Self-wiring in neural nets of point-like cortical neurons fails to reproduce cytoarchitectural differences

We propose a model for description of activity-dependent evolution and self-wiring between binary neurons. Specifically, this model can be used for investigation of growth of neuronal connectivity in the developing neocortex. By using computational simulations with appropriate training pattern sequences, we show that long-term memory can be encoded in neuronal connectivity and that the external stimulations form part of the functioning neocortical circuit. It is proposed that such binary neuron representations of point-like cortical neurons fail to reproduce cytoarchitectural differences of the neocortical organization, which has implications for inadequacies of compartmental models.Comment: 13 pages, 5 figure

Modeling of interstitial branching of axonal networks

A single axon can generate branches connecting with plenty synaptic targets. Process of branching is very important for making connections in central nervous system. The interstitial branching along primary axon shaft occurs during nervous system development. Growing axon makes pause in its movement and leaves active points behind its terminal. The new branches appear from these points. We suggest mathematical model to describe and investigate neural network branching process. The model under consideration describes neural network growth in which the concentration of axon guidance molecules manages axon's growth. We model the interstitial branching from axon shaft. Numerical simulations show that in the model framework axonal networks are similar to neural network.Comment: 12 pages, 7 figure

The simulation of the activity dependent neural network growth

It is currently accepted that cortical maps are dynamic constructions that are altered in response to external input. Experience-dependent structural changes in cortical microcurcuts lead to changes of activity, i.e. to changes in information encoded. Specific patterns of external stimulation can lead to creation of new synaptic connections between neurons. The calcium influxes controlled by neuronal activity regulate the processes of neurotrophic factors released by neurons, growth cones movement and synapse differentiation in developing neural systems. We propose a model for description and investigation of the activity dependent development of neural networks. The dynamics of the network parameters (activity, diffusion of axon guidance chemicals, growth cone position) is described by a closed set of differential equations. The model presented here describes the development of neural networks under the assumption of activity dependent axon guidance molecules. Numerical simulation shows that morpholess neurons compromise the development of cortical connectivity.Comment: 10 pages, 2 figure

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

Effects of Random External Background Stimulation on Network Synaptic Stability After Tetanization: A Modeling Study

We constructed a simulated spiking neural network model to investigate the effects of random background stimulation on the dynamics of network activity patterns and tetanus induced network plasticity. The simulated model was a “leaky integrate-and-fire” (LIF) neural model with spike-timing-dependent plasticity (STDP) and frequency-dependent synaptic depression. Spontaneous and evoked activity patterns were compared with those of living neuronal networks cultured on multielectrode arrays. To help visualize activity patterns and plasticity in our simulated model, we introduced new population measures called Center of Activity (CA) and Center of Weights (CW) to describe the spatio-temporal dynamics of network-wide firing activity and network-wide synaptic strength, respectively. Without random background stimulation, the network synaptic weights were unstable and often drifted after tetanization. In contrast, with random background stimulation, the network synaptic weights remained close to their values immediately after tetanization. The simulation suggests that the effects of tetanization on network synaptic weights were difficult to control because of ongoing synchronized spontaneous bursts of action potentials, or “barrages.” Random background stimulation helped maintain network synaptic stability after tetanization by reducing the number and thus the influence of spontaneous barrages. We used our simulated network to model the interaction between ongoing neural activity, external stimulation and plasticity, and to guide our choice of sensory-motor mappings for adaptive behavior in hybrid neural-robotic systems or “hybrots.

In silico framework to inform the design of repair constructs for peripheral nerve injury repair

Peripheral nerve injuries affect millions of people per year and cause loss of sensation and muscle control alongside chronic pain. The most severe injuries are treated through a nerve autograft; however, donor site morbidity and poor outcomes mean alternatives are required. One option is to engineer nerve replacement tissues to provide a supportive microenvironment to encourage nerve regeneration as an alternative to nerve grafts. Currently, progress is hampered due to a lack of consensus on how to arrange materials and cells in space to maximize rate of regeneration. This is compounded by a reliance on experimental testing, which precludes extensive investigations of multiple parameters due to time and cost limitations. Here, a computational framework is proposed to simulate the growth of repairing neurites, captured using a random walk approach and parameterized against literature data. The framework is applied to a specific scenario where the engineered tissue comprises a collagen hydrogel with embedded biomaterial fibres. The size and number of fibres are optimized to maximize neurite regrowth, and the robustness of model predictions is tested through sensitivity analyses. The approach provides an in silico tool to inform the design of engineered replacement tissues, with the opportunity for further development to multi-cue environments

Spatial Control of Mechanical Factors: a New Design Rationale for Nerve Tissue Engineering

Peripheral nerve injuries (PNI) result from traumatic injury, surgery or repetitive compression, and are reported in 3-5% of all trauma patients. The impact ranges from severe (major loss of sensory/motor function and/or intractable neuropathic pain) to mild (some sensory and/or motor deficits) and in both cases, is devastating for the patient. PNI affect ∼1M people in Europe and the US p.a. of whom 660,000 have surgery. PNI has high healthcare, unemployment, rehabilitation, societal costs and affects mostly young people. The current surgical practice for nerve gaps >3 cm is to bridge the site of injury with a graft taken from the patient. However, this involves additional time, cost and damage to a healthy nerve, limited supply, and unsatisfactory functional recovery (50% of the cases). For these reasons, research has focused on developing artificial nerve conduits to replace grafts, but to-date those available for clinical use do not match and/or exceed the functional performance of the autograft. This project develops a rational basis for promoting neurite growth through tissue-engineered conduits for peripheral nerve repair, by exploiting the response of cells to spatial variations in mechanical properties of conduits to inform their design. This is achieved through an interdisciplinary approach, that combines in vitro experimentation with mathematical modelling. First of all, the mechanical and structural properties of RAFTStabilised collagen gels (RsC) are explored, physiologically coherent RsC stiffness gradients are fabricated and characterised as well as the neuronal response to them. Finally, a predictive framework to inform the design of nerve conduits is parameterised and tested using experimental results and literature. The use of this multidisciplinary approach can help tissue engineers in the development of novel tissue repair solutions, as well as informing mathematical models of neurite behaviour which can contribute to the design process

Modelling Structure and Dynamics of Complex Systems: Applications to Neuronal Networks

Complex systems theory is a mathematical framework for studying interconnected dynamical objects. Usually these objects themselves are by construction simple, and their temporal behavior in isolation is easily predictable, but the way they are interconnected into a network allows emergence of complex, non-obvious phenomena. The emergent phenomena and their stability are dependent on both the intrinsic dynamics of the objects, the types of interactions between the objects, and the connectivity patterns between the objects. This work focuses on the third aspect, i.e., the structure of the network, although the other two aspects are inherently present in the study as well. Tools from graph theory are applied to generate and analyze the network structure, and the effect of the structure on the network dynamics is analyzed by various methods. The objects of interest are biological and physical systems, and special attention is given to spiking neuronal networks, i.e., networks of nerve cells that communicate by transmitting and receiving action potentials. In this thesis, methods for modelling spiking neuronal networks are introduced. Different point neuron models, including the integrate-and-fire model, are presented and applied to study the collective behaviour of the neurons. Special focus is placed on the emergence of network bursts, i.e., short periods of network-wide high-frequency firing. The occurrence of this behaviour is stable in certain regimes of connection strengths. This work shows that the network bursting is found to be more frequent in locally connected networks than in non-local networks, such as randomly connected networks. To gain a deeper insight, the aspects of structure that promote the bursting behaviour are analyzed by graph-theoretic means. The clustering coefficient and the maximal eigenvalue of the connectivity matrix are found the most important measures of structure in this matter, both expressing their relevance under different structural conditions. A range of different network structures are applied to confirm this result. A special class of connectivity is studied in more detail, namely, the connectivity patterns produced by simulations of growing and interconnecting neurons placed on a 2-dimensional array. Two simulators of growth are applied for this purpose. In addition, a more abstract class of dynamical systems, the Boolean networks, are considered. These systems were originally introduced as a model for genetic regulatory networks, but have thereafter been extensively used for more general studies of complex systems. In this work, measures of information diversity and complexity are applied to several types of systems that obey Boolean dynamics. The random Boolean networks are shown to possess high temporal complexity prior to reaching an attractor. Similarly, high values of complexity are found at a transition stage of another dynamical system, the lattice gas automaton, which can be formulated using the Boolean network framework as well. The temporal maximization of the complexity near the transitions between different dynamical regimes could therefore be a more general phenomenon in complex networks. The applicability of the information-theoretic framework is also confirmed in a study of bursting neuronal networks, where different types of networks are shown to be separable by the intrinsic information distance distributions they produce. The connectivities of the networks studied in this thesis are analyzed using graph-theoretic tools. The graph theory provides a mathematical framework for studying the structure of complex systems and how it affects the system dynamics. In the studies of the nervous system, detailed maps on the connections between neurons have been collected, although such data are yet scarce and laborious to obtain experimentally. This work shows which aspects of the structure are relevant for the dynamics of spontaneously bursting neuronal networks. Such information could be useful in directing the experiments to measure only the relevant aspects of the structure instead of assessing the whole connectome. In addition, the framework of generating the network structure by animating the growth of the neurons, as presented in this thesis, could serve in simulations of the nervous system as a reliable alternative to importing the experimentally obtained connectome