Allostery in a Coarse-Grained Model of Protein Dynamics

We propose a criterion for optimal parameter selection in coarse-grained models of proteins and develop a refined elastic network model (ENM) of bovine trypsinogen. The unimodal density-of-states distribution of the trypsinogen ENM disagrees with the bimodal distribution obtained from an all-atom model; however, the bimodal distribution is recovered by strengthening interactions between atoms that are backbone neighbors. We use the backbone-enhanced model to analyze allosteric mechanisms of trypsinogen and find relatively strong communication between the regulatory and active sites.

Figure 1

Density-of-states distribution for all-atom and elastic network models of trypsinogen. Frequency units are $(\mathrm{kcal}/\mathrm{mol}{\AA }^2{m}_p{)}^{1/2}=2.04\times {10}^{13}\mathrm{Hz}$, where $m_p$ is the proton mass. Densities were estimated by counting the number of modes in bins of width 0.2 and normalizing the integral to 663, which is the total number of nonzero modes.

Figure 2

Mean-squared displacements of alpha-carbon positions for trypsinogen residues 10–229 obtained from normal-modes simulations using charmm (dashed green line), a BENM with parameters that minimize $D_{{\mathbf{x}}_{\alpha }}$ with respect to charmm (dotted blue line), the same BENM but with $\gamma$ adjusted to better agree with charmm MSDs (fine-dotted magenta line), and an ENM with parameters adjusted to agree with charmm MSDs (dashed-dotted cyan line). Values were calculated at $T=300\mathrm{K}$ using the equipartition theorem. Harmonic vibrations at thermal equilibrium are known to inadequately model crystallographic MSDs, which include other sources of disorder (solid red line) [13].

Figure 3

Visualization of local sites on the surface of trypsinogen that exhibit a large change in the conformational distribution upon binding BPTI. Values of ${\overline{D}}_{\mathbf{x}}$ are mapped to a logarithmic temperature scale, with red coloring indicating large values. Changes are large both in the BPTI-binding site (left) and in the active site (right). There is a 90° rotation about the $x$ axis between the left and the right panels.