Hand-in task 2

Protein Physics SI2700 - Spring 2016 Hand-in assignment 2

Last submission date: March 4. You will get feedback within a couple of days and from that date you receive feedback you have 1 week to correct and hand in the final version.
(Must be completed and passed before taking exam)

A simple lattice model for protein folding

Lattice models have been used for a long time to study proteins, not because they are particularly representative for any real proteins, but if there are indeed general principles that govern protein folding it should apply to simplified models too.  In contrast to realistic molecular dynamics simulations lattice models have some special advantages. In particular, if the chain is reasonably short and we assume the lowest-energy states are the most compact ones (interactions are attractive on average), then you can often enumerate all states and compare their energies, and their simplicity also makes it possible to use quite efficient Monte Carlo algorithms with large moves when studying them. In this task, you will run a lattice simulation of a very small model (27 units, 3x3x3 compact states) sequence and analyze the results in terms of energy levels/landscape and what it means for stability. This is a tiny model by today's standards, but that also means you will be able to run it on your desktop without waiting for hours.

In preparation, you might want to read the paper “How does a protein fold?” by Sali, Shakhnovich and Karplus, Nature 369, 248-251 (1994) (see below). All these three authors are now rather famous senior professors at Harvard and UCSF, not only for this paper. YOU WILL HAVE TO READ THIS PAPER TO UNDERSTAND THE TASK.
Download the package with the lattice simulation programs from the course page. They should work both under windows, linux and mac (text -based in a terminal window). There is also source code if you want to compile yourself. The programs are not graphical though, so you have to open a terminal / command window and run them there.
The idea of the paper was to first generate sequences with random interactions between residues. Since we can enumerate all states on the 3x3x3 compact lattice it is then straightforward to calculate the entire energy spectrum/landscape for this particular set of interactions. The real test is what happens when you try to “fold” the protein as described in the Sali/Shakhnovich paper - does it find the lowest energy state, and how is that correlated with (i) the lowest energy and (ii) the energy gap to the second lowest energy?

Try to repeat the work of the paper.

 The packages on the home page contain three programs:

enumerate_compact: This program calculates all possible non- overlapping compact states on a 3x3x3 lattice, counts them, and writes the result to compact_conformations.dat.

 make_random_energy: This program generates random energy functions, as described in the paper. To save you some typing work, it can generate an arbitrary number of energy functions in one sweep, and write the lowest energy, energy gap, and suggested simulation temperature for you. For energy function “N”, the energy file is energyN.dat and the corresponding spectrum with the 500 lowest energies spectrumN.dat

 lattice_simulation: This program runs an actual lattice MC simulation. You can probably use up to 500,000,000 steps on a modern computer (but 100 million should be fine), and the rest of the parameters are output from the other programs.
Write a short (2p with figures) summary of your findings. How many compact states are there? Do any of the sequences you generate/choose fold? Which ones? Which ones donʼt fold? What happens to the ones that donʼt - what do they look like? The final structure is written to the file final_conformation.pdb, which you can open e.g. in PyMOL or VMD to look at.
Compare sequences with and without clear gaps in the spectrum. How is that related to the “foldability” of the sequence?

Good luck! Magnus

The Sali paper required for task 2

Programs required for hand-in task 2:

Mac OS X (Compiled on 10.6, Snow leopard): lattice_mac_osx.tgz
Linux (Compiled on Ubuntu 10.04 64 bit): lattice_linux.tgz
Windows (Compiled on Windows 7): lattice_windows.zip
Source code (if you want to compile yourself): lattice_source.tgz