Extracting Energy from Food

This post- especially the second half- is going to look deceptively like a recap of BIOC3004, but there's some new stuff in the first half, so read on!

Chemical potential energy; cost of ion pumps

Ion pumps move ions against their concentration gradients (i.e. from an area of low concentration to an area of high concentration). As ions don't like to move against their concentration gradients, this shit takes energy. Energy generally comes in the form of ATP.

We can figure out how much energy is required by using equations for electrical and chemical potential energy. If the sum of chemical and potential energy required is less than the amount of energy produced by ATP hydrolysis, then the pump will run. If this requirement is not met, the pump either will not run or will run backwards (which can also be a good thing, as we'll explore later).

The equations for chemical and electrical potential energy are as follows:
Chemical potential energy (μ_x) = nRT ln ([x]₁/[x]₂)
Electrical potential energy (μ_e) = zFnV
where n = number of moles, R = gas constant, T = temperature in Kelvin, [x] = concentration of ion in a given location, z = valence on the ion, F = Faraday's constant, V = voltage.
(At equilibrium, μ_x = μ_e, allowing for derivation of the Nernst equation, as discussed here.)

From the equations above, we can calculate the energy cost of running an ion pump. For example, let's take the Na+/K+ ATPase, which uses 1 ATP to exchange 3 Na+ ions for every 2 K+ ions. For the purposes of this example, we're going to use a temperature of 37°C (310°K) and the absolute value of the membrane potential as 70mV (0.07V).

Chemical potential energy of Na+ = 3*8.314*310*ln([150]/[15]) = 17.8 kJ/mol ATP
Chemical potential energy of K+ = 2*8.314*310*ln(140/5) = 17.2 kJ/mol ATP
Electrical potential energy = 1*96500*1*0.07 = 6.7 kJ/mol ATP

Add all of these up and you get the total cost of the ion pump: 42 kJ/mol ATP! This can be further converted into kcal (remember, scientific calories and food calories are different): 1kcal = 4.2kJ (or 1cal = 4.2J), so our ion pump costs around 10kcal/mol ATP.

Remember, to determine if an ion pump works or not, this total cost (10 kcal/mol ATP in this case) must be compared to the energy gained by hydrolysing ATP. If hydrolysis of ATP doesn't provide sufficient energy, the pump will either not work, or it will run backwards.

Potential energy in ATP

Okay, this is the part that I didn't 100% understand, so bear with me.

Here is an equation for the energy in a chemical reaction:

μ_c = ΔG = ΔG°' + nRT ln([Products]/[Reactants])

μ_c and ΔG are the same thing: they refer to the energy change in a reaction at STP (standard temperature and pressure) when all reactants are present at 1 mol. Physicists prefer the first term, and chemists prefer the second.

ΔG°' is very similar to the other two terms, but with a twist. Instead of using STP, ΔG°' uses a pH of 7.4, 37°C, and aqueous solution, as these are the conditions that you are likely to find in a biological system.

At standard state, the hydrolysis of ATP (ATP + H₂O <--> <-->ADP + PO₄^2- + H⁺) is around -7.5kcal/mol, meaning that the products (ADP and phosphate) have 7.5 kcal/mol less energy than ATP. (The negative sign means that the products have a lower energy state than the reactants.)
<-->
<-->Now here's the bit that confuses me: apparently, the measured chemical potential energy of ATP hydrolysis is not a measly -7.5 kcal/mol ATP, but rather somewhere between -10 and -14 kcal/mol ATP (averaging out at around -12 kcal/mol ATP). My best guess is that this is because, in real cells, ATP and ADP are not present in the same amounts. On the contrary, ATP is present in much larger quantities in the cell, which is why ATP will happily become hydrolysed into ADP to move closer towards equilibrium, releasing energy that can be used to move another reaction away from equilibrium (e.g. pumping ions against a concentration gradient).

Production of ATP

Glycolysis

See previous post: Glycolysis and the Pentose Phosphate Pathway

TCA cycle

See previous post: The TCA Cycle

Electron transport chain

See previous post: Electron Transport Chain and Oxidative Phosphorylation

Running an ion pump backwards

When the concentration gradient is too large to be overcome by the hydrolysis of ATP, an ion pump may be run backwards. This is actually what happens in the case of the H+ ATPase- the pump is run backwards by the large proton gradient, causing ATP to be formed, rather than hydrolysed.