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*Joseph N. Stember and Willy Wriggers*. Bend-Twist-Stretch Model for Coarse Elastic Network Simulation of Biomolecular Motion. J. Chem. Phys. 2009, 131:074112.

The empirical harmonic potential function of elastic network models (ENMs) is augmented by
three- and four-body interactions as well as by a parameter-free connection rule. In the new
bend-twist-stretch (BTS) model the complexity of the parametrization is shifted from the spatial
level of detail to the potential function, enabling an arbitrary coarse graining of the network.
Compared to distance cutoff-based Hookean springs, the approach yields a more stable
parametrization of coarse-grained ENMs for biomolecular dynamics. Traditional ENMs give rise to
unbounded zero-frequency vibrations when (pseudo)atoms are connected to fewer than three
neighbors. A large cutoff is therefore chosen in an ENM (about twice the average nearest-neighbor
distance), resulting in many false-positive connections that reduce the spatial detail that can be
resolved. More importantly, the required three-neighbor connectedness also limits the coarse
graining, i.e., the network must be dense, even in the case of low-resolution structures that exhibit
few spatial features. The new BTS model achieves such coarse graining by extending the ENM
potential to include three-and four-atom interactions (bending and twisting, respectively) in addition
to the traditional two-atom stretching. Thus, the BTS model enables reliable modeling of any
three-dimensional graph irrespective of the atom connectedness. The additional potential terms were
parametrized using continuum elastic theory of elastic rods, and the distance cutoff was replaced by
a competitive Hebb connection rule, setting all free parameters in the model. We validate the
approach on a carbon-alpha representation of adenylate kinase and illustrate its use with electron
microscopy maps of E. coli RNA polymerase, E. coli ribosome, and eukaryotic chaperonin
containing T-complex polypeptide 1, which were difficult to model with traditional ENMs. For
adenylate kinase, we find excellent reproduction (>90% 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 (70%–90% overlap) to those obtained from
significantly denser representations with ENM. Our Python-based algorithms of ENM and BTS
implementations are freely available.

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