Fig 1.
Spike frequency adaptation (SFA) and short-term synaptic depression (STD) are forms of negative feedback adaptation or gain control.
(a) SFA leads to a decrease in action potential firing rate in response to a continuous stimulus. Examples show single and multiple timescale adaption. (b) With adaptation fewer action potentials are generated in noiseless (upper panel) and noisy (lower panel) stimulus conditions. STD decreases postsynaptic membrane potentials in response to (c) fixed presynaptic firing rates and (d) noisy presynaptic firing rates. The membrane potential is normalized such that the mean of the steady-state non-adapted response (black) is one. Results are from Hodgkin-Huxley neuron models and synaptic-depression models with single or multiple timescales of adaptation (see Methods).
Table 1.
Parameters or variables used in the equations.
Fig 2.
Neuronal spike frequency adaptation (a) approximates fractional differentiation with order ~0.1–0.5. Properties for the fractional derivative transfer function (i2π)α include a power law amplitude response and frequency-independent phase response (see also S1 Text). (b) Higher fractional orders correspond to increased spike frequency adaptation, i.e., increased negative feedback inhibition.
Fig 3.
Multiple timescale adaptation can approximate fractional dynamics.
(a) Step responses and (b) frequency domain characteristics of three high-pass filters with three timescales (τ = 0.05s, 0.5s, 5s). The combination of the three high-pass filters is similar to an approximate power law with exponent -0.1, which is equivalent to fractional differentiation of order 0.1. (c) Fractional dynamics demonstrate a frequency-independent phase advance that can be approximated by multiple timescale adaptation with either one gain parameter (A1 = A2 = A3) or three gain parameters (A1≠ A2≠ A3). (d) Weighting each timescale equally (i.e. with one gain parameter) can provide a reasonable approximation of fractional dynamics, especially for α<0.5. The value of A (for one gain parameter) or median value of A (for three gain parameters) are similar as fractional order α increases.
Fig 4.
Model of neural components leading to LFP or EEG signals.
Colored noise inputs are filtered by high-pass and low-pass filtering mechanisms. Neural circuit topologies with parallel feed-forward connections and asymmetric time delays have similar computational components.
Fig 5.
Adaptation affects the gain and slope of neural power spectral densities.
(a) Example showing interaction of high-pass filters with low-pass filters. Eq (7) is plotted with three timescales (γ = k = c = x0 = 1, F = 0.5). (b) Relative steady-steady output for synaptic depression initially increases and then decreases as x0 increases (modeled via Eq (8) with n = 3, F = 0.5, γ = 2). (c) Adaptation alters the slope of PSDs, decreases the overall gain, and affects lower frequencies (e.g. 0–10 Hz) more than higher frequencies (e.g. 30–50 Hz). Adaptation interacts with input levels and includes Spike Frequency Adaptation (SFA) and Short-term Synaptic Depression (STD).
Fig 6.
Power spectra changes related to the seizure onset zone and increased adaptation.
(a) Previously published invasive EEG power spectra from 8 patients (left panel) [35] and 83 patients (right panel) [36] showing decreased low frequency activity and increased high frequency activity near the seizure onset zone (SOZ) compared to the non-SOZ. (b) Similar shapes can be obtained from constant input models (with one low-pass timescale to approximate membrane filtering) when more negative feedback is present (e.g., increased α or A), implemented either via fractional dynamics (left panel; α = 0.3, g = 0.7 or α = 0.1, g = 1; for both k = 100, τm = 0.3 s) or multiple timescales (right panel; A1 = A2 = A3 = 1.1, g1 = g2 = g3 = 1.3 or A1 = A2 = A3 = 1.5, g1 = g2 = g3 = 1.5; for both τ1 = 0.05 s, τ2 = 0.5 τ3 = 5 s, k = 500,τm = 5 s).
Fig 7.
Spiking neuron network model with spike frequency adaptation (SFA) and synaptic depression (STD).
(a) Feedforward neural network includes 100 conductance-based neurons with multiple timescales of SFA and STD. (b) PSDs show degrees of “tilt” or crossing when input is increased, and STD is decreased. Increasing SFA effectively decreases STD. (c) Increased adaptation, whether SFA or STD, generally leads to decreased power. However, increased SFA leads to decreased STD (rightmost panel). (d) Increasing input increases overall power when SFA is present. However, when STD is present, increasing the input leads to decreased overall power. When both SFA and STD are present, nonlinear effects are evident.