Synchronization of firing in cortical fast-spiking interneurons at gamma frequencies: a phase-resetting analysis

Fast-spiking (FS) cells in the neocortex are interconnected both by inhibitory chemical synapses and by electrical synapses, or gap-junctions. Synchronized firing of FS neurons is important in the generation of gamma oscillations, at frequencies between 30 and 80 Hz. To understand how these synaptic interactions control synchronization, artificial synaptic conductances were injected in FS cells, and the synaptic phase-resetting function (SPRF), describing how the compound synaptic input perturbs the phase of gamma-frequency spiking as a function of the phase at which it is applied, was measured. GABAergic and gap junctional conductances made distinct contributions to the SPRF, which had a surprisingly simple piecewise linear form, with a sharp midcycle break between phase delay and advance. Analysis of the SPRF showed how the intrinsic biophysical properties of FS neurons and their interconnections allow entrainment of firing over a wide gamma frequency band, whose upper and lower frequency limits are controlled by electrical synapses and GABAergi

BioNet: A Python interface to NEURON for modeling large-scale networks.

There is a significant interest in the neuroscience community in the development of large-scale network models that would integrate diverse sets of experimental data to help elucidate mechanisms underlying neuronal activity and computations. Although powerful numerical simulators (e.g., NEURON, NEST) exist, data-driven large-scale modeling remains challenging due to difficulties involved in setting up and running network simulations. We developed a high-level application programming interface (API) in Python that facilitates building large-scale biophysically detailed networks and simulating them with NEURON on parallel computer architecture. This tool, termed "BioNet", is designed to support a modular workflow whereby the description of a constructed model is saved as files that could be subsequently loaded for further refinement and/or simulation. The API supports both NEURON's built-in as well as user-defined models of cells and synapses. It is capable of simulating a variety of observables directly supported by NEURON (e.g., spikes, membrane voltage, intracellular [Ca++]), as well as plugging in modules for computing additional observables (e.g. extracellular potential). The high-level API platform obviates the time-consuming development of custom code for implementing individual models, and enables easy model sharing via standardized files. This tool will help refocus neuroscientists on addressing outstanding scientific questions rather than developing narrow-purpose modeling code

Computational performance.

<p>(<b>A</b>) Scaling of wall time duration (normalized by the duration on a single CPU core) with the number of CPU cores for the simulation set up (blue circles) and run (red circles) of the layer 4 model (see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0201630#pone.0201630.g005" target="_blank">Fig 5</a>). The ideal scaling is indicated by the dashed line. (<b>B</b>) Wall time increase when computing the extracellular potential for both set up (blue circles) and run (red circles) durations. (<b>C</b>) Scaling of the wall time with the simulated time for a long simulation. The non-ideal scaling with the increase in the number of cores corresponds to the deviations from the dashed line in (A).</p

Running simulations.

<p>(<b>A</b>) Relationships among various elements involved in running simulations with BioNet. The pre-built network (blue), is passed to the main Python script (pink) that loads custom user modules and runs BioNet/NEURON to produce the simulation output (purple). (<b>B</b>) The stages of the simulation executed by the main Python script. (<b>C</b>) Algorithm for distributing the cells over a parallel architecture. This simple example shows 10 cells distributed across 4 parallel processes (typically each parallel process corresponds to a CPU core). Cells are assigned to each process in turn (a “round-robin” assignment).</p

Building networks.

<p>(<b>A</b>) High-level specification of a simple example network (left) and corresponding builder API commands (right). The model is composed of two cell types: inhibitory (blue) and excitatory (red), which exchange connections both across and between the cell types. The API commands define the number of cells of each type to be created, connectivity rule (con_func) to use and associated parameters (con_func_params) as well as additional edge parameters (edge_type_params). (<b>B</b>) Illustration of creating cells (left) where each cell type may include both biophysical (morphological reconstruction) and LIF models (circles). The corresponding API commands for adding nodes for the biophysically detailed subset of excitatory populations are illustrated on the right. Here we specify the number of nodes to be created (N), a type of a model (model_type), the dynamical cell models (model_template) and the corresponding model parameters (dynamics_params), morphologies (morphology_file), and positions of cell somata (positions) that were computed with a user-defined function. (<b>C</b>) Illustration of connecting the cells into a network (left) and the corresponding API commands for adding a particular subset of connections (right). Here, the cells satisfying the query for both the source and target nodes will be connected using a function (connection_rule) with parameters (connection_params). The additional edge_type attributes are shared across the added edges and include the synaptic strength (syn_weight), function modulating synaptic strength (weight_function), dynamical synaptic model (model_template) and corresponding parameters (dynamics_params), a conduction delay (delay), as well as the locations where synapses could be placed on a cell (target_sections, distance_range).</p

Computing extracellular potential.

<p>(<b>A</b>) Schematic of the compartmental model of a cell in relationship to the recording electrode. The calculation of the extracellular potential involves computing the transfer resistances <i>R_mn</i> between each n-th dendritic segment and m-th recording site on the electrode. (<b>B</b>) Extracellular spike “signatures” of individual cells recorded on the mesh electrode (black dots), using two single-cell models from the layer 4 network model as examples: PV2 (left) and Nr5a1 (right). (<b>C</b>) Modeled extracellular recordings with the linear electrode positioned along the axis of the cylinder in the layer 4 model (left). Extracellular potential responses (right) show all simulated data (color map) as well as from six select channels (black traces superimposed on the color map).</p

Application example: Model of the layer 4 in mouse V1.

<p>(<b>A</b>) The <i>in silico</i> study [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0201630#pone.0201630.ref009" target="_blank">9</a>] mimicked <i>in vivo</i> visual physiology experiments (bottom), where a mouse watches visual stimuli such as, e.g., drifting gratings, while the activity of neurons in its cortex are recorded. (Center) The top view of the cortical surface, with boundaries of cortical areas delineated (VISp is V1). The inner boundary encloses part of the tissue that was modeled using biophysically detailed cells, whereas the tissue between the inner and outer circles was modeled using the simplified LIF cells. (Top) The 3D visualization of the layer 4 model (only 10% of cells are shown for clarity). (<b>B</b>) Example of synaptic innervation of the biophysically detailed cell models of each type. Synapses (depicted as spheres) are color coded according to their source cell type. (<b>C</b>) Rastergrams of the external inputs: (Top) “background” input (BKG, khaki) that switches between “ON” to “OFF” states, loosely representing different brain states; (Bottom) LGN input (green) corresponding to the visual response to 0.5 second gray screen (gray line) followed by 2.5 second drifting grating (black line). (<b>D</b>) The connection matrix showing the peak conductance strength for connections between each pair of cell types. (<b>E</b>) Simulation output: (Top) spike raster in the biophysical “core”. The node_ids are ordered such that cells with similar ids have similar preferred orientation angle. In this example, cells preferring ~0, ~180, and ~360 degrees are responding strongly to a horizontal drifting grating. (Bottom) somatic voltage traces and the corresponding calcium traces for example excitatory (red) and inhibitory (blue) cells.</p