Elsevier

Computers & Chemistry

Volume 25, Issue 2, March 2001, Pages 145-159
Computers & Chemistry

Stepwise assembling of polypeptide chain energy distributions

https://doi.org/10.1016/S0097-8485(00)00076-0Get rights and content

Abstract

The principles and application of conformational analysis software that makes use of a new algorithm are described. It is known that the existence of a local energy minimum in the energy landscape is in general related to the clustering of polypeptide chain conformations near that energy value or, in other words, to a high density of states. A criterion based on this principle is part of an algorithm employed to select subsets of polypeptide chain conformations in broad energy ranges. Chain fragments belonging to these subsets are then combined to build larger polypeptide chains and the corresponding energy distributions. The functionality of the various operations employed in the process is described and the FORTRAN 77 source code that defines the algorithm is listed. The methodology is illustrated with a calculation involving three chain fragments belonging to the cellular prion protein (PrPC).

Introduction

The exercise of a peptide chain bio-active function often requires a structural transition, i.e. more than one energy minimum is involved. Whereas protein folding calculations intend to predict the native structure, the purpose of calculations about bio-active peptides is usually to find the energy distribution of chain conformations and the biologically important states.

Bioactive polypeptide chain conformations are considered to correspond to the global minimum (Scheraga, 1996) or to meta stable states (Honeycutt and Thirumalai, 1992, Karplus, 1997). In either case, a broad sampling of the Potential Energy Landscape is necessary. It is important for the presently described calculations that a comparison between different methodologies shows that in Molecular Dynamics (Elber, 1996) or Monte Carlo (Ortiz et al., 1998) calculations the energy is part of the algorithm, whereas in calculations based on lattice algorithms (Skolnick et al., 1997, Bahar et al., 1997) conformations may be obtained without an initial regard to their energies. Consequently, a larger breadth of conformational space is sampled.

This is also an important feature of a conformational analysis software whose principles and functionality are described here. Based on results described in the literature (Jacchieri, 1997, Shortle et al., 1998) we have replaced the search of energy minima by a search of density of states maxima and minima in the energy distribution. A broad energy interval is considered in the calculation of the energy distribution.

Density of states calculations require an energy unbiased algorithm. For instance, the Metropolis Algorithm (Ortiz et al., 1998 and references quoted therein), by its very definition, distorts the density of states near energy minima. In this work a matrix algorithm that generates a uniform grid of main chain and side chain rotamers is employed in the conformational search.

The present methodology enables a generation of energy distributions rather than a prediction of the native state. However, the native (or active) conformation should be part of a representative distribution. By applying the methodology to a problem that involves a known structural transition we may evaluate the presence in the distribution of the initial and final states belonging to this transition.

We chose three regions of the prion protein (PrPC), whose structure has been recently determined (James et al., 1997), to illustrate the sampling of density of states maxima and minima.

The tertiary structure of the PrPC protein is formed by a natively unfolded, α-helix, β-sheet and loop regions. It is known that an α-helix to β-sheet transition is associated (Keh-Ming et al., 1993) with pathogenic activity. These are structural features and transitions that we want to describe theoretically.

The algorithm described in this manuscript has been applied to the helix-coil transition (Jacchieri and Richards, 1992), a characterization of possible α-MSH structural transitions (Jacchieri and Ito, 1995) from aqueous solution to membrane bound conformations, peptide chain structural transitions (Jacchieri et al., 1998) related to oligopeptidase specificity for conformation and, more recently, to the role (Jacchieri, 1998) of isolated β-strands in the formation of amyloid plaques.

Section snippets

The matrix algorithm

Nmer chain conformations are generated by the matrix productMn=M1⊗O2⊗O3⊗…⊗ON

Mi and Oi are matrices of statistical weights, the elements of matrices M and O are, respectively, the values of exp(−Eiξ/RT) and exp(−ΔEiξ/RT), where ξ are chain conformations, Ei are internal energies of a chain fragment having residue i in the carboxyl terminus and ΔEi are interaction energies of residue i with preceding residues.

The matrix multiplication in Eq. (1) generates a new set of chain conformations by

Methods

Five main chain rotamers (A:φ=−57, ψ=−47; B:φ=−139, ψ=135; G:φ=−60, ψ=−30, D:φ=−90, ψ=0 and E:φ=70, ψ=−60, for proline residues: A: φ=−75, ψ=158; B: φ=−75, ψ=149) are employed in the search. For side chain conformations we make use of the gauche minus, trans and gauche plus rotamers of the (Ponder and Richards, 1987) classification (the numerals 1, 2 and 3 indicate, respectively, the gauche minus, trans and gauche plus rotamers of χ1). Gas phase energies are calculated with the ECEPP/2 (

Results and discussion

The above-described algorithm was used to generate distributions of chain conformations adopted by fragments 106–129, 129–142 and 160–175 of the PrPC polypeptide chain. Fragment 106–129 belongs to the natively unfolded PrPC region (James et al., 1997) and undergoes α-helix–β-strand transitions (De Gioia et al., 1994, Zhang et al., 1995). Peptide 129–142 whose sequence is part of the PrPC structural core, is also subjected to α-helix–β-strand transitions (De Gioia et al., 1994, Zhang et al., 1995

Conclusion

Various methodologies are used to build polypeptide chains in stages, each stage comprehending a longer chain fragment. Since it is not possible to pursue the calculation taking into account all generated conformations a criterion must be adopted to select chain conformations and this criterion must not discard important conformations. Thus, in the Build up Procedure (Vasquez and Scheraga, 1985) very high energy conformations are discarded and in CONGEN (Bruccoleri and Karplus, 1987) and

Acknowledgements

This work was supported by a FAPESP grant. We thank Dr Gerrit Vriend for providing the Whatif software package.

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