BIO325 Laboratory Guide #10 (2024)
ACTION POTENTIALS II:
COMPUTER SIMULATIONS OF A
VOLTAGE-CLAMP EXPERIMENT
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Much of our understanding of action potential mechanisms comes from a series of experiments conducted by Hodgkin and Huxley in the early 1950s. For these experiments Hodgkin and Huxley (H-H) chose “giant” axons found in the squid Loligo. They recognized that generation of an action potential depends on changes in ionic conductances that, in turn, vary as functions of both voltage and time. We now refer to such conductances as being “voltage-gated”. H-H determined that the best way to separate the voltage- and time-dependence of these effects was to hold one of these variables constant. Lacking a time machine, they chose voltage. To do this, they employed an electronic apparatus, developed in 1947 by Cole, called a “voltage-clamp”, which they used to produce step changes in voltage across the squid axon while they monitored current. Based on the data they gathered using this instrument, they were able to successfully model the axonal membrane with a set of differential equations and, by plugging in experimentally-determined coefficients, produce a reasonable match of the time-course of an action potential.
Even though the voltage clamp is the key to understanding action potentials, under a voltage -clamp situation the membrane voltage is held at a constant value, so action potentials themselves do not occur. The voltage-clamp apparatus consists of two interconnected circuits. The first circuit monitors the membrane voltage. H-H used silver wires placed inside and outside the squid giant axon, but conventional glass pipette microelectrodes are more commonly used today. Your simulation uses a single large electrode which is sucked tightly onto a small patch of membrane, hence the term “patch-clamp”. The second circuit supplies whatever current is necessary to the axon to maintain a constant, predetermined voltage. In early experiments this current was supplied by a second pair of electrodes, but modern voltage-clamp amplifiers use a single electrode for both monitoring voltage and supplying current. H-H set their voltages manually, while modern devices are computer-controlled. According to Kirchoff’s current laws, the current supplied to the membrane must exactly equal the current flowing back across the membrane. Because the voltage clamp amplifier monitored both the instantaneous voltage and current across the membrane, the instantaneous conductance could be determined from Ohm’s Law (V = IR or g = I/V). By conducting a single experiment, H-H could determine the time course of conductance changes following a step change from a starting voltage to a particular test voltage. By comparing results for a set of such steps, they could determine the voltage-dependence of the conductance changes.
A typical modern conventional voltage-clamp experiment starts by penetrating a cell with a glass microelectrode or forming a “patch seal” and determining that the cell is healthy. Values and durations for a series of voltage steps are then determined. By convention, the initial voltage is called the “holding voltage” Vh. Subsequent voltage steps are called “clamp voltages” Vcl, Vc2, etc. During the experiment at least one of these values is systematically varied, to produce a “family” of curves. Conclusions about the voltage- and time-dependence of membrane conductances follow from comparisons of the curves within such a family.
After studying overall current flow through the axonal membrane, Hodgkin and Huxley were faced with the problem of isolating the constituent ionic currents and conductances. During an action potential the membrane voltages changes from its initial resting value to a depolarized value near the equilibrium potential of sodium ENa, then to a hyperpolarized value near the equilibrium potential of potasium EK, then back to its resting value. H-H reasoned correctly that the action potential must depend primarily on changes in membrane conductances to sodium and potassium, gNa and gK respectively. They had two ways to isolate these conductances. The first was to clamp the membrane at the equilibrium potential for one ion. At this value, any current flowing must be carried by the other ion. The second, more useful method, was to replace either sodium or potassium with an impermeant substitute monovalent cation, such as choline. In the squid giant axon, H-H could replace either the extracellular or intracellular fluid, and this was their primary method of isolating sodium and potassium currents and conductances.
We now have an additional and much more versatile method for isolating conductances, namely the use of pharmaceutical channel blockers. Tetraethylammonium (TEA) is a very specific blocker of voltage-gated potassium channels, while tetrodotoxin (TTX) is an equally specific blocker of voltage-gated sodium channels. In today’s exercise, you will be conducting a series of simulated voltage-clamp experiments on a patch-clamped region of membrane in the squid giant axon. Because this simulation works from the “bottom-up” and calculates conductances directly from the H-H equations, you will not have to expressly block either sodium or potassium conductances.
AP Mechanism PowerPoint
Patch Voltage Clamp tutorial
A. Setting Up
1) If you are running NIA2 on th elaboratory computers and wish to use the screen capture utility for printing your results, then activate the camera icon, as you have for previous labs.
2) Via My Computer open the C:/NIA2 folder. Double click on the NIA2PC shortcut icon. This will launch Neurons in Action as an interactive HTML application. Note: DO NOT MOVE THIS SHORTCUT ICON TO THE DESKTOP.
3) Click on Tutorials.
4) Select Voltage Clamping a Patch tutorial.
5) Read through the short introduction and goals sections.
6) Click on Start the Simulation to start the simulation. This will open several small control panels. At this point you will probably want to minimize (DO NOT CLOSE) the text windows to get them out of the way.
7) In the course of the first few exercises, refamiliarize yourself with the window controls, especially:
a) opening and manipulating parameter windows
b) opening, resizing, and positioning display windows
c) resealing display window plots
d) capturing windows for printing
B. Basic Tutorial
Complete all of the following sections of this tutorial, answering the in-text questions as you go:
Description of the Panels and Windows Customized or this Tutorial
Experiments and Observations
Observe the Na and K currents in response to a step depolarization
Observe the Na and K conductance changes in response to a step
depolarization
Observe families of currents
Observe “tail” currents
Demonstrate inactivation of the Na conductance
Observe the effect of temperature on the Na and K conductance
Return all of the simulation parameters to the default values when you are finished.
C. Peak Sodium and Potassium Currents
Return to the “Observe the Na and K currents in response to a step depolarization” section and look at item 3 (top of page 20 in the manual). Set up a series of depolarizing Vtest steps, ranging from -50mV to +100mV in 10 mV increments. For each of these, use the cursor in the current window to measure the maximum sodium current and the maximum potassium current. Repeat this process for the maximum conductances in the conductance window. Note that the maximum sodium current and conductance will occur at the peak of each INa curve, while the maximum potassium conductance and current are approached asymptotically by each IK curve. You may have to run several simulations, with varying parameters to accurately measure these values. For example, to get accurate values for maximum potassium currents and conductances, it will be necessary to increase the length of the testing level voltage step and the total # msec of the display to at least 10 msec. Transfer your data to an Excel spreadsheet to complete the following two Data Sheet Items and answer the associated questions.
Q1: Does your data match that of Moore and Cole (1960) as contained in the NIA link
under item 3?
Q2: Why does the sodium current change from an inward (negative) to an outward
(positive) current as Vtest changes from +50 to +60 mV?
Q3: If the simulation did not give you maximum conductance values, could you calculate
them from some algebraic combination of Vm, Vtest, and Imax? What formula would
you use? What law, named after Ohm, is the source of this formula?
D. Steady-State Conductance Curves – Potassium Activation
You will recall from earlier discussions and your readings that in the H-H model potassium channels are gated by a single set of gates, which tend to open “slowly” as the membrane is depolarized and close “slowly” as the membrane is repolarized or hyperpolarized. H-H termed this opening process “potassium activation” and represented it in their equations with the variable “n”:
gK = GKn4 where GK = maximal conductance for potassium
The value of n was, in turn determined as a dual function of membrane voltage and time.
The voltage-clamp setup allows us isolate the voltage-dependence of n from its time-dependence, by determining the “steady-state” value of n for a series of Vtest values. n is expressed as a dimensionless number between 0 and 1 and physically represents the proportion of potassium activation gates open if the cell is brought to a particular voltage and held at that voltage for an indefinitely long period of time.
You will first gather data to allow you to plot n as a function of membrane voltage, specifically Vtest. To do this:
1) Start with all of the simulation parameters at their default values. Set Total#(ms) under
the Run Control Window to 15ms. Set the Testing Level voltage step under VClamp in
the Stimulus Control window to 10ms duration and -60mV amplitude.
2) Click on VClamp Family and set the # of steps to 18. Click on Vary Test Level
to run the simulation.
3) Use the cursor to measure the peak potassium conductance GK for each Vtest value
Note: you may have to rerun several subsets of the V range to unambiguously identify
each curve. It may also help to selectively erase the sodium curves.
4) Enter this data into a new Excel spreadsheet as two columns (A and G): Vm (Vtest) and
GK. Find the largest value of GK. What Vtest does this correspond to? This value of GK
is GK(max).
5) For each Vtest value, n(steady-state) = GK/GK(max) . Divide each GK value by
GK(max) to determine the “steady-state” value of n. Calculate these n values into a
new Excel column (D). Your n values should range from 1 to approximately 0.
E. Steady-State Conductance Curves – Sodium Activation
In the H-H model sodium channels are gated by a two sets of gates. The first set of “fast” gates tend to open “rapidly” as the membrane is depolarized and close “rapidly” as the membrane is repolarized or hyperpolarized. H-H termed this opening process “sodium activation” and represented it in their equations with the variable “m”. The second set of “slow” gates have opposite properties. They close “slowly” as the membrane is depolarized and reopen “slowly” as the membrane is repolarized or hyperpolarized. H-H termed this closing process “sodium inactivation” and represented it in their equations with the variable “h”:
gNa = GNam3h where GNa = maximal conductance for potassium
In this experiment you will determine steady-state values for the activation coefficient m.
For H-H, m was determined as a dual function of membrane voltage and time. m is also expressed as a dimensionless number between 0 and 1 and physically represents the proportion of sodium activation gates open if the cell is brought to a particular voltage and held at that voltage for an indefinitely long period of time. Unfortunately, sodium conductances don’t go to sustained steady-states, because each individual sodium channel is turned-off by sodium inactivation. However, because sodium activation is much faster than sodium inactivation, steady-state values of m can be approximated by comparing peak conductances for a series of Vtest steps.
To approximate the steady-state voltage-dependence of m do the following:
1) Start with all of the simulation parameters at their default values. Set the Testing
Level voltage step under VClamp in the Stimulus Control window to -60mV
amplitude.
2) Click on VClamp Family and set the # of steps to 18. Click on Vary Test Level
to run the simulation.
3) Use the cursor to measure the peak sodium conductance GNa for each Vtest value.
Note: you may have to rerun several subsets of the V range to unambiguously identify each
curve. It may also help to selectively erase the potassium curves.
4) Enter this data into Excel as a new column (E): GNa (act). Find the largest
value of GNa. What Vtest does this correspond to? This value of GNa is GNa(max).
5) For each Vtest value, m(steady-state) = GNa/GNa(max) . Divide each GNa value by
GNa(max) to determine the “steady-state” value of m. Calculate these m values into a new
Excel column (B). Your m values should range from 1 to approximately 0.
F. Steady-State Conductance Curves – Sodium Inactivation
Again, in the H-H model sodium channels are gated by a two sets of gates:
gNa = GNam3h where GNa = maximal conductance for potassium
You approximated m values for the activation process above by comparing peak sodium conductance values for a set of Vtest voltages. Determining h values is conceptually tricky, but procedurally rather easy. The basic methodology is to “preset” the slow inactivation state by varying the initial conditioning level Vcond then stepping the membrane to a constant Vtest level. Because the activation process proceeds so rapidly, activation takes place before inactivation changes appreciably. You can therefore compare peak conductance amplitudes under this protocol to estimate the relative degree of inactivation h. As before h varies from 0 to 1 and physically represents the proportion of sodium inactivation “gates” open if the cell is brought to a particular voltage and held at that voltage for an indefinitely long period of time.
To approximate the steady-state voltage-dependence of h do the following:
1) Start with all of the simulation parameters at their default values. Set the Conditioning
Level voltage step under VClamp in the Stimulus Control window to -100mV
amplitude. Set the Testing Level voltage step under VClamp in the
StimulusControl window to 10mV amplitude.
2) Click on VClamp Family and set the # of steps to 10. Click on Vary
Conditioning Level to run the simulation.
3) Use the cursor to measure the peak sodium conductance GNa for each Vcond
value. Note: you may have to rerun several subsets of the V range to
unambiguously identify each curve It may also help to selectively erase the
potassium curves.
4) Enter this data into Excel as a new column (F): GNa (inact). Find the largest
value of GNa. What Vcond does this correspond to? This value of GNa is GNa(max).
5) For each Vcond value, h(steady-state) = GNa/GNa(max) . Divide each GNa value by
GNa(max) to determine the “steady-state” value of h. Calculate these h values into a new
Excel column (C). Your h values should range from 1 to approximately 0.
Choose Quit in the Panel & Graph Manager window to end the simulation.
Q4: How is time represented on this plot? Hint: what does “steady-state” mean?
V. PREPARATION OF THE LAB DATA SHEET
Your data sheet should include the FOUR items described in the boxes above Make sure that the axes of all of the graphs and print-outs are labeled and calibrated. You should certainly discuss your results and the answers to the questions with your partners and others in the lab. However, please work independently when you prepare your data sheet.
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