A New Bend-Twist-Stretch Model Enables Coarse Graining of Elastic Network Models and of Any 3D Graph Irrespective of Atom Connectedness

Abstract

A stable parameterization of biomolecular elastic network models (ENMs) is proposed to enable coarse graining of the representation and to model any 3D graph irrespective of the atom connectedness of a system. Traditional ENMs rely on a distance cutoff which is unforgiving in the presence of false negatives in the connectivity, giving rise to unbounded zero-frequency motions when atoms are connected to fewer than three neighbors. A large cutoff is therefore chosen in an ENM, resulting in many false positives in the connectivity that reduce the spatial detail that can be resolved. The required connectivity also has the undesired effect of limiting the coarse-graining, i.e. the network must be dense even in the case of low-resolution structures that exhibit few spatial features. To facilitate such a coarse graining, the newly proposed potential includes 3- and 4-atom interactions (bending and twisting, respectively), in addition to the traditional 2-atom stretching. Thus, in our new Bend-Twist-Stretch (BTS) model the complexity of the parameterization is shifted from the spatial level of detail to the potential function. The additional potential terms were parameterized using continuum elastic theory, and the distance cutoff was replaced by a parameter free competitive Hebb connection rule. We validate the approach on a carbon-alpha representation of adenylate kinase, and illustrate its use with electron microscopy maps of RNA polymerase, ribosome and CCT chaperonin, which were difficult to model with traditional ENMs. For adenylate kinase, we find excellent reproduction (>95% overlap) of the ENM modes and B-factors when BTS is applied to the carbon-alpha representation as well as to coarser descriptions. For the volumetric maps, coarse BTS yields similar motions (75-90% overlap) to those obtained from denser representations with ENM.