Chaok Seok

Use of the Weighted Histogram Analysis Method for the Analysis of Simulated and Parallel Tempering Simulations

The growing adoption of generalized-ensemble algorithms for biomolecular simulation has resulted in a resurgence in the use of the weighted histogram analysis method (WHAM) to make use of all data generated by these simulations. Unfortunately, the original presentation of WHAM by Kumar et al. is not directly applicable to data generated by these methods. WHAM was originally formulated to combine data from independent samplings of the canonical ensemble, whereas many generalized-ensemble algorithms sample from mixtures of canonical ensembles at different temperatures. Sorting configurations generated from a parallel tempering simulation by temperature obscures the temporal correlation in the data and results in an improper treatment of the statistical uncertainties used in constructing the estimate of the density of states. Here we present variants of WHAM, STWHAM and PTWHAM, derived with the same set of assumptions, that can be directly applied to several generalized ensemble algorithms, including simulated tempering, parallel tempering (better known as replica-exchange among temperatures), and replica-exchange simulated tempering. We present methods that explicitly capture the considerable temporal correlation in sequentially generated configurations using autocorrelation analysis. This allows estimation of the statistical uncertainty in WHAM estimates of expectations for the canonical ensemble. We test the method with a one-dimensional model system and then apply it to the estimation of potentials of mean force from parallel tempering simulations of the alanine dipeptide in both implicit and explicit solvent.

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 × 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.

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/.

Pulsating Tubules from Noncovalent Macrocycles

Slip-Sliding Apart One versatile means of synthesizing nanometer-scale cylinders has been to start with ring-shaped molecules that stack on top of each other. Huang et al. (p. 1521; see the Perspective by Zhang and Aida) took this approach a step further by giving the rings a flexible diameter. Specifically, rings were prepared consisting of six v-shaped building blocks with hydrophobic sides that could slide back and forth along one another and thereby expand or contract the pore at the center. The rings spontaneously stacked to form tubes in dilute aqueous solution, and heating induced contraction of the whole tube in a process that was readily reversible on cooling. Nanoscale tubes expand and contract with temperature changes through loose association of their constituent building blocks. Despite recent advances in synthetic nanometer-scale tubular assembly, conferral of dynamic response characteristics to the tubules remains a challenge. Here, we report on supramolecular nanotubules that undergo a reversible contraction-expansion motion accompanied by an inversion of helical chirality. Bent-shaped aromatic amphiphiles self-assemble into hexameric macrocycles in aqueous solution, forming chiral tubules by spontaneous one-dimensional stacking with a mutual rotation in the same direction. The adjacent aromatic segments within the hexameric macrocycles reversibly slide along one another in response to external triggers, resulting in pulsating motions of the tubules accompanied by a chiral inversion. The aromatic interior of the self-assembled tubules encapsulates hydrophobic guests such as carbon-60 (C60). Using a thermal trigger, we could regulate the C60-C60 interactions through the pulsating motion of the tubules.

Community-wide assessment of protein-interface modeling suggests improvements to design methodology

The CAPRI (Critical Assessment of Predicted Interactions) and CASP (Critical Assessment of protein Structure Prediction) experiments have demonstrated the power of community-wide tests of methodology in assessing the current state of the art and spurring progress in the very challenging areas of protein docking and structure prediction. We sought to bring the power of community-wide experiments to bear on a very challenging protein design problem that provides a complementary but equally fundamental test of current understanding of protein-binding thermodynamics. We have generated a number of designed protein-protein interfaces with very favorable computed binding energies but which do not appear to be formed in experiments, suggesting that there may be important physical chemistry missing in the energy calculations. A total of 28 research groups took up the challenge of determining what is missing: we provided structures of 87 designed complexes and 120 naturally occurring complexes and asked participants to identify energetic contributions and/or structural features that distinguish between the two sets. The community found that electrostatics and solvation terms partially distinguish the designs from the natural complexes, largely due to the nonpolar character of the designed interactions. Beyond this polarity difference, the community found that the designed binding surfaces were, on average, structurally less embedded in the designed monomers, suggesting that backbone conformational rigidity at the designed surface is important for realization of the designed function. These results can be used to improve computational design strategies, but there is still much to be learned; for example, one designed complex, which does form in experiments, was classified by all metrics as a nonbinder.

GalaxyRefine: protein structure refinement driven by side-chain repacking

The quality of model structures generated by contemporary protein structure prediction methods strongly depends on the degree of similarity between the target and available template structures. Therefore, the importance of improving template-based model structures beyond the accuracy available from template information has been emphasized in the structure prediction community. The GalaxyRefine web server, freely available at http://galaxy.seoklab.org/refine, is based on a refinement method that has been successfully tested in CASP10. The method first rebuilds side chains and performs side-chain repacking and subsequent overall structure relaxation by molecular dynamics simulation. According to the CASP10 assessment, this method showed the best performance in improving the local structure quality. The method can improve both global and local structure quality on average, when used for refining the models generated by state-of-the-art protein structure prediction servers.

Community-wide evaluation of methods for predicting the effect of mutations on protein-protein interactions

Community‐wide blind prediction experiments such as CAPRI and CASP provide an objective measure of the current state of predictive methodology. Here we describe a community‐wide assessment of methods to predict the effects of mutations on protein–protein interactions. Twenty‐two groups predicted the effects of comprehensive saturation mutagenesis for two designed influenza hemagglutinin binders and the results were compared with experimental yeast display enrichment data obtained using deep sequencing. The most successful methods explicitly considered the effects of mutation on monomer stability in addition to binding affinity, carried out explicit side‐chain sampling and backbone relaxation, evaluated packing, electrostatic, and solvation effects, and correctly identified around a third of the beneficial mutations. Much room for improvement remains for even the best techniques, and large‐scale fitness landscapes should continue to provide an excellent test bed for continued evaluation of both existing and new prediction methodologies. Proteins 2013; 81:1980–1987.

GalaxyWEB server for protein structure prediction and refinement

Three-dimensional protein structures provide invaluable information for understanding and regulating biological functions of proteins. The GalaxyWEB server predicts protein structure from sequence by template-based modeling and refines loop or terminus regions by ab initio modeling. This web server is based on the method tested in CASP9 (9th Critical Assessment of techniques for protein Structure Prediction) as ‘Seok-server’, which was assessed to be among top performing template-based modeling servers. The method generates reliable core structures from multiple templates and re-builds unreliable loops or termini by using an optimization-based refinement method. In addition to structure prediction, a user can also submit a refinement only job by providing a starting model structure and locations of loops or termini to refine. The web server can be freely accessed at http://galaxy.seoklab.org/.

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.

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/.