Article thumbnail

How Structure Determines Correlations in Neuronal Networks

By Volker Pernice, Benjamin Staude, Stefano Cardanobile and Stefan Rotter

Abstract

Networks are becoming a ubiquitous metaphor for the understanding of complex biological systems, spanning the range between molecular signalling pathways, neural networks in the brain, and interacting species in a food web. In many models, we face an intricate interplay between the topology of the network and the dynamics of the system, which is generally very hard to disentangle. A dynamical feature that has been subject of intense research in various fields are correlations between the noisy activity of nodes in a network. We consider a class of systems, where discrete signals are sent along the links of the network. Such systems are of particular relevance in neuroscience, because they provide models for networks of neurons that use action potentials for communication. We study correlations in dynamic networks with arbitrary topology, assuming linear pulse coupling. With our novel approach, we are able to understand in detail how specific structural motifs affect pairwise correlations. Based on a power series decomposition of the covariance matrix, we describe the conditions under which very indirect interactions will have a pronounced effect on correlations and population dynamics. In random networks, we find that indirect interactions may lead to a broad distribution of activation levels with low average but highly variable correlations. This phenomenon is even more pronounced in networks with distance dependent connectivity. In contrast, networks with highly connected hubs or patchy connections often exhibit strong average correlations. Our results are particularly relevant in view of new experimental techniques that enable the parallel recording of spiking activity from a large number of neurons, an appropriate interpretation of which is hampered by the currently limited understanding of structure-dynamics relations in complex networks

Topics: Research Article
Publisher: Public Library of Science
OAI identifier: oai:pubmedcentral.nih.gov:3098224
Provided by: PubMed Central

To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.

Suggested articles

Citations

  1. (2008). 3D structural imaging of the brain with photons and electrons.
  2. (2009). A kinetic theory approach to capturing interneuronal correlation: the feed-forward case.
  3. (2000). A quantitative analysis of the local connectivity between pyramidal neurons in layers 2/3 of the rat visual cortex.
  4. (2006). Auto- and Crosscorrelograms for the Spike Response of Leaky Integrate-and-Fire Neurons with Slow Synapses.
  5. (2005). Breathers in two-dimensional neural media.
  6. (2010). Cellular imaging of visual cortex reveals the spatial and functional organization of spontaneous activity.
  7. (1996). Chaos in neuronal networks with balanced excitatory and inhibitory activity.
  8. (2009). Complex brain networks: graph theoretical analysis of structural and functional systems.
  9. (2010). Complex network measures of brain connectivity: Uses and interpretations.
  10. (2008). Correlation and synchrony transfer in integrate-and-fire neurons: basic properties and consequences for coding.
  11. (2010). Correlation-based analysis and generation of multiple spike trains using Hawkes models with an exogenous input.
  12. (2008). Correlations and population dynamics in cortical networks.
  13. (2010). Correlations and synchrony in threshold neuron models. Phys Rev Lett 104:
  14. (2009). Correlations in spiking neuronal networks with distance dependent connections.
  15. (1999). Correlations without synchrony.
  16. (2010). Cross-correlations in high-conductance states of a model cortical network.
  17. (2010). Decorrelated neuronal firing in cortical microcircuits.
  18. (2010). Decorrelation of lowfrequency neural activity by inhibitory feedback.
  19. (2009). Disentangling the web of life.
  20. (2000). Dynamics of sparsely connected networks of excitatory and inhibitory spiking neurons.
  21. (2006). Eigenvalue spectra of random matrices for neural networks.
  22. (2009). Emergence of network structure due to spike-timing-dependent plasticity in recurrent neuronal networks IV.
  23. (2005). Excitatory cortical neurons form fine-scale functional networks.
  24. (2005). Fine-scale specificity of cortical networks depends on inhibitory cell type and connectivity.
  25. (2011). Fre ´gnac Y
  26. (2006). Graph-based methods for analysing networks in cell biology.
  27. (1999). Hebbian learning and spiking neurons.
  28. (2010). Higher-order correlations and cumulants.
  29. (2003). Higher-order statistics of input ensembles and the response of simple model neurons.
  30. (2009). How connectivity, background activity, and synaptic properties shape the cross-correlation between spike trains.
  31. (1997). Identification of synaptic connections in neural ensembles by graphical models.
  32. (2008). Ko ¨rding KP
  33. (2008). Kohn A
  34. (2007). Living with noisy genes: how cells function reliably with inherent variability in gene expression.
  35. (2008). Longtin A
  36. (2011). Network anatomy and in vivo physiology of visual cortical neurons.
  37. (2005). Neurogeometry and potential synaptic connectivity.
  38. (2010). Neurons hear their echo.
  39. (2009). Noise management by molecular networks.
  40. (2008). Noise propagation and signaling sensitivity in biological networks: a role for positive feedback.
  41. (2008). On how network architecture determines the dominant patterns of spontaneous neural activity.
  42. (2009). Origins of correlated activity in an olfactory circuit.
  43. (2010). Parallel processing of visual space by neighboring neurons in mouse visual cortex.
  44. (2008). Pinpointing connectivity despite hidden nodes within stimulus-driven networks.
  45. (1971). Point spectra of some mutually exciting point processes.
  46. (2010). Pooling and correlated neural activity.
  47. (2006). Pouget A
  48. (2007). Reyes A
  49. (2005). Role of delays in shaping spatiotemporal dynamics of neuronal activity in large networks.
  50. (2010). Sensitivity to perturbations in vivo implies high noise and suggests rate coding in cortex.
  51. (2010). Sparse coding and high-order correlations in fine-scale cortical networks.
  52. (1971). Spectra of some self-exciting and mutually exciting point processes.
  53. (2010). Structural motifs and correlation dynamics in networks of spiking neurons.
  54. (2002). Synaptic connections and small circuits involving excitatory and inhibitory neurons in layers 2-5 of adult rat and cat neocortex: triple intracellular recordings and biocytin labelling in vitro.
  55. (2001). Synaptic modi_cation by correlated activity: Hebb’s postulate revisited.
  56. (2010). The asynchronous state in cortical circuits.
  57. (1993). The highly irregular firing of cortical cells is inconsistent with temporal integration of random EPSPs.
  58. (2008). The statistics of repeating patterns of cortical activity can be reproduced by a model network of stochastic binary neurons.
  59. (1998). The variable discharge of cortical neurons: implications for connectivity, computation, and information coding.
  60. (2008). Theory of input spike auto-and crosscorrelations and their effect on the response of spiking neurons.
  61. (2005). van Oudenaarden A
  62. (2005). Waves, bumps, and patterns in neural field theories.