COGNITIVE SCIENCE 107A

Electrophysiology:

Electrotonic Properties 2

Jaime A. Pineda, Ph.D.

The Model Neuron Lab •  Your PC/CSB115 http://cogsci.ucsd.edu/~pineda/COGS107A/index.html •  Labs - Electrophysiology •  Home - ModelNeuron.zip •  Download ModelNeuron.zip •  Uncompress ModelNeuron.zip •  Double click on ccwin32 •  Do the assignment. *** PASSIVE.CCS=PASS.CCS, ACTIVE.CCS=ACTIV.CCS

Modern Electrophysiology

•  Many ion channels differ in: –  Trigger (ligand, voltage, stretch) –  Time course (transient/sustained) –  Sensitivity to Vm and ligands

•  (low/high threshold/affinity)

•  Ion channel distribution varies across neuron –  Nonuniform but not random

distribution –  Highest Na+ channel density in IS

•  Ion channels change frequently –  up/down regulation

Differences in Channel Currents

•  INat – rapidly activating/inactivating Na current

•  INap – “persistent” Na current, which does not inactivate; activated by subthreshold inputs; controls responsiveness of cell; responsible for “plateau” potentials - related to memory processes?

Differences in Channel Kinetics •  K channel

–  Ligand- and voltage-sensitive gate

–  Opens by depolarization of Vm (activates)

–  Closes by repolarization of Vm (deactivates)

•  Na channel –  Ligand and voltage-

sensitive gate –  Activates –  Deactivates –  Inactivates (despite

depolarization) –  Deinactivates (removal of

inactivation)

Ion Flow During an Action Potential

Na+ / K+ Pump

Restores equilibrium

(Transmembrane ATPase – an enzyme that catalyzes ATP into ADP and releases energy)

Na+-K+-ATPase The pump, with bound ATP, binds 3 intracellular Na+ ions. •  ATP is hydrolyzed, leading to phosphorylation of the

pump and subsequent release of ADP. •  A conformational change in the pump exposes the Na+

ions to the outside. The phosphorylated form of the pump has a low affinity for Na+ ions, so they are released.

•  The pump binds 2 extracellular K+ ions. This causes the dephosphorylation of the pump, reverting it to its previous conformational state, transporting the K+ ions into the cell.

•  The dephosphorylated form of the pump has a higher affinity for Na+ ions than K+ ions, so the two bound K+ ions are released. ATP binds, and the process starts again.

Advantages of myelination

•  Reduces number of ion channels •  Reduces number of Na+ / K+ pump •  Increases speed of conduction •  Reduces energy needs

Saltatory Conduction

Characteristic Patterns of Activity

•  Regular firing –  One spike at a time –  Intensity of stimulation

increases rate •  Rhythmic bursts

–  Regular/irregular •  Spike frequency

adaptation •  Slow oscillatory

NERNST EQUATION (Walter Nernst, 1888)

At body temperature (37o C): E = 61.5 x log10 [ion]o/[ion]i

Rule: The membrane potential of a cell will be closest to the equilibrium potential of the ion to which the membrane is most permeable.

ENa+ = +56 mV ECl- = - 60 mV EK+ = - 75 mV ECa++= +125mV

A way to determine the equilibrium potential for a specific ion – assumes no pump

Membrane Potential: Goldman-Hodgkin-Katz Equation

•  P = permeability (pK:pNa:pCl = 1:0.04:0.45) •  Net potential movement for all ions •  known Vm:Can predict direction of movement

of any ion ~

biological realism

Compartment Models

•  Neuron can be modeled as an electrical circuit with some simplifying assumptions: –  Segments are cylinders with a constant radius –  Current in a segment flows like in a cable

Other Assumptions

•  The lipid bilayer is represented as a capacitance (Cm)

•  Ion channels are represented by resistors or electrical conductances (gn)

•  The electrochemical gradients are represented by batteries

•  Ion pumps are represented by current sources (Ip)

INSIDE

POS

NEG

Electrochemical gradients resemble a battery

OUTSIDE

•  Electric current flows in accord with the following equations:

V = I x R (Ohm’s Law)

V = Vm – Er V = electrotonic potential

Vm = changed membrane potential

Er = resting membrane potential

Thus, one can construct an “equivalent circuit” per segment

Cm - capacitor Em - battery Rm - membrane resistance Ra - axial resistance Gm - conductance reciprocal of resistance I - current source

Compartment Models (assumptions cont.)

–  Electrotonic current is Ohmic in accord with the equation: V = I x R (Ohm’s Law)

–  Current divides into two local resistance paths: internal or axial (ri or ra) current membrane (rm) current

–  Axial current is inversely proportional to diameter •  ri = Ri/A where A = πr2

–  Membrane current is inversely proportional to membrane surface area (and density of channels)

•  rm = Rm/c where c=2πr

Steady-state solution

in centimeters

ri = Ri/A

rm = Rm/c

SPATIAL SUMMATION

Transient-state solution (the importance of membrane capacitance - Cm)

Capacitance how rapidly a membrane charges up (low pass filter)

TEMPORAL SUMMATION

•  Velocity of electrotonic spread is equal to 2 * (lambda/tau)

•  Synaptic integration is non-linear

Variables that contribute to integration

•  Cellular properties –  Space/time constants –  Membrane potential –  Thresholds –  Spike frequency

adaptation –  Delayed excitation

•  Synaptic properties –  Sign (+/-) –  Strength –  Time course –  Type of transmission

•  Chemical •  Electrical

Pyramidal cells… -75mV Thalamic cells…. -65mV Photoreceptors… -40mV

TTX (tetrodotoxin) And TEA (tetraethyl ammonium) – block INa and IK, respectively

Phases of the Action Potential

Firing threshold is the point at which the number of activated Na+ channels > inactivated Na+ channels

Absolute refractory period

Relative refractory period

Determining Rate of Firing

•  Absolute refractory period – mediated by the inactivation of Na+ channels.

•  Relative refractory period – occurs in the hyperpolarization phase.