New determinations and simplified representations of macromolecular surfaces

Perrot, Georges; Maigret, Bernard

doi:10.1016/0263-7855(90)80054-j

Cited by 19 publications

(4 citation statements)

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“…Evaluation of the derivatives of the expressions in eqs. (5) to (9) can be achieved in a manner that scales linearly ;artesian with the number of faces; hence, the overall determination of the Cartesian derivatives scales in the same way. Once the derivatives with respect to Cartesian coordinates are known, derivatives with respect to any other type of variable, such as dihedral angles, can be found using established formulas.…”

Section: Stepmentioning

confidence: 99%

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MSEED: A program for the rapid analytical determination of accessible surface areas and their derivatives

et al. 1992

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An algorithm for the rapid analytical determination of the accessible surface areas of solute molecules is described. The accessible surface areas as well as the derivatives with respect to the Cartesian coordinates of the atoms are computed by a program called "MSEED," which is based in part on Connolly's analytical formulas for determining surface area. Comparisons of the CPU time required for MSEED, Connolly's numerical algorithm DOT, and a program for surface area determination (ANA) based on Connolly's analytical algorithm, are presented. MSEED is shown to be as much as 70 times faster than ANA and up to 11 times faster than DOT for several proteins. The greater speed of MSEED is achieved partially because nonproductive computation of the surface areas of internal atoms is avoided. A sample minimization of an energy function, which included a term for hydration, was carried out on MET-enkephalin using MSEED to compute the solvent-accessible surface area and its derivatives. The potential employed was ECEPPiZ plus an empirical potential for solvation based on the solvent-accessible surface area of the peptide. The CPU time required for 150 steps of minimization with the potential that included solvation was approximately twice as great as the CPU time required for 150 steps of minimization with the ECEPP/2 potential only.

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Section: Stepmentioning

confidence: 99%

“…(5) to (9); hence, its derivatives can be found immediately from the derivatives of the quantities in eqs. (5) to (9). Finally, the derivatives of the area of one face are sums of contributions from expressions of the type given in eqs.…”

Section: Stepmentioning

confidence: 99%

MSEED: A program for the rapid analytical determination of accessible surface areas and their derivatives

et al. 1992

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“…If R1 ¢ R2, then the radius Ro of the circle of intersection is given by the equation (6) with the coefficients A, B, C and D given by the following equations:…”

Section: Proofmentioning

confidence: 99%

“…Both Connolly's and Richmond's methods have been modified by subsequent workers [6][7][8][9], and two recent algorithms based on these equations show promise of being fast enough for routine use in computations of the conformational energy of solvated polypeptides and proteins [7,9]. Both of these algorithms also compute the first derivatives of © J.C. Baltzer AG, Science Publishers…”

Section: Introductionmentioning

confidence: 99%

Gradient discontinuities in calculations involving molecular surface area

1994

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The free energy of solvation of a polypeptide or a protein can be expressed in terms of the accessible surface area of the molecule. Algorithms for energy minimization or for molecular dynamics, which involve the first derivatives of the energy, including the free energy of solvation, are commonly used in the conformational analysis of proteins. Discontinuities of the first derivatives, which occur in the accessible surface area and, hence, in the solvation energy, can cause serious numerical problems. In this paper, we describe all the situations in which the gradient of the molecular surface area becomes discontinuous. IntroductionThe computation of accessible surface area [1 ] and its first derivatives is becoming more and more important in the analysis of polypeptide and protein conformations. Partly, this is due to increasing reliance on space-f'ffling graphical representations by molecular models; partly, it is a consequence of the search for reasonably simple approaches to the problem of computing solvation free energies of peptides. One such simple approach associates a free energy density with each atom and calculates the contribution of that atom to the solvation free energy as the product of the free energy density and the accessible surface area; the total solvation free energy is then the sum of the contributions from all atoms exposed to the solvent [2,3].The most popular, and computationally most efficient methods for computing accessible surface areas analytically are those of Connolly [4] and Richmond [5], which treat the atoms as spheres and use the Gauss-Bonnet theorem from differential geometry to calculate the exposed area of each atom. Both Connolly's and Richmond's methods have been modified by subsequent workers [6][7][8][9], and two recent algorithms based on these equations show promise of being fast enough for routine use in computations of the conformational energy of solvated polypeptides and proteins [7,9]. Both of these algorithms also compute the first derivatives of © J.C. Baltzer AG, Science Publishers

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From secondary structure to three-dimensional structure: Improved dihedral angle probability distribution function for use with energy searches for native structures of polypeptides and proteins

1996

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An improved scheme to help in the prediction of protein structure is presented. This procedure generates improved starting conformations of a protein suitable for energy minimization. Trivariate gaussian distribution functions for the π, ψ, and χ1 dihedral angles have been derived, using conformational data from high resolution protein structures selected from the Protein Data Bank (PDB). These trivariate probability functions generate initial values for the π, ψ, and χ1 dihedral angles which reflect the experimental values found in the PDB. These starting structures speed the search of the conformational space by focusing the search mainly in the regions of native proteins. The efficiency of the new trivariate probability distributions is demonstrated by comparing the results for the α‐class polypeptide fragment, the mutant Antennapedia (C39 → S) homeodomain (2HOA), with those from two reference probability functions. The first reference probability function is a uniform or flat probability function and the second is a bivariate probability function for π and ψ. The trivariate gaussian probability functions are shown to search the conformational space more efficiently than the other two probability functions. The trivariate gaussian probability functions are also tested on the binding domain of Streptococcal protein G (2GB1), an α/β class protein. Since presently available energy functions are not accurate enough to identify the most native‐like energy‐minimized structures, three selection criteria were used to identify a native‐like structure with a 1.90‐Å rmsd from the NMR structure as the best structure for the Antennapedia fragment. Each individual selection criterion (ECEPP/3 energy, ECEPP/3 energy‐plus‐free energy of hydration, or a knowledge‐based mean field method) was unable to identify a native‐like structure, but simultaneous application of more than one selection criterion resulted in a successful identification of a native‐like structure for the Antennapedia fragment. In addition to these tests, structure predictions are made for the Antennapedia polypeptide, using a Pattern Recognition‐based Importance‐Sampling Minimization (PRISM) procedure to predict the backbone conformational state of the mutant Antennapedia homeodomain. The ten most probable backbone conformational state predictions were used with the trivariate and bivariate gaussian dihedral angle probability distributions to generate starting structures (i.e., dihedral angles) suitable for energy minimization. The final energy‐minimized structures show that neither the trivariate nor the bivariate gaussian probability distributions are able to overcome the inaccuracies in the backbone conformational state predictions to produce a native‐like structure. Until highly accurate predictions of the backbone conformational states become available, application of these dihedral angle probability distributions must be limited to problems, such as homology modeling, in which only a limited portion of the backbone (e.g., surface loops) must b...

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New determinations and simplified representations of macromolecular surfaces

Cited by 19 publications

References 4 publications

MSEED: A program for the rapid analytical determination of accessible surface areas and their derivatives

MSEED: A program for the rapid analytical determination of accessible surface areas and their derivatives

Gradient discontinuities in calculations involving molecular surface area

From secondary structure to three-dimensional structure: Improved dihedral angle probability distribution function for use with energy searches for native structures of polypeptides and proteins

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