Biomedical subjects

Chaok Seok

Publications and source records attributed to Chaok Seok.

6 recordsLinked to original sources

PubMed2005

Rotational superposition and least squares: the SVD and quaternions approaches yield identical results. Reply to the preceding comment by G. Kneller.

We clarify once again that Kabsch's method and the Quaternion method are mathematically equivalent methods, that is, that they contain identical information and, when properly understood and applied, lead to identical answers to any questions regarding least-squares rotational superposition, either by proper rotations or by rotation-reflections. We also provide the correct bounds for the eigenvalue spectrum.

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PubMed2005

The flexibility in the proline ring couples to the protein backbone.

In proteins, the proline ring exists predominantly in two discrete states. However, there is also a small but significant amount of flexibility in the proline ring of high-resolution protein structures. We have found that this side-chain flexibility is coupled to the backbone conformation. To study this coupling, we have developed a model that is simply based on geometric and steric factors and not on energetics. We show that the coupling between phi and chi1 torsions in the proline ring can be described by an analytic equation that was developed by Bricard in 1897, and we describe a computer algorithm that implements the equation. The model predicts the observed coupling very well. The strain in the C(gamma)-C(delta)-N angle appears to be the principal barrier between the UP and DOWN pucker. This strain is relaxed to allow the proline ring to flatten in the rare PLANAR conformation.

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PubMed2004

Using quaternions to calculate RMSD.

A widely used way to compare the structures of biomolecules or solid bodies is to translate and rotate one structure with respect to the other to minimize the root-mean-square deviation (RMSD). We present a simple derivation, based on quaternions, for the optimal solid body transformation (rotation-translation) that minimizes the RMSD between two sets of vectors. We prove that the quaternion method is equivalent to the well-known formula due to Kabsch. We analyze the various cases that may arise, and give a complete enumeration of the special cases in terms of the arrangement of the eigenvalues of a traceless, 4 x 4 symmetric matrix. A key result here is an expression for the gradient of the RMSD as a function of model parameters. This can be useful, for example, in finding the minimum energy path of a reaction using the elastic band methods or in optimizing model parameters to best fit a target structure.

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PubMed2004

Analytic density-functional self-consistent-field theory of diblock copolymers near patterned surfaces.

Analytical solutions are derived for the density profiles and the free energies of compressible diblock copolymer melts (or incompressible copolymer solutions) near patterned surfaces. The density-functional self-consistent-field theory is employed along with a Gaussian chain model for bonding constraints and a random mixing approximation for nonbonded interactions. An analytical solution is rendered possible by expanding the chain distribution function around an inhomogeneous reference state with a nontrivial analytical solution, by retaining the linear terms, and by requiring consistency with the homopolymer limit. The density profiles are determined by both real and complex roots of a sixth-degree polynomial that may easily be obtained by solving a generalized eigenvalue problem. This analytical formulation enables one to efficiently explore the large nine-dimensional parameter space and can serve as a first approximation to computationally intensive studies with more detailed models. Illustrative computations are provided for uniform and patterned surfaces above the order-disorder transition. The results are consistent with the previous self-consistent-field calculations in that lamellar ordering appears near the surface above the order-disorder transition and the lamella order perpendicular or parallel to the surface depending on the commensurability between the periods of the surface pattern and the density oscillations.

Journal Article↗

PubMed2004

A kinematic view of loop closure.

We consider the problem of loop closure, i.e., of finding the ensemble of possible backbone structures of a chain segment of a protein molecule that is geometrically consistent with preceding and following parts of the chain whose structures are given. We reduce this problem of determining the loop conformations of six torsions to finding the real roots of a 16th degree polynomial in one variable, based on the robotics literature on the kinematics of the equivalent rotator linkage in the most general case of oblique rotators. We provide a simple intuitive view and derivation of the polynomial for the case in which each of the three pair of torsional axes has a common point. Our method generalizes previous work on analytical loop closure in that the torsion angles need not be consecutive, and any rigid intervening segments are allowed between the free torsions. Our approach also allows for a small degree of flexibility in the bond angles and the peptide torsion angles; this substantially enlarges the space of solvable configurations as is demonstrated by an application of the method to the modeling of cyclic pentapeptides. We give further applications to two important problems. First, we show that this analytical loop closure algorithm can be efficiently combined with an existing loop-construction algorithm to sample loops longer than three residues. Second, we show that Monte Carlo minimization is made severalfold more efficient by employing the local moves generated by the loop closure algorithm, when applied to the global minimization of an eight-residue loop. Our loop closure algorithm is freely available at http://dillgroup. ucsf.edu/loop_closure/.

Journal Article↗

PubMed2003

MOPED: method for optimizing physical energy parameters using decoys.

We present a method called MOPED for optimizing energetic and structural parameters in computational models, including all-atom energy functions, when native structures and decoys are given. The present method goes beyond previous approaches in treating energy functions that are nonlinear in the parameters and continuous in the degrees of freedom. We illustrate the method by improving solvation parameters in the energy function EEF1, which consists of the CHARMM19 polar hydrogen force field augmented by a Gaussian solvation term. Although the published parameters for EEF1 correctly discriminate the native from decoys in the decoy sets of Levitt et al., they fail on several of the more difficult decoy sets of Baker et al. MOPED successfully finds improved parameters that allow EEF1 to discriminate native from decoy structures on all protein structures that do not have metals or prosthetic groups.

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