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 V m 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 I Nat rapidly activating/inactivating Na current I Nap 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 voltagesensitive gate Opens by depolarization of Vm (activates) Closes by repolarization of Vm (deactivates) Na channel Ligand and voltagesensitive gate Activates Deactivates Inactivates (despite depolarization) Deinactivates (removal of inactivation)
Ion Flow During an Action Potential
Na+ / K+ Pump (Transmembrane ATPase an enzyme that catalyzes ATP into ADP and releases energy) Restores equilibrium
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) A way to determine the equilibrium potential for a specific ion assumes no pump E Na+ = +56 mv E Cl- = - 60 mv E K+ = - 75 mv E Ca++ = +125mV At body temperature (37 o C): E = 61.5 x log 10 [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.
Membrane Potential: Goldman-Hodgkin-Katz Equation P = permeability (pk:pna:pcl = 1:0.04:0.45) Net potential movement for all ions known V m :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 (C m ) Ion channels are represented by resistors or electrical conductances (g n ) The electrochemical gradients are represented by batteries Ion pumps are represented by current sources (I p )
Electrochemical gradients resemble a battery OUTSIDE POS INSIDE NEG
Electric current flows in accord with the following equations: V = I x R (Ohm s Law) V = V m E r V = electrotonic potential V m = changed membrane potential E r = resting membrane potential Thus, one can construct an equivalent circuit per segment C m - capacitor E m - battery R m - membrane resistance R a - axial resistance G m - 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 (r i or r a ) current membrane (r m ) current Axial current is inversely proportional to diameter r i = Ri/A where A = πr 2 Membrane current is inversely proportional to membrane surface area (and density of channels) r m = R m /c where c=2πr
Steady-state solution in centimeters
r m = R m /c r i = R i /A
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
TTX (tetrodotoxin) And TEA (tetraethyl ammonium) block I Na and I K, respectively Pyramidal cells -75mV Thalamic cells. -65mV Photoreceptors -40mV
Phases of the Action Potential Absolute refractory period Relative refractory period Firing threshold is the point at which the number of activated Na+ channels > inactivated Na+ channels
Determining Rate of Firing Absolute refractory period mediated by the inactivation of Na + channels. Relative refractory period occurs in the hyperpolarization phase.