Structural and functional properties of a probabilistic model of neuronal connectivity in a simple locomotor network

Although, in most animals, brain connectivity varies between individuals, behaviour is often similar across a species. What fundamental structural properties are shared across individual networks that define this behaviour? We describe a probabilistic model of connectivity in the hatchling Xenopus tadpole spinal cord which, when combined with a spiking model, reliably produces rhythmic activity corresponding to swimming. The probabilistic model allows calculation of structural characteristics that reflect common network properties, independent of individual network realisations. We use the structural characteristics to study examples of neuronal dynamics, in the complete network and various sub-networks, and this allows us to explain the basis for key experimental findings, and make predictions for experiments. We also study how structural and functional features differ between detailed anatomical connectomes and those generated by our new, simpler, model (meta-model).

[1]  David J. Willshaw,et al.  Modelling the Effects of Electrical Coupling between Unmyelinated Axons of Brainstem Neurons Controlling Rhythmic Activity , 2015, PLoS Comput. Biol..

[2]  A. Roberts,et al.  Axon and dendrite geography predict the specificity of synaptic connections in a functioning spinal cord network , 2007, Neural Development.

[3]  Rodney J. Douglas,et al.  Frontiers in Computational Neuroscience , 2022 .

[4]  Marcus Kaiser,et al.  Newcastle University E-prints Citation for Item: Publisher's Copyright Statement: Neural Development Features: Spatio-temporal Development of the Caenorhabditis Elegans Neuronal Network , 2022 .

[5]  Alan Roberts,et al.  Locomotor rhythm maintenance: electrical coupling among premotor excitatory interneurons in the brainstem and spinal cord of young Xenopus tadpoles , 2009, The Journal of physiology.

[6]  Roman Borisyuk,et al.  A Developmental Approach to Predicting Neuronal Connectivity from Small Biological Datasets: A Gradient-Based Neuron Growth Model , 2014, PloS one.

[7]  Albert,et al.  Emergence of scaling in random networks , 1999, Science.

[8]  Mark E. J. Newman,et al.  Power-Law Distributions in Empirical Data , 2007, SIAM Rev..

[9]  R. Douglas,et al.  A Quantitative Map of the Circuit of Cat Primary Visual Cortex , 2004, The Journal of Neuroscience.

[10]  A. Roberts,et al.  How Neurons Generate Behavior in A Hatchling Amphibian Tadpole: An Outline , 2010, Front. Behav. Neurosci..

[11]  David J. Willshaw,et al.  Explorer Modelling Feedback Excitation , Pacemaker Properties and Sensory Switching of Electrically Coupled Brainstem Neurons Controlling Rhythmic Activity , 2016 .

[12]  Emma K. Towlson,et al.  The Rich Club of the C. elegans Neuronal Connectome , 2013, The Journal of Neuroscience.

[13]  Roman Borisyuk,et al.  Modeling the Connectome of a Simple Spinal Cord , 2011, Front. Neuroinform..

[14]  A. Roberts,et al.  Reconfiguration of a Vertebrate Motor Network: Specific Neuron Recruitment and Context-Dependent Synaptic Plasticity , 2007, The Journal of Neuroscience.

[15]  Srinivas C. Turaga,et al.  Space-time wiring specificity supports direction selectivity in the retina , 2014, Nature.

[16]  Olaf Sporns,et al.  The small world of the cerebral cortex , 2007, Neuroinformatics.

[17]  Alan Roberts,et al.  Primitive Roles for Inhibitory Interneurons in Developing Frog Spinal Cord , 2004, The Journal of Neuroscience.

[18]  A. Roberts,et al.  Sensory initiation of a co‐ordinated motor response: synaptic excitation underlying simple decision‐making , 2015, The Journal of physiology.

[19]  Andrew R. McKinstry-Wu,et al.  Connectome: How the Brain’s Wiring Makes Us Who We Are , 2013 .

[20]  Olaf Sporns,et al.  The Human Connectome: A Structural Description of the Human Brain , 2005, PLoS Comput. Biol..

[21]  D. A. Sprott.  The Method of Maximum Likelihood Applied to the Poisson Binomal Distribution , 1958 .

[22]  Michael L. Hines,et al.  The NEURON Book , 2006 .

[23]  Joshua M. Peterson,et al.  Graph Theoretical Model of a Sensorimotor Connectome in Zebrafish , 2012, PloS one.

[24]  Robert Merrison-Hort,et al.  The Generation of Antiphase Oscillations and Synchrony by a Rebound-Based Vertebrate Central Pattern Generator , 2014, The Journal of Neuroscience.

[25]  O. Sporns,et al.  Connectomics-Based Analysis of Information Flow in the Drosophila Brain , 2015, Current Biology.

[26]  T. Prescott,et al.  The brainstem reticular formation is a small-world, not scale-free, network , 2006, Proceedings of the Royal Society B: Biological Sciences.

[27]  Alan Roberts,et al.  Longitudinal neuronal organization and coordination in a simple vertebrate: a continuous, semi-quantitative computer model of the central pattern generator for swimming in young frog tadpoles , 2009, Journal of Computational Neuroscience.

[28]  A. Chiang,et al.  Automated in situ brain imaging for mapping the Drosophila connectome , 2015, Journal of neurogenetics.

[29]  Lav R. Varshney,et al.  Structural Properties of the Caenorhabditis elegans Neuronal Network , 2009, PLoS Comput. Biol..

[30]  A. Roberts,et al.  Specific Brainstem Neurons Switch Each Other into Pacemaker Mode to Drive Movement by Activating NMDA Receptors , 2010, The Journal of Neuroscience.

[31]  Alan Roberts,et al.  Role of type-specific neuron properties in a spinal cord motor network , 2007, Journal of Computational Neuroscience.

[32]  A. Roberts,et al.  Persistent Responses to Brief Stimuli: Feedback Excitation among Brainstem Neurons , 2006, The Journal of Neuroscience.

[33]  Marcus Kaiser,et al.  Nonoptimal Component Placement, but Short Processing Paths, due to Long-Distance Projections in Neural Systems , 2006, PLoS Comput. Biol..

[34]  Olaf Sporns,et al.  Complex network measures of brain connectivity: Uses and interpretations , 2010, NeuroImage.

[35]  O. Sporns,et al.  Complex brain networks: graph theoretical analysis of structural and functional systems , 2009, Nature Reviews Neuroscience.

[36]  A. Roberts,et al.  Can Simple Rules Control Development of a Pioneer Vertebrate Neuronal Network Generating Behavior? , 2014, The Journal of Neuroscience.

[37]  O. Sporns,et al.  Identification and Classification of Hubs in Brain Networks , 2007, PloS one.

[38]  R. Douglas,et al.  Developmental Origin of Patchy Axonal Connectivity in the Neocortex: A Computational Model , 2012, Cerebral cortex.

[39]  S. Soffe.  Roles of Glycinergic Inhibition and N‐Methyl‐D‐Aspartate Receptor Mediated Excitation in the Locomotor Rhythmicity of One Half of the Xenopus Embryo Central Nervous System , 1989, The European journal of neuroscience.

[40]  H. Seung,et al.  Neuronal Cell Types and Connectivity: Lessons from the Retina , 2014, Neuron.

[41]  S. Soffe,et al.  Two distinct rhythmic motor patterns are driven by common premotor and motor neurons in a simple vertebrate spinal cord , 1993, The Journal of neuroscience : the official journal of the Society for Neuroscience.

[42]  Xiaofan Wang,et al.  Unified index to quantifying heterogeneity of complex networks , 2008 .

[43]  E. Marder,et al.  Principles of rhythmic motor pattern generation. , 1996, Physiological reviews.