Structure-based model of allostery predicts coupling between distant sites

Abstract

Allostery is a phenomenon that couples effector ligand binding at an allosteric site to a structural and/or dynamic change at a distant regulated site. To study an allosteric transition, we vary the size of the allosteric site and its interactions to construct a series of energy landscapes with pronounced minima corresponding to both the effector bound and unbound crystal structures. We use molecular dynamics to sample these landscapes. The degree of perturbation by the effector, modeled by the size of the allosteric site, provides an order parameter for allostery that allows us to determine how microscopic motions give rise to commonly discussed macroscopic mechanisms: (i) induced fit, (ii) population shift, and (iii) entropy driven. These mechanisms involve decreasing structural differences between the effector bound and unbound populations. A metric (ligand-induced cooperativity) can measure how cooperatively a given regulated site responds to effector binding and therefore what kind of allosteric mechanism is involved. We apply the model to three proteins with experimentally characterized transitions: (i) calmodulin-GFP Ca(2+) sensor protein, (ii) maltose binding protein, and (iii) CSL transcription factor. Remarkably, the model is able to reproduce allosteric motion and predict coupling in a manner consistent with experiment.

Fig. 1.

General landscapes of allostery. In an approximation, energy landscapes can be projected onto an “order parameter” that separates conformations of the system based on the structure of the regulated site. There are two landscapes pertaining to the effector bound (E + E_effector) and unbound (E) states. Within each state there is an open substate, which occurs if the regulated site configuration is closer to that in the effector unbound crystal structure than to that of the effector bound crystal structure, and a closed substate, which occurs otherwise. The horizontal lines indicate different populated structures in each basin. Different proteins may have dissimilar landscapes, in terms of the relative heights of the barriers and basins as well as the entropy within each basin. There are three general scenarios: (A) induced fit, (B) population shift, and (C) entropy driven. For allosteric proteins, conformations not consistent with effector binding (left of the dashed line) must be less stable than bound conformations (right of the dashed line).

Fig. 2.

Allosteric and regulated sites. The crystal structures for (A) CaGFP, (B) MBP, and (C) CSL. The parts of the effector bound and unbound structures that differ from each other are shown in red and yellow, respectively. The effector ligand is shown in black. A radius around the effector ligand (r^AS) defines the allosteric site (green). The regulated region is shown in blue. Also shown for each structure are the distance(s) between the regulated and allosteric sites, the C^α rmsd between the bound and unbound crystal structures, and the similarity measure ΔQ between the bound and unbound crystal structures. The regulated site for CaGFP is a stretch of the sequence responsible for fluorescence (residues 219–226).

Fig. 3.

Coupling of distant sites. (A–C) The probability distributions of QI_diff for the regulated sites corresponding to a large r^AS (approximately half the distance between allosteric and regulated sites) for the effector bound (red, QI_diff > 0) and effector unbound (green, QI_diff < 0) simulations. (D–F) The P_overlap (overlapping area between the distributions) is shown as a function of r^AS, normalized by the distance between each regulated site and the allosteric site. The regulated sites experimentally demonstrated to be highly coupled to effector binding in solution are shown as lines with closed circles and other sites are shown as lines with open squares. Error bars represent the standard deviation calculated by randomly dividing the set of simulations into thirds.

Fig. 4.

Pseudocorrelation map. A pseudocorrelation map [PC^t-(j,i)] for the allosteric site (AS), regulated site (RS), and C-terminal (CT) domains of CSL is obtained by assigning all residues (or subsets of residues) into the effector bound or effector unbound substate using QI_diff. (Upper) The row corresponding to the regulated site, for PC^t-(297, i). A–C represent pseudocorrelations of single domains: Q_diff (RS), Q_diff (AS), and Q_diff(CT), respectively. D and E represent pseudocorrelations for contacts at the interface between domains, QI_diff(AS to RS) and QI_diff (CT to RS), respectively.

Fig. 5.

Allosteric networks. The allosteric networks are shown for (A) CaGFP, (B) MBP, and (C) CSL. Residues are colored red when in contact and well correlated with the regulated site (labeled with arrows). A residue is considered correlated if PC^t+(regulated site, i) has a value greater than two standard deviations above the mean PC^t+ (Z score > 2). Residues colored orange and yellow are in contact and well correlated with red and orange residues, respectively. The remaining residues are either colored green if they are in the allosteric site (within the r^AS radius) or blue if they are in the regulated region.

Fig. 6.

Allosteric mechanisms. (A) Diagram that qualitatively differentiates between allosteric mechanisms. LIC averaged over the whole protein (x axis) and LIC of the regulated site (y axis) are shown for CaGFP, MBP, and CSL. Points are shown for residues in the regulated site, which are defined by experimental studies, including six for MBP. Diagrams that show energy landscapes for a subset of residues in a protein are shown: (B) induced fit, (C) population shift, and (D) entropy-driven mechanisms. The arrows represent the equilibrium between the unbound (Left) and bound (Right) landscapes. The protein is divided in an allosteric site (green), regulated site (blue), allosteric network (red), and the rest (white). The sum of the contributions of individual interactions for the mechanisms in B–D results in landscapes shown in Fig. 1 A–C, respectively. Higher LIC values across the whole protein often coincide with a large allosteric network and involve the cooperative motions of many residues between the allosteric site and the regulated site.