For lecture 6, we start by recapping some of the math from yesterday. Then we will talk about how helix & coil can mix in the simple one-dimensional system formed by an amino acid chain, and how this can be measured e.g. with CD spectroscopy - which in fact is the way most "helical propensities" were derived a long time ago.

This helps us formulate slightly more detailed equations that also gives some hints about the time used for initiation and extension/elongation of helices.

In the same way we can go through beta sheet formation and simply introduce and define the properties we think we need. One of the hardest questions is to determine how long it takes for the initiation. Just as for alpha helices, this barrier is caused by the most unfavorable conformation we need to pass on our way to folding. Think of it this way: If we were not yet at the top of the barrier, we would need to add even more (free) energy before the sheet is extended naturally. Similarly, if we are already past the barrier, we would already be going downhill free-energy-wise. These states are called transition states, and the typical property is exactly this: Their relative free energy determines how hard it is for the reaction to happen.

Thus, we will spend some time identifying this transition state for sheet formation, what its properties are, and if this can help us say something about what is required for beta sheets to form (it will). It will also give us some deep insight about why beta sheet formation is often very slow.

We further talk about misfolding of proteins, and why some structures might make conformational transitions and then turn our attention to the "coil" or "random coil", which turns out to be more interesting than you might think. We can make some simple reasoning about how large a completely random coil will be, and how this is related to actual proteins (where the coil cannot cross itself due to steric clashes).

Armed with all this theory stuff, we can now approach modeling of real proteins. We will think about their energy landscape, and how we can minimize the energy to fix bad clashes, and then we look more into real molecular dynamics simulations using Newton's Equations of motions and how they (in contrast to energy minimization) are used to calculate and predict properties that we otherwise measure in the lab.

Finally, we look at some protein simulations and talk a little bit about ensembles.

Reading instructions

Book chapter 9: Helices, sheets and coil

Lecture notes: Simulations of real biomolecules

Study questions

What is the difference between thermodynamics and kinetics?
What feature of the energy landscape determines thermodynamics and stability?
What is most important for kinetics?
What is the point of separating initiation and elongation free energies? Roughly how large are they for a typical helix?
How are numbers like that determined?
What type of transition is alpha helix folding?
Roughly how long does it take to fold a typical helix?
How is beta sheet folding different from a kinetics point of view?
What type of transition is beta sheet folding?
How long does beta sheet folding typically take?
How does the end-to-end distance vary with the number of residues in a coil?
What terms do we need to model a real biomolecule, e.g. a protein?
What is the role of energy minimization? What do you not get from it?
What does a simulation really do?
What do you get from a simulation? What do you not get from it?

Study questions

What is the difference between thermodynamics and kinetics?
What feature of the energy landscape determines thermodynamics and stability?
What is most important for kinetics?
What is the point of separating initiation and elongation free energies? Roughly how large
are they for a typical helix?
How are numbers like that determined?
What type of transition is alpha helix folding?
Roughly how long does it take to fold a typical helix?
How is beta sheet folding different from a kinetics point of view?
What type of transition is beta sheet folding?
How long does beta sheet folding typically take?
How does the end-to-end distance vary with the number of residues in a coil?
What terms do we need to model a real biomolecule, e.g. a protein?
What is the role of energy minimization? What do you not get from it?
What does a simulation really do?
What do you get from a simulation? What do you not get from it?

Slides

Handout-format slides for lecture 6

Full-format slides for lecture 6