Outline Ohm’s Law Voltage Clamp Current-Voltage Relationships Components/ conductances of an action potential

Ohm’s Law V = IR The potential difference between two points (A, B) linked by current path with the conductance (G) and current (I) is as follows: A B

Definition V=IR V=voltage, I=current, R=resistance g=1/R g=conductance   g=1/R g=conductance Vm=membrane voltage Vr=voltage of membrane at rest

Permeability and Conductance gna is low at Vr because sodium channels are closed. gk is higher than gna at Vr because some potassium channels are open.

Definitions Current=net flow of ions per unit time 1 ampere of current represents movement of 1 coulomb of charge per second Resistance- frictional forces that resists movement of ions or charges measured in ohm Current (I)= V/R

Definitions Conductance is the reciprocal of resistance and measures the ease with which current flows in an object. Measured in siemens (S) Capacitance refers to the ability of plasma membrane to store or separate charges of opposite signs. Myelin has high capacitance so stores charges and ions do not move across the membrane Measured in Farads

Conductance = g How many charges (ions) enters or leaves cell (inverse of resistance) due to: number of channels/membrane area Highest density at axon hillock number of open channels ion concentration on either side of membrane Measured in Siemens (S).

Action Potential Changes in Ion Permeability allows inward Na flux and triggers an increased outward K flux through voltage gated ion channels Causes transient change in Membrane Potential The change in ion permeability is triggered by transient depolarization of the membrane

Historical Figures Hodgkin and Huxley won Nobel Prize for Voltage clamp in 1961 used to identify the ion species that flowed during action potential Clamped Vm at 0mv to remove electric driving force than varied external ion concentration and observed ion efflux during a voltage step Sakman and Nehr won Nobel Prize for Patch Clamp in 1991 measured ion flow through individual channels shows that each channel is either in open or closed configuration with no intermediate. The sum of many recordings gives you the shape of sodium conductance.

Voltage Clamp Itotal = IC + Iionic where IC = C(dV/dt) Measures the amount of current needed to hold the cell at a given potential Itotal = IC + Iionic where IC = C(dV/dt) when clamping the cell at a certain voltage, at steady state, dV/dt=0, thus Itotal = II Vhold Battery: imposes a voltage drop across the cell membrane V-clamp I-clamp I

Voltage Clamp Vhold V-clamp I-clamp Can compensate for the capacitive current with amplifier. (ie. can force the Ic=0) By injecting an equal and opposite amount of current Iinj Vm Thus have full control over the membrane potential of the cell. Thus, can measure the conductance of the cell due to Iionic at any voltage

Box 3A The Voltage Clamp Technique neuro4e-box-03-a-0.jpg

Voltage Clamp vs. Current Clamp glut I-clamp V-clamp Upward deflections are depolarizing; downward are hyperpolarizing Downward (negative deflections) are inward currents; upward are outward

Figure 3.1 Current flow across a squid axon membrane during a voltage clamp experiment (Part 1) neuro4e-fig-03-01-1r.jpg

Figure 3.1 Current flow across a squid axon membrane during a voltage clamp experiment (Part 2) neuro4e-fig-03-01-2r.jpg

Figure 3.2 Current produced by membrane depolarizations to several different potentials (Part 1) neuro4e-fig-03-02-1r.jpg

Figure 3.3 Relationship between current amplitude and membrane potential neuro4e-fig-03-03-0.jpg

Figure 3.4 Dependence of the early inward current on sodium neuro4e-fig-03-04-0.jpg

Figure 3.5 Pharmacological separation of Na+ and K+ currents neuro4e-fig-03-05-0.jpg

Figure 3.6 Membrane conductance changes underlying the action potential are time- and voltage-dependent (Part 1) neuro4e-fig-03-06-1r.jpg

Figure 3.6 Membrane conductance changes underlying the action potential are time- and voltage-dependent (Part 3) neuro4e-fig-03-06-3r.jpg

Figure 3.7 Depolarization increases Na+ and K+ conductances of the squid giant axon neuro4e-fig-03-07-0.jpg

Figure 3.8 Mathematical reconstruction of the action potential neuro4e-fig-03-08-0.jpg

Figure 3.9 Feedback cycles responsible for membrane potential changes during an action potential neuro4e-fig-03-09-0.jpg

Action Potentials The Hodgkin-Huxley Model The squid giant axon action potential had only sodium and potassium currents…. Other cells’ action potentials are shaped by a number of other conductances.

Squid Axon Action Potentials Current clamp Voltage clamp Assymetrical currents w/ depol or hyperpol V-steps ie. non-Ohmic I-V relationship

Ion Permeability Changes during action potential The plasma membrane becomes permeable to sodium ions Permeability increases from 0.02 to 20=1000 fold increase Causes Em aka Vr to approach Ena at positive voltages = +20mV

6 Characteristics of an Action Potential #1 Triggered by depolarization a less negative membrane potential that occurs transiently Understand depolarization, repolarization and hyperpolarization

#2 Threshold Threshold depolarization needed to trigger the action potential 10-20 mV depolarization must occur to trigger action potential

#3 All or None Are all-or- none event Amplitude of AP is the same regardless of whether the depolarizing event was weak (+20mV) or strong (+40mV).

#4 No Change in Size The shape (amplitude & time) of the action potential does not change as it travels along the axon Propagates without decrement along axon

#5 Reverses Polarity At peak of action potential the membrane potential reverses polarity. Becomes positive inside as predicted by the Ena Called OVERSHOOT Return to membrane potential to a more negative potential than at rest Called UNDERSHOOT

#6 Refractory Period Absolute refractory period follows an action potential. Lasts 1 msec During this time another action potential CANNOT be fired even if there is a transient depolarization. Limits firing rate to 1000AP/sec

Nerve Impulse Conduction Conduction of action potentials is not like conduction of charge along a wire conductor. The axon is a poor conductor of electrical charge and is leaky to charge in the form of ions. Within a short distance, the flow of electrical charge is greatly diminished. However, this passive electrotonic spread of charge in an axon is an important component of the propagation of action potentials down the axon.

Propagation of the Action Potential The action potential is regenerated all along the axon like a series of relay stations. Localized flow of current from the region undergoing an action potential depolarizes the adjacent membrane. Voltage gated Na+ channels in the adjacent membrane respond by opening their activation gates. A new action potential is triggered in the adjacent membrane. This sequence is repeated down the length of the axon. Action potentials don’t decay in strength as they are conducted down the axon.

Unidirectional Propagation Propagation of the action potential only moves in one direction, from the axon hillock to the axon terminals. The region just recovering from an action potential (K+ outflow region) cannot be stimulated by local current flow. During the repolarizing and undershoot phases, the inactivation gates of the Na+ channels are still closed, blocking any Na+ influx even if the activation gates were to open. Refractory period

2 ways to increase AP propagation speed Increase internal diameter of axon which decreases the internal resistance to ion flow. Increase the resistance of the plasma membrane to charge flow by insulating it with myelin.

Myelinated Neurons Many vertebrate peripheral neurons have an insulating sheath around the axon called myelin which is formed by Schwann cells. Myelin sheathing allows these neurons to conduct action potentials much faster than in non-myelinated neurons.

Saltatory Conduction in Myelinated Axons Myelin sheathing is interrupted by bare patches of axon called nodes of Ranvier where ion channels are concentrated. Action potentials jump from node to node without depolarizing the region under the myelin sheath - called saltatory conduction. Myelin sheathing improves the ability of electrical charge to flow far enough down the axon to reach the next node.

Myelinated Neurons Conduct Faster Than Non-myelinated Myelin sheathing and saltatory conduction improves the speed of nerve impulse conduction. This allows small diameter neurons to conduct impulses rapidly. Invertebrates, which don’t have myelinated neurons, have to increase axon diameter to speed up conduction. The larger the cross-sectional area of a neuron, the further it can conduct electrical charge along the axon. Giant axons are found in some invertebrates like earthworms and squid that need to rapidly conduct nerve impulses to distant muscles for escape responses.