The provided code models synaptic dynamics based on the principles of Spike-Timing-Dependent Plasticity (STDP), following concepts from Abigail Morrison's STDP model. STDP is a well-established biological mechanism underlying synaptic plasticity, which is crucial for learning and memory processes in the brain. Here's a description of the biological basis: ### Biological Basis 1. **Synaptic Plasticity:** - Synaptic plasticity refers to the ability of synapses, the connections between neurons, to strengthen or weaken over time in response to increases or decreases in neural activity. This code models this by adjusting the synaptic weight `w` over multiple spike pair interactions. 2. **Spike-Timing-Dependent Plasticity (STDP):** - STDP is a form of synaptic plasticity dependent on the precise timing of pre- and postsynaptic spikes. It is characterized by changes in synaptic strength that are determined by the temporal order and timing difference between pre- and postsynaptic action potentials (or spikes). 3. **Timing Dependence:** - The code incorporates timing variables `delta_t`, `dt_plus`, and `dt_minus`, which represent the timing differences between pre- and postsynaptic spikes. The timing determines whether Long-Term Potentiation (LTP) or Long-Term Depression (LTD) occurs. - **LTP**: If the presynaptic neuron fires just before the postsynaptic neuron (positive `delta_t`), synaptic strength typically increases. - **LTD**: If the presynaptic neuron fires just after the postsynaptic neuron (negative `delta_t`), synaptic strength typically decreases. 4. **Exponential Decay:** - The exponential decay terms `exp(-dt_plus/tau)` and `exp(-dt_minus/tau)` reflect the temporal window of STDP, where the influence of a spike pair on synaptic strength decays exponentially with time. The `tau` parameter represents the time constant for this decay. 5. **Parameters:** - `alpha`, `mu`, and `lambda` are parameters that scale the amount of potentiation or depression. - `alpha`: Modulates the ratio of depression to potentiation. - `mu`: Non-linear potentiation term that accounts for dependence on the current synaptic weight. - `lambda`: Learning rate that controls how quickly synaptic weights are updated. 6. **Dendritic Delay:** - The code considers `delay`, representing the transmission delay often observed in biological dendrites. This adds realism by simulating the delays encountered in neural signal travel. ### Conclusion Overall, this code simulates a key neurobiological process, capturing how the precise timing between neuronal spikes affects synaptic strength changes. This model plays a critical role in understanding the cellular and molecular underpinnings of learning and memory formation in neural circuits.