How Many ATP Molecules Are Used in a Single Bicep Muscle Contraction?

[Kawrae]

>> Calculate approximately how many molecules of ATP are required for a standard muscle like the biceps during the contraction phase of a single twitch.

I honestly do not even know where to begin here... I don't think he wants us to go through and just outline Glycolysis/Kreb's Cycle/ETC because that's just producing ATP in general, not for a specific contraction. And that's not saying how much is NEEDED...

I've looked around on the internet but can't really seem to come up with an answer. I know that calcium is needed but again, I can't figure out how much.

Does anyone think they could help me out? Thanks

 

[TeethWhitener]

There are tons of different ways to approach this problem, from the very simple to the very involved. I'll go a very simple way. Let's take the bicep, for instance. Let's say you lift a 10kg weight 0.5m directly upward (using only your bicep somehow). This requires your bicep to do:
$$W = mgh = (10kg)(9.8m/s^2)(0.5m) = 49J$$
worth of work. ATP hydrolysis releases 30.5 kJ mol^-1. This means that the number of moles of ATP required to do 49 J worth of work is:
$$\frac{49J}{30500J\cdot mol^{-1}}=1.6\times 10^{-3} mol$$
To get number of molecules, simply multiply by Avogadro's number:
$$(1.6\times 10^{-3} mol)(6.022 \times 10^{23} mol^{-1}) = 9.6 \times 10^{20}$$
So an order of magnitude estimate would be roughly 10²¹ molecules of ATP per muscle contraction.