Single Cell Physiology: Concepts and Methods

First post of the new academic year! This one is for PHYL3001: Physiology of Membranes, Muscles and Signalling.

This post is supposedly revision if you did PHYL2002: Physiology of Cells. I didn't do that unit, and I also didn't do physics in year 11/12, so some of this is new to me.

Review of membrane properties

Yay, a section that isn't particularly new to me! Main things you need to know are that the membrane is a lipid bilayer that lets through some things more easily than others, but there are also channels that can help carry through stuff that won't readily diffuse through the membrane (mainly ions and larger polar molecules).

Here are some posts that you can read for more information:

• Cell Membrane Structure
• Membrane Diffusion and Osmosis
• Lipids- Membranes as Dynamic Molecular Barriers

I did write other stuff on membranes back when I was doing CHEM1004/SCIE1106, but those three posts are the most relevant ones.

Importance of electrical phenomena for all cells

The movement of ions and other charged particles is pretty important. Aside from controlling phenomena such as signalling, enzyme cascades and so forth, ions are the most abundant dissolved solutes, so their concentrations in different compartments can contribute greatly to the osmotic balance in cells. This, in turn, can lead to the control of fluid flow, such as in the reabsorption processes in the kidney.

Principles of membrane potential generation

Membrane potential relies on different concentrations of ions on either side of the cell membrane. (My understanding of "potential" is all of that energy that those ions could produce if they could just smash through the membrane and move down their concentration gradients, but I could be wrong. Despite my dad being a lecturer of electronic engineering, electrical stuff was never my strong suit.) This, in turn, relies on the membrane being selectively permeable to ions (if the membrane was 100% permeable, then ions would just diffuse across until there were equal amounts on either side of the membrane). As I alluded to in the first section, this permeability is helped along by channels and so forth that can help carry some ions (but not others) across the cell membrane.

There are several different types of channels. Uniports only bring one substance across the membrane. A symport can bring two substances across at once: sometimes one that is moving up its concentration gradient, coupled with one that is moving down its concentration gradient (so that no energy is required). An antiport works similarly to a symport, but the two substances are moving in opposite directions across the membrane.

As well as channels, there are also pumps, which use ATP in order to move solutes against the concentration gradient. The most well-known example of a pump is the Na⁺-K⁺ ATPase, which moves 3 Na⁺ ions out for every 2 K⁺ ions in.

Concept of electrochemical equilibrium

Electrochemical equilibrium is probably a bit easier to explain with an example. Due to the action of the Na⁺-K⁺ ATPase, there is usually more K⁺ inside a cell than outside of it. When a K⁺ channel opens, K⁺ begins to move down its concentration gradient. However, it never gets to the stage where there are equal amounts of K⁺ inside and outside of the cell. This is because the outward movement of K⁺ makes the outside more positive than the inside, and K⁺, being a positive ion, is drawn towards the negative charges. Eventually the electrical force pulling K⁺ into the cell balances out the chemical force pulling K⁺ out of the cell, so there is no further net movement of K⁺. When this happens, K⁺ is in electrochemical equilibrium.

Driving force on ions across membranes- generate simple IV curves

Before I go any further, I'm going to go through some definitions. These should be revision from high school physics (I say "should be," because back when we did electricity in year 9 physics, I had a teacher with an accent that I couldn't understand).

• Charge (Q): The imbalance between positively- and negatively-charged particles. Measured in coulombs (C).
• Avogadro's number (N): The number of protons (or whatever) in one mole of a substance. Equal to 6.02*10^23.
• Faraday's constant (F): The magnitude of electric charge in one mole of protons. This is equal to the charge on one proton (1.6*10^(-19)C) multiplied by the number of protons in a mole (which is simply Avogadro's number), giving a Faraday's constant of ~96 500 C/mole.
• Valence (z): The charge on an ion.
• Current (I): The movement of charge over a certain amount of time (I = Q/t). Measured in amperes (amps).
• Voltage (V): The difference in electrical potential between two points. (And it has to be more than one point, because you can't have a difference over one point, unless you're Donald Trump.) Measured in volts.
• Resistance (R): A quantity that measures how a material reduces the flow of current. Measured in ohms (Ω). Cell membranes have a high resistance, so good thing that they have a shit ton of ion channels.
• Conductance (G): The reciprocal of resistance (i.e. 1/R), conductance is the ease with which an electric current passes. Measured in siemens (S).
• Capacitance (C): The ability to store charges of opposite sign on opposite sides of an insulating layer. Measured in farads (F). Capacitance is proportional to the surface area of the membrane and inversely proportional to the thickness. Cell membranes are thin and thus have a high capacitance.

You also need to learn (or remember, if you've learned this in the past), some of the relationships between the quantities above.

Firstly, voltage developed due to storage of different charges across a membrane (i.e. capacitance) is proportional to the amount of charge separated (Q) and inversely proportional to capacitance (C). This relationship can be written as V = Q/C, which can also be rearranged to Q = CV or C = Q/V.

A possibly more important relationship to know, however, is Ohm's Law, which relates current, voltage and resistance. This is V = IR, which can be rearranged to I = V/R or R = V/I.

Electrochemical driving force and the Nernst equation

I'm going to take a bit of a hiatus here to talk about the electrochemical potential energy difference, which is the main driving force behind ion movement. This ties in with the concept of electrochemical equilibrium, as discussed above. Essentially, if the electrical and chemical forces are not in balance, there's an electrochemical potential energy difference, which causes ions to move. The electrochemical potential energy difference can be summed up in an equation:

Δμ_x = RT ln(([X]_i)/([X]_o)) + z_xF(ψ_i - ψ_o)

That looks really scary, so let's break it down. The Δμ_x refers to the electrochemical potential energy difference. This is essentially just the sum of the chemical potential energy difference (RT ln(([X]_i)/([X]_o))) and the electrical potential energy difference (z_xF(ψ_i - ψ_o)). R is the gas constant, which is around 8.3 J/mol/K, T is the absolute temperature in Kelvin, the two terms in the natural log refer to the concentration of the ion in question inside and outside of the cell, z_x refers to the valency of the ion, F is Faraday's constant and (ψ_i - ψ_o) is the voltage across the membrane (which can also be abbreviated as V_m).

The Nernst equation can be derived from the above. It uses the fact that, at equilibrium, Δμ_x should be equal to 0. This allows us to do the following rearrangements:

0 = RT ln(([X]_i)/([X]_o)) + z_xFV_m
-RT ln(([X]_i)/([X]_o)) = z_xFV_m

V_m = -(RT/z_xF) ln(([X]_i)/([X]_o))
V_m = -2.303(RT/z_xF) log(([X]_i)/([X]_o)) (the -2.303 comes from turning the natural log into a base 10 log)
V_m = E_x =  -2.303(RT/z_xF) log(([X]_i)/([X]_o))

E_x is the theoretical membrane potential at which the ion in question is in equilibrium. I say "theoretical" because in reality there are a whole lot of ions that are trying to get themselves into equilibrium, and a perfect solution is pretty much never reached. If V_m = E_x then there is no net flow of the ion, but if they are different then there is a net flow in some direction. This can be expressed by the following equation:

I_x = G_x(V_m - E_x) where I_x is the current and G_x is the membrane conductance.

If you think about it, this equation is similar to Ohm's Law. Remember, V = IR can be rearranged to I = V/R, or I = (V)(1/R). Conductance is equal to 1/R, so this can be simplified to I = VG (or I = GV if you want to keep the terms in the same order as the equation above).

Oh, Ohm's Law! That goes nicely with my next part...

IV Curve

Nope, this has nothing to do with intravenous medication, which is what I thought of first when I saw "IV curve" on the lecture outcomes slide. In this case, IV simply stands for current and voltage. It is a graph in which the voltage is on the x-axis, and the current is on the y-axis. Since I = V/R (from Ohm's Law), this produces a linear curve which is steeper if R is lowered. Positive values of I generally indicate flow of the ion out of the cell, whereas negative values generally indicate flow into the cell.