Effects of Adaptation on Discrimination of Whisker Deflection Velocity and Angular Direction in a Model of the Barrel Cortex

Abstract

Two important stimulus features represented within the rodent barrel cortex are velocity and angular direction of whisker deflection. Each cortical barrel receives information from thalamocortical (TC) cells that relay information from a single whisker, and TC input is decoded by barrel regular-spiking (RS) cells through a feedforward inhibitory architecture (with inhibition delivered by cortical fast-spiking or FS cells). TC cells encode deflection velocity through population synchrony, while deflection direction is encoded through the distribution of spike counts across the TC population. Barrel RS cells encode both deflection direction and velocity with spike rate, and are divided into functional domains by direction preference. Following repetitive whisker stimulation, system adaptation causes a weakening of synaptic inputs to RS cells and diminishes RS cell spike responses, though evidence suggests that stimulus discrimination may improve following adaptation. In this work, I construct a model of the TC, FS, and RS cells comprising a single barrel system-the model incorporates realistic synaptic connectivity and dynamics and simulates both angular direction (through the spatial pattern of TC activation) and velocity (through synchrony of the TC population spikes) of a deflection of the primary whisker, and I use the model to examine direction and velocity selectivity of barrel RS cells before and after adaptation. I find that velocity and direction selectivity of individual RS cells (measured over multiple trials) sharpens following adaptation, but stimulus discrimination using a simple linear classifier by the RS population response during a single trial (a more biologically meaningful measure than single cell discrimination over multiple trials) exhibits strikingly different behavior-velocity discrimination is similar both before and after adaptation, while direction classification improves substantially following adaptation. This is the first model, to my knowledge, that simulates both whisker deflection velocity and angular direction and examines the ability of the RS population response to pinpoint both stimulus features within the context of adaptation.

Keywords: barrel cortex; deflection direction; deflection velocity; direction discrimination; feedforward inhibition; velocity discrimination; whisker.

Figure 1

Diagram of connectivity in barrel model. Arrow heads indicate excitation; bar heads indicate inhibition. TC cells are divided into eight direction groups, with each group assigned a preferred angular direction of whisker deflection (1 = 180°, 2 = 225°, 3 = 270°, 4 = 315°, 5 = 0°, 6 = 45°, 7 = 90°, 8 = 135°). TC cells are not explicitly simulated; rather, spike times of TC cells are drawn from a distribution (stimulus velocity determines the synchrony of TC cell spikes, while stimulus direction determines the quantity of TC spikes across direction groups). RS cells are split into 8 direction domains, with each domain aligned to the TC direction group shown directly below. The density of TC → RS synapses depends on TC group-RS domain alignment; the diagram shows connection densities from the TC group with a direction preference of 0° (line/arrow thickness represents synapse density). Connectivity is analogous for other TC direction groups. TC cells uniformly excite a population of FS cells, which uniformly inhibit the RS cell population. Connectivity among RS cells is all-to-all. See text for details.

Figure 2

Membrane potential, net TC input current, and net FS input current to a sample RS cell within the 0° direction domain during a single trial. Data shown are for a high velocity (top row) and low velocity (bottom row) deflection, both before adaptation (left column) and after adaptation (right column). Stimulus deflection direction is fixed at 0° in all plots. The inverse of the standard deviation of the TC spike time distribution is used as a stand-in for deflection velocity.

Figure 3

Behavior of an RS cell within the 0° direction domain to deflections of varying velocity, before and after adaptation. The left panel shows the probability that the RS cell spikes, while the middle panel shows the jitter (standard deviation) in the timing of the RS cell spike, as a function of deflection velocity (deflection direction is fixed at 0°). The right panel shows the velocity tuning ratio (response to highest velocity/average response over all velocities) of the RS cell as a function of deflection direction (data are averaged over deflection directions equidistant from preferred). Data are gathered over 600 trials.

Figure 4

Membrane potential, net TC input current, and net FS input current to a sample RS cell within the 0° direction domain during a single trial. Data shown are for a deflection at the preferred (top row) and opposite-to-preferred (bottom row) deflection direction, both before adaptation (left column) and after adaptation (right column). Stimulus deflection velocity is fixed at 1 in all plots (the inverse of the standard deviation of the TC spike time distribution is used as a stand-in for deflection velocity).

Figure 5

Behavior of an RS cell within the 0° direction domain to deflections of varying angular direction, before and after adaptation. The left panel shows the probability that the RS cell spikes, while the middle panel shows the jitter (standard deviation) in the timing of the RS cell spike, as a function of deflection direction (data are averaged over deflection directions equidistant from preferred; deflection velocity is fixed at 1). The right panel shows the direction tuning ratio (response to preferred direction/average response over all directions) of the RS cell as a function of deflection velocity. The inverse of the standard deviation of the TC spike time distribution is used as a stand-in for deflection velocity. Data are gathered over 600 trials.

Figure 6

Direction and velocity dependence of RS population responses, before and after adaptation. The top row shows the probability that an RS cell spikes for RS cells within one direction domain as a function of deflection velocity, before (left) and after (right) adaptation (deflection direction is fixed at the preferred direction of the domain). The bottom row shows the probability that an RS cell spikes for RS cells within one direction domain as a function of deflection direction, before (left) and after (right) adaptation (data from directions equidistant from the preferred direction of the domain are aggregated; deflection velocity is fixed at 1). For a particular symbol type, data points represent the responses of individual RS cells within the domain, and symbol type is varied with velocity of the simulated deflection (hence there are 20 data points for each velocity; top row) or direction of the simulated deflection (since data are aggregated over directions equidistant from preferred, there are 40 data points for the 45°, 90°, 135° cases and 20 data points for the 0°, 180° cases; bottom row). The solid line shows the mean response of the RS direction domain. Data are gathered over 600 trials.

Figure 7

Velocity discrimination by the net cortical RS response, before and after adaptation. Left: Mean net cortical response as a function of deflection velocity, normalized by the response at a velocity of 1 (deflection direction is fixed). Net cortical response is defined as the total number of RS cell spikes in a trial; the mean is calculated over 600 trials. Middle: Fraction of correctly classified trials of each velocity (600 trials per velocity). The midpoints between the mean net cortical responses for adjacent velocities are set as classification cutoffs; a trial is defined as correctly classified if the net cortical response falls between the upper and lower cutoffs. Right: Data on fraction of correctly classified trials aggregated over all velocities (3,000 total trials; 600 trials of each velocity). The inverse of the standard deviation of the TC spike time distribution is used as a stand-in for deflection velocity.

Figure 8

Direction discrimination by the cortical RS response, before and after adaptation, for a stimulus deflection direction of 0°. Left: Mean response of the 0° RS direction domain divided by the mean cortical response as a function of deflection velocity. Mean response is defined as number of spikes per cell averaged over RS cells (either cells in the 0° direction group or the entire cortex) in a trial; data shown are averaged over 600 trials. Middle: Fraction of correctly classified trials as a function of deflection velocity (600 trials per velocity). The midpoint between the mean response of the 0° RS direction domain divided by the mean cortical response (averaged over 600 trials) and the mean response of the 45°/315° RS direction domain divided by the mean cortical response (averaged over 600 trials) is set as the classification cutoff; a trial is defined as correctly classified if the mean response of the 0° RS direction domain divided by the mean cortical response for the trial exceeds the cutoff. Right: Data on fraction of correctly classified trials aggregated over all velocities (3,000 total trials; 600 trials of each velocity). The inverse of the standard deviation of the TC spike time distribution is used as a stand-in for deflection velocity.