Biology for Engineers: Cellular and Systems Neurophysiology

1. Biology for Engineers: Cellular and Systems Neurophysiology Christopher Fiorillo BiS 521, Fall 2009 042 350 4326, fiorillo@kaist.ac.kr Part 3: Dynamic Regulation of Membrane Voltage Reading: Bear, Connors, and Paradiso Chapter 4

2. The Action Potential • Graded changes in current cause graded changes in voltage. • If voltage is depolarized beyond a threshold (about -50 mV), an action potential is triggered.

3. An Action Potential is “All-or-None” • At a brief moment in time (~1 ms), an action potential either occurs or it does not • The shape of an action potential is always the same (almost) • The magnitude of the current and depolarization that triggered the action potential do not matter (but the depolarization must reach threshold)

4. Firing Rate Depends on Current Magnitude • The frequency of action potentials (“firing rate”) depends on the magnitude of depolarizing current (assuming that the current lasts long enough).

5. Why Do Neurons Have Action Potentials? • Current that enters the cell at one point will spread passively through the cytosol of a dendrite. • Because of membrane permeability, current leaks out of the neuron as it travels along a dendrite. • Thus information cannot be conveyed over long distances through passive spread of current. • An action potential is “regenerative” and therefore it can reliably carry information over long distances. • Trade-off: Digital (action potential) versus Analog (membrane voltage) • Most neurons have action potentials. • Many neurons that do not need to transmit information over long distances do not have action potentials.

6. Phases of the Action Potential • Rising phase • Overshoot • Falling phase • Undershoot

7. Properties of the Action Potential • Threshold • Caused by positive feedback among Na+ channels • Requires high density of Na+ channels • Rising phase • Increase in Na+ conductance • Overshoot • Positive membrane voltage (no functional significance) • Falling phase • Inactivation of Na+ conductance • Activation of K+ conductance • Undershoot (After-Hyperpolarization) • K+ conductance greater than before start of action potential • Absolute refractory period • Na+ channel inactivation makes it impossible to elicit another action potential • Relative refractory period • High K+ conductance means that a large depolarizing current is necessary to elicit another action potential

8. The Hodgkin-Huxley Model • Hodgkin and Huxley described the ionic basis of the action potential (1952) • This is considered the most important single achievement in cellular neurophysiology. • Their approach: Experiments on the squid giant axon • Two electrode voltage clamp (1 mm diameter axon) • Measured the voltage-dependence and kinetics of sodium and potassium currents • Ion substitution experiments • They derived a relatively simple but detailed mathematical and biophysical model of the action potential • Their model is still the “textbook” model • The utility of their model extends beyond the action potential. It is useful for understanding all voltage-dependent ion channels • Their model predicted some of the key properties of ion channels • It was about 30 years later (~1980) that scientists were able to identify and record single ion channels • It was about 10 years after that (~1990) that people began to clone ion channels (to discover their amino acid sequence) • It was about 10 years after that (~2000) that the 3-dimensional structure and function of ion channels began to be understood (Rod Mackinnon)

9. The Patch Clamp Method • Developed by Erwin Neher • Very useful for electrophysiology • Enables the recording of single channels

10. Recordings of Single Na+ Channels • Channels exist in discrete states: Open or closed • The channels “behavior” will not be the same, even under identical conditions. It is “stochastic.” • Inactivation occurs after the channel opens

11. Relationship between single channel and cellular currents • Macroscopic currents in the cell result from the summation of many microscopic single channel currents • Although single channel currents are stochastic, currents within the cell are not. They are highly reproducible. • Single sodium channels do not have a threshold voltage at which they open • The action potential threshold depends on positive feedback between many sodium channels • Action potentials require a high density of sodium channels • A sufficient number of channels must be deinactivated (ready to be opened)

12. Structure of Ion Channels Na+ channel • The Voltage-Gated Sodium Channel • Four subunits • Each has 6 transmembrane alpha-helices • Voltage sensor (positive charges) on S4 • Selectivity filter • Gate K+ channel

13. The Voltage-gated Sodium Channel • Structure – gating and pore selectivity • Positive charges move with changes in voltage • Conformational change in protein • Gating current can be measured • Ion selectivity is possible because of the difference in size between sodium and potassium

14. An Ion Channel Has Many States (Conformations) • States of a glutamate-gated ion channel (4 subunits) are shown • Open states require that glutamate is bound • There are many desensitized (inactivated) states • Gray states are seldom visited • This is typical of many ion channels, including voltage-gated ion channels • This is probably more simplistic than reality

15. Three Key Properties of Voltage-gated Ion Channels • Ion selectivity • Voltage-dependence • Time-dependence (Kinetics)

16. Voltage-Dependence of Ion Channels in HH model • ‘n-infinity’ is the steady-state probability that a K+ channel subunit “gate” is in the “open” conformation • The channel is only open when all four subunit gates are in open conformation • Thus, the steady-state probability that a channel is open: • Po = ninfinity4 • The Na+ channel has three activation gates (m) and one inactivation gate (h) • Thus, the steady-state probability that a channel is open: • Po = minfinity3h

17. Summary of Voltage-Dependence of Parameters in HH model

18. ventricular myocytes 200 ms Kv4.3 2000 ms Diversity of K+ Channel Kinetics

19. Kinetics of Ion Channels Underlying the Action Potential • Sodium channels activate and inactivate quickly • Potassium channels activate slowly

20. The Spread of Current Through Neurons • Passive spread of current DVx = DV0e-x/l • = square root (rm/ra) • Lambda is the “length constant” • At a distance lambda, the change in voltage will be 1/e of the original change in voltage • Actual length constants are 0.1 - 1.0 mm

21. Action Potential Conduction • Propagation of the action potential • It is an active, regenerative process, but it still relies upon the passive spread of current • Orthodromic: Action potential travels from soma to terminal • Antidromic (experimental): Backward propagation (towards soma)

22. Conduction Velocity • Conduction velocity (0.5-80 m/s) • Two means of increasing velocity • Diameter of axon (or dendrite) • Increases speed by decreasing axial resistance • Squid Giant Axon: 1 mm • Insulation • Myelination by glia • Increases membrane resistance and decreases membrane capacitance • Some information needs to be transmitted quickly, some does not • Large axons and myelination are each costly • Some axons are small and unmyelinated

23. Myelination • Some axons are insulated by glial cells • Node of Ranvier • Gap in myelin sheath • High density of Na+ channels • Current decays as it passes from one node to another • Multiple sclerosis is caused by degeneration of myelin

24. Initiation and propagation of action potentials • Requires a high density of sodium channels • High density is found in: • Axon • Nerve endings of primary somatosensory neurons • Dendrites have lower density, but some dendrites can have action potentials • Dendritic action potentials are not always all-or-none • Forward and backward propagation

25. Beyond the Action Potential • We have focused on action potentials, but the HH model can be extended (by changing parameter values) to include many other types of voltage-gated ion channels • Voltage-gated ion channels do not only mediate the action potential. They also influence the pattern of action potentials. • Different neurons express different sets of voltage-regulated ion channels • Therefore, different neurons have different firing patterns in response to the same excitatory input

26. Measuring the Current-Voltage Relationship • The Current-Voltage relationship of a cloned Na+ channel • At very negative potentials, the channels are closed • At very positive potentials, the current is small, or positive, because of inactivation and the sodium reversal potential • It would be useful to measure the I-V curve when the sodium channels are open • A “tail current” protocol can be used for this purpose

27. Measuring the Current-Voltage Relationship • A “Tail Current” protocol activates channels and then measures the I-V function at a brief moment in time • A voltage protocol is delivered that is designed to strongly activate the channels • The voltage is then stepped to different potentials, and the instantaneous “tail” current is measured at each potential • An I-V curve is constructed • Another I-V curve can be constructed without the first “activating” voltage protocol • The second I-V curve is then subtracted from the first. The resulting curve shows the I-V relationship of the isolated current. • In this example (from glial cells), the reversal potential of the current matches the theoretical K+ reversal potential • The I-V function is linear because it follows Ohm’s Law. • no time is allowed for the channels to open or close at the “new” voltage

29. Voltage-regulated ion channels • Na+ channels • depolarization activated • Ca2+ channels • depolarization activated • L-type, T-type, N-type, P-type, Q-type, R-type • Cl- channels • depolarization activated • not common • Cation channel (non-selective; Na+ and K+) • Hyperpolarizaton activated • “H” current • K+ channels • Depolarization activated • Most diverse • A-type, M-type, delayed rectifier, inward rectifier, etc. • Multiple types of calcium-activated K+ channels (BK, SK, etc)

30. K+ channel diversity • This shows only genetic diversity (~100 genes) • There is great diversity created by non-genetic mechanisms, such as alternative splicing of mRNA, post-translational modifications, varying subunit composition, and phosphorylation • There are probably hundreds, or even thousands, of functionally distinct K+ channels • A typical neuron might express about 10 types, or more

31. ventricular myocytes 200 ms Kv4.3 2000 ms Diversity of K+ Channel Kinetics

32. The After-Hyperpolarization in Hippocampal Pyramidal Neurons • Three components to the AHP, mediated by 4 K+ channel types • Fast • BK-type K+ channels, activated synergistically by calcium and voltage • Medium • M-type K+ channel, voltage-activated • Calcium-activated K+ channel • Slow • Calcium-activated K+ channel

33. H-current (HCN channels) • HCN channels are hyperpolarization activated, non-selective cation channels that underlie the “H-current”

34. Representation of Space and Time • Inputs to a neuron: • Non-synaptic, voltage-regulated ion channels carry information from the past • The conductance of these channels depends on the history of a neuron’s voltage • Different types of channels represent different periods of the past, depending on their kinetics • Synaptic inputs represent points in space • Different synapses represent different points in space • A neuron’s output depends on integration of the conductance of all of its ion channels