Collective dynamics underlying allosteric transitions in hemoglobin

Abstract

Hemoglobin is the prototypic allosteric protein. Still, its molecular allosteric mechanism is not fully understood. To elucidate the mechanism of cooperativity on an atomistic level, we developed a novel computational technique to analyse the coupling of tertiary and quaternary motions. From Molecular Dynamics simulations showing spontaneous quaternary transitions, we separated the transition trajectories into two orthogonal sets of motions: one consisting of intra-chain motions only (referred to as tertiary-only) and one consisting of global inter-chain motions only (referred to as quaternary-only). The two underlying subspaces are orthogonal by construction and their direct sum is the space of full motions. Using Functional Mode Analysis, we were able to identify a collective coordinate within the tertiary-only subspace that is correlated to the most dominant motion within the quaternary-only motions, hence providing direct insight into the allosteric coupling mechanism between tertiary and quaternary conformation changes. This coupling-motion is substantially different from tertiary structure changes between the crystallographic structures of the T- and R-state. We found that hemoglobin's allosteric mechanism of communication between subunits is equally based on hydrogen bonds and steric interactions. In addition, we were able to affect the T-to-R transition rates by choosing different histidine protonation states, thereby providing a possible atomistic explanation for the Bohr effect.

Figure 1. Illustration of the separation procedure of the MD trajectories into tertiary-only and quaternary-only trajectories.

At the top it is shown how a single MD snapshot is decomposed (B) with respect to the reference structure (A). This procedure is applied to all snapshots yielding the two desired trajectories of tertiary-only and quaternary-only motions (C). The schematic system was chosen to resemble Hb with its four chains.

Figure 2. Functional Mode Analysis input data and fit results.

Projections of the concatenated MD trajectories onto cQ (blue) and onto the constructed model cT (orange) are shown. The first half of the data has been used for constructing the model and the second half for cross-validation. Pearson correlation coefficients comparing MD data and FMA model for both parts are shown on top. The x-axis is the consecutive simulation time and the y-axis the projection onto the principal quaternary eigenvector in nm. The projections for the T- and R-state X-ray structures are marked in grey.

Figure 3. Graphical representation of the vdW overlap analysis.

Overlaps were calculated for structures in the plane spanned by cQ (x-axis) and cTew (y-axis). For the extreme structures in the four corners a zoomed-in part on the N-terminal region of the -chain (green), the -chain (blue) and the -chain (yellow) of Hb is shown to illustrate the motions. Projections of the original simulation data onto this plane are shown as white dots.

Figure 4. Inter-chain contact analysis.

(A) The matrix of observed contacts pairs along cQ-cTew is shown. The colour of the dot indicates when along cQ-cTew the two residues are in contact and thereby defines the contact class. (B) An exemplary close-up on a contact region, which allowed us to identify contacts that are part of the ‘switch’ and ‘hinge’ region (structure shown in (D)) as measured by Balakrishnan et al. . The arrows mark contacts of the and the residues in which one contact partner switches when going from T-state (orange) to the R-state (green). (C) Schematic representation of the contact classifications along cQ-cTew.