26 KiB
Voltage dependent membrane permeability
- Hodgkin and Huxley hypothesis– Action potential can be explained by voltage-gated ion channels
- Experiment– Measure ion permeability at varying membrane potentials
- Problem– Difficult to systematically vary the cell potential and also measure ion permeability
- Solution– Voltage clamping. Fix membrane potential in a cell without triggering an action potential while measuring ion permeability
Note:
We learned last time that the experiments of Hodgkin, Huxley, and Katz showed that the Vm during an AP approaches ENa. And they thought that this might be due to changes in permeability for Na in the cell membrane that changes during the course of an action potential. Thus Hodgkin and Huxley hypothesized that APs can be explained by ion channels that change their permeability due to voltage— that these channels are voltage-gated.
Alan Hodgkin and Andrew Huxley began this work in the late 1930s, and quickly finished one paper before helping with the British war effort during WWII. Indeed Hodgkin said that he lost all interest in neurophysiology during those dark years as one might imagine. But as things calmed down after the war they renewed their collaboration and got back to the business of neuronal excitability.
So they needed to proved that ion permeability changes according to membrane potential but there was an issue— how to vary the membrane potential in a systematic way and also measure the ion permeabilities?
The solution was to build an electrophysiological recording apparatus with feedback circuitry such that you can fix or clamp the voltage across the cell membrane.
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Action potential summary video
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Summary of last time…
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More Vm examples
- Given a cell with intracellular: 1 mM NaCl, 10 mM KCl; extracellular: 10 mM NaCl, 1 mM KCl
- What is the resting potential of the cell at room temperature (20ºC + 273 = 293 K) if the membrane is only permeable to K⁺?
(58/1)*log10(1/10) = -58 mV
- Only permeable to Na⁺?
(58/1)*log10(10/1) = +58 mV
- Only permeable to Cl⁻?
(58/-1)*log10(11/11) = 0 mV
- Equally permeable to K⁺ and Na⁺?
Pk = 0.5; Pna = 0.5; Pcl = 0; kOut = 1; kIn = 10; naOut = 10; naIn = 1; clIn = 11; clOut = 11(58)*log10( (Pk*kOut + Pna*naOut + Pcl*clIn) / (Pk*kIn + Pna*naIn + Pcl*clOut) ) = 0 mV
Note:
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(58/1)*log10(1/10) = -58 mV
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(58/1)*log10(10/1) = +58 mV
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(58/-1)*log10(11/11) = 0 mV
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0 mV:
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Pk = 0.5; Pna = 0.5; Pcl = 0; kOut = 1; kIn = 10; naOut = 10; naIn = 1; clIn = 11; clOut = 11
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(58)log10( (PkkOut + PnanaOut + PclclIn) / (PkkIn + PnanaIn + Pcl*clOut) ) = 0 mV
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0 mV:
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Pk = 1; Pna = 1; Pcl = 0; kOut = 1; kIn = 10; naOut = 10; naIn = 1; clIn = 11; clOut = 11
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(58)log10( (PkkOut + PnanaOut + PclclIn) / (PkkIn + PnanaIn + Pcl*clOut) )
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-59 mV (room temp and low Pna):
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Pk = 1; Pna = 0.001; Pcl = 0.5; kOut = 1; kIn = 10; naOut = 10; naIn = 1; clIn = 1; clOut = 11
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(58)log10( (PkkOut + PnanaOut + PclclIn) / (PkkIn + PnanaIn + Pcl*clOut)
-62 mV (body temp and low Pna):
- R = 8.3; F = 9.6e4; T = (273+37)
- Pk = 1; Pna = 0.001; Pcl = 0.5; kOut = 1; kIn = 10; naOut = 10; naIn = 1; clIn = 1; clOut = 11
- ((RT)/F)log( (PkkOut + PnanaOut + PclclIn) / (PkkIn + PnanaIn + PclclOut) )
-69 mV (body temp and low Pna and physiol concentrations):
- R = 8.3; F = 9.6e4; T = (273+37)
- Pk = 1; Pna = 0.05; Pcl = 0.45; kOut = 5; kIn = 140; naOut = 145; naIn = 5; clIn = 5; clOut = 110
- ((RT)/F)log( (PkkOut + PnanaOut + PclclIn) / (PkkIn + PnanaIn + PclclOut) )
Calculate the total concentration of all ions for these solutions. For every one NaCl that dissolves, two ions are produced (one Na⁺ and one Cl¯). Thus for 10 mmol/L NaCl outside there are (10 mmol/L)x(1 total Cl ions/NaCl) = 10mM. And for 1mM KCl outside there are (1 mmol/L)x(1 total Cl ions/KCl) = 1mM. Thus the total number of Cl⁻ ions per liter is 11mmol/L = 11mM
The voltage clamp method
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This is an illustration of the voltage clamp recording method.
One internal electrode measures membrane potential and is connect to the voltage clamp amplifier.
voltage clamp amplifier compares membrane potential to the desired command potential
When Vm is different from the command potential the clamp amplifier injects current ion the axon through a second electrode. This feedback arrangement causes the membrane potential to become the same as the command potential.
The current flowing back into the axon and thus across its membrane can be measured.
**This electronic feedback circuit holds the membrane pot at the desired level, even in the face of permeability changes that would normally alter the membrane potential. (such as those generated during the action potential). Most importantly, the device permits the simultaneous measure of the current needed to keep the cell at a given voltage. This current is exactly equal to the amount of current flowing across the neuronal membrane, allowing direct measurement of these membrane currents.
An amplifier, electronic amplifier or (informally) amp is an electronic device that can increase the power of a signal. It does this by taking energy from a power supply and controlling the output to match the input signal shape but with a larger amplitude.
A differential amplifier is a type of electronic amplifier that amplifies the difference between two input voltages but suppresses any voltage common to the two inputs.[1]
An operational amplifier (often op-amp or opamp) is a DC-coupled high-gain electronic voltage amplifier with a differential input and, usually, a single-ended output.[1] In this configuration, an op-amp produces an output potential (relative to circuit ground) that is typically hundreds of thousands of times larger than the potential difference between its input terminals.[2]
Hodgkin and Huxley 1952
- Do neuronal membranes have voltage-dependent permeability?
- Which ions are changing their permeability?
- Experiment– Change potential to make neuron membrane potential more negative (hyperpolarize). No currents need to be injected into cell to maintain that potential. Therefore no current is moving from inside and outside of cell
- Change potential– Depolarize cell, now see both inward and outward currents between the inside and outside of cell
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Hodgkin and Huxley published a series of seminal papers in 1952 that summarized their investigations using this voltage clamp method to examine voltage dependent ion flux.
They asked…
So the experiment was to hold the membrane potential at different voltages and measure charge flux into or out of the cell... —>
Electric current flow across a squid axon membrane during voltage clamp
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And so here are the results from this type of voltage clamp experiment.
If you command that the cell membrane potential be hyperpolarized, you get very little or negligible current flowing across the membrane except for a very brief capacitive current that you always see in these voltage clamp experiments.
This is because the cell membrane essentially acts as a parallel RC circuit where a resistor and a capacitor are connected in parallel and to a constant current source. Ion channels are resistors, lipid bilayer with the extracellular and intracellular environments act as capacitor, storing charge in the form of ions accumulating near the surface of the membrane. When a switch is turned on in an RC circuit current flows from the battery to the capacitor until the capacitor is charged to a voltage that is same as the battery.
However when Hodgkin and Huxley depolarized the membrane, a transient inward current occurs followed by a slow outward current.
A capacitor (originally known as a condenser) is a passive two-terminal electrical component used to store electrical energy temporarily in an electric field. Consists of two parallel conductors. Lipid membrane with the inner and outer cellular environment acts as this. The membrane capacitance per unit areas is mostly constant at about 1 µF/cm2.
- When the voltage is constant, the current through the capacitative pathway is zero because the capacitor has acquired the charge Q (coulombs) according to the relationship Q=CV. C is capacitance (farads) Ic is capacitive current. Ic = C(dV/dt)
- as long as V is changing with time, there will be a current flowing towards the capacitor.
- if V is constant in time, there is no capacitive current.
- product of resistance and capacitance has the unit of time and is called the time constant. Time constant defines how quickly capacitors charge or discharge over time.
http://nerve.bsd.uchicago.edu/med98c.htm
Current produced by different membrane depolarizations during voltage clamp
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This show several different voltage steps (with the brief capacitive current omitted for clarity)
...Notice as we approach ENa the inward current disappears.
Relationship between current amplitude and membrane potential
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This summarizes the peak magnitude of these these two currents at different Vm
How do we prove the inward current is sodium?
- Prediction– If you could change the Na⁺ concentrations in the system, for example have less sodium outside than inside (instead of the normal high outside low inside), Nernst equation would predict an early outward current instead of an early inward current
- Experiment– Change the Na⁺ concentration in the bath. Normally 440 mM NaCl outside & 50 mM inside for squid axon, now make it 50 mM inside & 0 mM outside
Note:
So it seems like this inward current may be carried by Na ions.
Dependence of the early inward current on sodium
Note:
Choline is a water-soluble nutrient. It is usually grouped within the B-complex vitamins. Choline generally refers to the various quaternary ammonium salts containing the N,N,N-trimethylethanolammonium cation. (X− on the right denotes an undefined counteranion.)
The cation appears in the head groups of phosphatidylcholine and sphingomyelin, two classes of phospholipid that are abundant in cell membranes. Choline is the precursor molecule for the neurotransmitter acetylcholine, which is involved in many functions including memory and muscle control.
Voltage clamp method summary
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Pathways of the two currents are distinct
- Question– Do Na⁺ and K⁺ go through the same channels? Or do they have distinct channels?
- Experiment– Add tetrodotoxin (TTX) to block inward current but not outward current
- Experiment– Add tetraethylammonium (TEA) to block outward current but not inward current
- TTX inactivates Na⁺ channels, TEA blocks K⁺ channels
Note:
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Neurotoxins as pharmacological tools
- Fugu (puffer fish or blow fish)
- TTX concentrated in their livers (don’t eat it)
- TTX blocks voltage-gated Na⁺ channels
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Its mechanism of action, selective blocking of the sodium channel, was shown definitively in 1964 by Toshio Narahashi and professor John W. Moore at Duke University, using the sucrose gap voltage clamp technique (Narahashi et al, J Gen Physiol 1964)
Pharmacological separation of inward and outward currents into Na⁺ and K⁺ dependent components
Note:
Tetramethylammonium chloride is one of the simplest quaternary ammonium salts.
https://en.wikipedia.org/wiki/Tetramethylammonium_chloride
TTX and TEA experiments from Moore 1967 J Gen Physiol; Armstrong and Binstock, 1965 J Gen Physiol
Voltage dependent membrane conductances of Na⁺ and K⁺
- Another way of describing permeability is using membrane conductance (g). Conductance (measured in siemens, S) is the reciprocal of resistance
- g = 1/R
- Ohm’s law:
- I = V/R
- I = gV
- For an ion x,
- Ix = ionic current flow, Ex = equilibrium potential
- The membrane potential (Vm) minus the equilibrium potential (Ex) is the electrochemical driving force acting on an ion, thus V = Vm - Ex
- Ix = gx
- Ix = gx(Vm - Ex)
- Solve for g:
- gx = Ix/(Vm - Ex)
- Ix determined from measurement of current changes plus or minus ion (or during pharmacological inhibition)
- Ex calculated from Nernst equation using concentrations of inside and outside ions
Note:
For our purposes, we can consider conductance to be another way of describing permeability.
technically conductance is the degree to which an object conducts electricity, calculated as the ratio of the current that flows to the potential difference present. It deals with the movement of charge, whereas permeability refers to the ability of a specific ion to move across the cell membrane.
Ohms law= Voltage = Current times resistance.
Can use this to calculate the dependence of Na and K conductances vs. time and membrane potential.
Membrane conductance changes are time and voltage dependent
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Depolarization increases Na⁺ and K⁺ conductances of the squid giant axon
Note:
Determine the peak conductance of ions at different membrane potentials.
Description of an action potential using Na⁺ and K⁺ conductances
- At rest (-70 mV), voltage-gated Na⁺ and K⁺ channels are closed. Non voltage-gated K⁺ channels are open and dictate the resting potential, together with the distribution of ions across cell membranes
- A stimulus raises the membrane potential in the cell. Depolarization causes voltage-gated Na⁺ channels to open, which allows Na⁺ to rush in the cell which increases the membrane potential, which causes more Na⁺ channels to open, which causes more Na⁺ to rush in which causes higher membrane potential (a positive feedback loop). As membrane potential is approaching ENa, the further depolarization causes Na⁺ channels to inactivate which prevents more Na⁺ from from flowing through these channels
- Depolarization also opens voltage gated K⁺ channels, which causes K⁺ to flow out, thus lowering the membrane potential
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Ion conductances underlying the action potential
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Properties of action potentials explained
- Question– Why do APs exhibit an all-or-nothing threshold?
- Answer– When membrane potential (Vm) is below threshold there is not enough Na⁺ channels open to raise Vm high enough to open more channels. When Vm is above threshold the action potential cycle is activated.
- Question– Why to APs exhibit an undershoot?
- Answer– During the AP voltage-gated K⁺ conductance slowly increases (delayed activation of voltage-gated K⁺ channels) and during the falling phase these K⁺ channels are still open and active whereas voltage-gated Na⁺ channels are inactivated… as Vm approaches Ek there is briefly more K⁺ flowing out than at rest and the hyperpolarization inactivates voltage-gated K⁺ channels. K⁺ leak channels and ion transporters bring back cell to resting potential.
Note:
The threshold is a point of criticality in the system like trying to balance on a knifes edge. Just imagine any self-organized phenomena in nature: a snow field suddenly turning into an avalanche, liquid water turning into gas or solid forms, videos of cats or korean pop stars suddenly going viral. The point at which the states of these systems veer on the edge of order or disorder is the point of criticality also known to physicists as a phase transition.
Properties of action potentials explained
- Action potential propagation and directionality?
- Refractory periods?
- What does myelin do?
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Next we will look at the following properties of APs such as:
Action potential propagation
- Charge flowing in through Na⁺ channels can diffuse inside the axon. This passive current cannot diffuse very far because of current leakage. Potentials below threshold taper out fast (like passive conduction of subthreshold depolarizations).
- Potentials above threshold cause increased depolarization (due to more Na⁺ channels open). Now there is enough current to diffuse laterally and still be above threshold for a new set of Na⁺ channels.
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First let’s talk about AP propagation.
During an action potential, inward current through Na⁺ channels
Passive current flow in an axon
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bottom graph shows the peak Vm
Propagation of an action potential
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bottom graph shows the peak Vm
Action potential conduction requires both active and passive current flow
Note:
Active and Passive current flow.
- Na+ chan locally open in response to stimulus, generating an AP
- Depolarzing current passively flows down axon
- Local passive depolarization causes nearby Na chan to open and another AP is generated
- Na chan upstream inactivate and K chan open. Vm repolarizes and is refractory to further AP generation upstream
- Process repeated downstream, propagating AP along the axon
Why is there a refractory period?
- Remember during the falling to undershoot phase of an action potential K⁺ channels are still open but Na⁺ are channels inactivated (decreased gNa), leading to temporary hyperpolarization more negative than the resting membrane potential
- Therefore (1) inactivation of Na⁺ channels and (2) slow K⁺ channel kinetics are responsible for the refractory period
- This makes it harder to initiate a new AP either from a new stimulus or for an AP to propagate backwards
- Different axons will have different refractory periods (and thus different maximal firing rates) depending on the particular subtypes of Na⁺ and K⁺ channels they express
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Voltage-gated channel states during an action potential
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What does myelin do?
- Rate of action potential formation limits the flow of information
- How to speed up AP conduction?
- Increase the diameter of the axon– bigger axon diameters have less resistance (decreased resistance to passive current flow)
- Myelin insulates the axon, reducing current leak. Example AP conduction velocities for axons: unmyelinated 0.5–10 m/s, myelinated 150 m/s
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Nodes of Ranvier
- Can’t insulate the whole axon because transmembrane current flow is required to generate the action potential
- Current from one action potential flows passively to next node where a new action potential is made
- Action potentials have saltatory conduction– meaning from node to node
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Nodes of Ranvier
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saltatory action potential condution along a myelinated axon.
red indicates imaged expression of voltage gated Na channels. green indicates a protein (Caspr) associated with the nodes of Ranvier.
Speed of action potential conduction in unmyelinated versus myelinated axons
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figure comparing action potential propagation speed in an unmyelinated and myelinated axon.
action potential genaration occurs only at specific points, the nodes of Ranvier, along the myelinated axon
The Nobel Prize in Physiology or Medicine (1963)
"for their discoveries concerning the ionic mechanisms involved in excitation and inhibition in the peripheral and central portions of the nerve cell membrane"
Alan Lloyd Hodgkin
Andrew Fielding Huxley
Note:
Painless dentistry
- Lidocaine blocks some types of Na⁺ channels
- Blocks action potentials in sensory axons
- Pain signals do not reach the brain
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Multiple sclerosis
- Disease caused by myelination defects and loss of neurons
- Seems like an autoimmune disease
- 1/750 of population in US get multiple sclerosis (MS)
- 1/40 risk if a parent has it
- 1/3 if an identical twin gets it
- Genetic and environmental risk factors
Note:
onset between ages 20-40.
blindness, motor weakness, paralysis.
ultimate cause of MS remains unclear. Immune system contributes to damage and is key component. Immune cells in CSF and injection of myelin in animals can cause EAE. Autoimmune disorder. Or persistent infection with a human retrovirus?
- women to men ratio 3/2
- Genetic component is likely the effect of multiple genes