Thursday, September 30, 2010

The Battle of the E in biology and physics

Today's biological physics class is extremely exhilarating, despite the fact that I was probably lost half the time, but I could stilll follow some of the equations and treatments that Prof D went. He was extremely fast, so was J, our TA, when he mentioned something and he rattled on like water.
Basically, class today was talking about the contention between entropy and (internal) energy of a system, in order to achieve minimal free energy of a system.

Entropy is loosely defined as the quantification of consistency of certain (micro)states with its meso/macrostates; so by the law of thermodynamics, it increases, OR simply, a measure of the system that you did not know about (ignorance). I shan't go into the treatment of entropy. But here, let me tease apart the energy components that we are defining here. So, free energy here, typically refers to Gibbs' free energy - remember the enzyme energy curve that we always draw in JC, where we are always trying to achieve as negative a delta G as possible, in order for the forward reaction to be driven forward. Loosely put, the resultant products are of lower (internal) energy = more stability than the reactants. In nature generally, things aim to minimize free energy to achieve equilibrium state. In order to do that, we have to apply energy to the system, for the system to do work, in this case, to minimise free energy. You can also see free energy as the amount of energy available to do work (by the system). But free energy is also dependent on entropy as well. To keep things short,

free energy = (internal) energy - temperature * entropy of the system,
where temperature is kept constant

So, contextualising the above physics in a familiar biological scenario: osmotic pressure. Typically, in biology, we name that phenomenon based on the fact that there is a pressure exerted (on a semipermeable membrane) by the solutes in a solution against the inward flow of water/solvent, due to osmosis. Imagine we have our standard osmotic pressure experiment, where we have a box, divided into 2 sections by a semi-permeable membrane. In one section of V volume, you place N molecules in it. To keep this concentration of solutes in place, work has to be done by the system to keep the solutes from moving out too and this corresponds to the amount of free energy available to do work. And using the free energy equation above, if we assume all the solutes to be ideal solutes (which is like ideal gas assumption, where each particle is pointlike, totally random and non-interacting), the "internal energy" of the system as a whole can be ignored. Work done is also defined by the pressure * volume, so to counteract the water moving in, work done by the solute = the osmotic pressure * volume occupied by each solute. If you can imagine, then the amount of work done which is dependent on your free energy (to do work) per unit volume would correspond to your osmotic potential, which after a semi-long mathematical treatment, would give you:

osmotic potential = n * K (Boltzmann constant) * T

I do not know about you, but when I saw that, the IMMEDIATE thing that came to mind, was the equation of the ideal gas, pV = nRT (and I am surprised myself how fast that came, considering the last time I used that was, like 10 years ago!!)! And it turns out, it IS the ideal gas equation, since n in the ideal gas refers to number in moles!

SO, long story short, the conclusion was that osmotic pressure AND ideal gas pressure are really forces that a system exerts in its attempt to increase its entropy (2nd law of thermodynamics). Contrast these mechanical systems (where no energy assumed due to idealized particles) with a simple mechanical system, of a spring, where no entropy is involved, only aim was to reduce the free energy, you end up with a entropy-energy spectrum representing all situations, where in real-life situations, systems are really in the intermediates, a competition between minimizing energy and maximising entropy to obtain an optimal minimum free energy state.

Prof D ended the class with an analogy from amoeba being placed in pure water. In high-school biology, we often viewed that as a proof of osmosis in hypotonic solution, where the amoeba eventually burgeons (and explodes if left too long) when the cell semipermeable membrane cannot withstand the rapid increase in volume. But if you look at it in the physical point of view, the law of thermodynamics in entropy is STILL a universal governing law! In fact, the solutes is trying to get out of the amoeba, IN ADDITION TO, the water getting into the amoeba!

I couldn't find a good "bursting" experiment video, this is the best I could find on YouTube for RBC: not that great IMO LOLX

No comments: