Markus Butz’s research while affiliated with Bernstein Center for Computational Neuroscience Berlin and other places

Supercomputing facilities are becoming increasingly available for simulating activity dynamics in large-scale neuronal networks. On today's most advanced supercomputers, networks with up to a billion of neurons can be readily simulated. However, building biologically realistic, full-scale brain models requires more than just a huge number of neurons. In addition to network size, the detailed local and global anatomy of neuronal connections is of crucial importance. Moreover, anatomical connectivity is not fixed, but can rewire throughout life (structural plasticity)—an aspect that is missing in most current network models, in which plasticity is confined to changes in synaptic strength (synaptic plasticity). The papers in this Ebook, which may broadly be divided into three themes, aim to bring together high-performance computing with recent experimental and computational research in neuroanatomy. In the first theme (fiber connectivity), new methods are described for measuring and data-basing microscopic and macroscopic connectivity. In the second theme (structural plasticity), novel models are introduced that incorporate morphological plasticity and rewiring of anatomical connections. In the third theme (large-scale simulations), simulations of large-scale neuronal networks are presented with an emphasis on anatomical detail and plasticity mechanisms. Together, the articles in this Ebook make the reader aware of the methods and models by which large-scale brain networks running on supercomputers can be extended to include anatomical detail and plasticity. Download the book from: http://www.frontiersin.org/books/Anatomy_and_Plasticity_in_Large-Scale_Brain_Models/1082

Supercomputing facilities are becoming increasingly available for simulating electrical activity in large-scale neuronal networks. On today's most advanced supercomputers, networks with up to a billion of neurons can be readily simulated. However, building biologically realistic, full-scale brain models requires more than just a huge number of neurons. In addition to network size, the detailed local and global anatomy of neuronal connections is of crucial importance. Moreover, anatomical connectivity is not fixed, but can rewire throughout life (structural plasticity)—an aspect that is missing in most current network models, in which plasticity is confined to changes in synaptic strength (synaptic plasticity). The papers in this research topic, which may broadly be divided into three themes, aim to bring together high-performance computing with recent experimental and computational research in neuroanatomy. In the first theme (fiber connectivity), new methods are described for measuring and data-basing microscopic and macroscopic connectivity. In the second theme (structural plasticity), novel models are introduced that incorporate morphological plasticity and rewiring of anatomical connections. In the third theme (large-scale simulations), simulations of large-scale neuronal networks are presented with an emphasis on anatomical detail and plasticity mechanisms. Together, the papers in this research topic contribute to extending high-performance computing in neuroscience to encompass anatomical detail and plasticity.

After brain lesions caused by tumors or stroke, or after lasting loss of input (deafferentation), inter- and intra-regional brain networks respond with complex changes in topology. Not only areas directly affected by the lesion but also regions remote from the lesion may alter their connectivity—a phenomenon known as diaschisis. Changes in network topology after brain lesions can lead to cognitive decline and increasing functional disability. However, the principles governing changes in network topology are poorly understood. Here, we investigated whether homeostatic structural plasticity can account for changes in network topology after deafferentation and brain lesions. Homeostatic structural plasticity postulates that neurons aim to maintain a desired level of electrical activity by deleting synapses when neuronal activity is too high and by providing new synaptic contacts when activity is too low. Using our Model of Structural Plasticity, we explored how local changes in connectivity induced by a focal loss of input affected global network topology. In accordance with experimental and clinical data, we found that after partial deafferentation, the network as a whole became more random, although it maintained its small-world topology, while deafferentated neurons increased their betweenness centrality as they rewired and returned to the homeostatic range of activity. Furthermore, deafferentated neurons increased their global but decreased their local efficiency and got longer tailed degree distributions, indicating the emergence of hub neurons. Together, our results suggest that homeostatic structural plasticity may be an important driving force for lesion-induced network reorganization and that the increase in betweenness centrality of deafferentated areas may hold as a biomarker for brain repair.

In networks with small-world topology, which are characterized by a high clustering coefficient and a short characteristic path length, information can be transmitted efficiently and at relatively low costs. The brain is composed of small-world networks, and evolution may have optimized brain connectivity for efficient information processing. Despite many studies on the impact of topology on information processing in neuronal networks, little is known about the development of network topology and the emergence of efficient small-world networks. We investigated how a simple growth process that favors short-range connections over long-range connections in combination with a synapse formation rule that generates homeostasis in post-synaptic firing rates shapes neuronal network topology. Interestingly, we found that small-world networks benefited from homeostasis by an increase in efficiency, defined as the averaged inverse of the shortest paths through the network. Efficiency particularly increased as small-world networks approached the desired level of electrical activity. Ultimately, homeostatic small-world networks became almost as efficient as random networks. The increase in efficiency was caused by the emergent property of the homeostatic growth process that neurons started forming more long-range connections, albeit at a low rate, when their electrical activity was close to the homeostatic set-point. Although global network topology continued to change when neuronal activities were around the homeostatic equilibrium, the small-world property of the network was maintained over the entire course of development. Our results may help understand how complex systems such as the brain could set up an efficient network topology in a self-organizing manner. Insights from our work may also lead to novel techniques for constructing large-scale neuronal networks by self-organization.

Lasting alterations in sensory input trigger massive structural and functional adaptations in cortical networks. The principles governing these experience-dependent changes are, however, poorly understood. Here, we examine whether a simple rule based on the neurons' need for homeostasis in electrical activity may serve as driving force for cortical reorganization. According to this rule, a neuron creates new spines and boutons when its level of electrical activity is below a homeostatic set-point and decreases the number of spines and boutons when its activity exceeds this set-point. In addition, neurons need a minimum level of activity to form spines and boutons. Spine and bouton formation depends solely on the neuron's own activity level, and synapses are formed by merging spines and boutons independently of activity. Using a novel computational model, we show that this simple growth rule produces neuron and network changes as observed in the visual cortex after focal retinal lesions. In the model, as in the cortex, the turnover of dendritic spines was increased strongest in the center of the lesion projection zone, while axonal boutons displayed a marked overshoot followed by pruning. Moreover, the decrease in external input was compensated for by the formation of new horizontal connections, which caused a retinotopic remapping. Homeostatic regulation may provide a unifying framework for understanding cortical reorganization, including network repair in degenerative diseases or following focal stroke.

Small-world networks display enhanced signal-propagation speed, computational power, and synchronizability. Neuronal networks in the brain share properties of small-world networks and, in addition, dynamically rewire their connectivity by forming and deleting synapses. It is unclear whether small world networks are best in repairing damages caused by loss of connections and input. Neuronal networks show a reciprocal interaction between topology and the flow of neuronal (electrical) activity they generate. Topology determines the activity flow through the network, whereas on a longer timescale, the flow of activity guides new connections to be formed or existing ones to be removed. Importantly, neurons thereby try to maintain their electrical activity at a certain setpoint (homeostasis of electrical activity). That is, if neurons loose synaptic input due to a lesion, they respond with a local change in connectivity to obtain more connections and activity from other sources. Here we investigate by a computational modelling study based on a model for activity-dependent structural plasticity [1,2], first, how local changes in synaptic connectivity alter global network topology after a circumscribed loss of input; and second, which topologies best support network repair re-establishing homeostasis in electrictal activity of all neurons. We found that reorganizing networks become more random as they form more long-range connections after a loss of input and those neurons losing their input increase their betweenness centrality. Interestingly, an increased randomness and betweenness centrality has recently been found in functional connectivity of ipsilateral cortical and contralateral cerebellar networks following subcortical stroke [3]. As a second important result we found that small-world networks recover fastest (Fig. (Fig.1),1), compared to regular and random networks, from a loss of input in the sense that all neurons return to homeostasis in electrical activity. The small-worldness of brain networks may therefore have an evolutionary advantage since those networks are more robust against lesions than regular (and random) networks. Figure 1 Number of connectivity updates required to completely repair the network as dependent on a small-world parameter γ of the network. Small-world networks go fastest back into homeostasis.

Recently evidence has accumulated that many neural networks exhibit self-organized criticality. In this state, activity is similar across temporal scales and this is beneficial with respect to information flow. If subcritical, activity can die out, if supercritical epileptiform patterns may occur. Little is known about how developing networks will reach and stabilize criticality. Here we monitor the development between 13 and 95 days in vitro (DIV) of cortical cell cultures (n = 20) and find four different phases, related to their morphological maturation: An initial low-activity state (≈19 DIV) is followed by a supercritical (≈20 DIV) and then a subcritical one (≈36 DIV) until the network finally reaches stable criticality (≈58 DIV). Using network modeling and mathematical analysis we describe the dynamics of the emergent connectivity in such developing systems. Based on physiological observations, the synaptic development in the model is determined by the drive of the neurons to adjust their connectivity for reaching on average firing rate homeostasis. We predict a specific time course for the maturation of inhibition, with strong onset and delayed pruning, and that total synaptic connectivity should be strongly linked to the relative levels of excitation and inhibition. These results demonstrate that the interplay between activity and connectivity guides developing networks into criticality suggesting that this may be a generic and stable state of many networks in vivo and in vitro.

Derivation of the nullcline of the model. (0.03 MB PDF)