Hello All,
Membrane Potentials is a difficult concept to grasp because the simple movement of ions and it reaching an equilibrium when the concentration and electrical gradients are equal goes against what we typically think of as equilibrium (when the concentrations are equal). However, potentials really ARE an important thing to grasp to understand how the communicative physiology of the body works. If you are struggling, PLEASE come see me or work with your fellow colleagues to grasp these concepts. Unfortunately this is NOT one you can just miss these questions on the test and move on, this is one that will continue to come up, so lets struggle with it now and reap the benefits for semesters to come! Here are a number of questions that I have gotten from many of you already. As always, if you have others, please feel free to leave a comment and we can work through them together!
1. I was wondering if you could explain the first
example question from todays lecture (membrane potential). I am just confused
as to why the concentration gradient would not be altered significantly (answer
3) if the driving force is from 155mM to 4mM. It seems that ion flow is not
only possible with it being selectively permeable, but is needed. Also does the
Mannitol make any differences?
Mannitol is only in the system to start the system off with electric neutrality so there is no difference in charges across the membrane to begin with. However, struggling with the movement of the molecules themselves is precisely what I am teaching in this lecture and mentioned above. The concentrations DO NOT change because the concentration gradient becomes balanced by the electrical gradient. THAT is what causes the system to reach an equilibrium when we are discussing charged ions. That, therefore, prevents the concentrations themselves from adjusting very much.
Precisely, a very few number of ions moving from the area of 155mM to 4mM does occur. This causes a HUGE electrical gradient to occur (which quickly with very view ions becomes approximately 90mV gradient) and that prevents any more ions from moving. Therefore, the concentrations themselves that started (155mM may become 153mM while 4mM may become 6mM, but those concentrations do not change). It is the BALANCE of this concentration gradient with the electrical gradient that cause the molecule concentrations to stay.
2. This is about the question the with KCl + mannitol
solution to the membrane only permeable to K.
Electrical and chemical gradients...can they actually be
calculated and have an actual value? I know the difference is delta mu, so I
wasn't sure if there were actual numbers involved. If so, they are equal but
opposite, correct?
Maybe I'm getting ahead of myself without knowing the
answer to my previous question, but if they can be calculated and have equal
but opposite values, and hypothetically one has a value of 2 and the other has
a equal but opposite value of -2, wouldn't the difference between those be 4
and not 0? Or maybe I'm thinking way too much of magnitude/direction in physics
and the values would both be 2 just in opposite directions, making the
difference 0?
Electrical gradients can DEFINITELY be
calculated (using the Nernst equation). Chemical gradients are a bit
more complicated and the equations we have all boil down to the Nernst
equation essentially. The Nernst equation is calculating, however, the absolute
value of these gradients. It gives you a voltage (that indicates the
difference in charges across the membrane) of the value of the
electrical gradient that counteracts the chemical gradient. Therefore,
it is not quite so much that there are actual numbers involved for each
gradient, but that there is an absolute value of each gradient and
they are in opposite directions.
I understand the nit-picking of the math as well and understand your confusion. These gradients are of an absolute value vector of driving force and happen to go in opposite directions, therefore if you take the difference between their absolute value, you would in fact mathematically get zero as well.
3. For question #3 that we did in lecture today, I
don't understand why chloride ion would leave the right compartment negative
when itself is a negative ion?
Turningpoint question #3 has a situation given below. If you made the membrane solely permeable to Cl- it would, just like the other ions if it were permeable to them, go initially down its concentration gradient (if the membrane was not permeable to anything to begin with there was no electrical gradient as the membrane potential was equal to 0mV). Since there is more Cl- on the left side of the system than the right it would move down its concentration gradient from left to right. It would bring with it its negative charge (as you indicated above), thereby making the right side of the system negative with respect to the left.
4. Also on slide 21, why are the chemical and electrical gradient for sodium the
same direction (into the cell)? Are we not taking into consideration the NA/K
Pump?
I'm going to assume you mean slides 23/24 similar to the picture below because on slide 21 the gradients are going in opposite directions. However, I will explain the following picture: We are looking at here the electrochemical gradients for K+, Na+, Cl- and Ca2+ for a typical neuronal cell at rest with a Vm of -70mV (as indicated). The arrows are indeed representing the chemical and electrical gradients as you mentioned. Remember that the chemical driving force is the force that is causing the molecules to move from an area of high concentration of molecule (K, Na, Cl, or Ca) to an area of low concentration (ex. Na concentration is high in the ECF and low in the ICF while K concentration is high in the ICF and low in the ECF). Therefore the chemical gradient or driving force for K is from the inside of the cell to the outside and for Na is from the outside of the cell to the inside (as indicated). Electrical driving force, on the other hand, is the driving force for the charge (either + or -) and also goes from an area of high like-charge to an area of low like-charge (or another way of thinking about it is opposite charges attract). Therefore, since the inside of the cell has a negative charge (-70mV to be exact), the electrical charge for BOTH K and Na would be into the cell because BOTH molecules are positively charged.
The electrochemical gradients, therefore, are a COMBINATION of the chemical gradient or driving force and electrical gradient or driving force. This can ONLY be determined by determining the equilibrium potential (or Nernst potential) for a given ion. As we have calculated the equilibrium potentials for a typical neuronal cell you know that the EK is ~-90mV and the ENa is ~+60mV, therefore the electrochemical gradient in the cell below for K+ would be out of the cell (the direction K+ needs to move to bring the membrane potential from -70 mV to -90 mV) and for Na+ it would be into the cell (the direction Na+ needs to move to bring the membrane potential from -70mV to +60mV).
The Na/K pump, remember simply MAINTAINS these gradients. The primary active transporter, by definition, moves molecules AGAINST their concentration gradients and therefore does not effect the electrochemical gradients except for to maintain them.
5. I think there is a
mistake in the Goldman-Hodgkin-Katz
voltage equation. Is the intracellular chloride concentration supposed to be
divided by the extracellular concentration, and not the other way around?
Shouldn't anions be treated differently than cations when
calculating their contribution to a cell's membrane potential.
Indeed anions SHOULD be treated differently than cations. However, in the equation on the slide the negative sign out front simply accounts for that. Alternatively, you could write the equation like the simplified Nernst equation and put the intracellular chloride concentration divided by the extracellular chloride concentration (as is written in the notes section of the same slide).
Hopefully these help. If you have any other questions please do not hesitate to contact me on here or via whatever other method you like best. If you are having trouble with the MetiLS practice questions please feel free to contact me as well!
