De novo protein structure prediction from amino acid sequence is one of the most challenging problems in computational biology. As one of the extensively explored mathematical models for protein folding, Hydrophobic-Polar (HP) model enables thorough investigation of protein structure formation and evolution. Although HP model discretizes the conformational space and simplifies the folding energy function, it has been proven to be an NP-complete problem. In this paper, we propose a novel protein folding framework FoldingZero, self-folding a de novo protein 2D HP structure from scratch based on deep reinforcement learning. FoldingZero features the coupled approach of a two-head (policy and value heads) deep convolutional neural network (HPNet) and a regularized Upper Confidence Bounds for Trees (R-UCT). It is trained solely by a reinforcement learning algorithm, which improves HPNet and R-UCT iteratively through iterative policy optimization. Without any supervision and domain knowledge, FoldingZero not only achieves comparable results, but also learns the latent folding knowledge to stabilize the structure. Without exponential computation, FoldingZero shows promising potential to be adopted for real-world protein properties prediction.
Approximation algorithms offer rigorous mathematical tools and fold a protein structure within polynomial time. However, it may lead to a weak approximation ratio, resulting in a structure far from the optimal solution. Hart and Istrail proposed an approximation algorithm with ratio 3 8 of the optimal score for the 3D cubic lattice structure @cite_16 . An improved approximation algorithm with 2 5 performance guarantees was further developed by the same authors @cite_1 . For the 2D square lattice, an approximation algorithm @cite_7 can achieve the approximation ratio of 1 3.
@cite_16 @cite_1 @cite_7
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We consider the problem of protein folding in the HP model on the two-dimensional square lattice. This problem is combinatorially equivalent to folding a string of 0's and 1's so that the string forms a self-avoiding walk on the lattice and the number of adjacent pairs of 1's is maximized. We present a linear-time 1 3-approximation algorithm for this problem, improving on the previous best approximation factor of 1 4. The approximation guarantee of this algorithm is based on an upper bound presented by Hart and Istrail [6] and used in all previous papers that address this problem. We show that this upper bound cannot be used to obtain an approximation factor better than 1 2. We prove new results for approximating the graph-TSP and some related problems. We obtain polynomial-time algorithms with improved approximation guarantees. For the graph-TSP itself, we improve the approximation ratio to 7=5. For a generalization, the minimum T-tour problem, we obtain the first nontrivial approximation algorithm, with ratio 3=2. This contains the s-t-path graph-TSP as a special case. Our approximation guarantee for finding a smallest 2-edge-connected spanning subgraph is 4=3. The key new ingredient of all our algorithms is a special kind of ear-decomposition optimized using forest representations of hypergraphs. The same methods also provide the lower bounds (arising from LP relaxations) that we use to deduce the approximation ratios. ABSTRACT This paper considers the protein energy minimization problem for lattice and off-lattice protein folding models that explicitly represent side chains. Lattice models of proteins have proven useful tools for reasoning about protein folding in unrestricted continuous space through analogy. This paper provides the first illustration of how rigorous algorithmic analyses of lattice models can lead to rigorous algorithmic analyses of off-lattice models. We consider two side chain models: a lattice model that generalizes the HP model (Dill, 1985) to explicitly represent side chains on the cubic lattice and a new off-lattice model, the HP Tangent Spheres Side Chain model (HP-TSSC), that generalizes this model further by representing the backbone and side chains of proteins with tangent spheres. We describe algorithms with mathematically guaranteed error bounds for both of these models. In particular, we describe a linear time performance guaranteed approximation algorithm for the HP side chain model that...