 The cell models correspond to regular-spiking excitatory cells and fast-spiking interneurons (PV+); whereas non-PV+ interneurons do exist in L4, they are a relative minority [34], and therefore were neglected for simplicity. Furthermore, 35,000 much simpler leaky-integrate-and-fire (LIF) neurons, with only two groups–excitatory and inhibitory–were placed around the biophysically detailed “core” to prevent boundary artefacts (see SI). The complete model accounted for over half of V1 L4 cells (45,000 out of ~70,000). Below, we primarily focus on the properties of the biophysical core circuit.
Fig 1. Construction of the model.
(a) The biophysical and LIF portions of the model on the cortical surface with delineations of cortical areas (top; “VISp” is V1; the other labels starting with “VIS” correspond to higher visual areas) and with individual cells rendered (bottom; only a small subset of cells is shown for clarity). (b) Morphologies and action potential shapes of the five neuron models used to generate the L4 network; numbers of cells of each type are listed. (c-e) Connection probability (c,d) and synaptic weights (e) of excitatory (E) or inhibitory (I) cell targets and sources. The rules incorporate the dependence on the distance between somata (c) or difference of the assigned preferred orientations, Δori (d, e). Rules dependent on Δori were applied to E-to-E connections only, and synaptic weights for all connections were independent of distance. (f) Connection probability computed for cells within 50 μm using actual preferred orientation observed in simulations (cf. [24]). Numbers of connected and total pairs, used to obtain the probability, are shown inside the bars. (g) Three types of LGN filters (ON, OFF, and ON/OFF), superimposed onto an image, providing inputs to a L4 cell. Example filter’s spatial and temporal profiles are at the bottom. (h) The proportion of excitatory thalamocortical synapses (VGLUT2+) in the neuropil of V1 L4, as determined experimentally using EM. Proportions for individual samples of tissue are in gray; mean and s.e.m. for each mouse are in black. Right, an exemplar EM image of a putative VGLUT2+ synapse from the LGN onto an L4 neuron (Sp, spine; Bt, bouton; arrows: postsynaptic densities within the spine).
Three independent instantiations were generated using different random seeds. The connectivity and inputs into these three model instantiations were distinct, but all followed the rules described below. All simulations were performed using the Python 2.7 code (an early version of the BioNet package [35]) employing NEURON 7.4 [36].
Recurrent connections (Fig 1C) were established randomly according to probability decaying with intersomatic distance (e.g., [37]). Recent experiments [25, 26, 27, 29] showed that excitatory neurons in the mouse V1 L2/3 exhibit more likely and stronger connections if neurons prefer similar stimuli (“like-to-like connectivity”). We sought to investigate how such a rule affects neural activity. The rule (Fig 1D) was applied to all excitatory cells by assigning a preferred orientation to each excitatory neuron (which was also used to select LGN inputs, see below) and using the difference between such orientations to compute a probability of connection. A similar like-to-like rule was applied to the amplitude of synaptic weights (Fig 1E). The like-to-like rules were parameterized to correspond approximately to the observations for L2/3 [25] (Fig 1F) and did not apply to pairs containing one or more inhibitory neurons. See Methods (section “Connectivity within the Network” and “Synaptic characteristics”) for further details.
We directly converted visual stimuli to spikes of LGN cells (which provide the input to L4) via space-time separable linear-nonlinear Poisson (LNP) filters (Fig 1G; see, e.g., [38, 39, 40]) of ON, OFF, and ON/OFF types (see Methods), all of which produced relatively transient responses. Such a considerable simplification of the wide variety of response types that the LGN cells exhibit (see, e.g., [41, 42, 17]) was necessary to make the model tractable, especially because rules of connectivity from various functional LGN cell types and L4 in the mouse are largely unknown. Because the retinotopy of the complete model did not cover the entire field of view, we employed 9,000 LGN filters–approximately half of the mouse LGN. Based on the experimental data about receptive fields of L4 neurons [6, 7, 17], we used retinotopy of L4 cells to “pool” inputs from LGN filters with similar retinotopy, and the assigned preferred orientation (see above) to establish the geometry of the ON and OFF subfields (Fig 1G; see Methods). This helped to establish orientation selectivity in the combined LGN inputs to individual L4 cells [17]. Due to the distance dependence of recurrent connections and retinotopy of LGN inputs, the L4 cells that were connected to each other had a higher chance to receive inputs from the same LGN cells, in comparison with unconnected L4 cells (see Methods). This is consistent with recent experimental observations for L4 and L2/3 cells [27].
The numbers of synapses for recurrent connections were chosen based on the literature (see Methods). Using electron microscopy (EM), we found (Fig 1H) that LGN synapses constitute 15–30% of all synapses in the neuropil in L4 (see Methods for details), consistent with observations for mouse S1 and M1 [43]. This corresponds to over 1,000 synapses from the LGN per excitatory L4 neuron (given ~8,000 synapses total per mouse V1 cell [33] on average, we assume relatively small L4 neurons to receive ~6,000 synapses). Thus, the number of LGN-to-L4 synapses is an order of magnitude higher in the mouse than in the cat V1 (for which this number has been long established to be ~100 [44]). These new data determined the numbers of LGN-to-L4 synapses in the model (see Methods for further details). For the majority of connections, multiple synapses per connection were assigned, typically in the 3–7 range (see Methods). Synaptic dynamics was described by a sum of two decaying exponentials. We assumed no short-term plasticity as it is plausible that in vivo synapses operate at steady-state conditions [18]. Long-term plasticity was neglected because simulations covered several seconds at most.
To account for inputs from the rest of the brain and for different brain states, we introduced externally generated waves of background activity sweeping across the L4 model (Fig 2A), inspired by reports of activity propagation over cortical surface in vivo [45]. Poisson spike generators were distributed within the cortical plane and were activated whenever the wave swept through their positions, sending spikes to the nearby L4 cells. This enabled the L4 model (Fig 2B) to operate with an extremely simple analogue of distinct cortical states (see, e.g., [46, 47, 48]), which we call “Bkg. on” and “Bkg. off.” (see Methods). The random generation of the background waves, as well as random generation of background spike trains from the wave profiles and of LGN spike trains from deterministic filter outputs were the sole sources of indeterminacy, leading to differences between individual trials.
Fig 2. Examples of simulated responses to various visual stimuli.
(a) Spontaneous activity in the model was generated by waves of background excitation (“Bkg. on”, yellow arrow denotes the direction of motion of the yellow bar-like region) alternated with intervals of no background excitation (“Bkg. off”). (b) Model activity in a gray screen trial. Examples of membrane potential traces from simulated biophysical cells are in the middle. (c) Spike raster in response to a drifting grating (TF = 4 Hz, at 0 degrees direction). Bottom, example orientation tuning curves for an excitatory and inhibitory cell from simulation. (d) Spikes in response to a 50 ms full-field flash. (e) Spike raster for a single trial of a natural movie (top) and for a temporally scrambled version of the same movie (bottom). The raster in (b) shows all neurons and those in (c-e) for clarity show the 10,000 cells in the biophysical core of the model (inset on top of (c) zooms in on 200 cells). All rasters are examples from one trial; all trials used unique combinations of “Bkg. on” and “Bkg. off” states (shown at the bottom of plots), which overlapped (or not) in different ways with the visual stimuli.
After the steps above, all parameters were fixed except the synaptic weights (conductance amplitudes). The LGN-to-L4 weights were selected to produce experimentally observed excitatory currents from LGN [17]. The weights for recurrent connections were then manually optimized, while constraining post-synaptic potentials and currents (PSPs and PSCs) to the experimentally reported range for mouse cortex [49] (see Methods). The weights were not adjusted individually; instead, we uniformly scaled all weights belonging to a particular connection type, such as, for example, excitatory-to-Rorb connections or inhibitory-to-Nr5a1 connections. Optimization was limited to two training stimuli–a single trial of a drifting grating and one of a gray screen, 500 ms each. The target was to reproduce the mean spontaneous firing