L3 - Postsynaptic Potentials: Size, Decay, Summation & Dendritic Integration

Overview

• Focus: biophysical determinants of postsynaptic potentials (PSPs) – their size, decay, and summation.
  • Types: Excitatory (EPSPs, typically glutamate opening non-selective cation channels) vs. Inhibitory (IPSPs, typically GABA opening Cl⁻ channels).
  • Two main themes explored:
  • Factors that set the initial amplitude of an EPSP/IPSP at the synapse.
  • How distance and time alter that amplitude before it reaches the soma and trigger zone.

Determinants of EPSP/IPSP Size at the Synapse

• Neurotransmitter identity & channel type opened.
• Number of vesicles released (quantal content).
• Postsynaptic receptor density & properties.
• Driving force for ions (membrane potential relative to ion equilibrium potentials).
• Experimental example (neuromuscular junction):
  • Preparation placed in low [Ca^{2+}]{o} / high [Mg^{2+}]{o} bath.
  • Low Ca^{2+} → few vesicles released per stimulus.
  • Recorded PSP amplitudes showed discrete steps: failures, unit, double, quadruple.
  • Histogram: peaks at 0.4\,\text{mV}, 0.8\,\text{mV}, 1.2\,\text{mV} … ⇒ quantization.
  • Miniature PSP (mPSP): response to single vesicle, stereotyped amplitude.

Quantal Nature of Neurotransmitter Release

• Vesicles are uniform packages; each contains roughly the same number of transmitter molecules.
• Release is probabilistic; with very low Ca^{2+} you isolate single-vesicle events.
• In normal physiological Ca^{2+} many vesicles fuse simultaneously → larger PSPs.
• Key consequence: synaptic strength can be modulated by altering probability of release (presynaptic) or vesicle size (rare) or postsynaptic receptor count.

Distance-Dependent Decay: Space (Length) Constant \lambda

• Passive spread in dendrites described by exponential decay:
  • V(x)=V_0 e^{-x/\lambda}
• \lambda (space/length constant): distance where voltage falls to 1/e \approx 37\% of initial.
• \lambda = \sqrt{\frac{rm}{ri}} (qualitative)
  • rm: membrane resistance (fewer leak channels ↑ rm ↑ \lambda).
  • ri: internal (axial) resistance (larger diameter ↓ ri ↑ \lambda).
• Experiment: inject constant current at one dendritic point, record at multiple distances.
  • Plot of % peak depolarization vs. distance matched exponential curve.
  • Demonstrates charge leakage through K_{2P} (leak K⁺) channels.

Time Constant \tau and Temporal Summation

• \tau = Rm Cm (membrane resistance × capacitance).
• Long \tau:
  • Slow decay of a PSP; successive inputs summate even if widely spaced.
  • Good for integrating activity but blurs precise timing.
• Short \tau:
  • Fast decay; requires high-frequency inputs for summation.
  • Preserves temporal precision but reduces likelihood of reaching threshold.
• Example: two identical synaptic currents separated in time.
  • Long \tau cell achieves summation ≥ threshold.
  • Short \tau cell fails to summate.

Spatial Summation & Proximity Effects

• Two simultaneous synapses at different dendritic sites.
  • Long \lambda → both contribute strongly to soma → summation.
  • Short \lambda → only proximal site exerts large effect.
• Rule of thumb analogy:
  • Influence someone by standing close (proximal synapse) and/or speaking loudly (larger local PSP).

Bidirectional Passive Spread

• Hyperpolarizations (IPSPs) also propagate.
  • Experiment with two inhibitory synapses: distal input produces large local hyperpolarization, small somatic; proximal input shows opposite.
  • Demonstrates passive current can flow toward or away from soma.

Active Conduction in Dendrites

• Some dendrites possess sparse voltage-gated Na⁺ or Ca²⁺ channels.
  • Provide "boost" to decaying PSPs but rarely generate full axonal-like action potentials.
  • Increase likelihood a distal EPSP influences soma (partial regenerative amplification).
  • Still graded, not all-or-none.

Triple-Patch Experiment (Soma + Proximal + Distal)

• Slice, fill neuron, patch three electrodes (red = soma, blue = proximal apical dendrite, green = distal apical dendrite ~750 µm away).
• Spontaneous PSPs categorized by origin:
  1. Distal origin: largest at green, medium at blue, tiny/negligible at red.
  2. Proximal origin: largest at blue, medium both directions.
  3. Somatic origin: largest at red, decays bidirectionally.
• Aggregate data:
  • Local dendritic PSP amplitude grows with distance from soma (distal synapses "shout louder").
  • Somatic amplitude falls with distance; compensation not perfect.
  • Plot: increasing dendritic amplitude vs. distance but decreasing somatic impact.
• Physiological implication: distal synapses can compensate for distance by larger conductance or cooperative inputs (e.g., clustered synapses, active boosting).

Plasticity Mechanisms Affecting PSP Size

• Synaptic rearrangement (structural plasticity):
  • Neuron A loses contacts; Neuron B gains → changes network weight.
• Long-Term Potentiation (LTP) of receptor density:
  • Initially few AMPA receptors → after LTP additional receptors inserted → same glutamate release causes larger EPSP.
• Both mechanisms alter effective quantal amplitude and/or probability, underpinning learning & memory.

Numerical & Conceptual Summary

• Quantal amplitude example: \approx 0.4\,\text{mV} per vesicle (neuromuscular prep).
• Failure rate example: 18/# trials showed 0 mV change under low Ca^{2+}.
• Length constant experimental value (illustrative): decay to 1/e within ~200–300 µm for many dendrites (exact graph values context dependent).
• Triple-patch distal PSP example: local 1.2\,\text{mV} at 700 µm → 0.1\,\text{mV} at soma.

Key Equations & Definitions

• Miniature PSP (mPSP): postsynaptic voltage change produced by a single vesicle.
• Spatial decay: V(x)=V_0 e^{-x/\lambda}.
• Space constant: \lambda=\sqrt{Rm/ Ri} (qualitative; exact derivation uses specific resistances).
• Temporal decay (charging curve): V(t)=V0 (1-e^{-t/\tau}) for current step; decay V(t)=V0 e^{-t/\tau} after current stops.
• Time constant: \tau = Rm Cm.

Real-World & Conceptual Connections

• Quantal theory pioneered at neuromuscular junction extends to CNS synapses.
• Clinical/drug relevance: agents altering Ca^{2+} influx or leak conductances modulate synaptic efficacy (e.g., Ca²⁺ channel blockers, anesthetics via K_{2P} channels).
• Computational neuroscience: dendritic integration underpinning logical operations (AND via summation, NOT via IPSPs).
• Learning & memory: LTP, dendritic spine dynamics, and activity-dependent pruning are cellular substrates for experience-dependent plasticity.

Ethical & Philosophical Notes

• Animal tissue slicing experiments raise welfare considerations; governed by ethical review boards.
• Understanding dendritic computation influences AI/ML architectures (neuromorphic chips) and philosophical debates on localization of neural processing vs. distributed networks.

Take-Home Analogies

• "Proximity + Volume" analogy: To influence the soma (decision center), be near and speak loudly; distal synapses compensate by louder voices, sometimes with a megaphone (active conductance) or by recruiting friends (synaptic clustering).