Biological Basis of the Spike Timing Dependent Weight Adjuster

The provided code models synaptic plasticity, specifically the spike-timing dependent plasticity (STDP) mechanism, which is foundational to learning and adaptation in neural circuits. STDP refers to the changes in the synaptic strength between neurons based on the precise timing of spikes from the pre- and post-synaptic neurons.

Key Biological Concepts

Spike-Timing Dependent Plasticity (STDP)

• STDP Principle: The code is based on the principle of STDP, where the relative timing of spikes (action potentials) of pre- and post-synaptic neurons determines synaptic strengthening (long-term potentiation, LTP) or weakening (long-term depression, LTD).
• Hebbian Learning: The concept is rooted in Hebbian learning, often summarized as "cells that fire together, wire together," but with a critical twist where timing determines whether the connection strengthens or weakens. If a pre-synaptic spike occurs shortly before a post-synaptic spike, LTP is induced. Conversely, if the post-synaptic spike precedes the pre-synaptic spike, LTD occurs.

Biological Relevance of Parameters

• Decay Times: The parameters tauLTP and tauLTD represent the decay times for LTP and LTD, respectively. These decay times influence how quickly the effects of past spikes diminish and are grounded in empirical observations from studies like those by Song and Abbott (2001).

• Amplitude Parameters: The parameters aLTP and aLTD denote the amplitudes of the potentiation and depression steps, controlling the magnitude of synaptic weight changes during LTP and LTD events. These values reflect experimentally observed ratios between potentiation and depression.

• Soft Weight Limits: The maximum weight (wmax) and pruning weight (wprune) parameters imply biological constraints on synaptic strength. Synapses have upper bounds to prevent runaway excitation in neural circuits, and pruned synapses can be seen as those that are weakened beyond a functional threshold.

Synaptic Weight Adjustment

• Synaptic Weight Changes: The variable wsyn represents the synaptic weight, which changes according to calculated changes (deltaw). The direction and magnitude of changes are determined by the calculated LTP or LTD effects, based on the intervals between spikes.

• Exponential Decays: The use of exponential decay functions in calculating P (LTP function) and M (LTD function) mimics the physiological decay of synaptic potentials over time, making the model biologically plausible.

Global Learning Switch

• Learning Toggle: The on variable serves as a switch allowing for global control of synaptic plasticity. This simulates biological scenarios where learning can be modulated by neuromodulatory inputs, such as in different behavioral or developmental states.

In summary, the code aims to emulate the biological phenomenon of STDP through a computational model, capturing how precise spike timing influences synaptic modifications. These modifications are crucial for encoding information, learning, and memory formation in neural circuits.