Julian Lee

Unbiased global optimization of Lennard-Jones clusters for N < or =201 using the conformational space annealing method.

We apply the conformational space annealing method to the Lennard-Jones clusters and find all known lowest energy configurations up to 201 atoms, without using extra information of the problem such as the structures of the known global energy minima. In addition, the robustness of the algorithm with respect to the randomness of initial conditions of the problem is demonstrated by ten successful independent runs up to 183 atoms. Our results indicate that this method is a general and yet efficient global optimization algorithm applicable to many systems.

Protein loop modeling by using fragment assembly and analytical loop closure

Protein loops are often involved in important biological functions such as molecular recognition, signal transduction, or enzymatic action. The three dimensional structures of loops can provide essential information for understanding molecular mechanisms behind protein functions. In this article, we develop a novel method for protein loop modeling, where the loop conformations are generated by fragment assembly and analytical loop closure. The fragment assembly method reduces the conformational space drastically, and the analytical loop closure method finds the geometrically consistent loop conformations efficiently. We also derive an analytic formula for the gradient of any analytical function of dihedral angles in the space of closed loops. The gradient can be used to optimize various restraints derived from experiments or databases, for example restraints for preferential interactions between specific residues or for preferred backbone angles. We demonstrate that the current loop modeling method outperforms previous methods that employ residue‐based torsion angle maps or different loop closure strategies when tested on two sets of loop targets of lengths ranging from 4 to 12. Proteins 2010.

Prediction of protein solvent accessibility using fuzzy k -nearest neighbor method

MOTIVATION The solvent accessibility of amino acid residues plays an important role in tertiary structure prediction, especially in the absence of significant sequence similarity of a query protein to those with known structures. The prediction of solvent accessibility is less accurate than secondary structure prediction in spite of improvements in recent researches. The k-nearest neighbor method, a simple but powerful classification algorithm, has never been applied to the prediction of solvent accessibility, although it has been used frequently for the classification of biological and medical data. RESULTS We applied the fuzzy k-nearest neighbor method to the solvent accessibility prediction, using PSI-BLAST profiles as feature vectors, and achieved high prediction accuracies. With leave-one-out cross-validation on the ASTRAL SCOP reference dataset constructed by sequence clustering, our method achieved 64.1% accuracy for a 3-state (buried/intermediate/exposed) prediction (thresholds of 9% for buried/intermediate and 36% for intermediate/exposed) and 86.7, 82.0, 79.0 and 78.5% accuracies for 2-state (buried/exposed) predictions (thresholds of each 0, 5, 16 and 25% for buried/exposed), respectively. Our method also showed slightly better accuracies than other methods by about 2-5% on the RS126 dataset and a benchmarking dataset with 229 proteins. AVAILABILITY Program and datasets are available at http://biocom1.ssu.ac.kr/FKNNacc/ CONTACT jul@ssu.ac.kr.

Prediction of protein tertiary structure using PROFESY, a novel method based on fragment assembly and conformational space annealing

A novel method for ab initio prediction of protein tertiary structures, PROFESY (PROFile Enumerating SYstem), is proposed. This method utilizes the secondary structure prediction information of a query sequence and the fragment assembly procedure based on global optimization. Fifteen‐residue‐long fragment libraries are constructed using the secondary structure prediction method PREDICT, and fragments in these libraries are assembled to generate full‐length chains of a query protein. Tertiary structures of 50 to 100 conformations are obtained by minimizing an energy function for proteins, using the conformational space annealing method that enables one to sample diverse low‐lying local minima of the energy. We apply PROFESY for benchmark tests to proteins with known structures to demonstrate its feasibility. In addition, we participated in CASP5 and applied PROFESY to four new‐fold targets for blind prediction. The results are quite promising, despite the fact that PROFESY was in its early stages of development. In particular, PROFESY successfully provided us the best model‐one structure for the target T0161. Proteins 2004.

The FALC-Loop web server for protein loop modeling

The FALC-Loop web server provides an online interface for protein loop modeling by employing an ab initio loop modeling method called FALC (fragment assembly and analytical loop closure). The server may be used to construct loop regions in homology modeling, to refine unreliable loop regions in experimental structures or to model segments of designed sequences. The FALC method is computationally less expensive than typical ab initio methods because the conformational search space is effectively reduced by the use of fragments derived from a structure database. The analytical loop closure algorithm allows efficient search for loop conformations that fit into the protein framework starting from the fragment-assembled structures. The FALC method shows prediction accuracy comparable to other state-of-the-art loop modeling methods. Top-ranked model structures can be visualized on the web server, and an ensemble of loop structures can be downloaded for further analysis. The web server can be freely accessed at http://falc-loop.seoklab.org/.

Exact partition function zeros and the collapse transition of a two-dimensional lattice polymer

We study the collapse transition of the lattice homopolymer on a square lattice by calculating the exact partition function zeros. The exact partition function is obtained by enumerating the number of possible conformations for each energy value, and the exact distributions of the partition function zeros are found in the complex temperature plane by solving a polynomial equation. We observe that the locus of zeros closes in on the positive real axis as the chain length increases, providing the evidence for the onset of the collapse transition. By analyzing the scaling behavior of the first zero with the polymer length, we estimate the transition temperature T(θ) and the crossover exponent φ.

Refinement of protein termini in template‐based modeling using conformational space annealing

The rapid increase in the number of experimentally determined protein structures in recent years enables us to obtain more reliable protein tertiary structure models than ever by template‐based modeling. However, refinement of template‐based models beyond the limit available from the best templates is still needed for understanding protein function in atomic detail. In this work, we develop a new method for protein terminus modeling that can be applied to refinement of models with unreliable terminus structures. The energy function for terminus modeling consists of both physics‐based and knowledge‐based potential terms with carefully optimized relative weights. Effective sampling of both the framework and terminus is performed using the conformational space annealing technique. This method has been tested on a set of termini derived from a nonredundant structure database and two sets of termini from the CASP8 targets. The performance of the terminus modeling method is significantly improved over our previous method that does not employ terminus refinement. It is also comparable or superior to the best server methods tested in CASP8. The success of the current approach suggests that similar strategy may be applied to other types of refinement problems such as loop modeling or secondary structure rearrangement. Proteins 2011;

Folding of small proteins using a single continuous potential

Extensive Monte Carlo folding simulations for four proteins of various structural classes are carried out, using a single continuous potential (united-residue force field). In all cases, collapse occurs at a very early stage, and proteins fold into their nativelike conformations at appropriate temperatures. We also observe that glassy transitions occur at low temperatures. The simulation results demonstrate that the folding mechanism is controlled not only by thermodynamic factors but also by kinetic factors: The way a protein folds into its native structure is also determined by the convergence point of early folding trajectories, which cannot be obtained by the free energy surface.

Parallel algorithm for calculation of the exact partition function of a lattice polymer

We develop a parallel algorithm that calculates the exact partition function of a lattice polymer, by enumerating the number of conformations for each energy level. An efficient parallelization of the calculation is achieved by classifying the conformations according to the shape of the box spanned by a conformation, and enumerating only those in a given box at a time. The calculation time for each box is reduced by preventing the conformations related by symmetries from being generated more than once. The algorithm is applied to study the collapse transition of a lattice homopolymer on a square lattice, by calculating the specific heat for chain lengths up to 36.

Nonadditive entropies yield probability distributions with biases not warranted by the data.

Different quantities that go by the name of entropy are used in variational principles to infer probability distributions from limited data. Shore and Johnson showed that maximizing the Boltzmann-Gibbs form of the entropy ensures that probability distributions inferred satisfy the multiplication rule of probability for independent events in the absence of data coupling such events. Other types of entropies that violate the Shore and Johnson axioms, including nonadditive entropies such as the Tsallis entropy, violate this basic consistency requirement. Here we use the axiomatic framework of Shore and Johnson to show how such nonadditive entropy functions generate biases in probability distributions that are not warranted by the underlying data.