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Protein folding pathways and state transitions described by classical equations of motion of an elastic network model.

ABSTRACT: Protein topology defined by the matrix of residue contacts has proved to be a fruitful basis for the study of protein dynamics. The widely implemented coarse-grained elastic network model of backbone fluctuations has been used to describe crystallographic temperature factors, allosteric couplings, and some aspects of the folding pathway. In the present study, we develop a model of protein dynamics based on the classical equations of motion of a damped network model (DNM) that describes the folding path from a completely unfolded state to the native conformation through a single-well potential derived purely from the native conformation. The kinetic energy gained through the collapse of the protein chain is dissipated through a friction term in the equations of motion that models the water bath. This approach is completely general and sufficiently fast that it can be applied to large proteins. Folding pathways for various proteins of different classes are described and shown to correlate with experimental observations and molecular dynamics and Monte Carlo simulations. Allosteric transitions between alternative protein structures are also modeled within the DNM through an asymmetric double-well potential.

SUBMITTER: Williams G

PROVIDER: S-EPMC3009412 | biostudies-literature | 2010 Dec

REPOSITORIES: biostudies-literature

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Protein folding pathways and state transitions described by classical equations of motion of an elastic network model.

Williams Gareth G Toon Andrew J AJ

Protein science : a publication of the Protein Society 20101201 12

Protein topology defined by the matrix of residue contacts has proved to be a fruitful basis for the study of protein dynamics. The widely implemented coarse-grained elastic network model of backbone fluctuations has been used to describe crystallographic temperature factors, allosteric couplings, and some aspects of the folding pathway. In the present study, we develop a model of protein dynamics based on the classical equations of motion of a damped network model (DNM) that describes the foldi ...[more]

PMID: 20954241

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Project description: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.

Dataset Information

Protein folding pathways and state transitions described by classical equations of motion of an elastic network model.

Publications

Protein folding pathways and state transitions described by classical equations of motion of an elastic network model.

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