5. Plasticity and development of neural circuits

Plasticity refers to the brain's ability to change and adapt in response to experience, learning, or injury. This includes changes in the strength of synaptic connections (synaptic plasticity), the formation of new neurons (neurogenesis), and structural reorganization of neural pathways.

Neural circuits are interconnected networks of neurons that work together to process specific types of information and generate coordinated responses. These circuits underlie all brain functions, from simple reflexes to complex cognitive behaviors.

• activity independent

  • These are genetically programmed and occur before sensory experience begins.

  • They include:

    • Neurogenesis (creation of neurons)

    • Axon pathfinding (growth cones guided by molecular cues)

    • Target selection and initial synapse formation

  • These mechanisms ensure the basic scaffold of the nervous system is correctly laid out.

• activity dependent

  • These occur after circuits are in place and are shaped by neural activity and experience.

  • They include:

    • Synaptic strengthening/weakening (e.g., LTP/LTD)

    • Pruning of unused connections

    • Experience-driven plasticity (like in sensory maps)

• short term plasticity

  • Temporary modulation of signal transmission

• long term plasticity

  • Long-term strengthening or weakening of synaptic connections

• intrinsic plasticity

  • Altering neuron’s firing properties without changing synaptic connections

This phrase summarizes Hebbian plasticity:

When a presynaptic and postsynaptic neuron fire together repeatedly, the synapse between them strengthens.

This is a key mechanism in learning and memory formation, often observed as long-term potentiation (LTP).

This phrase describes anti-Hebbian plasticity or long-term depression (LTD):

If two neurons do not fire together, or their activity is uncorrelated, the synapse between them weakens.

This helps refine neural circuits by eliminating inefficient or unused connections.

LTD -> 3 Hz

LTP -> 50 Hz

• learning rule

• p = presynaptic neurons

• v = postsynaptic neurons

form of synaptic plasticity where changes in synaptic strength depend on the average firing rate of pre- and postsynaptic neurons, rather than the precise timing of their spikes

• Measures co-activation: if both pre- and postsynaptic neurons fire with high average rate, the synapse is strengthened.

• Leads to long-term potentiation (LTP) if co-activation is strong.

• original equation does not messure LTD

• Synaptic change depends on the average co-activity of two neurons over a time window twtw​.

• Allows both LTP and LTD, depending on whether the activity is positively or negatively correlated.

• Detects consistent patterns in co-activation beyond chance.

• Synaptic changes depend on how much both neurons deviate from their average firing rates.

• Detects structured co-activation, filtering out background or random noise.

• Produces LTP when both are above average together, and LTD when they vary oppositely.

O = Mittelwert der Feuerrate

Covariance-based learning can lead to unstable synaptic growth. Two core mechanisms used to stabilize it are:

• subtractive normalization

  • The same constant is subtracted from all synaptic weights, independent of individual weight size.

  • Creates strong competition: smaller weights are affected more.

  • Keeps total input constant

• divisive normalization

  • A value proportional to each weight is subtracted (or all weights are scaled).

  • creates a graded distribution of weights

  • preserves realtive differences between weights

• Measures the postsynaptic activity relative to a dynamic threshold; if activity is above the threshold → LTP, below → LTD, and the threshold adjusts over time.

• threshold θM​ is activity-dependent and adaptive

• Δw∝rpre​⋅rpost​⋅(rpost​−θM​):

  • θM​: sliding modification threshold (depends on average rpostrpost​)

  • If rpost>θM >θM​: LTP

  • If rpost<θM <θM​: LTD

    
    

• Balances synaptic strengthening and weakening

• Implements metaplasticity: the rules of plasticity themselves adapt

• Explains how neurons maintain stable but flexible connectivity

STDP (Spike-Timing-Dependent Plasticity): Synaptic strength changes based on the relative timing of spikes.

• Pre before post → LTP (causal = reinforce)

• Post before pre → LTD (non-causal = weaken)

• Captures temporal sensitivity of biological learning

• Shapes synaptic refinement, sensory map development, and learning sequences.

• relative timing

• neuromodulation

• firing pattern

Phenomenological (what)

• observed behavior or effects without necessarily explaining the underlying biological mechanisms in detail.

into

Biophysical (how)

• resolve parts of the underlying biological machinery invovlved in the induction of plasticity

Triplet STDP is an extension of classical STDP that considers sequences of three spikes (e.g., pre–post–post or post–pre–pre) to better capture how synapses change during repetitive or burst-like activity.

• Captures effects of burst timing, spike trains, and recent firing history.

Classical pair-based STDP cannot explain:

• Frequency dependence of plasticity

• Strong potentiation from bursts

• Nonlinear synaptic effects

BTDP is a plasticity rule based on the relative timing of spike bursts, not individual spikes.

1. If presynaptic burst occurs before postsynaptic → LTP

2. If postsynaptic burst occurs before presynaptic → LTD

• Captures plasticity from burst-based activity

• Reflects developmental learning, sensory refinement, and sequence encoding

• More robust than STDP in burst-driven systems

• based on postsnyaptic potential

• calcium based model

• additive weight change

• multiplicative weight change

• synaptic bounds

1. additive weight change

   1. at each pre-synaptic spike: change weight according to post-synaptic trace

   2. at each post-synaptic spike: change weight according to pre-synaptic trace

2. multipicative weight change

   1. at each pre-synaptic spike: change weight according to post-synaptic trace and weight

   2. at each post-synaptic spike: change weight according to pre-synaptic trace and weight

3. synaptic bounds:

   1. at each pre-synaptic spike: change weight according to post-synaptic trace or zero

   2. at each post-synaptic spike: change weight according to pre-synaptic trace or zero

Hebbian Rule

“Fire together, wire together”

LTP only Co-activation of pre- and post-synaptic neurons strengthens the synapse

No LTD, no timing involved

BCM Rule

Plasticity depends on postsynaptic activity relative to a sliding threshold

Above threshold → LTP Below threshold → LTD Threshold adapts over time for stability

Covariance Rule

Synaptic change depends on deviation from mean activity

Only co-activation above average leads to strengthening

Below average leads to weakening Unstable without normalization

Correlation/ STDP (Spike-Timing-Dependent Plasticity)

Plasticity depends on the exact timing of spikes Pre before post → LTP Post before pre → LTD Millisecond precision required

Correlation/ BTDP (Burst-Timing-Dependent Plasticity)

Like STDP, but based on timing of spike bursts

Burst timing determines direction of plasticity

Common in early development and some neural systems

In early brain development, neurons show spontaneous activity even without external input. This activity is often patterned (e.g. waves) and plays a key role in shaping and refining synaptic connections. It helps form initial circuits, guides synaptic strengthening or weakening, and supports experience-independent wiring of sensory systems (like visual or auditory pathways).

• Spontaneous activity: Neurons generate activity before sensory input arrives (e.g. retinal waves)

• Activity-dependent refinement: Synaptic connections are strengthened or eliminated based on neural activity

• Guidance cues: Chemical signals help neurons grow toward correct targets

• Critical periods: Time windows where circuits are especially sensitive to experience

• Synaptic plasticity mechanisms (e.g. Hebbian, STDP) shape functional connectivity

• The relative timing of pre- and postsynaptic spikes determines whether synapses are strengthened (LTP) or weakened (LTD)

• This principle is captured by STDP (Spike-Timing-Dependent Plasticity)

  • Pre before post (within ~20 ms) → LTP

  • Post before pre → LTD

• This precise timing encodes causality and helps in forming meaningful neural connections based on experience

The paper shows that the studied synapses exhibit synaptic depression so that their postsynaptic effect cannot be described by a single synaptic-strength parameter.

The synapses exhibit long-term potentiation of the “use-dependent efficacy” (which can be

interpreted as the neurotransmitter release probability) but not of the “absolute efficacy”, as

might have been expected.

This phenomenon provides a constraint for firing-rate codes and shows that synaptic dynamics

can effect neural coding properties.

(Tsodyks & Markram showed that synapses depress with repeated use,and LTP affects dynamic release probability, not total strength —meaning that synaptic dynamics shape how neurons encode information.)