Undergraduate Research in Engineering at Rice
Allison Heath, Junior Computer Science student
Conformational Analysis of Biomolecules
with Dr. Lydia KavrakiUnderstanding how molecules interact with each other is a fundamental concept in biochemistry. One important application of molecule interaction is drug design. Drugs work by binding one molecule, the ligand, to another, usually larger, molecule. To approximate this interaction the structures are considered to be rigid. Of course in reality this is not true: the molecules are flexible and can change to conform to each other. We hope to develop the ability to predict how these molecules will interact with each other. Part of this ability includes being able to come up with natural states of these flexible molecules. Since they are able to move they can take on many different conformations. In nature the molecule tends to move towards conformations that have lower energy, and thus are more stable. So we need a way to examine a certain conformation and move it towards a local energy minimum. This will help us in finding conformations of a ligand that have the potential to interact with a specific receptor.
Over the summer I worked to develop a program that would change a given molecule conformation so that the resulting conformation was located in a local energy minimum. The energy of the molecule was calculated using the CHARMM force field. This is a function that takes in the location of each atom and the bonds between them and comes up with a number representing the energy of the molecule. By taking the gradient of this function I could use numerical methods to find a local minimum of the energy. The first method that was implemented was steepest descent. This is a simple method where one moves along the gradient towards the minimum. However, this method is not a very good one. Therefore a better method called conjugate gradient was implemented. The conjugate gradient method moves along the gradient of the energy function until the line minimum in that direction is found. Then it repeats the process from this point until the local minimum is found. Once it has reached the line minimum it moves along the gradient, but perpendicular to the direction we just moved in order to not spoil the minimization that was just done. If the function to be minimized were quadratic, then conjugate gradient would be able to find the minimum in n iterations, where n is the number of atoms in the molecule. However, the CHARMM function is not quadratic, so it will take more than n iterations. Past work has shown that better results are obtained if the conjugate gradient method is restarted. In my program I implemented a restart procedure that moves in the steepest descent direction after n iterations. Conjugate gradient is the choice of many software packages that minimize the conformation of a molecule. It is quick and does not require the storage of matrices like variable metric, quasi-Newton and second-order methods do.
In the future such optimization as limiting the non-bonded interactions to within a certain distance will be added. Other force fields will also be implemented and tested to calculate and minimize the energy of a molecule depending on the type of molecule being used.
Department of Computer Science
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