3resting Potential & Action Potential

Chapter 5 Resting Potential & Action Potential

Outline Outline • Measuring membrane potential • Ionic basis of resting potential & action potential • Initiation and propagation of action potential

Historical Background on Nerve Impulses 

Greeks 



Some thought the brain secreted fluids or "spirits" that flow through the nerves to the muscles

Luigi Galvani 1791 

Discovered that frog muscles can be stimulated by electricity, postulated the existence of "animal electricity" in nerves and muscles, study of frog legs lead to recognition of current electricity, before only static electricity was known, led to development of electric battery

Historical Background on Nerve Impulses 

Carlo Matteuci 1840's 



Obtained the first evidence of the electrical nature of the nerve impulse

Emil du Bois Reymond 1840's 

Followed up Matteuci's work, did extensive work on nerve impulses

Historical Background on Nerve Impulses 

Herman von Helmholtz 1850 

Colleague of du Bois Reymond, famous physicist, physiologist, determined velocity of nerve impulse in large nerves of frog, as about 40 m/sec or 140 km/hr, or 88 mi/hr

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Demonstrated that nerve impulse was active biological process, different from the passage of a current through a wire

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For some, slow speed was evidence for dualism ie. mind is separate from body, immaterial soul (The concept that human beings have two basic natures, the physical and the spiritual)

§5.1 Measuring Membrane

Potential

Much of our early knowledge of nerve electrical activity came from the study of giant squid axons. Because of their size, it was easy to insert electrodes into them for accurate measurements of the membrane potential.

Microelectrode

Making fine tip of pipette with resistance around 30 mΩ , diameter ≤ 1µ m by puller

Resting Potential

a

a.Microelectrodes applied to the membrane surface record no voltage change.

b. When microelectrode b

1 is inserted into the axoplasm, a voltage change is recorded. The graphs chart the voltage change over time.

Concept of the Resting Potential Rest potential (RP) defined as at rest, a potential difference across cell membrane, also termed as transmembrane resting potential.

Resting Membrane Potential (Difference)  The

resting membrane potential is the electrical gradient across the cell membrane.  Potential: the electrical gradient created by the active transport of ions is a source of stored or potential energy, like chemical gradients are a form of potential energy.  Resting: the membrane potential has reached a steady state and is not changing.  Difference: the difference in the electrical charge inside and outside the cell (this term is usually omitted)

Properties Properties of of Resting Resting Potential Potential 



RP is a constant, steady direct current, with the interior of the cell negative with respect to the exterior. The size of the resting potential varies, but in neuron or muscle it runs about –70 to -90 (mV).

Terminology 

Polarization state 

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Hyperpolarization 

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An increase in charge separation or cell becomes more negative inside than at rest

Depolarization 



polarity of potential across membrane or charge separation

A reduction of the charge separation or cell becomes less negative inside than at rest

Repolarization 

With the completion of depolarization, the membrane potential returns to its resting state

Action Potential 

Action potential (AP) : A brief transient reversal of membrane potential that sweeps along the membrane of a cell in response to the appropriate stimulus.

Characteristics of the action potential (AP)  





Action potential is temporary, lasts only about 1 millisecond at any one point on membrane Generation of an action potential at one location on membrane induces an action potential in adjacent membrane, thus AP propagates down axon For AP to be elicited, neuron must be stimulated strongly enough that membrane is depolarized to threshold AP is all or none, once elicited always of same amplitude

Terminology Spike

Overshoot

potential



Overshoot



Upstroke (rise) of the AP

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Downstroke (fall) of the AP

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Positive after potential

Rising phase

Falling phase

Positive after-potential

§5.2 Ionic Basis of Resting Potential and Action Potential

 Membrane hypothesis 1. The concentration differences of ions [Na+] : outside the cell > inside the cell (about 10 times) Julius Bernstein 1839-1917

[ K+ ] : inside the cell > outside the cell (about 20 times)

2. Membrane Permeability to different kinds of ion changes with membrane potential. The membrane is permeable only to K+ at rest, and that this selectivity breaks down during the action potential. 3. A sodium/potassium pump maintains concentrations gradient.

Permeability and Conductance 



Opening of gated ion channels alters permeability of membrane to the ion that can pass through the channel For convenience, neurophysiologists use conductance, because more readily measured, conductance is inverse of electrical resistance, and is a measure of how difficult it is for a charged particle to move through a conductor

Factors Determining Membrane Conductance 1.

Availability (concentration) of the ion 

Under normal conditions this is not a limiting factor, concentration of ions inside and outside the neuron do not change significantly

Factors Determining Membrane Conductance Density of channels for the ion

2. 





In squid giant axon, there are 300 voltage sensitive Na+ channels and 20-30 voltage sensitive K+ channels per square micron If 1 square micron of membrane scaled up to size of football field 4.1 yds (3.9 m) between adjacent Na+ channels, K+ channels 13.3-16.3 yds (12.2 to 14.9 m) apart, density of leakage channels unknown Number of channels in a patch of membrane may change over days or weeks, but not on the timescale of APs

Factors Determining Membrane Conductance 3.

Number of those channels that are open 

In resting neuron nearly all Na+ channels, and most K+ channels closed. When neuron at rest, most ions cross membrane via leakage channels (along with those transported by Na+/K+ exchange pump

Resting potential and K+ equilibrium potential

Ion distributions in a living cell ICF

K 136.0 Cl3.5 Na+ 9.0 HCO-3 1.0 An- 140.5 +

ECF

4.0 119.0 141.0 26.0 --

Na+ and Cl- are more concentrated outside the cell K+ and organic anions (organic acids and proteins) are more concentrated inside.

What happened to K? 

At the beginning, concentration fore acted on K+



Then, outward movement of K+ generated a second force acting on K+ ( electrical force), an electrical potential directed opposite to the concentration (chemical) force.

Intuitively……. 





There is a quantitative relationship between Ek (electrical force) & the K concentration gradient (chemical force) The ratio [K]o/[K]I is a measure of the concentration gradient therefore,

[ K ]o Ek = ( factor ) [ K ]i

Calculating equilibrium potentials for single ions: Nernst Equation

Eion

RT [ K ]o = ln zF [ K ]i

for K+ at 20°C, the Nernst Equation become: [ K ]o Ek =58 log [ K ]i

K+

Concentration gradient { [K]o/[K]i} Electrical gradient (potential)

At rest, if K is only resting permeable ion, membrane resting potential should be close to or at Ek

Predicated & measured the RP

But, in fact, at rest…… The cell membrane permeates not only K+, but also Na+ & Cl-. Each permeant ion attempts to drive membrane potential (Vm) towards its own equilibrium potential. The highest permeability or conductance at rest, the greatest contribution to the resting potential Na+

Na

+

K

+

Cl-

Cl

K+

So, what determines how much of an ionic species passes through the membrane at rest?

When Vm is: a) determined by 2 or more (permeant) ions and b) not changing ( i.e. at steady state) Thus, a way of evaluating the contribution each ion makes to the membrane potential is by using Goldman equation (pp53):

or

Pk PNa Em = Ek + E Na Pk + PNa PK + PNa GNa GK Em = EK + E Na GK + GNa GK + GNa

Comparison

Actual Em is similar to calculated one by Goldman equation

Consider Cl:

Cl “feels “ a strong concentration gradient pushing it inward, and the resting permeability to Cl is high, so Cl is free to enter.

[Cl ]O ECl = −58 log [Cl ]i

Cl: Cl-

Vm ⇒ Ek Cl-

But the relative excess of negative charge inside the membrane tend to push chloride ions back out of the cell

For Cl- distributes passively, Em, rest is closed to Ek, closed to ECl. As long as PCl remains high, Cl tends to resist changes in Vm away from Vm,rest and thus exerts a “buffering action” on Vm.

Equilibrium potential of different ions

Summary 

The resting potential arises from two activities: 

The sodium/potassium ATPase : its activity results in a net loss of positive charges within the cell.

Ungated ion channels allow ions to diffuse across the plasma membrane.  given that gNa is considerably less than gk, the membrane potential is close to the potassium equilibrium potential, (Em is about -60 to –90 millivolts (negative inside) 

Action Potential and Na+ equilibrium potential

Recall: 

At the RP, Na+ is in severe disequilibrium (ENa is 100 to 150 mV more positive than the RP)



If Em= -68mV, ENa=54mV, EK=-74.4mV Then, there is a large driving force for Na+ but a small one for K+: Em-ENa= -68-(+54)= -122mV Em-EK= -68-(-74.4)= +6.4mV

Recall :

Na+ or K+ that enters or leaves the cells at rest are pumped actively by Na+/K+ ATPase to counteract these inward (Na+) and outward (K+) movements to maintain “the cell’s batteries.

Now, to the action potential……

Study on Ionic Basis of Action Potential 

We have known that the action potential arises from changes in the membrane conductance to Na+ and K+ 



differences in the voltage and time-dependence of these conductance Na+: dual voltage-dependence 

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during early phase, conductance increases with depolarization during later phase, conductance decreases with depolarization

in unmyelinated neurons, gK increases with depolarization, but relatively slowly

How do we first learn all this? 

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

Key evidence comes from voltage clamp studies carried out by A. L. Hodgkin and A. F. Huxley, with the early participation of B. Katz they shared the 1963 Nobel prize for Physiology & Medicine foundation for all modern work on electrical excitability

Hodgkin and Huxley, two famous physiologists at University of Cambridge in England

Hodgkin’s early experiment

Hodgkin & Katz, 1949 : Reducing [Na+]o, and hence ENa, reduces the amplitude (degree of overshoot) of the AP. Conclusion: AP is due to a large, transient increase in membrane PNa+

Obviously: 

Something caused a changes in gNa while a proper stimulation was applied to a cell membrane



Overshoot of the AP should be closed to or equal to ENa

Inference of Conductance from Voltage Clamp Data 

Ohm's law 





V=IR

[R is inversely related to g (R=1/g) ]

To determine membrane conductance, put electrode in neuron, pass known current through membrane, measure voltage difference produced, then compute membrane conductance using g = I/V (V=driving force) So, Iion = gion (Em - Eion )

Voltage Clamp 

The voltage clamp is a method by which the membrane voltage can be set at a specified command voltage. A feedback amplifier compares the membrane voltage to the command voltage and sends a signal to a current passing amplifier that injects current to make the membrane voltage equal to the command voltage. The injected current is measured and is equal in magnitude but opposite in sign to the current produced by the ion channels. The feedback amplifier can inject current much faster than the ion channels can change conformation to allow current to pass.

Measure Total Membrane Current Obtained total transmembrane current carried by both Na+ and K+ by performing experiment with normal sea water

How to isolate Na+ and K+ components? 

  

take advantage of differences in time course of conduction changes manipulate ionic environment use toxins once isolated, can work out driving force and hence, conductance

Demonstration that rising phase of action potential depends on Na+ 1. change extracellular fluid so that [Na+]o = [Na+]i • INa is now forced to equal zero • remaining current must be IK • having thus isolated IK, we can now calculate INa by subtracting IK from

Experiments (from Hodgkin & Huxley)

Demonstration that rising phase of action potential depends on Na+ Using voltage clamp, from holding potential of –65mV 2. Step Vm to ENa results: a) transient inward current abolished b) delayed outward current remains conclusion: transient inward current is carried by Na+

Demonstration that rising phase of action potential depends on Na+ 3. Replace extracellular Na+ with another cation (such as strontium) results: a) transient inward current abolished b) delayed outward current unchanged conclusion: transient inward current is carried by Na+

Demonstration that repolarization in squid axon depends on K+ using voltage clamp, from holding potential of -65mV 1. Step Vm to EK results: a) early inward current still present b) delayed outward current abolished conclusion: delayed outward current is carried by K+

Blocking of ionic channels with pharmacological agents

Time and voltage dependence of changes in gNa and gK

The process, in the Hodgkin-Huxley model, determining the variation of sodium conductance with depolarization and repolarization with voltage clamp.

In the Hodgkin-Huxley model, the process determining the variation of potassium conductance with depolarization and repolarization with voltage clamp.

Relation between gNa & gK and the action potential for squid axon

Comparison of gNa and gK  Both

Na+ and K+ channel open were caused by depolarization of membrane potential  With membrane potential was depolarized more, the number of opened channel increased.

Comparison of gNa and gK But:  The rate of channel open for Na+ is different from K+, (Na+> K+)  The duration of channel open for Na+ is different from K+, (inactivation of Na+ is faster than that of K+)

Mechanisms of changes in conductance of ion channel H-H model from Hodgkin and Huxley

Two gates that control + Na channels 

 

m gate that response to depolarization h gate that response to repolarization Three states of Na+ channel state m h g resting state closed opened 0 active state opened opened high inactive state opened closed 0

Terms Resting activation Recovery

Active inactivation Inactive

Single Channel Recording Erwin Neher , Bert Sakmann were awarded “Nobel prize in physiology or Medicine 1991” for their discoveries concerning “the function of single ion channels in cells".

Neher and Sakmann's contributions have meant a revolution for the field of cell biology, for the understanding of different disease mechanisms, and opened a way to develop new and more specific drugs.

A model of equipment for single channel recording

Summary

§5.3 Excitability & Excitation

• Excitable

cells

- neuron, muscle, gland • Excitability • Excitation

Extension: Excitability is an ability or property of generation of the action potential while a excitable cell responds to appropriate stimuli. Excitation is a process of the AP was generated.

Three essential parameters regarding stimulation 

Parameters Intensity 刺激强度 Duration 刺激作用时间 Rate of change （ in intensity ） 强度对时间的变率



Terms Threshold intensity 阈强度 Threshold stimulus 阈刺激 Subthreshold stimulus 阈下刺激 Suprathreshold stimulation 阈上刺激 只有阈和阈上刺激才能触发动作电位

Changes of excitability during excitation 

Absolute refractory period 绝对不应期



Relative refractory period 相对不应期 Supernormal period 超常期 Subnormal period 低常期

 

Absolute 



During an action potential, a second stimulus will not produce a second action potential (no matter how strong that stimulus is) corresponds to the period when the sodium channels are open (typically just a millisecond or less)

Relative:  



Another action potential can be produced, but only if the stimulus is greater than the threshold stimulus corresponds to the period when the potassium channels are open (several milliseconds) the nerve cell membrane becomes progressively more 'sensitive' (easier to stimulate) as the relative refractory period proceeds. So, it takes a very strong stimulus to cause an action potential at the beginning of the relative refractory period, but only a slightly above threshold stimulus to cause an action potential near the end of the relative refractory period.

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在绝对不应期内，可兴奋细胞不可能 立即接受刺激爆发另一个新的 AP 。

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不应期的长短决定了细胞在单位时间 内可以产生动作电位的数目（频率） ，而 AP 的频率是可兴奋细胞接受刺激 后编码信息的一种方式。

The factors that effects on excitability of the cell 

Resting potential-[K+]o/[K+]I.



Threshold



Ca++ concentration outside of the cells (surface charge)

§5.4 Initiation and Propagation of the Action Potential Initiation of the Action Potential

How does depolarization open voltage-gated channels? 

There is a threshold for generation of action potential; i.e.small random fluctuations in the membrane potential are not interpreted as useful information.

Why is that? 

The stimulus might be produced by a sensory receptor, an action potential in nearby parts of the cell or from an electrical current applied experimentally. Current flowing into the cell lowers the membrane potential towards zero.

There are two immediate effects: 1. The difference between Vm and the EK increases – more K+ flows out of the cell. This tends to repolarize the cell. 2. The voltage-gated Na+ channels are opened allowing Na+ to flow down its gradient into the cell. This tends to produce further depolarization.

The result is determined by the relative sizes of these two effects.  With small depolarizations, the effect on the IK is larger than that on INa and the outward IK exceeds the inward INa. 



If stimulus is greater, the effect on INa exceeds that on the IK and then, the inward INa exceeds the outward IK, leading more depolarization to a point at which AP takes place. The smallest level of depolarization that can generate action potential is called threshold potential *(In general, TP is about 15 mV above the RP of the cell)

The process to generate action potential is just like shoot with a gun! The key that AP is evoked is that energy used in depolarization should be greater enough to bring membrane potential to the threshold potential.

Once membrane potential is depolarized to threshold potential, then the occurrence of an action potential is inevitable. Because…

A process of positive feedback

Note: 

A key to generate action potential is to make membrane depolarization to the threshold level no matter what kind of manner. The peak of the action potential is determined not by the depolarizing stimulus but rather by the sodium equilibrium potential

Again:

Subthreshold stimulus and local response

Graded (electrotonic) Potential Now consider subthreshold stimuli –the membrane potential doesn’t reach the threshold voltage –The local currents still flow but slowly the membrane potential returns to the resting value If the stimulation is restricted to a small area of membrane –the depolarization will be greatest at that point and will fall exponentially with distance because the effect is ‘local’ to the stimulus, these are called ‘electrotonic’ or ‘local’ potentials

Properties of local response Importantly, local potentials: – do not induce refractoriness –are graded bigger stimulus = bigger response! –Summate (spatial or temporal summation) multiple stimuli = summed response

Experiment

Voltage response (%)

stimulus

100

Recording electrodes

37 0

3

6

Distance (mm)

Comparison of the Action Potential and Local Potential  

 

Action potential “All” or “none” Propagation without decrement Refractory Regenerated Na influx that rely on Na concentration out of cell

   

Local response Graded ( 等级的 ) Electrotonic ( 电紧 张 ) propagation Summation ( 总和 ) Small amount of Na influx in response to subthreshold stimulus

Propagation of the action potentials along nervous or muscle fiber

The role of the action potential, which is a local event in excitable cells, is to generate an electrical signal which is conducted along the surface of excitable cells as a command or a message, a piece of information.

动作电位是细胞的语言，是细胞携带或传递信息的方式  细胞以动作电位的频率编码信息量、信息种类等 For example: In muscle a rapidly conducted action potential ensures that the whole contractile of mechanism of a cell is activated at once; In nerves, when the message reached the terminals, the information is transmitted to adjacent cells by the release of neurotransmitters. 

Mechanism of propagation  Propagation

of action potential down a unmyelinated ( 无髓鞘 的） nerve or muscle by the spread of local current from active regions to adjacent resting regions in a continuous manner.

Mechanism of propagation 

In myelinated nerves, action potentials are not generated at all points along the nerve but only at gaps in the myelin (nodes) where the nerve membrane is not covered. This is called saltatory (leaping) conduction ( 跳跃式传导） .

Properties of propagation of action potential along nerve  

 

“All” or “none” (“ 全”或“无”） Two way directional propagation （双向传导） Insulation （绝缘传导） Relative fatigueless ( 相对不疲劳）

Landmark 1952 Papers on Electrical Activity in the Squid Giant Axon (I) 1. HodgKin AL, Huxley AF, Katz B (1952) Measurement of current-voltage relations in the membrane of the giant axon of Loligo. Journal of Physiology 116: 424-448 2. HodgKin AL, Huxley AF (1952) Currents carried by sodium and potassium ions through the membrane of the giant axon of Loligo. Journal of Physiology 116: 449-472 3. HodgKin AL, Huxley AF (1952) The components of membrane conductance in the giant axon of Loligo. Journal of Physiology 116: 473-496

Landmark 1952 Papers on Electrical Activity in the Squid Giant Axon (II) 4.HodgKin AL, Huxley AF (1952) The dual effect of membrane potential on sodium conductance in the giant axon of Loligo. Journal of Physiology 116: 497-506 5.HodgKin AL, Huxley AF (1952) A quantitative description of membrane current and its application to conduction and excitation in nerve.

Declan A. Doyle, Joa˜ o Morais Cabral, Richard A. Pfuetzner, Anling Kuo, Jacqueline M. Gulbis, Steven L. Cohen, Brian T. Chait, Roderick MacKinnon*. The Structure of the Potassium Channel: Molecular Basis of K1Conduction and Selectivity. SCIENCE ,VOL, 280, APRIL (1998):69-77

Useful terms 

Equilibrium potential: 当驱动离子跨膜转运的浓差与阻碍离子转 运的电位差达到大小相等、方向相反时的状 态称作电化学平衡（ electrochemical balance) ，此时的电位即平衡电位。



Electrochemical driving force:



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If there are many open channels in the membrane for a particular ion, the resistance of the membrane to the passage of the ion is low, and its conductance for that ion is high In resting neuron Na+ conductance gNa is low. K+ conductance gK is higher than Na+, but still not large, because at rest only some K+ channels are open, along with leak channels that admit small amounts of both K+ and Na+