Systematic multiscale parameterization of heterogeneous elastic network models of proteins - PubMed (original) (raw)

Systematic multiscale parameterization of heterogeneous elastic network models of proteins

Edward Lyman et al. Biophys J. 2008.

Abstract

We present a method to parameterize heterogeneous elastic network models (heteroENMs) of proteins to reproduce the fluctuations observed in atomistic simulations. Because it is based on atomistic simulation, our method allows the development of elastic coarse-grained models of proteins under different conditions or in different environments. The method is simple and applicable to models at any level of coarse-graining. We validated the method in three systems. First, we computed the persistence length of ADP-bound F-actin, using a heteroENM model. The value of 6.1 +/- 1.6 microm is consistent with the experimentally measured value of 9.0 +/- 0.5 microm. We then compared our method to a uniform elastic network model and a realistic extension algorithm via covariance Hessian (REACH) model of carboxy myoglobin, and found that the heteroENM method more accurately predicted mean-square fluctuations of alpha-carbon atoms. Finally, we showed that the method captures critical differences in effective harmonic interactions for coarse-grained models of the N-terminal Bin/amphiphysin/Rvs (N-BAR) domain of amphiphysin, by building models of N-BAR both bound to a membrane and free in solution.

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Figures

FIGURE 1

FIGURE 1

Two views of an α_-carbon heteroENM model of myoglobin. Pairs of C_α atoms separated on average by <15 Å are connected by a harmonic spring, indicated by colored lines. Stiffness of the spring is represented by its color on a logarithmic scale, from ∼100 kcal mol−1Å−2 (red) to 0.01 kcal mol−1Å−2 (blue). The N-terminus is indicated by a red ball (at left), and the plane of the heme is indicated by a black line (right). The image was rendered with Kinemage, next generation (54).

FIGURE 2

FIGURE 2

Spring constant as a function of equilibrium length _x_0 for the myoglobin heteroENM model in Fig. 1. Points are colored to indicate whether they are between neighboring _α_-carbons (1–2 interactions), next-neighbor _α_-carbons (1–3 interactions), etc. Interactions cluster into distinct groups, even as far out as 1–6 related _α_-carbons.

FIGURE 3

FIGURE 3

Per-residue mean-square fluctuations computed from atomistic MD simulation, heteroENM, REACH, and single-parameter ENM. Neither the heteroENM nor REACH models were parameterized to reproduce these data. Agreement between the MD simulation and ENM models, as measured by linear correlation coefficient r, is best for the heteroENM model.

FIGURE 4

FIGURE 4

Side view of bound N-BAR domain model, comparing backbone level structure (left) with heteroENM model (right). The CG-site definitions are symmetric across the homodimer. Residues corresponding to CG sites are 26–31, 32–55, 56–103, 104–132, 133–150, 151–163, 164–173, 174–192, 193–218, and 219–244. Ribbon diagram was rendered using visual molecular dynamics (55), and network diagram was rendered using Kinemage, next generation (54).

FIGURE 5

FIGURE 5

(Top) Comparison of spring constants determined by a heteroENM calculation between membrane-bound and unbound N-BAR domains. The horizontal axis labels the CG harmonic bonds; the vertical axis is logarithmic to emphasize the difference between the two cases. (Bottom) Close-up of A for bonds numbered 100–150. To test whether observed differences were significant, error bars were calculated by performing the heteroENM calculation separately for five adjacent 2-ns blocks of atomistic simulations, and computing the standard deviation of resultant spring constants. Error bars are typically on the order of 1–5%. Many of the spring constants differ by far more than the range of their error bars. Moreover, error bars address the convergence of the heteroENM model by demonstrating that k values computed from 2-ns blocks agree with those computed from the full 10-ns trajectory.

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