Geometry optimization for peptides and proteins: Comparison of Cartesian and internal coordinates

Exploration of biochemical reactivity with a QM/MM growing string method

In this work, we have implemented the single-ended growing string method using a hybrid internal/Cartesian coordinate scheme within our in-house QM/MM package, QoMMMa, representing the first implementation of the growing string method in the QM/MM framework. The goal of the implementation was to facilitate generation of QM/MM reaction pathways with minimal user input, and also to improve the quality of the pathways generated as compared to the widely used adiabatic mapping approach. We have validated the algorithm against a reaction which has been studied extensively in previous computational investigations - the Claisen rearrangement catalysed by chorismate mutase. The nature of the transition state and the height of the barrier was predicted well using our algorithm, where more than 88% of the pathways generated were deemed to be of production quality. Directly compared to using adiabatic mapping, we found that while our QM/MM single-ended growing string method is slightly less efficient, it readily produces reaction pathways with fewer discontinuites and thus minimises the need for involved remapping of unsatisfactory energy profiles.

Improving double-ended transition state searches for soft-matter systems

Transitions between different stable configurations of biomolecules are important in understanding disease mechanisms, structure-function relations, and novel molecular-scale engineering. The corresponding pathways can be characterized efficiently using geometry optimization schemes based on double-ended transition state searches. An interpolation is first constructed between the known states and then refined, yielding a band that contains transition state candidates. Here, we analyze an example where various interpolation schemes lead to bands with a single step transition, but the correct pathway actually proceeds via an intervening, low-energy minimum. We compare a number of different interpolation schemes for this problem. We systematically alter the number of discrete images in the interpolations and the spring constants used in the optimization and test two schemes for adjusting the spring constants and image distribution, resulting in a total of 2760 different connection attempts. Our results confirm that optimized bands are not necessarily a good description of the transition pathways in themselves, and further refinement to actually converge transition states and establish their connectivity is required. We see an improvement in the optimized bands if we employ the adjustment of spring constants with doubly-nudged elastic band and a smaller improvement from the image redistribution. The example we consider is representative of numerous cases we have encountered in a wide variety of molecular and condensed matter systems.

Two Perturbations for Geometry Optimization of Off-lattice Bead Protein Models

Referring to the optimization algorithm previously developed for atomic clusters, the present author develops an efficient method for geometry optimization of a coarse-grained protein model expressed with two kinds of beads (hydrophilic and hydrophobic ones). In the method, two types of geometrical perturbations, center-directed bead move and one bead rotation, are used to explore new configurations and local optimizations are performed after the perturbations. The center-directed bead move is used for hydrophobic beads and the one bead rotation is performed for both hydrophobic and hydrophilic beads. The optimization method was applied to protein models consisting of 13, 20, 21, and 34 beads. The present method produced the global minima of the 13-, 21-, and 34-bead models reported in the literature and updated the lowest energies of the protein models with 20 beads. These results indicate that the present method is efficient for searching for optimal structures of proteins.