Complexity in Neuronal Networks (original) (raw)
Related papers
Destexhe A. Complexity in Neuronal Networks
2016
The brain can be thought of as a collective ensemble ranging in the spatial domain from microscopic elements (molecules, receptors, ionic channels, synapses) to macroscopic entities (layers, nuclei, cortical areas, neural networks) (Figure 1). The same multi-scale analysis can be replicated in the temporal domain, when decomposing brain activity in a multitude of dynamic
Proceedings of The National Academy of Sciences, 1994
In brains ofhigher vertebrates, the functional segregation of local areas that differ in their anatomy and physiology contrasts sharply with their global ination during perception and behavior. In this paper, we introduce a measure, called neural complexity (CN), that captures the interplay between these two dental aspects of brain organization. We express functional segregation within a neural system in terms of the relative statistical independence of small subsets of the system and functional integration in terms of signicant deviations from independence of large subsets. CN is then obtained from estimates of the average deviation from statistical independence for subsets of increasing size. CN is shown to be high when functional segregation coexists with integration and to be low when the components of a system are either completely independent (segregated) or completely dependent (integrated). We apply this complexity measure in computer simulations of cortical areas to examine how some basic principles of neuroanatomical organization constrain brain dynamics. We show that the connectivity patterns of the cerebral cortex, such as a high density of connections, strong local connectivity ornizing cells into neuronal groups, patchiness in the connectivity am neuronal groups, and prevalent reciprocal connections, are associated with hi values of CN. The approach outlined here may prove useful in analyzing complexity in other biological domains such as gene regulation and embryogenesis.
Neural engineering: Unraveling the complexities of neural systems
IEEE Canadian Review, 2003
L'incroyable, souvent subtile complexité des systèmes neuronaux semble être le cauchemar de l'ingénieur. Mais quand on examine ces systèmes soigneusement, ils peuvent devenir le rêve de l'ingénieur -un moyen pour étudier des systèmes robustes et complexes. En utilisant des techniques de la théorie de l'information, théorie du contrôle, et l'analyse des signaux et systèmes, il est possible de formuler un cadre pour construire de grandes et biologiquement plausibles simulations de systèmes neuronaux. Ces simulations nous aident à apprendre comment fonctionnent les systèmes neuronaux sous-jacent et comment obtenir de bonnes solutions aux complexes problèmes faisant face à ces systèmes.
Geometric and functional organization of cortical circuits
Nature neuroscience, 2005
Can neuronal morphology predict functional synaptic circuits? In the rat barrel cortex, 'barrels' and 'septa' delineate an orderly matrix of cortical columns. Using quantitative laser scanning photostimulation we measured the strength of excitatory projections from layer 4 (L4) and L5A to L2/3 pyramidal cells in barrel- and septum-related columns. From morphological reconstructions of excitatory neurons we computed the geometric circuit predicted by axodendritic overlap. Within most individual projections, functional inputs were predicted by geometry and a single scale factor, the synaptic strength per potential synapse. This factor, however, varied between projections and, in one case, even within a projection, up to 20-fold. Relationships between geometric overlap and synaptic strength thus depend on the laminar and columnar locations of both the pre- and postsynaptic neurons, even for neurons of the same type. A large plasticity potential appears to be incorporate...
Connectivity and complexity: the relationship between neuroanatomy and brain dynamics
Neural Networks, 2000
Nervous systems facing complex environments have to balance two seemingly opposing requirements. First, there is a need quickly and reliably to extract important features from sensory inputs. This is accomplished by functionally segregated (specialized) sets of neurons, e.g. those found in different cortical areas. Second, there is a need to generate coherent perceptual and cognitive states allowing an organism to respond to objects and events, which represent conjunctions of numerous individual features. This need is accomplished by functional integration of the activity of specialized neurons through their dynamic interactions. These interactions produce patterns of temporal correlations or functional connectivity involving distributed neuronal populations, both within and across cortical areas. Empirical and computational studies suggest that changes in functional connectivity may underlie specific perceptual and cognitive states and involve the integration of information across specialized areas of the brain. The interplay between functional segregation and integration can be quantitatively captured using concepts from statistical information theory, in particular by defining a measure of neural complexity. Complexity measures the extent to which a pattern of functional connectivity produced by units or areas within a neural system combines the dual requirements of functional segregation and integration. We find that specific neuroanatomical motifs are uniquely associated with high levels of complexity and that such motifs are embedded in the pattern of long-range cortico-cortical pathways linking segregated areas of the mammalian cerebral cortex. Our theoretical findings offer new insight into the intricate relationship between connectivity and complexity in the nervous system. ᭧
Complexities and uncertainties of neuronal network function
The nervous system generates behaviours through the activity in groups of neurons assembled into networks. Understanding these networks is thus essential to our understanding of nervous system function. Understanding a network requires information on its component cells, their interactions and their functional properties. Few networks come close to providing complete information on these aspects. However, even if complete information were available it would still only provide limited insight into network function. This is because the functional and structural properties of a network are not fixed but are plastic and can change over time. The number of interacting network components, their (variable) functional properties, and various plasticity mechanisms endows networks with considerable flexibility, but these features inevitably complicate network analyses. This review will initially discuss the general approaches and problems of network analyses. It will then examine the success of these analyses in a model spinal cord locomotor network in the lamprey, to determine to what extent in this relatively simple vertebrate system it is possible to claim detailed understanding of network function and plasticity.
Brain Complexity: Analysis, Models and Limits of Understanding.
Manifold initiatives try to utilize the operational principles of organisms and brains to develop alternative, biologically inspired computing paradigms. This paper reviews key features of the standard method applied to complexity in the cognitive and brain sciences, i.e. decompositional analysis. Projects investigating the nature of computations by cortical columns are discussed which exemplify the application of this standard method. New findings are mentioned indicating that the concept of the basic uniformity of the cortex is untenable. The claim is discussed that non-decomposability is not an intrinsic property of complex, integrated systems but is only in our eyes, due to insufficient mathematical techniques. Using Rosen’s modeling relation, the scientific analysis method itself is made a subject of discussion. It is concluded that the fundamental assumption of cognitive science, i.e., cognitive and other complex systems are decomposable, must be abandoned.
Computational Neuroscience of Neuronal Networks
Neuroscience in the 21st Century, 2013
Through multiscale modeling, computer simulation typically utilizes multiple simplifications, each providing a different view. The various models then provide complementary insights into a system that is too large, and too complex, to grasp directly. Each simplification will match, albeit always imperfectly, some important aspect of the system under study. In the story of the blind men and the elephant, each blind man takes hold of a different part of the elephant's anatomy. Each, from his own limited observation, declares the elephant to be something quite different: long and tufted (tail), long and muscular (trunk), flat and broad (ear), thick like a tree (leg), etc. Each of these models of the elephant is accurate but limited. Taking these models together, adding in additional information as to the location of each blind man, one could begin to build a preliminary idea of the elephant as a whole. While multiscale modeling emphasizes the use of different models at different scales, multiple views are also often useful at a single scale. The multiple scales of multiscale may be spatial (microns to millimeters to centimeters to meters) or temporal (milliseconds to seconds to minutes up to years). Whether multiscale or not, a major challenge in modeling is the same as it is in the elephant story: make the connections between models so as to build a coherent
Functional structure of cortical neuronal networks grown in vitro
Physical Review E, 2007
We apply an information theoretic treatment of action potential time series measured with microelectrode arrays to estimate the connectivity of mammalian neuronal cell assemblies grown in vitro. We infer connectivity between two neurons via the measurement of the mutual information between their spike trains. In addition we measure higher point multi-informations between any two spike trains conditional on the activity of a third cell, as a means to identify and distinguish classes of functional connectivity among three neurons. The use of a conditional three-cell measure removes some interpretational shortcomings of the pairwise mutual information and sheds light into the functional connectivity arrangements of any three cells. We analyze the resultant connectivity graphs in light of other complex networks and demonstrate that, despite their ex vivo development, the connectivity maps derived from cultured neural assemblies are similar to other biological networks and display nontrivial structure in clustering coefficient, network diameter and assortative mixing. Specifically we show that these networks are weakly disassortative small world graphs, which differ significantly in their structure from randomized graphs with the same degree. We expect our analysis to be useful in identifying the computational motifs of a wide variety of complex networks, derived from time series data.