Interaction of short-term depression and firing dynamics in shaping single neuron encoding

Abstract

We investigated how the two properties short-term synaptic depression of afferent input and postsynaptic firing dynamics combine to determine the operating mode of a neuron. While several computational roles have been ascribed to either, their interaction has not been studied. We considered two types of short-term synaptic dynamics (release-dependent and release-independent depression) and two classes of firing dynamics (regular firing and firing with spike-frequency adaptation). The input-output transformation of the four possible combinations of pre- and post-synaptic dynamics was characterized. Adapting neurons receiving input from release-dependent synapses functioned largely as coincidence detectors. The other three configurations showed properties consistent with integrators, each with distinct features. These results suggest that the operating mode of a neuron is determined by both the pre- and post-synaptic dynamics and that studying them together is necessary to understand emergent properties and their implications for neuronal coding.

Keywords: emergent properties; firing properties; operating modes; short-term depression; synaptic integration.

Figure 1

(A1) Response of type 1 (top left) and type 2 (top right) synapses to 30 Hz stimulation. For a current injection of 0.5 nA response of class 1 (bottom left) and class 2 (bottom right) neurons are shown. (A2) Illustration of stimulus. In the example, 1000 Gaussian-distributed (in time) presynaptic spikes are relayed through 75 synapses. (B) Synaptic conductance if synapses were static; σ_stim = 60 (B1) or 120 ms (B2). (C,F) Synaptic conductances with type 1 (C) synapses and type 2 (F) synapses. (D,E) With type 1 synapses, raster of spiking response over 1000 iterations for class 1 (D) and class 2 (E) neurons. (G,H) With type 2 synapses, raster of spiking response over 1000 iterations for class 1 (G) and class 2 (H) neurons. Dashed line signifies stimulus mean (μ_stim) while solid lines indicate response mean (μ_resp). Gray boxes indicate ±0.5·σ_stim in (B,C, and F) and ±0.5·σ_resp in (D,E,G, and H).

Figure 2

Cellular response with varying number of synapses and background noise correlation. (A) Contour plots showing precession (A1) and reliability (A2) of response Gaussian distribution with respect to the stimulus distribution and changing background noise correlation (N_syn set to 100). Contour lines join points of equal value thus indicating regions in the two-dimensional parameter space (stimulus synchrony vs. noise correlation) in which an response characteristic of the system is similar even while parameter values change. In addition, contour lines are useful in visualizing regions which are lesser or greater than a specified value. (B) Contour plots showing precession (B1) and reliability (B2) of response Gaussian distribution with respect to the stimulus distribution and synapse number (τ_N is set to 50 ms).

Figure 3

Reliability of the cellular response with varying number of synapses and background noise correlation. (A) Contour plots reliability for varying noise correlation (A1) and number of synapses (A2) for class 1-type 1 configuration. (B) Contour plots showing reliability for varying noise correlation (B1) and number of synapses (B2) for class 2-type 1 configuration. (C) Contour plots showing reliability for varying noise correlation (C1) and number of synapses (C2) for class 2-type 2 configurations. In all of the above contour plots, when noise correlation is varied, N_syn is set to 1000 and when number of synapses is varied, τ_N is set to 50 ms. (D) Analysis of the slope of relationship between stimulus synchrony and response jitter. Graphs are plotted with the number of synapses (D1) or the noise correlation (D2) systematically changing along the abscissa with the corresponding slope plotted along the ordinate. (D1) For N_syn = 100 and τ_N = 50, plot showing the relationship between number of synapses and ratio between response and stimulus dispersion. A straight line was fit and the slope computed. This was repeated for all parameter values to obtain relationship between number of synapses and the slope (D2) for T1C1 (solid), T2C1 (dashed), and T2C2 (dotted).

Figure 4

Sharpening of the cellular response with varying number of synapses and background noise correlation. (A–C) Heat plots showing response sharpening for varying noise correlation (A1) and number of synapses (A2) for T1C1, T2C1, (B1 and B2), and T2C2 (C1 and C2) configurations. In all of the above heat plots, when noise correlation is varied, N_syn is set to 100 and when number of synapses is varied, τ_N is set to 50 ms. Scaling of the heat plot is linear from values of 0.5 to 8. The white line in (A1,A2, and B1) is an isocline with a value of 1.5. The area circumscribed by this isocline encompasses sharpening values less than or equal to 1.5. The corresponding area in the other graphs is negligible.

Figure 5

Sharpening of the cellular response of T1C1 with varying number of synapses and background noise correlation. (A–C) Heat plots showing sharpening for varying noise correlation (A1) and number of synapses (A2) when total number of presynaptic spikes (N_tot; see Methods) was set to 500, 750 (B1 and B2), and 1000 (C1 and C2). In all of the above heat plots, when noise correlation is varied, N_syn is set to 100 and when number of synapses is varied, τ_N is set to 50 ms. Scaling of the heat plot is linear from values of 0.5 to 8. The white line in all the above graphs is an isocline with a value of 1.5. The area circumscribed by this isocline encompasses sharpening values less than or equal to 1.5.

Figure 6

Sharpening of the cellular response of T2C2 with varying number of synapses and background noise correlation. (A–C) Heat plots showing sharpening for varying noise correlation (A1) and number of synapses (A2) when total number of presynaptic spikes (N_tot; see Methods) was set to 500, 750, (B1 and B2) and 1000 (C1 and C2). In all of the above heat plots, when noise correlation is varied, N_syn is set to 100 and when number of synapses is varied, τ_N is set to 50 ms. Scaling of the heat plot is linear from values of 0.5 to 8. The white line in all the above graphs is an isocline with a value of 3.0. The area circumscribed by this isocline encompasses sharpening values less than or equal to 3.0.