes within the mitochondria and is directly associated with mitochondrial metabolism and integrity. The retina is the site of the highest concentration for neuroglobin and has been reported to be up to 100-fold higher than in the brain. Since neuroglobin was especially abundant in retinal ganglion cell layer, we investigated its abundance in optic nerves. Remarkably in optic nerves, neuroglobin is observed, as expected, in retinal ganglion cell axon profiles but also astrocyte processes, in physiological conditions, possess high levels of the protein. Neuroglobin mRNA and protein levels are ~10-fold higher in optic nerves than in retinas, indicating an important accumulation of neuroglobin in these support cells. Additionally, neuroglobin levels increase in Müller cells during reactive gliosis in response to eye injury. This suggests the pivotal role of neuroglobin in retinal glia involved in neuronal support and/or healing. This article is part of a Special Issue entitled: Oxygen Binding and Sensing Proteins.

Axonal and glial microstructural information obtained with diffusion-weighted magnetic resonance spectroscopy at 7T

Diffusion-weighted magnetic resonance spectroscopy (DWS) offers unique access to compartment-specific microstructural information on tissue, and potentially sensitive detection of compartment-specific changes in disease. The specificity of DWS is, however, offset by its relative low sensitivity, intrinsic to all MRS-based methods, and further exacerbated by the signal loss due to the diffusion weighting and long echo times. In this work we first provide an experimental example for the type of compartment-specific information that can be obtained with DWS from a small volume of interest (VOI) in brain white matter. We then propose and discuss a strategy for the analysis of DWS data, which includes the use of models of diffusion in compartments with simple geometries. We conclude with a broader discussion of the potential role of DWS in the characterization of tissue microstructure and the complementarity of DWS with less-specific but more sensitive microstructural tools such as diffusion tensor imaging.

The role of tissue microstructure and water exchange in biophysical modelling of diffusion in white matter

Biophysical models that describe the outcome of white matter diffusion MRI experiments have various degrees of complexity. While the simplest models assume equal-sized and parallel axons, more elaborate ones may include distributions of axon diameters and axonal orientation dispersions. These microstructural features can be inferred from diffusion-weighted signal attenuation curves by solving an inverse problem, validated in several Monte Carlo simulation studies. Model development has been paralleled by microscopy studies of the microstructure of excised and fixed nerves, confirming that axon diameter estimates from diffusion measurements agree with those from microscopy. However, results obtained in vivo are less conclusive. For example, the amount of slowly diffusing water is lower than expected, and the diffusion-encoded signal is apparently insensitive to diffusion time variations, contrary to what may be expected. Recent understandings of the resolution limit in diffusion MRI, the rate of water exchange, and the presence of microscopic axonal undulation and axonal orientation dispersions may, however, explain such apparent contradictions. Knowledge of the effects of biophysical mechanisms on water diffusion in tissue can be used to predict the outcome of diffusion tensor imaging (DTI) and of diffusion kurtosis imaging (DKI) studies. Alterations of DTI or DKI parameters found in studies of pathologies such as ischemic stroke can thus be compared with those predicted by modelling. Observations in agreement with the predictions strengthen the credibility of biophysical models; those in disagreement could provide clues of how to improve them. DKI is particularly suited for this purpose; it is performed using higher b-values than DTI, and thus carries more information about the tissue microstructure. The purpose of this review is to provide an update on the current understanding of how various properties of the tissue microstructure and the rate of water exchange between microenvironments are reflected in diffusion MRI measurements. We focus on the use of biophysical models for extracting tissue-specific parameters from data obtained with single PGSE sequences on clinical MRI scanners, but results obtained with animal MRI scanners are also considered. While modelling of white matter is the central theme, experiments on model systems that highlight important aspects of the biophysical models are also reviewed.

Molecular mechanisms of retinal ganglion cell degeneration in glaucoma and future prospects for cell body and axonal protection

Glaucoma, which affects more than 70 million people worldwide, is a heterogeneous group of disorders with a resultant common denominator; optic neuropathy, eventually leading to irreversible blindness. The clinical manifestations of primary open-angle glaucoma (POAG), the most common subtype of glaucoma, include excavation of the optic disc and progressive loss of visual field. Axonal degeneration of retinal ganglion cells (RGCs) and apoptotic death of their cell bodies are observed in glaucoma, in which the reduction of intraocular pressure (IOP) is known to slow progression of the disease. A pattern of localized retinal nerve fiber layer (RNFL) defects in glaucoma patients indicates that axonal degeneration may precede RGC body death in this condition. The mechanisms of degeneration of neuronal cell bodies and their axons may differ. In this review, we addressed the molecular mechanisms of cell body death and axonal degeneration in glaucoma and proposed axonal protection in addition to cell body protection. The concept of axonal protection may become a new therapeutic strategy to prevent further axonal degeneration or revive dying axons in patients with preperimetric glaucoma. Further study will be needed to clarify whether the combination therapy of axonal protection and cell body protection will have greater protective effects in early or progressive glaucomatous optic neuropathy (GON).

Modeling extracellular electrical stimulation: II. Computational validation and numerical results

The validity of approximate equations describing the membrane potential under extracellular electrical stimulation (Meffin et al 2012 J. Neural Eng. 9 065005) is investigated through finite element analysis in this paper. To this end, the finite element method is used to simulate a cylindrical neurite under extracellular stimulation. Laplace's equations with appropriate boundary conditions are solved numerically in three dimensions and the results are compared to the approximate analytic solutions. Simulation results are in agreement with the approximate analytic expressions for longitudinal and transverse modes of stimulation. The range of validity of the equations describing the membrane potential for different values of stimulation and neurite parameters are presented as well. The results indicate that the analytic approach can be used to model extracellular electrical stimulation for realistic physiological parameters with a high level of accuracy.