Based on lecture 2, we will dig deeper into the energy of different conformations. This turns out to be intimately related to another very important concept: The Boltzmann distribution that tells you what states of a molecule will be occupied depending on their energy and the current temperature.

Armed with this, we are able to introduce the concepts of free energy and entropy, which are important when there are many "microscopic" states sharing the same absolute value of energy - since on the macroscopic scale we think of all these collected state as a single state, but with more freedom - or entropy.

One of the key results here is that entropy is actually pretty simple: it's merely a way to count that some states have more internal states, and then we introduce a convenience notation for it. We also expand the free energy concept and separate it into Helmholz vs. Gibbs free energies. This is an important formal definition difference, since the latter introduces the constant pressure we typically have in the lab. However, for proteins this difference is typically negligible since we deal with extremely low concentrations - so for the rest of the course we will typically just talk about "free energy", we will use the letters (G) corresponding to the Gibbs one, but because of the small difference we never bother about pressure.

We will show you how the temperature actually comes out as a natural definition from the F=E-TS equation, and this is the proper thermodynamic definition of temperature. We then go back and revisit the hydrophobic effect, but now we can describe it properly with the free energy nomenclature, and also start relating it to protein folding.

We'll spend some time on quizzes and thinking - the key concept you need to get from this lecture is to start "working" with free energy, entropy, and enthalpy. Look around in your daily life (ice, water, order/disorder, any other process you can imagine) and try to assess what they mean in terms of entropy and enthalpy. It's also instructive to think in terms of probabilities - why is it that a brick can drop, but not fly up?

Another important conclusion from the lecture will be that the Boltzmann distribution gives us an energy scale to which we can compare other energies! You need to know what "kT" is in kcal/mol (and kJ/mol ;-) - you will remember it better if you look it up yourself, so I won't write the value here, though! Energies clearly smaller than kT will just be "gravel on the road" in the sense that we can easily get across those barriers, while energies significantly higher than kT will turn into "brick walls" that will take very long to surmount - but the intermediate energies we identified last lecture will define different states between which we can exchange populations.

Lecture recording

Playlist of all lecture 3 concepts

Isolated concepts:

Slides with still images from videos

(Some students found these useful to take notes)
Full-format stills
Handout-format stills

Reading instructions

Finkelstein/Protein Physics chapters 4, 5 & 6

Study questions

Papers / reading

Debunking polywater

The courious case of polywater

Gerstein & Levitt Scientific American paper on simulating water