Molecular Neuro (HW1 + HW2)
current
(I) measured in amperes or charge/sec (C/s); rate of flow of positive charge; flow of ions across the membrane
charge
(Q) measured in coulombs (C); refers to the physical property of IONS being positive/negative
Reversal potential of Na+
+ 55 mV
Reversal potential of Ca2+
+145 mV
It is important here to remember the sign convention for these currents.
- First, current is taken as the direction of positive charge flow. - Second, a positive current is taken as an outward current—it goes from the inside of the cell to the outside. - Third, a negative current is taken as an inward current
Reversal potential of Cl-
-60 mV
(T/F) Membrane capacitance is easy to change, therefore the time constant is always changing in response to the needs of the neuron.
False.
How to calculate the equilibrium potential?
Nernst equation
Given your answer from A, if the conductance of this ion were to decrease to half of its current conductance, how would this affect the membrane potential? membrane potential would become more positive [correct answer] membrane potential would become more negative [my answer] membrane potential would not change
Ohm's law
How are all these "physics" concepts related to each other?
Ohm's law.
Voltage is always inside in comparison w/...
outside
Voltage-gated Na+ channels
rapid time to onset and rapid time to offset
Voltage-gated Na channels open...
rapidly and close rapidly
Consider point E. What directions are the two ions flowing?
red+ is flowing outward, green- is flowing inward
Voltage-gated K+ channels
slow time to onset and slow time to offset
In order for diffusion you need...
the channels (the membrane to be permeable to the specific ion)
Vm is the closest to Em at rest b/c it has...
the most leak ion channels @ rest, therefore K+ is the most permanent at rest
(T/F) the current of a particular ion is dependent on the conductance of that ion and its particular concentration.
The second one: True. If we look at the modified Ohm's law, then current is equal to the conductance times * the (Vm - Ex)
A new neurotoxin was identified from a marine snail. Scientists wanted to figure out the effect the toxin might have on action potential generation. Two voltage clamp experiments in the squid giant axon were performed; one in the presence and one in the absence of the new neurotoxin. The data are shown below. Select all statements that are correct.
The toxin leads to the loss of the early inward current.
(T/F) In a neuron at rest, if the membrane was perfectly permeable to sodium, then sodium ions would flow in to the neuron.
True. Negative inside sodium is positive BAM!
In an equivalent circuit, the Nernst potential for a particular ion is represented by a battery symbol for that ion.
True. Orientation depends on the signage.
Sketch an IV plot with a line representing each of the ions. Mark an X over the resting membrane potential on the graph as well.
Use the reversal potential for an x-int and the conductance for a slope. As far as the RMP, goes remember: Ohm's law (extended). And that restraining membrane potential is when the current = 0. Therefore, if we add up all three currents and set them equal to 0....
What is the reversal potential for this ion?
[can tell by looking at x intercept of the IV plot]
Graded potentials are not very...
efficient, which means it is decaying over transmission.
Resistance and conductance refer to
how easily current can flow through - And b/c the membrane is closed these are directly tied to the number of ion channels
resistance and conductance
(R and G) Ohms and Siemens; are inverses of each other; how much of the flow of charge is impeded; # of open ion channels
voltage
(V or J/C) measured in volts; difference of electrical potential; difference in potential between the extra/intracellular space
(T/F) the Nernst equation is dependent on the starting membrane potential?
First one: No or false. Nowhere on the Nernst equation do we see the starting membrane potential.
length constant (lambda)
:a measure of how far a charge in membrane potential travels down the axon before it decays to zero. One length constant is the distance at which the membrane potential is 37% of the maximum.
Time constant
A measure of how fast a change in membrane potential reaches its maximum. You can think of this like the membrane "charging up" with the voltage. One time constant is the time at which the membrane potential is 63% of the maximum.
(T/F) The "capacitance" of a neuron is characterized by the presence or absence of open ion channels?
Also false b/c that is referring to the conductance although, technically could be argue to be true given that capacitance requires the lipid bilayers ability to separate charge etc...
Similar to Goldman equation in concept but uses conductances of the channels. This gives a formula for the membrane potential.
Equivalence circuit equation
Changes in a cell's membrane potential are classified as either graded or action potentials.
- In graded potentials, the amplitude of the change is proportional to the magnitude of the input. In action potentials, the amplitude of the change is independent of input ("all-or-none"). - also graded potentials (or passive conduction) decays over distance
Electrical gradient
- Net movement occurs in response to electrical attraction/repulsion - Depends on both the charge of the ion AND the electrical potential of environment
Consider an IV plot for a leak ion channel. Is it possible to have a negative slope? Why or why not?
- This is in fact, not possible b/c G (conductance) cannot be a negative value - must remember, that conductance depends on the number of leak ion channels open (you can't have a negative amount of channels)
58 mv would be the point where there is no more net flux of potassium ions (aka the sweet spot) - "equilibrium potential" or "reversal potential"
- above this point we se outwards flux of positive charge - and below we see inwards flux of positive charge {stays the same regardless of the ions charge}
Chemical gradient (aka. the concentration gradient)
- this only looks at the specific ion of interest - Net movement occurs in response to diffusion - will move ions from area to high concentration to low concentration
Reversal potential of K+
-75 mV
How can we measure these things experimentally? Compare: voltage, current, and patch-clamp techniques.
Current clamp technique ~ "clamps" current at an experimenter-controlled value, (independent variable being controlled) allows voltage to vary (dependent variable) Voltage clamp technique (exactly the opposite) ~ "clamps" voltage at an experimenter-controlled value, (independent variable being controlled) and instead allows current to vary (dependent variable) And finally Patch clamp technique (a special type of voltage clamp) ~ "clamps" the voltage of a single channel, measures current through that channel
In an equivalence circuit, the representation of a "resistor" corresponds to the number of open leak channels for that ion, and is typically measured in amps.
False, that is amps for current. Ohms/siemen for resistance.
Which of the following statements is true (may be more than one)? A. In the 'voltage clamp' technique, the current is controlled by the experimenter and the membrane potential is allowed to vary B. In the 'current clamp' technique, the membrane potential is controlled by the experimenter and the current is allowed to vary C. In the 'voltage clamp' technique, , the membrane potential is controlled by the experimenter and the current is allowed to vary D. In the 'current clamp' technique, the current is controlled by the experimenter and the membrane potential is allowed to vary E. 'Patch clamp' is a type of voltage clamp technique that measures current through a single ion channel.
False; False; True; True; True
Furthermore, Hodkin and Katz did an experiment with extracellular [K+] in 1949 that goes in line w/the Goldman equation:
Furthermore, Hodkin and Katz did an experiment with extracellular [K+] in 1949 that goes in line w/the Goldman equation:
Calculate the resting membrane potential of a cell using the information provided below, use all ions given. {provided with permeability and intra/extracellular conc.]
Goldman equation (note: the extra/intracellular conc. for Cl- are flipped b/c of its charge)
What are some of the differences/similarities between graded and action potentials that we can observe?
Graded potentials - decay - variable - sub-threshold Action potentials - no decay - necessary to reach threshold (faster once this is met) - stereotyped
The Current Convention Is that an...
Outward Current Is Positive
How to account for more than one ion?
The Goldman Equation Emore than one ion = sum of the permeability of each ion * the Nernst equilibrium for that ion This equation will tell us the resting membrane potential
The same cell is then placed in a solution with an abnormally high concentration of potassium, so that the concentration of potassium outside the cell is greater than inside the cell. How would this change affect the IV plot of each of the ions? Re-draw the graph and put an X on the x-axis to represent the approximate value of the new membrane potential.
This one refers to knowledge that [K+] conc. is typically higher intracellular than extracellular. If it was higher on the outside than the reversal potential would become more positive shifting this line (and only this ion) --- keep the same "slope" conductance just move the x-intercept. B/c K+ has the highest permeability it plays the largest role in establishing the RMP, so it would drag it up from the previously calculated negative value to somewhere in the positive area.
(T/F) An axon with very few leak channels would have further-reaching grading potentials than an axon with many leak channels, all else equal.
True.
(T/F) An equivalent circuit gives another way, in addition to the Goldman equation, to mathematically calculate membrane potential.
True. It gives us the preferred way.
The dog-tor tells you that the ion has a charge of paws-itive 2 (+2) and that the extracellular concentration of the ion is 6.5535 mM and the intracellular concentration of the ion is 3.1802 mM. What is the body temperature of an alien dog (in Kelvin)? (Dogs cannot use thermometers.)
[can calculate by using the 'full' Nernst potential equation and solving for temperature.]
Calculate the conductance of this ion channel.
a ~ [159 pS. Conductance is determined by the slope of the line. Taking the difference between the y points over the difference between the x points gives us the slope.]
This E.T. has a body temperature equal to that of room temperature and a concentration of extracellular Cl- ions equal to 500 mM. What is the concentration of intracellular Cl- ions at room temperature? At human body temp?
ans ~ [500 mM. You could do the math with the Nernst equation or recognize that a reversal potential of 0 describes equal concentrations of intracellular and extracellular ions regardless of temperature.]
Draw a cartoon of the molecular structure of voltage-gated K+ channel within a membrane, labeling components. Describe how this structure changes in response to changing membrane potential.
ans ~ [A correct response would include: voltage-sensing domains, pore/selectivity filter. A correct response would include a description of how the positively-charged voltage-sensing domains are normally flexed towards the negative intracellular environment, closing the pore and disallowing ion flow, but with a neuronal depolarization, this attraction is weakened such that the VSD move away from the intracellular side of the membrane and open the channel, allowing for ion flow.]
As depicted on the graph, this ion has a reversal potential of -90 mV. What causes the reversal potential to be negative?
ans ~ [A negative reversal potential indicates a higher intracellular concentration of the ion and a lower extracellular concentration for cations. Potassium is known to have a greater concentration inside the cell, which means that the potassium ions want to move down their concentration gradient towards the outside of the cell to an area of lower concentration. As a positive charge is exiting the cell, this leaves the inside of the cell negative which correlates to a negative reversal potential.]
Explain why the overall membrane potential is most similar to that of K+. Why is that? What would need to change in order to have a membrane potential be closer to Na+?
ans ~ [Because the equivalence circuit is a weighted average of the reversal potentials, K+ having the highest conductance would push the Vm closer to that of K+. To have the overall membrane potential be closer to Na+, you could either lower the conductance of K+, raise the conductance of Na+, or do both.]
Unfortunately, a student who was tasked with finding the conductance value for Cl- skipped class one too many times. They were unsure which of the following was the true conductance but was certain that one of them was. Cl- = 3 nS OR Cl- = -3 nS Assuming one is correct, which of the two possible conductance values for Cl- is correct? How do you know?
ans ~ [Conductance cannot be a negative number, as it is simply a metric of how much the ion is allowed to flow. You cannot have negative flow of an ion.]
A scientist uses microelectrodes to record a membrane potential of -70mV in a wild type mammalian neuron. She would like to manipulate the membrane potential to become more negative. Which of the following choices is the best way for her to achieve her goal? a. Decrease the efficiency of the Na+/K+ pump b. Decrease the K+ conc by 10 fold in the external solution c. Use a drug to open voltage-gated Na+ channels d. Inject positive ions inside the neuron Explain your answer using mathematical justification.
ans ~ [Correct answer could use multiple modes of reasoning, but MUST include some reference to a formula in order to show sufficient mathematical justification. One option would be to use the Nernst equation to show that reversal potential of potassium would be more negative, then say that the reversal potential of potassium is critical to establishing the membrane potential (potentially using the equivalence circuit equation for such a justification). Another option would be to use the Goldman equation to show that membrane potential would become more negative, taking into account that K+ has the highest permeability coefficient.]
Why is the membrane an effective barrier to ion flow? Describe relevant physical characteristics of the lipid bilayer.
ans ~ [correct concepts necessary to mention: hydrophobic/hydrophilic regions, ions are polar and can't go thru hydrophobic portion, hydrophobic nature is due to the hydrocarbon/fatty acid/lipid tails]
The class of drugs known as diuretics are used to rid the body of excess salt and water. However, when used for extended periods of time, they can cause decreased extracellular sodium levels resulting in fatigue, lethargy, and confusion. Explain how these drugs would affect membrane potential. Max 4 sentences
ans ~ [Correct answer could use one of a few methods of justification. One option is to say, if extracellular sodium is decreased, then the reversal potential of sodium is decreased (via the Nernst equation), which means the membrane potential would be more negative (via the equivalence circuit equation). One option is to justify the answer using the Goldman equation, that if there is less extracellular sodium in the numerator of this equation, the membrane potential will be more negative. Lastly, one could say that since the Ena would be less positive (via Nernst equation) and that the membrane potential is a weighted average of all permeant ions, the membrane potential would be more negative.]
Consider an alien species that has leak channels for ions red+ and green-. Consider the following sketch of an IV plot showing/describing these leak channels. Which point best describes the resting membrane potential?
ans ~ [Correct answer is D. We know it has to be a point on the x axis, since the x-axis gives the possible ranges of membrane potentials. We know that it must be between the two x-intercepts, since the membrane potential is an average of the contributing ions' reversal potentials. We know it's going to be closer to the red line, since the higher slope means that the red ion has higher conductance, and therefore a greater impact on Vm. Another way to think of this would be to find the x-value at which all the y-values add up to zero, since Itotal = Ired + Igreen at Vm.]
Below are single channel recordings (in cell-attached mode) of the two types of voltage-gated channels that give rise to an action potential in neurons. What is the identity of the channel shown in A? What about B?
ans ~ [Correct answer: VGNa+ channel. Keynote: notice the rapid, early, inward current.] vs. ans ~ [Possible answers could include discussing the delay in current change that we commonly associate with K+ channels.]
Which of the following statements is false? a. if the extracellular concentration of the ion decreases, then the reversal potential will also decrease. [This one is false/but the answer I selected] b. when the dog neuron is hyperpolarized, then the ion will exit the cell [This one was the right one; aka. false] c. an ion with the exact same relative concentrations but a charge of +1 would have a more positive reversal potential d. doubling BOTH the extracellular AND the intracellular concentration of the ion will have no effect on the reversal potential
ans ~ [Hyperpolarization means very negative membrane potential, so we're looking at the left side of the graph. When the line is negative, that means positive charge ENTERING the cell. In the case of cations, that means the ion is entering the cell, not exiting.] also just read the question slower; I missed the fact it was asking for which statement was false and chose a true one.
Episodic ataxia type 1 is characterized by the loss of voluntary motor abilities. It results from a mutation in the voltage-gated potassium channel. Given what you know about these channels, how could a mutation lead to the observed motor symptoms?
ans ~ [If episodic ataxia type 1 is caused by a mutation in the voltage-gated potassium channel, then that means that something is not working properly regarding the flow of K+ ions out of the neuron or regarding the pace of the VGK channels opening and closing. If a patient with episodic ataxia type 1 loses their ability for voluntary motor movement, then that means that not enough K+ ions are flowing out of the cell to cause hyperpolarization. If the VGK channels didn't open slowly, stay open during depolarization, and then close slowly, then the cell would only stay depolarized and wouldn't be able to hyperpolarize, which would lead to a loss of voluntary motor movement because action potentials allow for controlled, planned movement.]
Explain 2 similarities and 2 differences between channels and pumps.
ans ~ [Similarities: Can move ions across a membrane; Are transmembrane proteins; Are specific to particular ions. Differences: Channels only allow ions to flow down their gradient; Pumps can force ions against their gradient; Pumps require energy]
Examine the voltage clamp traces below, which were generated by Hodgkin and Huxley in the squid giant axon. They recorded the current in response to different membrane depolarizations (from -65mV to +26mV, +39 mV, +52mV, +65 mV, and +78mV). Notice these two observations: 1.) The early inward current shifts direction with increased depolarizing voltage steps. 2.) Conversely, the late outward current only gets more positive with increasing depolarizing voltage steps. Explain why these observations occur using any appropriate equations. Please limit your answer to a MAXIMUM of six sentences.
ans ~ [There are four critical components to a correct response. 1.) Early current is due to Na+. 2.) late current is due to K+. 3.) Na+ crosses over its reversal potential (Ena) as Vm increases. 4.) K+ stays at Vms more positive than its own reversal potential (Ek) as Vm increases]
Consider an alien species that has leak channels for ions red+ and green-. Consider the following sketch of an IV plot showing/describing these leak channels. Which point best describes the resting membrane potential? Explain your answer using mathematical reasoning. Please limit your answer to four sentences.
ans ~ [There are several ways to correctly justify your answer. One option would be to say that the total current from all ionic sources must be zero, so you picked the x-value at which all the y-values add up to zero. Another option is to use the equivalence circuit equation to justify your choice.]
Multiple sclerosis is a disease which causes the demyelination of neuronal axons, resulting in a broad array of neurological symptoms including visual disturbances and general muscle weakness. Using mathematical equations and discussing membrane resistance, explain how demyelination affects the time and length constants of an axon.
ans ~ [Uses the length constant equation and explains how a smaller Rm will decrease the length constant. Uses the time constant equation and explains that it will stay relatively constant because a decreased Rm will only slightly affect the time constant. Ex: -length: Demyelination decreases Rm, as it becomes easier for an ion to cross the membrane without the presence of myelin. As Rm decreases, the length constant decreases (in numerator of equation), meaning that a change in membrane potential will not travel as far down the axon. - time: Demyelination decreases Rm, as it becomes easier for an ion to cross the membrane without the presence of myelin. As Rm decreases, the time constant stays relatively constant (multiplied by capacitance of the membrane).]
Molecules such as glucose....
can have a concentration gradient but not an electrical gradient b/c it has no charge
What technique is being used here?
current clamp
As mentioned earlier, the reversal potential is the potential at which...
current reverses direction: it changes from positive to negative.
Also, the Goldman equation in one sentence is:
essentially a weighted average of contributors from all relevant permeant ions
Nernst equation vs shortcut
ln and Volts vs log and MV
Vrest
resting membrane potential Note that E(K, Na, Cl) = RMP = Vrest [Ca is really small] RMP is the measure of the difference in neuron between the inside of the neuron and the outside of the neuron when nothing else is going o
Voltage-gated K channels open...
slowly and stay open
Keep in mind that the values we covered and the equations are a....
statement of theory - In reality, it is very unlikely that the membrane potential will be exactly at the reversal potential
Equilibrium potential (Ex)
the electric potential that achieves electrochemical equilibrium for a given ion, X
how can we define "reversal potential"?
the electrical potential at which the flow of ions reverses
[Reversal potential, Nernst, equilibrium]
the electrical potential difference between the inside and outside of a membrane that give rise to the electrochemical equilibrium for a single ion given in VOLTS
The membrane resistance is a function of... and the axial resistance is generally a function of...
the number of open ion channels the diameter of the axon.
Given the information above, and your choice for Question 1, what is the membrane potential (assuming no other ions are present)? {conductances and reversal potentials]
use the equivalent circuit equation
You are given a cell that contains a sodium conductance of 2uS, a potassium conductance of 4uS, and a chloride conductance of 3uS. Solve for the resting membrane potential {your are given the conductance values and approximate reversal potentials]
use the equivalent circuit equation
Thought question: if we knew an ion's reversal potential and the conductance of its ion channels, how could we calculate the current due to that ion?
using Ohm's law
In the Goldman equation why are extra/intracellular chloride conc. switched?
well, b/c of the charge
Electrochemical equilibrium
when the chemical and electrical gradients perfectly offset each other
note: should probably remember the relative concentrations of these ions (at least the mammalian ones) Potassium is the only one out of the four that will ALWAYS be greater inside (vs extracellular)
{extra/intra} potassium ~ 5/140 mM sodium ~ 145/5-15 mM chloride ~ 110/4-30 mM calcium ~ (negligible) but higher outside regardless
