Model-Based Search to Determine Minima in Molecular Energy Landscapes

Search for the global minimum in a molecular energy landscape populated with numerous local minima is a difficult task. Search techniques relevant to such complex spaces can be classified as either global or local. Global search explores the entire space, guaranteeing the global extremum will be found. To accomplish this, the number of samples required grows exponentially with the number of dimensions. Since this is clearly not computationally tractable, global search is impractical in highdimensional spaces. Local search, on the other hand, employs gradient descent to avoid searching the entire exponential space. Gradient descent methods are susceptible to getting stalled in local minima and consequently, no guarantees can be made about finding the global minimum. We propose a middle ground that minimizes the effects of exponential space and local minima by integrating domain knowledge and information generated during search into a model, and then using this model to focus computation on regions of increasing relevance. Directing resources to multiple relevant regions prevents oversampling local minima. At the same time the exploration of only significant regions avoids the intractable computational requirements of high-dimensional spaces. The proposed method, called Model-Based Search (MBS), is compared to the local search method Monte Carlo as implemented in Rosetta currently considered the best computational protein structure prediction method. The results indicate that MBS is significantly better at finding lower energy minima than the Monte Carlo technique implemented as part of Rosetta. This effect is amplified as the dimensionality of the search space increases.