Residue interaction potentials

M, Obatake and G. M. Crippen,/. Phys. Chem., 85, 1 187 (1981). A Residue-Residue Interaction Potential for Protein Conformational Calculations,... 

We have developed such a force field, named SPEEDY (Simplified Parameters for Energy Evaluation and DYnamics). SPEEDY uses the QPACK protein model and residue interaction potentials.- The terms of the potential function are analogous to those used in molecular mechanics calculations. Since the backbone virtual dihedral and bond angles are dependent on the complicated geometry of the polypeptide backbone, these terms are not represented independently. Residue interactions are represented by Lennard-Jones type functions scaled by their... 

We have recently introduced a combined structural, computational, and experimental approach for the de novo design of novel inhibitors such as variants of the synthetic cyclic peptide Compstatin. A novel two-stage computational protein design method is used not only to select and rank sequences for a particular fold but also to validate the stability of the fold for these selected sequences. To correctly select a sequence compatible with a given backbone template that is flexible and represented by several NMR structures, an appropriate energy function must first be identified. The proposed sequence selection procedure is based on optimizing a pairwise distance-dependent interaction potential. A number of different parameterizations for pairwise residue interaction potentials exist the one employed here is based on the discretization of alpha carbon distances into a set of 13 bins to create a finite number of interactions, the parameters of which were derived from a linear optimization formulated to favor native folds over... 

In this section we discuss mainly three types of potential terms computed from statistical analyses (Figure 2) (a) the residue-residue interaction potentials considered to represent local and nonlocal interactions between residues along the polypeptide chain (b) the local backbone potential, representing local interactions such as those associated with secondary structure propensities and (c) the profile-like potentials, considered to represent the interactions of individual residues with their three-dimensional environment. In contrast to molecular mechanics force fields, which have converged to a small number of functional forms and parameter sets, the implementations of these various potentials remain rather diverse. In the following we illustrate these implementations with some specific examples, and use these as the basis to review the approaches taken by various authors. 

Inspired by earlier work by Miyazawa and co-workers, distance dependent residue-residue interaction potentials were introduced by Sippl and collaborators and developed further in subsequent studies by many authors. We illustrate them here using the specific implementation of Kocher et al. ... 

In the latter implementation, the residue interaction potentials measure the propensities P l °j (dij) of amino acid pairs at positions / and j along the sequence to be separated by a given spatial distance d. Residue pairs are partitioned according to the number of positions / — j that separates them along the polypeptide sequence. In order to try and distinguish between local contributions associated with secondary structure propensities and nonlocal tertiary interactions, pairs of consecutive residues are not considered, because their spatial distance is roughly constant. For pairs separated by 2-8 sequence positions (1 < f — j < 8), probabilities are computed for each separation individually, yielding seven... 

Figure 2 Schematic illustration of the different types of potential terms derived from statistical analyses of known protein structures, (a) The residue-residue interaction potential computed from the frequencies of finding specific residue pairs at a given. spatial distance d from each other in known protein. structures, (b) The local backbone potential, representing the influence of amino acids on the backbone conformation of neighboring residues along the sequence, (c) The profile-like, or environment, potential, representing the interactions of individual residues with the field provided by their environment in the protein...

The corre.sponding seven middle range residue-residue interaction potentials A (C) (1 < ot < 8) ate given by... 

There are some alternative RPA schemes also delivering self-consistent factorization of the two-body residual interaction, see e.g. [21, 27-29] for atomic nuclei and [30,31] for atomic clusters. However, these schemes are usually not sufficiently general. Some of them are limited to analytic or simple numerical estimates [21,27,30], next ones start from phenomenological single-particle potentials and thus are not fully self-consistent [28], the others need a large number of the separable terms to get an appropriate numerical accuracy [29,31]. SRPA has evident advantages as compared with these schemes. 

A more detailed model can be constructed for the nucleons in terms of a central potential that holds all the nucleons together plus a residual potential or residual interaction that lumps together all of the other nucleon-nucleon interactions. Other such important one-on-one interactions align the spins of unlike nucleons (p-n) and cause the pairing of like nucleons (p-p, n-n). The nucleons are then allowed to move independently in these potentials, that is, the Schrodinger equation is solved for the... 

A residual interaction that is also quite simple has been developed and applied with good results. Recall that the nucleon-nucleon force is attractive and very short ranged, so one might image that the nucleons must be in contact to interact. Thus, the simplest residual interaction is an attractive force that only acts when the nucleons touch or a 8 interaction (in the sense of a Kronecker 8 from quantum mechanics). This can be written as V(r, r%) = a where a is the strength of the interaction, and the 8 function only allows the force to be positive when the nucleons are at exactly the same point in space. In practice, the strength of the potential must be determined by comparison to experimental data. Notice,... 

We assume that, after the protein has entered the proteasome, the protein-proteasome interaction is characterized by a spatially periodic asymmetric potential U(x) with the period P equal to the distance between amino adds in the protein. In reality there is a basic periodicity, namely the periodidty of the protein (or peptide) backbone, that is superposed by a nonperiodic (in our sense irregular) part that is attributed to the amino add-spedfic residues. Below we consider also the influence of the nonperiodic constituent. The spatial asymmetry results from breaking the symmetry by entering the proteasome from one end, as well as from the C — N asymmetry of the protein (or peptide) backbone. Figure 14.3 (left) plots several examples of such asymmetric periodic potential. The detailed form of the asymmetric periodic interaction potential is of less importance for this qualitative study. 

For obtaining the residual stresses in the hollow cylinder, do as advised below. The edges of the cylinder cut are moved apart through angle > and some deficit material is put there. The surrounding of the inner cylinder surface is in the tensile state, and the area of the outer surface is in the compression state. The hydrogen atoms interact with the residual stresses of the opposite signs. The interaction potential for dimensional effect is defined by the known relation [2]... 

Mao, W., Rupasinghe, S.G., Zangerl, A.R., Berenbaum, M.R. and Schuler, M.A. (2007) Allelic variation in the Depressaria pastinacella CYP6AB3 protein enhances metabolism of plant allelochemicals by altering a proximal surface residue and potential interactions with cytochrome P450 reductase. /. Biol. Chem., 282,10544—52. 

Liwo, A., Odziej, S., Pincus, M. R., Wawak, R. J., Rackovsky, S. and Scheraga, H. A. (1997). A united-residue force field for off-lattice protein-structure simulations. I. Functional forms and parameters of long-range side-chain interaction potentials from protein crystal data. J. Comp. Chem., 18, 849-873. 

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