Numerical methods and computer models for simulation of proteins [electronic resource]
Keywords: Mechanical Engineering

Computational biology is a multidisciplinary field in which biology, mathematics, physics and computer science are integrated to study biological systems. Main challenges in this field include the speed and scalability of the algorithms to better utilize computer hardware and perform intensive calculations in biological systems, efficiency of the algorithms for better search and predictions, and the accuracy of the models for proteins and macro-molecules. In this work, we studied three different problems, each focusing on one of the challenges mentioned above. In the first part of the thesis, we introduced a new parallel algorithm to enhance the speed of electrostatic force calculations by better utilizing parallel computer clusters. The fast multipole method (FMM) and smooth particle mesh Ewald (SPME) are well known fast algorithms to evaluate long range electrostatic interactions in molecular dynamics and other fields. FMM is a multi-scale method which reduces the computation cost by approximating the potential due to a group of particles at a large distance using few multipole functions. This algorithm scales like O(N) for N particles. SPME algorithm is an O(N log N) method which is based on an interpolation of the Fourier space part of the Ewald sum and evaluating the resulting convolutions using fast Fourier transform (FFT). Those algorithms suffer from relatively poor efficiency on large parallel machines especially for midsize problems around hundreds of thousands of atoms. A variation of the FMM, called PWA, based on plane wave expansions is presented in this paper. A new parallelization strategy for PWA, which takes advantage of the specific form of this expansion, is described. Its parallel efficiency is compared with SPME through detail time measurements on two different computer clusters. In the second part of this thesis, we studied the accuracy of current force field models to simulate antimicrobial peptides with a dominant helical secondary structure. Secondary structures of antimicrobial peptides play an important role in their activity. The antimicrobial peptide cecropin P1, like most other anti-microbial peptides, is known to form a helix at the interface of bacterial cell membranes. This structure is fundamental to its activity and its ability to destroy the membrane. In contrast, as reported in experimental measurements, this peptide unfolds in bulk water. We analyzed this behavior using two different force fields, CHARMM22/CMAP and AMBER ff99SB. Although these two force fields are commonly used in molecular dynamics and have been extensively validated, we observed two sharply different results. A sodiumdodecylsulfate (SDS) micelle was used to model the bacterial membrane using Molecular Dynamics simulations. CHARMM22 resulted in a peptide that stays mostly folded in both environments (bulk water and SDS), while AMBER correctly predicted the unfolding in bulk water and produced results that closely match the available experimental data. We further computed the free energy of folding and unfolding, using the adaptive biasing force method, to get a complete picture of the energy barriers and the different metastable states. To get further insights into the interaction of the peptide with its environment, we computed the average number of hydrogen bonds between different components vs the folding reaction coordinate. In the third part of this thesis, we introduced an algorithm for fast protein structure search and predictions. We particularly applied this algorithm to study a certain type of ion channel, ASIC1a. Gating mechanism is an essential part of ion channel activities. We studied acid sensing ion channel 1a (ASIC1a) to better understand its gating mechanism. Although there are some resolved structures for ASIC1a, the open and conductive conformation of this channel is not yet fully known. We used a two steps method, each step with a different level of fidelity, to efficiently search for the possible open conformations. We searched for conformations which had minimal structural changes from the known closed structure. The two steps search helped reduce the multidimensional search space by splitting the search parameters. In the first step, we searched for conformations at the subunit level dealing with the relative orientation of the two transmembrane helices and their packing agains each other. In the second step, the results from the first step were used to explore the relative orientation of the chains in the transmembrane domain of the channel. We were able to identify several possible stable open conformations for the channel. The obtained candidates for the open structure met experimentally known characteristics for the open channel. This led to some theories on how the gating mechanism takes place in this channel.