Backbone degrees of freedom

L. Piela, H.A. Scheraga, On the multiple-minima problem in the conformational analysis of polypeptides. I. Backbone degrees of freedom for a perturbed a-helix. Biopolymers 26, S33-S58 (1987)... 

L. Piela and H. A. Scheraga, Biopolymers, 26, S33 (1987). On the Multiple-Minima Problem in the Conformational Analysis of Polypeptides. I. Backbone Degrees of Freedom for a Perturbed a-Helix. 

All the calculations described below were done with the program MOIL [28]. Moil is a freely available molecular simulation package with a focus on reaction path and rate calculations. Structures selected from the trajectory described in the previous paragraph were fed into MOIL. They were refined into a detailed SDP from a helix to a coil conformation with the action formnlation of Olender and Elber [29]. The SDP was computed in a rednced snbspace of coarse variables, namely the positions of the C -s of the peptide. We are making the plausible assumption that side chain motions equilibrate more rapidly than backbone degrees of freedom. 

To understand the function of a protein at the molecular level, it is important to know its three-dimensional stmcture. The diversity in protein stmcture, as in many other macromolecules, results from the flexibiUty of rotation about single bonds between atoms. Each peptide unit is planar, ie, oJ = 180°, and has two rotational degrees of freedom, specified by the torsion angles ( ) and /, along the polypeptide backbone. The number of torsion angles associated with the side chains, R, varies from residue to residue. The allowed conformations of a protein are those that avoid atomic coUisions between nonbonded atoms. 

Analysis and prediction of side-chain conformation have long been predicated on statistical analysis of data from protein structures. Early rotamer libraries [91-93] ignored backbone conformation and instead gave the proportions of side-chain rotamers for each of the 18 amino acids with side-chain dihedral degrees of freedom. In recent years, it has become possible to take account of the effect of the backbone conformation on the distribution of side-chain rotamers [28,94-96]. McGregor et al. [94] and Schrauber et al. [97] produced rotamer libraries based on secondary structure. Dunbrack and Karplus [95] instead examined the variation in rotamer distributions as a function of the backbone dihedrals ( ) and V /, later providing conformational analysis to justify this choice [96]. Dunbrack and Cohen [28] extended the analysis of protein side-chain conformation by using Bayesian statistics to derive the full backbone-dependent rotamer libraries at all... 

Peptide bond resonance has several important consequences. First, it restricts free rotation around the peptide bond and leaves the peptide backbone with only two degrees of freedom per amino acid group rotation around... 

US studies can produce informative free energy landscapes but assume that degrees of freedom orthogonal to the surface equilibrate quickly. The MD time needed for significant chain or backbone movement could exceed the length of typical US simulations (which are each typically on the nanosecond timescale). However, in spite of this caveat, US approaches have been very successful. One explanation for this success lies in the choice of initial conditions US simulations employ initial coordinates provided by high-temperature unfolding trajectories, which themselves have been found to yield predictive information about the nature of the relevant conformational space. 

There are many further issues that can be addressed by the model of the kind described here. Clearly, the HA model is amenable to a number of generalizations that allow one to study more sophisticated features of amphiphilic copolymers, including, for instance, backbone stiffness, orientational degrees of freedom, or additional structural constraints such as the saturation of monomer-monomer interactions [98], which are crucial, e.g., for the folding of RNA. Also, it is easy to introduce dipole moments for side H - P bonds and specific directional interactions (like hydrogen bonds) for some of the chain units. These additional factors can result in the formation of intramolecular secondary structures and lead to an increase in the stability of globules formed by such polymers. 

---