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Estimating absolute configurational entropies of macromolecules: the minimally coupled subspace approach.

ABSTRACT: We develop a general minimally coupled subspace approach (MCSA) to compute absolute entropies of macromolecules, such as proteins, from computer generated canonical ensembles. Our approach overcomes limitations of current estimates such as the quasi-harmonic approximation which neglects non-linear and higher-order correlations as well as multi-minima characteristics of protein energy landscapes. Here, Full Correlation Analysis, adaptive kernel density estimation, and mutual information expansions are combined and high accuracy is demonstrated for a number of test systems ranging from alkanes to a 14 residue peptide. We further computed the configurational entropy for the full 67-residue cofactor of the TATA box binding protein illustrating that MCSA yields improved results also for large macromolecular systems.

SUBMITTER: Hensen U

PROVIDER: S-EPMC2826394 | biostudies-literature | 2010

REPOSITORIES: biostudies-literature

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Estimating absolute configurational entropies of macromolecules: the minimally coupled subspace approach.

Hensen Ulf U Lange Oliver F OF Grubmüller Helmut H

PloS one 20100223 2

We develop a general minimally coupled subspace approach (MCSA) to compute absolute entropies of macromolecules, such as proteins, from computer generated canonical ensembles. Our approach overcomes limitations of current estimates such as the quasi-harmonic approximation which neglects non-linear and higher-order correlations as well as multi-minima characteristics of protein energy landscapes. Here, Full Correlation Analysis, adaptive kernel density estimation, and mutual information expansion ...[more]

PMID: 20186277

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Project description:The hypothetical scanning molecular dynamics (HSMD) method is used here for calculating the absolute free energy of binding, ?A(0) of the complex of the protein FKBP12 with the ligand SB2 (also denoted L8) - a system that has been studied previously for comparing the performance of different methods. Our preliminary study suggests that considering long-range electrostatics is imperative even for a hydrophobic ligand such as L8. Therefore the system is modeled by the AMBER force field using Particle Mesh Ewald (PME). HSMD consists of three stages applied to both the ligand-solvent and ligand-protein systems. (1) A small set of system configurations (frames) is extracted from an MD trajectory. (2) The entropy of the ligand in each frame is calculated by a reconstruction procedure. (3) The contribution of water and protein to ?A(0) is calculated for each frame by gradually increasing the ligand-environment interactions from zero to their full value using thermodynamic integration (TI). Unlike the conventional methods, the structure of the ligand is kept fixed during TI, and HSMD is thus free from the end-point problem encountered with the double annihilation method (DAM); therefore, the need for applying restraints is avoided. Furthermore, unlike the conventional methods, the entropy of the ligand and water is obtained directly as a byproduct of the simulation. In this paper, in addition to the difference in the internal entropies of the ligand in the two environments, we calculate for the first time the external entropy of the ligand, which provides a measure for the size of the active site. We obtain ?A(0) = -10.7 ±1.0 as compared to the experimental values -10.9 and -10.6 kcal/mol. However, a protein/water system treated by periodic boundary conditions grows significantly with increasing protein size and the computation of ?A(0) would become expensive by all methods. Therefore, we also apply HSMD to FKBP12-L8 described by the GSBP/SSBP model of Roux's group (implemented in the software CHARMM) where only part of the protein and water around the active site are considered and long-range electrostatic effects are taken into account. For comparison this model was also treated by the double decoupling method (DDM). The two methods have led to comparable results for ?A(0) which are somewhat lower than the experimental value. The ligand was found to be more confined in the active site described by GSBP/SSBP than by PME where its entropy in solvent is larger than in the active site by 1.7 and by 5.5 kcal/mol, respectively.

Project description:BACKGROUND: Genomes of lower organisms have been observed with a large amount of horizontal gene transfers, which cause difficulties in their evolutionary study. Bacteriophage genomes are a typical example. One recent approach that addresses this problem is the unsupervised clustering of genomes based on gene order and genome position, which helps to reveal species relationships that may not be apparent from traditional phylogenetic methods. RESULTS: We propose the use of an overlapping subspace clustering algorithm for such genome classification problems. The advantage of subspace clustering over traditional clustering is that it can associate clusters with gene arrangement patterns, preserving genomic information in the clusters produced. Additionally, overlapping capability is desirable for the discovery of multiple conserved patterns within a single genome, such as those acquired from different species via horizontal gene transfers. The proposed method involves a novel strategy to vectorize genomes based on their gene distribution. A number of existing subspace clustering and biclustering algorithms were evaluated to identify the best framework upon which to develop our algorithm; we extended a generic subspace clustering algorithm called HARP to incorporate overlapping capability. The proposed algorithm was assessed and applied on bacteriophage genomes. The phage grouping results are consistent overall with the Phage Proteomic Tree and showed common genomic characteristics among the TP901-like, Sfi21-like and sk1-like phage groups. Among 441 phage genomes, we identified four significantly conserved distribution patterns structured by the terminase, portal, integrase, holin and lysin genes. We also observed a subgroup of Sfi21-like phages comprising a distinctive divergent genome organization and identified nine new phage members to the Sfi21-like genus: Staphylococcus 71, phiPVL108, Listeria A118, 2389, Lactobacillus phi AT3, A2, Clostridium phi3626, Geobacillus GBSV1, and Listeria monocytogenes PSA. CONCLUSION: The method described in this paper can assist evolutionary study through objectively classifying genomes based on their resemblance in gene order, gene content and gene positions. The method is suitable for application to genomes with high genetic exchange and various conserved gene arrangement, as demonstrated through our application on phages.

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Estimating absolute configurational entropies of macromolecules: the minimally coupled subspace approach.

Publications

Estimating absolute configurational entropies of macromolecules: the minimally coupled subspace approach.

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