2 Neuroscience2.4 Cells
2.4.3 Modelling single neurons and their combination in circuits
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Written by Resident Doctor Committee · Published
Passive membrane
The membrane acts as a capacitor with conductances: current either charges it or flows through channels.
In a passive model, capacitance times the rate of voltage change equals injected current minus leak conductance times driving force.
The membrane time constant is resistance times capacitance, and a larger constant lets the neuron integrate inputs for longer.
Cable models join segments through axial resistance to describe how signals spread and attenuate.
A passive cable cannot spike, because it lacks regenerative voltage-dependent currents.
Single-neuron models
Model | How it works | Represents well | Omits |
|---|---|---|---|
Passive membrane and cable | Charging and leak only | Charging, decay, subthreshold spread | Spike generation |
Integrate-and-fire | Inputs accumulate to a threshold, then a spike, reset and refractory period | Summation, spike timing | Ionic waveform |
Conductance-based | Currents from conductance times driving force | Currents, spike shape, channel effects | Some geometry and biochemistry |
Leaky integrate-and-fire models let voltage decay between inputs.
Hodgkin-Huxley models use voltage- and time-dependent gating: sodium drives depolarisation and potassium drives repolarisation.
Extra currents and compartments add parameters, and different parameter combinations can produce similar traces.
Rate models summarise average activity for slower population dynamics, while spiking models keep timing, synchrony and timing-dependent plasticity.
Connections
Synaptic weight sets a connection's effect, but conductance models, using reversal potentials, capture shunting inhibition better than signed weights.
Convergence brings many inputs onto one target; divergence sends one source to many targets.
Circuit arrangements
Arrangement | Organisation | Consequence |
|---|---|---|
Feedforward | Successive stages | Transforms input; inhibition narrows response timing |
Feedback | Later activity influences earlier stages | Context, amplification, stabilisation |
Recurrent | Units interconnect | Persistence, competition, instability |
Lateral inhibition | Units inhibit neighbours | Contrast enhancement |
Disinhibition raises output by suppressing inhibition, so similar output changes can arise from different mechanisms.
Emergent properties
Circuits show properties absent from single units: oscillation, synchrony, persistent activity and pattern completion.
An attractor is a stable state or trajectory reached from several starting conditions: fixed-point attractors settle, cyclic attractors repeat.
Changing one parameter can switch a network between quiet, sustained, oscillatory and unstable activity.
What a working model proves
Reproducing data shows a mechanism works in the model, not that the brain uses it.
Models are tested against anatomy and physiology, by parameter recovery, and by predictions on new data or perturbations.