Response of the simple 2-gate kinetic receptor model to a single pulse of neurotransmitter of amplitude 1 mM and duration1 ms. Rates are α = 1  /mM.ms and β = 1 /ms. Conductance waveform scaled to an amplitude of 1 and compared with an alpha function with τ = 1 ms (dotted line).

Simulated action potential travelling along two axons that are joined by a gap junction half-way along their length. Membrane potentials are recorded at the start, middle and end of the axons. (a,b) Axon in which an action potential is initiated by a current injection into one end. (c) Other axon, with a 1 nS gap junction. (d) Other axon, with a 10 nS gap junction. Axons are 100 μm long, 2 μm in diameter with standard Hodgkin-Huxley sodium, potassium and leak channels.

Three distinct trials of a complete synapse model with 500 independent active zones. Each active zone uses the stochastic vesicle-state model of short-term synaptic dynamics combined with the 2-gate kinetic model of AMPA receptors. Phenomenological model of facilitation: p₀ = 0.2; Δp = 0.05; τ_f = 100 ms. Vesicle-state model: k^∗_n = k_r = 0.2 s⁻¹; n_s = 0. 2-gate kinetic receptor model: α = 4 mM⁻¹ms⁻¹, β = 1 ms⁻¹. E_syn = 0 mV, with postsynaptic cell clamped at −65 mV. Synapse stimulated at 100Hz.

Facilitation and depression in deterministic models of short-term synaptic dynamics. Phenomenological model of facilitation: p₀ = 0.2; Δp = 0.05; τ_f = 100 ms. (a) vesicle-state model: k^∗_n = k_r = 0.2 /s. (b) release-site model: n_T = 1; k_n = k_r = 0.2 /s. Solid lines: n_s = 0; dotted lines: n_s = 0.1. Synapse stimulated at 50Hz.

Facilitation of release probability in the basic phenomenological model. Stimulation at 50Hz with p0 = 0.1, dp = 0.1 and τf = 100 ms.

Facilitation of transmitter release in a kinetic 2-gate model. Left-hand column shows stimulation at 50 Hz. Right-hand column shows release and gating transients at the tenth pulse. Fast gate: k+1 = 200 /mM.ms, k−1 = 3 /ms; Slow gate: k+2 = 0.25 /mM.ms, k−2 = 0.01 /ms; square-wave [Ca2+]r pulse: 1 mM amplitude, 1 ms duration.

Here is some Matlab code that reproduces Figure 7.2[img_assist|nid=19|title=Figure 7.2|desc=Synaptic conductance waveforms|link=none|align=right|width=370|height=113]

Postsynaptic current in response to 100Hz stimulation from (a) 2-gate kinetic receptor model, α = 4 /mM.ms, β = 1 /ms; (b) 5-gate desensitising model, Rb = 13 /mM.ms, Ru1 = 0.3 /ms, Ru2 = 200 /ms, Rd = 10 /ms, Rr = 0.02 /ms, Ro = 100 /ms, Rc = 1 /ms. Each presynaptic action potential is assumed to result in the release of a vesicle of neurotransmitter, giving a square-wave transmitter pulse amplitude of 1 mM and duration of 1 ms. The current is calculated as Isyn(t) = gsyn(t)(V(t) − Esyn). Esyn = 0 mV and the cell is clamped at −65 mV. The value of gsyn(t) approaches 0.8 nS on the first pulse.

Example STDP weight change curves. The weight is increased if the postsynaptic spike occurs at the time of, or later than the presynaptic spike; otherwise the weight is decreased. The magnitude of the weight change decreases with the time interval between the pre- and postsynaptic spikes. No change occurs if the spikes are too far apart in time.

Stochastic vesicle-state model of short-term dynamics at a single synaptic active zone. (a) A single simulation run, showing the release probability p, the actual number of releasable vesicles, n (initially 1), and neurotransmitter release, T. (b) Average values of these variables, taken over 10000 trials. Phenomenological model of facilitation: p₀ = 0.2; Δp = 0.05; τ_f = 100 ms. Vesicle-state model: k^∗_n = k_r = 0.2 s⁻¹; n_s = 0.1. Synapse stimulated at 50Hz.

Three waveforms for synaptic conductance: (a) single exponential decay with τ = 3 ms, (b) alpha function with τ = 1 ms, and (c) dual exponential with τ₁ = 3 ms and τ₂ = 1 ms. Response to a single presynaptic action potential arriving at time=1ms. All conductances are scaled to a maximum of 1 (arbitrary units).

Alpha function conductance with τ = 10 ms responding to action potentials occurring at 20, 40, 60 and 80 ms. Conductance is scaled to a maximum of 1 (arbitrary units).