Tim Dellinger |
Jennifer Gerbi |
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Various approaches have been taken to solve the protein folding problem. A top-down solution involves "Taxonomic" [1] methods, by which large catalogs of known proteins are compared in all their complexity. (Some of these databanks can be found in the links of interest below). Computer models are used in the opposite sense: from bottom up, using the modelled underlying mechanisms to generate the protein structures. There are many versions of these models, ranging from the general which only investigate a few conformations of the large number available, to simple exact models, which consider all possible conformations. Simple Exact models, while limited in scope due to sheer computing power issues, enable the calculation of the partition function and related quantities.
Our aim with this project was to research and develop a simple exact model, which was extended to include second nearest neighbor interactions. We simulated various sequences of amino acids and their resulting conformations. By analyzing the degeneracies of the energies, "good" protein sequences can be seperated from the "bad" ones, using the ideas of degeneracy with positive and negative design outlined above. In other words, our goal was an amino acid sequence and a set of monomer interaction rules which would show a small number of conformations with very low energy. It is believed that seeing such behavior in simple exact models demonstrates the fundimental aspect of protein behavior.
The standard exact model proposed by Dill [1],[2] is called the "HP nearest neighbor model". In this model, there are only two types of amino acids used: H for hydrophopic and P for polar. Proteins tend to arrange themselves such that the H are folded in on, and the P are at the interface with the water surrounding the molecule. The energy of the conformation is calculated by the nearest-neighbor interactions (NOT counting the interactions between bonded H and/or P, which are those linked together on the sequence chain). Usually, all are neglected except for H H which is -1. Such models are based on the experimental observation that conformations of real proteins almost always bury hydrophobic amino acids, keeping the polar monomers on the surface.
We wrote a computer program that calculates all possible conformations from a set of complete permutations of the moves up,down,left,and right. A possible conformation is one which does not try and put an amino acid on an already occupied site. Of the sucessful conformations, the energies are calculated for two situations: nearest neighbor only, and both nearest neighbor and second nearest neighbor interactions. Additionally, we enable up to four different amino acid types to be input in the sequence, and we have a user input table of the interaction energies between all of them to enable easy modification of the model.
Following are selected results from our simulations. First, a simple example of a 6-chain is presented. The possible conformations and their energies are placed in a histogram, which illustrates the degeneracies of various energies.
Second, the difference between two different sequences, and the expanded model with second nearest neighbor intereractions, is presented.
Note here that there are two different effects. One is the sequence of the protein only. the HPHPPH is a "better" protein than the PHHHHP, becuase it can both achieve a lower energy state, and has a lower degeneracy at that state.
The second effect is that of the nearest neighbor interactions. The energy graphs show more clearly the trends of degeneracy, and in both cases lower energy states are reached. However, the lowest degeneracy of the first sequence is again very clearly realized at all lower energy conformations.
We believe simple models such as this are fundamental to understanding protein folding. The sequence itself is the key to why the protein folds as it does, and sequential effect is very evident even in our very basic model. Additionally, considering second nearest neighbors may be of use in analyzing the density of states of the protein, and deciding what is a "good" vs. a "bad" sequence to perform further studies on.
References:
[1] Chan, Hue Sun. Dill, Ken A. "The protein folding problem" Physics Today v.46 (Feb. 93), p 24-32.
[2] Dill, Ken A. et al "Principles of protein folding- A perspective from simple exact models"Protein Science (1995), 4:561-602
[3] Nunes, Nicole L, Chen, Kaiqi, Hutchinson, John S. "A flexible lattice model to study protein folding" J. Phys. Chem (1996), 100: 10443-10449
Additionally, the Project Links below all provided helpful information and should be considered as references.
Protein Folding Simulation Project: Abstract 10-15-98
Tim Dellinger
Jennifer Gerbi
Ioannis Tziligakis
Protein folding studies investigate the mechanism by which a protein molecule obtains an observed preferred spatial orientation, or conformation. Proteins are complex molecules, and these studies have involved correspondingly elaborate computer simulations. Nevertheless, there are many unanswered questions in this field, and the topic is very active.
We propose to investigate the computer simulation method of protein folding by researching and developing a simple model of this phenomenon. Small, two dimensional "pseudoproteins" will be used, with the molecule consisting of only "a" and "b" amino acids (e.g. a-b-a-b-b-a-a-b etc.) on the order of 16 units long. A lattice model will be used, by which the units can only move to a chosen set of coordinates. Additionally, only nearest neighbor interactions will be considered to define the potential. The metropolis monte carlo technique will be used to "anneal" the molecule. Depending on the temperature, the amino acid sequence in the chain, and the initial conformation of the chain, a number of different transitional and final conformations are possible. Our goal is to develop an energy minimizing algorithm to find the energetically preferred conformation, and to maximize the efficiency of this algorithm.
Using our program, we will contrast the characteristics of various systems by varying four items: the anneal temperature, inital protein conformation, initial protein sequence, and nearest neighbor potential. We will investigate and compare certain properties of each system, including the relaxation time that it takes for the molecule to reach the final preferred conformation, the metastable conformations and energies, and the final conformation and energy.
Finally, it would be of interest to investigate some of the three dimensional, more complex models that are available for immediate use. Running simulations under similar beginning conditions to our model would enable us to very roughly contrast our results, and gain insight on what has been accomplished in the field recently.