The mechanics of state-dependent neural correlations

Abstract

Simultaneous recordings from large neural populations are becoming increasingly common. An important feature of population activity is the trial-to-trial correlated fluctuation of spike train outputs from recorded neuron pairs. Similar to the firing rate of single neurons, correlated activity can be modulated by a number of factors, from changes in arousal and attentional state to learning and task engagement. However, the physiological mechanisms that underlie these changes are not fully understood. We review recent theoretical results that identify three separate mechanisms that modulate spike train correlations: changes in input correlations, internal fluctuations and the transfer function of single neurons. We first examine these mechanisms in feedforward pathways and then show how the same approach can explain the modulation of correlations in recurrent networks. Such mechanistic constraints on the modulation of population activity will be important in statistical analyses of high-dimensional neural data.

Figure 1. Schematic illustration of correlation transfer in networks of spiking neurons

We consider a pair of unconnected neurons (black triangles) that receive input from a presynaptic population of excitatory neurons (red triangles) and inhibitory neurons (blue circles). Covariability, Cov(P₁, P₂), in the presynaptic inputs, P₁ and P₂, to the postsynaptic pair is due to a combination of shared anatomical projections leading to a shared input (overlap between P₁ and P₂) and correlations between the activity of the presynaptic populations. This presynaptic activity along with internal synaptic and cellular fluctuations, N_i, determine the postsynaptic currents, x_i (i = 1, 2) in each of the two postsynaptic cells. Finally, the nonlinear spike generation mechanism translates these postsynaptic currents into the output spike trains, y₁ and y₂.

Figure 2. Three mechanisms for correlation modulation

(a) The presynaptic excitatory (E) population (red) and the inhibitory population (blue) both project to the postsynaptic neuron pair. In state A the presynaptic populations are weakly driven, with a slight asymmetry favoring the E population (a1). In contrast, both presynaptic E and I populations are driven strongly in state B (a2). The increase in presynaptic rate uncovers an anticorrelation between the E and I currents, ultimately decorrelating the overall synaptic inputs to the postsynaptic pair (a3). The result of the modulation from state A to B is to both increase the postsynaptic firing rate (a4, green) and decrease spike count correlation (a4, black). (b) The synapses linking presynaptic activity to postsynaptic current are probabilistic, with activity dependent reliability of vesicle release (we show only the E population for schematic brevity). In state A the presynaptic populations are weakly driven and the number of vesicles released per presynaptic spike, and their reliability, is high (b1). In contrast, in state B the presynaptic population fires at a higher rate, resulting in less reliable synaptic transmission (b2). The decrease in synaptic reliability from state A to B increases the synaptic noise to signal ratio, 1 + R (b3). As in a4, the transition from state A to B has the effect of both increasing the postsynaptic firing rate (b4, green) and decreasing the spike count correlation (b4, black). (c) The presynaptic E and I populations project balanced, conductance based inputs to the postsynaptic pair. In state A the firing rates of the presynaptic populations are low, and the overall synaptic fluctuations are small (c1). In contrast, in state B the presynaptic rates are higher, resulting in larger fluctuations in the input to the postsynaptic pair (c2). The increase in conductance based fluctuations between state A and B reduces the spike response gain (L) (c3). As in a4, the transition from state A to B increases the postsynaptic firing rate (c4, green) and decreases the spike count correlation (c4, black).

Figure 3. Dissecting correlation modulation

(a) Output correlation coefficient ρ as a function of the window T over which spike trains are counted. The pre-synaptic correlations (column 1), internal fluctuation (column 2), and neural transfer (column 3) examples are identical to those of Figure 2. (b) The Fano factor F(n) = Var(n)/〈n〉 for the same data as panel a. (c) The co-Fano factor CoF(n₁, n₂) = Cov(n₁, n₂)/〈n〉 for the same data as panel a.

Figure 4. Correlation modulation in recurrent networks

a. Schematic of recurrent excitatory (E) and inhibitory (I) network. The neurons in the network receive a global source of shared fluctuations, alongside individual sources of private variability. b. Spike train rasters (top) and instantaneous firing rates (bottom) of the E-neuron population in state A and B. c. Change in spike response gain (L) as modulatory drive (state) is varied. d. Change in presynaptic correlation to a representative pair of neurons within the population as modulatory drive (state) is varied. e. The result of the modulation from state A to B is to both increase the postsynaptic firing rate (green) and decrease spike count correlation (black). f. Schematic showing a silencing of a portion of the inhibitory population through activation of halorhodopsin. g. Same as e) but with half of the inhibitory neurons hyperpolarized.