We optimize a physical energy function for proteins with the use of the available structural database and perform three benchmark tests of the performance: (1) recognition of native structures in the background of predefined decoy sets of Levitt, (2) de novo structure prediction using fragment assembly sampling, and (3) molecular dynamics simulations. The energy parameter optimization is based on the energy landscape theory and uses a Monte Carlo search to find a set of parameters that seeks the largest ratio deltaE(s)/DeltaE for all proteins in a training set simultaneously. Here, deltaE(s) is the stability gap between the native and the average in the denatured states and DeltaE is the energy fluctuation among these states. Some of the energy parameters optimized are found to show significant correlation with experimentally observed quantities: (1) In the recognition test, the optimized function assigns the lowest energy to either the native or a near-native structure among many decoy structures for all the proteins studied. (2) Structure prediction with the fragment assembly sampling gives structure models with root mean square deviation less than 6 A in one of the top five cluster centers for five of six proteins studied. (3) Structure prediction using molecular dynamics simulation gives poorer performance, implying the importance of having a more precise description of local structures. The physical energy function solely inferred from a structural database neither utilizes sequence information from the family of the target nor the outcome of the secondary structure prediction but can produce the correct native fold for many small proteins.

Predicting protein tertiary structure by folding-like simulations is one of the most stringent tests of how much we understand the principle of protein folding. Currently, the most successful method for folding-based structure prediction is the fragment assembly (FA) method. Here, we address why the FA method is so successful and its lesson for the folding problem. To do so, using the FA method, we designed a structure prediction test of ''chimera proteins.'' In the chimera proteins, local structural preference is specific to the target sequences, whereas nonlocal interactions are only sequence-independent compaction forces. We find that these chimera proteins can find the native folds of the intact sequences with high probability indicating dominant roles of the local interactions. We further explore roles of local structural preference by exact calculation of the HP lattice model of proteins. From these results, we suggest principles of protein folding: For small proteins, compact structures that are fully compatible with local structural preference are few, one of which is the native fold. These local biases shape up the funnel-like energy landscape.computational protein design ͉ energy landscape ͉ fragment assembly ͉ Go model ͉ SIMFOLD N atural proteins have the algorithm of finding the global minimum of their free energy surface within a biologically relevant timescale (1). One of the most stringent tests of how much we understand the algorithm may be to predict protein tertiary structures by simulating processes that are analogous to folding, which is often called de novo structure prediction. Recently, significant progress has been made in de novo structure prediction, in which the most successful method is the fragment assembly (FA) method developed by Baker and coworkers (2) and others (3-6). The FA method shows considerable promise for new fold targets of recent Critical Assessments of Techniques for Protein Structure Prediction (CASPs), the community-wide blind tests of structure prediction (7-11). In the FA method, the protocol is separated into two stages: First, we collect structural candidates for every short segment of the target sequence, retrieving them from the structural database. The second stage is to assemble͞fold these fragments for constructing tertiary structures that have low energies.Simple questions arose as to why the FA method is so successful and what we can learn about protein folding from the success of the FA method. According to Baker and coworkers (12,13), the FA method is based on the experimental observation that local sequence of a protein biases but does not uniquely decide its local structure. To what extent does the modest local bias influence tertiary structures generated? How is the FA method related to recently developed protein folding theory (14, 15)? In this work, we address these questions.For this purpose, we need structure prediction software that uses the FA method. Here, we use the in-house-developed software, SIMFOLD. SIMFOLD employs a coarse-grained protei...

Predicting protein tertiary structures by in silico folding is still very difficult for proteins that have new folds. Here, we developed a coarse-grained energy function, SimFold, for de novo structure prediction, performed a benchmark test of prediction with fragment assembly simulations for 38 test proteins, and proposed consensus prediction with Rosetta. The SimFold energy consists of many terms that take into account solvent-induced effects on the basis of physicochemical consideration. In the benchmark test, SimFold succeeded in predicting native structures within 6.5 A for 12 of 38 proteins; this success rate was the same as that by the publicly available version of Rosetta (ab initio version 1.2) run with default parameters. We investigated which energy terms in SimFold contribute to structure prediction performance, finding that the hydrophobic interaction is the most crucial for the prediction, whereas other sequence-specific terms have weak but positive roles. In the benchmark, well-predicted proteins by SimFold and by Rosetta were not the same for 5 of 12 proteins, which led us to introduce consensus prediction. With combined decoys, we succeeded in prediction for 16 proteins, four more than SimFold or Rosetta separately. For each of 38 proteins, structural ensembles generated by SimFold and by Rosetta were qualitatively compared by mapping sampled structural space onto two dimensions. For proteins of which one of the two methods succeeded and the other failed in prediction, the former had a less scattered ensemble located around the native. For proteins of which both methods succeeded in prediction, often two ensembles were mixed up.

The fragment assembly method is currently one of the most successful methods for the de novo protein structure prediction, where conformational change by fragment replacement is repeated with the simulated annealing scheme. We point out here that the conventional fragment replacement algorithm violates the detailed balance condition. This precludes application of various generalized ensemble algorithms, which would have made conformational sampling more efficient. We develop here a reversible variant of the fragment assembly algorithm which satisfies the detailed balance and thus is applicable to the generalized ensemble techniques. We combine this method with the multicanonical ensemble Monte Carlo, one of the generalized ensemble approaches, and test its performance in the structure prediction of three proteins. We show that the new method can find low energy conformations more efficiently than the conventional simulated annealing method. Also importantly, the lowest energy structures found by the new method are closer to the native than those by the simulated annealing. It seems that conformations with more complex topology can be generated by the new algorithm.

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