cognitive science 107apineda/cogs107a/lectures...[ion] o /[ion] i rule: the membrane potential of a...
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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.