Guaranteed Discrete Energy Optimization on Large Protein Design Problems

Abstract

In Computational Protein Design (CPD), assuming a rigid backbone and amino-acid rotamer library, the problem of finding a sequence with an optimal conformation is NP-hard. In this paper, using Dunbrack's rotamer library and Talaris2014 decomposable energy function, we use an exact deterministic method combining branch and bound, arc consistency, and tree-decomposition to provenly identify the global minimum energy sequence-conformation on full-redesign problems, defining search spaces of size up to 10(234). This is achieved on a single core of a standard computing server, requiring a maximum of 66GB RAM. A variant of the algorithm is able to exhaustively enumerate all sequence-conformations within an energy threshold of the optimum. These proven optimal solutions are then used to evaluate the frequencies and amplitudes, in energy and sequence, at which an existing CPD-dedicated simulated annealing implementation may miss the optimum on these full redesign problems. The probability of finding an optimum drops close to 0 very quickly. In the worst case, despite 1,000 repeats, the annealing algorithm remained more than 1 Rosetta unit away from the optimum, leading to design sequences that could differ from the optimal sequence by more than 30% of their amino acids.

Computational protein design for given backbone: recent progresses in general method-related aspects

“…Common simplifications in this aspect include fixed backbone and discretized side chain rotamer state. Under such simplifications either heuristic or deterministic [23,24] optimization algorithms can be applied to optimize the sequence. However, these simplifications are often inconsistent with the use of high-resolution terms in the energy function, such as atomic van der Waals interactions.…”

PLUG (Pruning of Local Unrealistic Geometries) removes restrictions on biophysical modeling for protein design

“…This precomputation dramatically speeds up protein design calculations. An energy matrix can be used to efficiently perform simulated annealing 4,27,48 , which can yield an answer quickly with no guarantees of accuracy and with error that empirically increases for larger designs 44 , or as input to a search algorithm with provable guarantees of accuracy. Many algorithms with such guarantees are available, including DEE/A* 5,10,13,17,22,29,36 , integer linear programming 26,40 , branch-24 and tree 50 decomposition-based methods, and weighted constraint satisfaction algorithms 40,46,47 .…”

Guaranteed Weighted Counting for Affinity Computation: Beyond Determinism and Structure

“…Monte-Carlo methods including Markov Chain Monte Carlo methods [16] offer asymptotic convergence /s, but convergence is impractically slow. Indeed, there are recent significant examples showing that the time needed for Monte Carlo methods to converge can be easily under-estimated [36]. Practical MCMC based tools also rely on heuristics that destroy these theoretical guarantees.…”