In this lecture we formulate two important results: Anfinsen's Dogma (or the "Thermodynamic hypothesis") arguing the native state of proteins is the global free energy minimum, and Levinthal's paradox pointing out that there is no way for a protein to visit every possible state to find this minimum. Both are key for this class!

We will look more into specific amino acids such as Proline & Glycine, but also hydrophobic residues - what do their properties mean e.g. for entropy, packing and folding of proteins? Now we also discuss the disulphide bridges of Cysteine, and how Tryptophan is big & bulky - which incidentally is a key feature of the world's smallest protein Trp-Cage. It turns out the charged amino acids are also critical for stabilizing and strengthening effects of the alpha helices, and the geometry of alpha helices and beta sheets can give them a "hydrophobic moment". We also talk about the titratable amino acids and the concept of "pKa value", and why the charges can be exceptionally important for function.

However, before you draw a deep sigh of relief that we are done with the math and statistical physics: as we look at real proteins, we will increasingly interpret structure, folding, and function with these tools, so it is imperative that you understand them well - in particular:

F=E-TS.

We will talk about different ways to look at protein structures and how to classify them, ranging from primary through secondary and tertiary to quaternary structure, we will look at the stability properties of helices, and how we can rewrite this into free energy of formation combined with a free energy of elongation. This will help us investigate the helix/coil transition, and we will reason why these parts can co-exist in the 1-dimensional chain - it is thus not a true phase transition, but an equilibrium with a sliding transition over ~10K. We'll also look at kinetics to justify why helices form so fast. This will then be repeated for sheets, i.e. investigating their stability and formation timescales, which leads us to the striking results that the beta sheet formation time can range from microseconds to years since the stability shows up in the exponent (in contrast to the helix). This appears to be the explanation for several misfolding diseases such as prions, meaning there are exceptions (but very few...) to the rule that the native state is the global minimum in free energy. Finally, we take a look at the coil and show that the expected end-to-end distance only grows as the square root of the number of residues.

Lecture recording

Playlist with all lecture 5 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 chapters 9, 10 - and partly repetition of previous ones. After this lecture you need to know the basics in-and-out, because now we'll head on first to simulations, and then looking at real proteins using these tools :-)

Study questions

Why are amino acids chiral?
Suggest a couple of conceptual ways to organise amino acid side chains!
Name at least one common place for glycine to occur!
Why does proline tend to break helices?
What is special with cysteine?
What is special with proline?
What are the Phi & Psi dihedral angles? Omega? Chi?
How many atoms are restricted to a plane by the peptide bond?
Why are helices and sheet so common?
What is tertiary structure?
What is quaternary structure?
What is Anfinsen’s Dogma?
What is Levinthal’s Paradox?
Why is there no left-handed alpha helix?
Why do helices tend to pack at an angle rather than in parallel fashion?
What determines if helices are stable? What determines their kinetics of formation?
What do we mean by “hydrophobic moment”?
What’s the difference between parallel and antiparallel beta sheets?
Why is sheet formation a phase transition while helix formation is not?
Why is the range of formation rates for sheets large while it is not so for helices?
What is a prion?

Other material

Trp-cage folding movie