Growth-Driven Percolations: The Dynamics of Community Formation in Neuronal Systems

The quintessential property of neuronal systems is their intensive patterns of selective synaptic connections. The current work describes a physics-based approach to neuronal shape modeling and synthesis and its consideration for the simulation of neuronal development and the formation of neuronal communities. Starting from images of real neurons, geometrical measurements are obtained and used to construct probabilistic models which can be subsequently sampled in order to produce morphologically realistic neuronal cells. Such cells are progressively grown while monitoring their connections along time, which are analysed in terms of percolation concepts. However, unlike traditional percolation, the critical point is verified along the growth stages, not the density of cells, which remains constant throughout the neuronal growth dynamics. It is shown, through simulations, that growing beta cells tend to reach percolation sooner than the alpha counterparts with the same diameter. Also, the percolation becomes more abrupt for higher densities of cells, being markedly sharper for the beta cells.Comment: 8 pages, 10 figure

Graphene-Based Nanomaterials for Neuroengineering: Recent Advances and Future Prospective

Graphene unique physicochemical properties made it prominent among other allotropic forms of carbon, in many areas of research and technological applications. Interestingly, in recent years, many studies exploited the use of graphene family nanomaterials (GNMs) for biomedical applications such as drug delivery, diagnostics, bioimaging, and tissue engineering research. GNMs are successfully used for the design of scaffolds for controlled induction of cell differentiation and tissue regeneration. Critically, it is important to identify the more appropriate nano/bio material interface sustaining cells differentiation and tissue regeneration enhancement. Specifically, this review is focussed on graphene-based scaffolds that endow physiochemical and biological properties suitable for a specific tissue, the nervous system, that links tightly morphological and electrical properties. Different strategies are reviewed to exploit GNMs for neuronal engineering and regeneration, material toxicity, and biocompatibility. Specifically, the potentiality for neuronal stem cells differentiation and subsequent neuronal network growth as well as the impact of electrical stimulation through GNM on cells is presented. The use of field effect transistor (FET) based on graphene for neuronal regeneration is described. This review concludes the important aspects to be controlled to make graphene a promising candidate for further advanced application in neuronal tissue engineering and biomedical use

Fast Primal-Dual Gradient Method for Strongly Convex Minimization Problems with Linear Constraints

In this paper we consider a class of optimization problems with a strongly convex objective function and the feasible set given by an intersection of a simple convex set with a set given by a number of linear equality and inequality constraints. A number of optimization problems in applications can be stated in this form, examples being the entropy-linear programming, the ridge regression, the elastic net, the regularized optimal transport, etc. We extend the Fast Gradient Method applied to the dual problem in order to make it primal-dual so that it allows not only to solve the dual problem, but also to construct nearly optimal and nearly feasible solution of the primal problem. We also prove a theorem about the convergence rate for the proposed algorithm in terms of the objective function and the linear constraints infeasibility.Comment: Submitted for DOOR 201

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Mathematical modelling and numerical simulation of the morphological development of neurons

BACKGROUND: The morphological development of neurons is a very complex process involving both genetic and environmental components. Mathematical modelling and numerical simulation are valuable tools in helping us unravel particular aspects of how individual neurons grow their characteristic morphologies and eventually form appropriate networks with each other. METHODS: A variety of mathematical models that consider (1) neurite initiation (2) neurite elongation (3) axon pathfinding, and (4) neurite branching and dendritic shape formation are reviewed. The different mathematical techniques employed are also described. RESULTS: Some comparison of modelling results with experimental data is made. A critique of different modelling techniques is given, leading to a proposal for a unified modelling environment for models of neuronal development. CONCLUSION: A unified mathematical and numerical simulation framework should lead to an expansion of work on models of neuronal development, as has occurred with compartmental models of neuronal electrical activity

Innate Synchronous Oscillations in Freely-Organized Small Neuronal Circuits

BACKGROUND: Information processing in neuronal networks relies on the network's ability to generate temporal patterns of action potentials. Although the nature of neuronal network activity has been intensively investigated in the past several decades at the individual neuron level, the underlying principles of the collective network activity, such as the synchronization and coordination between neurons, are largely unknown. Here we focus on isolated neuronal clusters in culture and address the following simple, yet fundamental questions: What is the minimal number of cells needed to exhibit collective dynamics? What are the internal temporal characteristics of such dynamics and how do the temporal features of network activity alternate upon crossover from minimal networks to large networks? METHODOLOGY/PRINCIPAL FINDINGS: We used network engineering techniques to induce self-organization of cultured networks into neuronal clusters of different sizes. We found that small clusters made of as few as 40 cells already exhibit spontaneous collective events characterized by innate synchronous network oscillations in the range of 25 to 100 Hz. The oscillation frequency of each network appeared to be independent of cluster size. The duration and rate of the network events scale with cluster size but converge to that of large uniform networks. Finally, the investigation of two coupled clusters revealed clear activity propagation with master/slave asymmetry. CONCLUSIONS/SIGNIFICANCE: The nature of the activity patterns observed in small networks, namely the consistent emergence of similar activity across networks of different size and morphology, suggests that neuronal clusters self-regulate their activity to sustain network bursts with internal oscillatory features. We therefore suggest that clusters of as few as tens of cells can serve as a minimal but sufficient functional network, capable of sustaining oscillatory activity. Interestingly, the frequencies of these oscillations are similar those observed in vivo

Shaping Embodied Neural Networks for Adaptive Goal-directed Behavior

The acts of learning and memory are thought to emerge from the modifications of synaptic connections between neurons, as guided by sensory feedback during behavior. However, much is unknown about how such synaptic processes can sculpt and are sculpted by neuronal population dynamics and an interaction with the environment. Here, we embodied a simulated network, inspired by dissociated cortical neuronal cultures, with an artificial animal (an animat) through a sensory-motor loop consisting of structured stimuli, detailed activity metrics incorporating spatial information, and an adaptive training algorithm that takes advantage of spike timing dependent plasticity. By using our design, we demonstrated that the network was capable of learning associations between multiple sensory inputs and motor outputs, and the animat was able to adapt to a new sensory mapping to restore its goal behavior: move toward and stay within a user-defined area. We further showed that successful learning required proper selections of stimuli to encode sensory inputs and a variety of training stimuli with adaptive selection contingent on the animat's behavior. We also found that an individual network had the flexibility to achieve different multi-task goals, and the same goal behavior could be exhibited with different sets of network synaptic strengths. While lacking the characteristic layered structure of in vivo cortical tissue, the biologically inspired simulated networks could tune their activity in behaviorally relevant manners, demonstrating that leaky integrate-and-fire neural networks have an innate ability to process information. This closed-loop hybrid system is a useful tool to study the network properties intermediating synaptic plasticity and behavioral adaptation. The training algorithm provides a stepping stone towards designing future control systems, whether with artificial neural networks or biological animats themselves

Convergence among Non-Sister Dendritic Branches: An Activity-Controlled Mean to Strengthen Network Connectivity

The manner by which axons distribute synaptic connections along dendrites remains a fundamental unresolved issue in neuronal development and physiology. We found in vitro and in vivo indications that dendrites determine the density, location and strength of their synaptic inputs by controlling the distance of their branches from those of their neighbors. Such control occurs through collective branch convergence, a behavior promoted by AMPA and NMDA glutamate receptor activity. At hubs of convergence sites, the incidence of axo-dendritic contacts as well as clustering levels, pre- and post-synaptic protein content and secretion capacity of synaptic connections are higher than found elsewhere. This coupling between synaptic distribution and the pattern of dendritic overlapping results in ‘Economical Small World Network’, a network configuration that enables single axons to innervate multiple and remote dendrites using short wiring lengths. Thus, activity-mediated regulation of the proximity among dendritic branches serves to pattern and strengthen neuronal connectivity

Pogostick: A New Versatile piggyBac Vector for Inducible Gene Over-Expression and Down-Regulation in Emerging Model Systems

Non-traditional model systems need new tools that will enable them to enter the field of functional genetics. These tools should enable the exploration of gene function, via knock-downs of endogenous genes, as well as over-expression and ectopic expression of transgenes.We constructed a new vector called Pogostick that can be used to over-express or down-regulate genes in organisms amenable to germ line transformation by the piggyBac transposable element. Pogostick can be found at www.addgene.org, a non-profit plasmid repository. The vector currently uses the heat-shock promoter Hsp70 from Drosophila to drive transgene expression and, as such, will have immediate applicability to organisms that can correctly interpret this promotor sequence. We detail how to clone candidate genes into this vector and test its functionality in Drosophila by targeting a gene coding for the fluorescent protein DsRed. By cloning a single DsRed copy into the vector, and generating transgenic lines, we show that DsRed mRNA and protein levels are elevated following heat-shock. When cloning a second copy of DsRed in reverse orientation into a flanking site, and transforming flies constitutively expressing DsRed in the eyes, we show that endogenous mRNA and protein levels drop following heat-shock. We then test the over-expression vector, containing the complete cDNA of Ultrabithorax (Ubx) gene, in an emerging model system, Bicyclus anynana. We produce a transgenic line and show that levels of Ubx mRNA expression rise significantly following a heat-shock. Finally, we show how to obtain genomic sequence adjacent to the Pogostick insertion site and to estimate transgene copy number in genomes of transformed individuals.This new vector will allow emerging model systems to enter the field of functional genetics with few hurdles