13.2 Conduction Velocity, Synaptic Transmission & Postsynaptic Summation

13.2 Conduction Velocity, Synaptic Transmission & Postsynaptic Summation

Biophysics of Conduction Velocity: Axon Diameter vs. Myelination

Conduction velocity ($v$) of an action potential depends directly on the passive electrical cable properties of the axonal cylinder: membrane resistance ($r_m$), internal/axial resistance ($r_i$), and membrane capacitance ($c_m$):

• Length Constant ($\lambda = \sqrt{r_m / r_i}$): Reflects how far an electrical potential will spread passively before decaying to 37% of its original amplitude. A larger $\lambda$ promotes faster conduction.
• Time Constant ($\tau = r_m \cdot c_m$): The time required for the membrane potential to charge or discharge to 63% of its steady-state value. A smaller $\tau$ permits faster charging of adjacent membrane segments.

Increasing axonal diameter increases cross-sectional area (proportional to $r^2$), which dramatically decreases internal axial resistance ($r_i$), allowing electrotonic current to flow rapidly downstream. However, vertebrate biology cannot accommodate gigantic axons for millions of neurons. Instead, vertebrates evolved myelination:

• Myelin acts as a thick dielectric insulator, which increases membrane resistance ($r_m$) by preventing ions from leaking out through the internodal internode.
• Simultaneously, by increasing the physical separation between intracellular anions and extracellular cations, myelin drastically decreases membrane capacitance ($c_m$).
• Consequently, passive current flows nearly instantaneously along the myelinated internode without discharging the capacitor. At the unmyelinated nodes of Ranvier, where $Na_V$ channels are densely packed (>1,000 per square micrometer), the depolarizing current rapidly regenerates a full action potential. This jumping of the impulse from node to node is termed saltatory conduction and elevates transmission velocity up to $120\text{ m/s}$ (>250 mph). In demyelinating pathologies such as multiple sclerosis (CNS) or Guillain-Barré syndrome (PNS), the loss of myelin increases capacitance and leak, leading to conduction slowing or block.

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Chemical Synapses and Neurotransmitter Release Mechanics

When an action potential reaches the presynaptic axon terminal, electrical signaling must be converted into chemical signaling across the narrow (20-40 nm) synaptic cleft:

1. Depolarization of Axon Terminal: The arrival of the action potential depolarizes the presynaptic bouton, activating voltage-gated calcium channels ($Ca_V$).
2. Calcium Influx: Calcium rushes down its steep concentration gradient ($[Ca^{2+}]_{out} \approx 1-2\text{ mM}$ vs. $[Ca^{2+}]_{in} \approx 100\text{ nM}$) into the terminal cytoplasm.
3. SNARE-Mediated Vesicular Fusion: Intracellular free $Ca^{2+}$ binds to synaptotagmin, a calcium-sensor protein located on the membrane of neurotransmitter-filled synaptic vesicles. Synaptotagmin interacts with the SNARE complex:
   • v-SNARE: Synaptobrevin (VAMP) on the vesicle membrane.
   • t-SNAREs: Syntaxin-1 and SNAP-25 on the presynaptic plasma membrane. Binding triggers a conformational change that pulls the lipid bilayers together, mediating pore formation and vesicular exocytosis of neurotransmitter into the cleft.
4. Postsynaptic Receptor Binding: Neurotransmitter molecules diffuse across the synaptic cleft and bind specific postsynaptic receptors:
   • Ionotropic Receptors: Ligand-gated ion channels. Binding directly opens an integral pore, mediating rapid, millisecond-scale electrical responses (e.g., Nicotinic acetylcholine receptor, $GABA_A$, AMPA, NMDA).
   • Metabotropic Receptors: G-protein coupled receptors (GPCRs). Binding activates heterotrimeric G-proteins ($G_s, G_i, G_q$), triggering downstream intracellular second-messenger cascades (e.g., cAMP, $IP_3$/DAG, phosphorylation). Responses are slower in onset but sustained, modulatory, and amplified (e.g., Muscarinic acetylcholine receptors, $GABA_B$, adrenergic receptors).

Termination of Neurotransmitter Action

To prevent constant stimulation or desensitization, neurotransmitters must be rapidly cleared from the synaptic cleft via three classic mechanisms:

1. Enzymatic Degradation: Specific enzymes hydrolyze the neurotransmitter in the cleft. For example, acetylcholinesterase (AChE) cleaves acetylcholine into acetate and choline (which is taken back up via high-affinity choline transporters). Inhibition of AChE by organophosphates or sarin nerve gas causes toxic accumulation of acetylcholine, leading to SLUDGE syndrome (salivation, lacrimation, urination, defecation, GI upset, emesis) and flaccid muscle paralysis.
2. Reuptake into Presynaptic Terminals: Specific secondary active sodium-symporters reabsorb intact transmitter (e.g., Norepinephrine Transporter [NET], Serotonin Transporter [SERT], Dopamine Transporter [DAT]). Selective Serotonin Reuptake Inhibitors (SSRIs) block SERT to prolong serotonin signaling.
3. Glial Uptake and Diffusion: Astrocytes express excitatory amino acid transporters (EAATs) that clear glutamate from the cleft, converting it into glutamine via glutamine synthetase to prevent excitotoxicity.

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Postsynaptic Potentials and Summation Mechanics

Binding of neurotransmitters produces localized, graded electrical responses termed postsynaptic potentials:

• Excitatory Postsynaptic Potentials (EPSPs): Graded local depolarizations driven by inward flow of positive ions ($Na^+$ or $Ca^{2+}$) via ligand-gated channels. EPSPs shift $V_m$ closer to threshold (e.g., glutamate acting on AMPA receptors).
• Inhibitory Postsynaptic Potentials (IPSPs): Graded local hyperpolarizations driven by inward flow of anions ($Cl^-$) or outward flow of cations ($K^+$). IPSPs shift $V_m$ further from threshold (e.g., GABA acting on $GABA_A$ chloride channels, or glycine in the spinal cord).

Because an individual EPSP is typically minute (0.5-2 mV) and decays passively over distance, a single input rarely fires an action potential. The neuron integrates thousands of inputs at the axon hillock through two distinct summation mechanisms:

• Temporal Summation: Multiple high-frequency action potentials generated by a single presynaptic neuron in rapid succession arrive before previous postsynaptic potentials decay, incrementally compounding depolarization toward threshold.
• Spatial Summation: Graded potentials generated simultaneously by multiple distinct presynaptic inputs at physically separate dendritic or somatic locations converge and combine algebraically at the axon hillock.

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Summation and Postsynaptic Potentials

Whether a neuron fires is decided at the axon hillock by the algebraic sum of graded potentials, so both the source and the sign of each input matter.