Fig. 3: Synaptic modeling and deep learning.
a Digitized trace (black line) from a CA2 Pyramidal cell to a CA2 Narrow-Arbor Basket PV+ cell82. The corresponding 9-point reconstruction of each spike (red circles), based on initiation, peak, decay (filled circles), and 6 interpolations (hollow circles), are used to optimize the simulated signal (green). b The Tsodyks-Pawelzik-Markram (TPM) model describes synaptic amplitude, kinetics, and short-term plasticity in terms of utilization rate (u), activation (A), deactivation (D), and recovery (R) dynamics. State A represents the portion of activated synapses; state D corresponds to deactivated synapses that are still bound to neurotransmitter and therefore cannot be reactivated; R is the portion of synapses detached from neurotransmitter and ready to be reactivated. The kinetics of the transition from A to D is determined by the synaptic decay constant τd. The recovery rate is instead mostly determined by τr. In terms of postsynaptic ionotropic neurotransmitter receptors, the TPM model assumes that ligand-gated channel opens instantaneously. The portion of recovered synapses that are instantly activated after a synaptic event is indicated by u (lower case). During deactivation, the gate is closing while the neurotransmitter is still attached to the channel receptor. For a full recovery, the neurotransmitter needs to detach from the receptor for presynaptic reuptake. The time constant τr measures that recovery speed. While τd mainly defines synaptic decay, it can affect ST-P as well when presynaptic firing is very fast. TPM model combined with Ohm’s law can simulate voltage-clamp experiments (synaptic current, Isyn) by using experimentally measured reversal potential (Erev), junction potential (Ej), and holding potential (Vh). To simulate current-clamp experiments (synaptic potential, Vsyn), we fed the Isyn to a simple membrane model (Resistor-Capacitor circuit), which depends on experimentally measured steady-state potential (Vss), membrane capacitance (Cm), and membrane time constant (τm, that could be calculated knowing Cm and input conductance, gin). A genetic algorithm yields the best-fitting values of 5 synapse-specific parameters: conductance (g), single-exponential decay time constant (τd), recovery time constant (τr), facilitation time constant (τf), and utilization ratio (U, capital letter). c The predictive machine learning model of synaptic electrophysiology used a deep learning architecture with five hidden layers and error backpropagation. The input layer encoded the (typically fuzzy) presynaptic and postsynaptic neuron types (122 × 2 nodes) and all covariates (75 nodes). The output layer consisted of one node for each of the 5 synapse-specific parameters. Model training used the best-fitting TPM parameters corresponding to the available 2,621 reconstructed traces and matching covariates (corresponding to ∼84% of 3120 potential connections). The model outputs the five predicted synapse-specific parameters for any directional pair of neuron types and desired choice of covariates. We used random forest to complete the missing ST-P values (τr, τr, and U) in training data, and deep learning to predict synaptic properties of potential connections for which no data existed, including experimental conditions and potential connections that have never been studied before.
