We study temporal correlations of interspike intervals, quantified by the network-averaged serial correlation coefficient (SCC), in networks of both current- and conductance-based purely inhibitory integrate-and-fire neurons. Numerical simulations reveal transitions to negative SCCs at intermediate values of bias current drive and network size. As bias drive and network size are increased past these values, the SCC returns to zero. The SCC is maximally negative at an intermediate value of the network oscillation strength. The dependence of the SCC on two canonical schemes for synaptic connectivity is studied, and it is shown that the results occur robustly in both schemes. For conductance-based synapses, the SCC becomes negative at the onset of both a fast and slow coherent network oscillation. We then show by means of offline simulations using prerecorded network activity that a neuron's SCC is highly sensitive to its number of presynaptic inputs. Finally, we devise a noise-reduced diffusion approximation for current-based networks that accounts for the observed temporal correlation transitions.

VL - 99 IS - 3-1 U1 - https://www.ncbi.nlm.nih.gov/pubmed/30999498?dopt=Abstract ER - TY - JOUR T1 - Mesoscale Mapping of Mouse Cortex Reveals Frequency-Dependent Cycling between Distinct Macroscale Functional Modules. JF - J Neurosci Y1 - 2017 A1 - Vanni, Matthieu P A1 - Chan, Allen W A1 - Balbi, Matilde A1 - Silasi, Gergely A1 - Murphy, Timothy H KW - Animals KW - Brain Waves KW - Calcium Signaling KW - Cerebral Cortex KW - Computer Simulation KW - Connectome KW - Female KW - Male KW - Mice KW - Mice, Transgenic KW - Models, Neurological KW - Nerve Net KW - Rest KW - Spatio-Temporal Analysis KW - Voltage-Sensitive Dye Imaging AB -Connectivity mapping based on resting-state activity in mice has revealed functional motifs of correlated activity. However, the rules by which motifs organize into larger functional modules that lead to hemisphere wide spatial-temporal activity sequences is not clear. We explore cortical activity parcellation in head-fixed, quiet awake GCaMP6 mice from both sexes by using mesoscopic calcium imaging. Spectral decomposition of spontaneous cortical activity revealed the presence of two dominant frequency modes (<1 and ∼3 Hz), each of them associated with a unique spatial signature of cortical macro-parcellation not predicted by classical cytoarchitectonic definitions of cortical areas. Based on assessment of 0.1-1 Hz activity, we define two macro-organizing principles: the first being a rotating polymodal-association pinwheel structure around which activity flows sequentially from visual to barrel then to hindlimb somatosensory; the second principle is correlated activity symmetry planes that exist on many levels within a single domain such as intrahemispheric reflections of sensory and motor cortices. In contrast, higher frequency activity >1 Hz yielded two larger clusters of coactivated areas with an enlarged default mode network-like posterior region. We suggest that the apparent constrained structure for intra-areal cortical activity flow could be exploited in future efforts to normalize activity in diseases of the nervous system.Increasingly, functional connectivity mapping of spontaneous activity is being used to reveal the organization of the brain. However, because the brain operates across multiple space and time domains a more detailed understanding of this organization is necessary. We usedwide-field calcium imaging of the indicator GCaMP6 in head-fixed, awake mice to characterize the organization of spontaneous cortical activity at different spatiotemporal scales. Correlation analysis defines the presence of two to three superclusters of activity that span traditionally defined functional territories and were frequency dependent. This work helps define the rules for how different cortical areas interact in time and space. We provide a framework necessary for future studies that explore functional reorganization of brain circuits in disease models.

VL - 37 IS - 31 U1 - http://www.ncbi.nlm.nih.gov/pubmed/28674167?dopt=Abstract ER - TY - JOUR T1 - Nonstationary Stochastic Dynamics Underlie Spontaneous Transitions between Active and Inactive Behavioral States. JF - eNeuro Y1 - 2017 A1 - Melanson, Alexandre A1 - Mejias, Jorge F A1 - Jun, James J A1 - Maler, Leonard A1 - Longtin, Andre KW - Animals KW - Behavior KW - Computer Simulation KW - Electric Fish KW - Electric Organ KW - Locomotion KW - Models, Biological KW - Monte Carlo Method KW - Nonlinear Dynamics KW - Stochastic Processes KW - Time Factors AB -The neural basis of spontaneous movement generation is a fascinating open question. Long-term monitoring of fish, swimming freely in a constant sensory environment, has revealed a sequence of behavioral states that alternate randomly and spontaneously between periods of activity and inactivity. We show that key dynamical features of this sequence are captured by a 1-D diffusion process evolving in a nonlinear double well energy landscape, in which a slow variable modulates the relative depth of the wells. This combination of stochasticity, nonlinearity, and nonstationary forcing correctly captures the vastly different timescales of fluctuations observed in the data (∼1 to ∼1000 s), and yields long-tailed residence time distributions (RTDs) also consistent with the data. In fact, our model provides a simple mechanism for the emergence of long-tailed distributions in spontaneous animal behavior. We interpret the stochastic variable of this dynamical model as a decision-like variable that, upon reaching a threshold, triggers the transition between states. Our main finding is thus the identification of a threshold crossing process as the mechanism governing spontaneous movement initiation and termination, and to infer the presence of underlying nonstationary agents. Another important outcome of our work is a dimensionality reduction scheme that allows similar segments of data to be grouped together. This is done by first extracting geometrical features in the dataset and then applying principal component analysis over the feature space. Our study is novel in its ability to model nonstationary behavioral data over a wide range of timescales.

VL - 4 IS - 2 U1 - http://www.ncbi.nlm.nih.gov/pubmed/28374017?dopt=Abstract ER - TY - JOUR T1 - Improved Simulation of Electrodiffusion in the Node of Ranvier by Mesh Adaptation. JF - PLoS One Y1 - 2016 A1 - Dione, Ibrahima A1 - Deteix, Jean A1 - Briffard, Thomas A1 - Chamberland, Eric A1 - Doyon, Nicolas KW - Action Potentials KW - Animals KW - Computer Simulation KW - Diffusion KW - Electricity KW - Finite Element Analysis KW - Humans KW - Models, Neurological KW - Nerve Net KW - Ranvier's Nodes AB -In neural structures with complex geometries, numerical resolution of the Poisson-Nernst-Planck (PNP) equations is necessary to accurately model electrodiffusion. This formalism allows one to describe ionic concentrations and the electric field (even away from the membrane) with arbitrary spatial and temporal resolution which is impossible to achieve with models relying on cable theory. However, solving the PNP equations on complex geometries involves handling intricate numerical difficulties related either to the spatial discretization, temporal discretization or the resolution of the linearized systems, often requiring large computational resources which have limited the use of this approach. In the present paper, we investigate the best ways to use the finite elements method (FEM) to solve the PNP equations on domains with discontinuous properties (such as occur at the membrane-cytoplasm interface). 1) Using a simple 2D geometry to allow comparison with analytical solution, we show that mesh adaptation is a very (if not the most) efficient way to obtain accurate solutions while limiting the computational efforts, 2) We use mesh adaptation in a 3D model of a node of Ranvier to reveal details of the solution which are nearly impossible to resolve with other modelling techniques. For instance, we exhibit a non linear distribution of the electric potential within the membrane due to the non uniform width of the myelin and investigate its impact on the spatial profile of the electric field in the Debye layer.

VL - 11 IS - 8 U1 - http://www.ncbi.nlm.nih.gov/pubmed/27548674?dopt=Abstract ER -