Dynamically Driven Protein Allostery Exhibits Disparate Responses for Fast and Slow Motions

Abstract

There is considerable interest in the dynamic aspect of allosteric action, and in a growing list of proteins allostery has been characterized as being mediated predominantly by a change in dynamics, not a transition in conformation. For considering conformational dynamics, a protein molecule can be simplified into a number of relatively rigid microdomains connected by joints, corresponding to, e.g., communities and edges from a community network analysis. Binding of an allosteric activator strengthens intermicrodomain coupling, thereby quenching fast (e.g., picosecond to nanosecond) local motions but initiating slow (e.g., microsecond to millisecond), cross-microdomain correlated motions that are potentially of functional importance. This scenario explains allosteric effects observed in many unrelated proteins.

Main Text

Allostery, whereby ligand binding at a distal site affects binding affinity or catalytic activity at the active site, is traditionally considered as mediated through conformational transition (1). In 1951, Wyman and Allen (2) described a scenario of cooperative oxygen binding to hemoglobin in terms of conformational entropy. Later it was proposed that an allosteric ligand may produce changes in protein dynamics within a given conformational state without a switch in conformational states (3). A growing list of proteins has been characterized as exemplars of such dynamically driven allostery (4–12). Our molecular-dynamics (MD) simulations (12) along with the NMR data of Namanja et al. (7) suggest that a main consequence of substrate binding to the WW domain of Pin1 is rigidification of the loops around the catalytic site of the PPIase domain. Previous theoretical work of dynamically driven allostery has focused on free energy, not dynamics per se, and indeed this type of allostery has been referred to as entropic allostery (3,13,14). Here we examine generic features of dynamics in dynamically driven allostery.

For the purpose of considering conformational dynamics, we may simplify a protein molecule into a number of relatively rigid microdomains connected by joints. For example, allosteric network methods use data from MD simulations to partition proteins into communities and edges between them (8,10,12). Our premise is that the binding of an allosteric activator adds physical coupling between nearby microdomains and strengthens other intermicrodomain coupling. The stronger coupling, as illustrated on a simple model, leads to disparate responses for fast and slow motions, which are actually observed in Pin1 and many other proteins.

Our simple model, inspired by community analysis on Pin1 (12), represents three main microdomains of Pin1 as springs for describing local motions (Fig. 1). In apo Pin1, intermicrodomain coupling is weak. We extremitize this situation by assuming that the three springs are totally uncoupled. The potential energy of the model is then

$$U_0\left(x_1,x_2,x_3\right)={\sum }_{i=1}^3\left(k_i/2\right)x_i^2,$$ (1)

where x_i denote the internal coordinates for the local motions and k_i denote the spring constants. Upon binding to the WW domain, a phosphopeptide with sequence FFpSPR acts as a bridge between microdomains 1 and 3 via direct physical contact. In addition, the coupling between the other two pairs of microdomains is also strengthened. Representing the intermicrodomain coupling by harmonic potentials, we obtain the total potential energy

$$U\left(x_1,x_2,x_3\right)={\sum }_{i=1}^3\left(k_i/2\right)x_i^2+{\sum }_{i=1}^3\left(J_i/2\right){\left(x_{i+1}-x_i\right)}^2,$$ (2)

where J_i denote the strengths of intermicrodomain coupling, and x₄ ≡ x₁ (for the circular coupling pattern). We are interested in the strong coupling regime, where J_i > k_i.

Figure 1.

Dynamic model of protein allostery. The community analysis results for (A) apo and (B) FFpSPR-bound Pin1 from Guo et al. (12) are shown as motivation for the dynamic model. The communities are shown in different colors as cartoon structures (left) or as circles (middle). Intercommunity connections are shown as lines, with width proportional to the cumulative betweenness of intercommunity edges (middle). The three largest communities are represented in the dynamic model, each by a spring (right). The springs are weakly coupled in the apo form but are strongly coupled in the FFpSPR-bound form. Motions of the internal coordinates are assumed to be diffusive. To see this figure in color, go online.

We assume that the motions are diffusive in nature. In apo Pin1, the local motions are uncoupled and each internal coordinate is assigned its own diffusion coefficient d_i. Each coordinate then undergoes diffusion in a harmonic well. This situation is similar to the diffusion-in-a-cone model for bond vector internal (e.g., picosecond to nanosecond) motions in interpreting NMR relaxation data (15). For the diffusion in a harmonic well, the time correlation function is a single exponential: 〈x_i(t)x_i(0)〉 = 〈x_i²〉exp(–t/τ_i), where 〈x_i²〉 = k_BT/k_i, with k_B denoting Boltzmann’s constant, T denoting the absolute temperature, and relaxation time τ_i = k_BT/k_id_i.

When the microdomains become strongly coupled as occurs upon FFpSPR-WW binding, a major consequence on the dynamics is that the effective diffusion coefficient, D, for the coupled motions is orders-of-magnitude smaller than the diffusion coefficients, d_i, for the local motions. Intuitively, one certainly expects D/d_i < 1, but there is also direct experimental support. By measuring residue-residue contact formation rates in unstructured peptides, it was found that relative diffusion of two residues in a peptide chain is an order-of-magnitude slower than the relative diffusion of free amino acids (16). Even more dramatically, the intramolecular diffusion coefficient in unfolded protein L was found to decrease 2–3 orders of magnitude as the concentration of the denaturant GdnHCl was reduced from 6 to 0 M (17). Removing the denaturant had the effect of increasing intramolecular coupling, but still the diffusion studied was in the unfolded (though compact) protein. Because d_i describe local motions of essentially free amino acids whereas D describes coupled motions within a folded protein, it would not be surprising if the values of D/d_i are even smaller than implicated by these experiments.

The problem of diffusion in the potential of Eq. 2 can be solved analytically. When all the spring constants k_i are identical (= k) and all the coupling constants J_i are identical (= J), the time correlation functions of all the coordinates are 〈x_i(t)x_i(0)〉 = (k_BT/3k)exp(–t/τ_s) + (2k_BT/3(k + 3J)) exp(–t/τ_f). The first exponential has a relaxation time τ_s = k_BT/kD that is orders-of-magnitude longer than those (τ_i = k_BT/k_id_i) for local motions in the apo protein. Compared to the first exponential, the second exponential has a much shorter relaxation time τ_f = k_BT/(k + 3J)D as well as a much smaller amplitude (note that J > k). The normalized cross correlation, 〈x_ix_j〉/(〈x_i²〉〈x_j²〉)^1/2, is J/(k + J) and approaches 1, indicating highly synchronous motions of the internal coordinates. So the binding of the allosteric ligand strengthens intermicrodomain coupling, and consequently quenches fast, asynchronous motions but initiates slow, synchronous motions.

These predicted dynamic consequences are precisely what had been found by Namanja et al. Their side-chain methyl ²D relaxation data indicated quenched picosecond-to-nanosecond dynamics upon FFpSPR binding (7). On the other hand, microsecond-to-millisecond exchange dynamics, as captured by the product of the longitudinal and transverse relaxation rates of side-chain methyl ¹³C, was enhanced (18). In our MD simulations, the allosteric action of FFpSPR-WW binding is manifested by rigidification of the catalytic-site loops (12). To further dissect the allosteric mechanism, we investigated whether the effects of FFpSPR-WW binding could be mimicked by artificially enhancing intra- or intermicrodomain coupling in the form of conformational restraints in MD simulations. Artificial enhancement of coupling within microdomain 1 or 2 or between microdomains 2 and 3 was ineffective, but artificial coupling of microdomains 1–3 together produced the same allosteric action as FFpSPR-WW binding. This observation provides support to our modeling of allosteric binding as strengthening intermicrodomain coupling.

Our model predicts that allosteric action reduces with weakening of ligand-induced intermicrodomain coupling. Namanja et al. (7,18,19) found that a second phosphopeptide, from the mitotic phosphatase Cdc25C, produced less prominent effects on both picosecond-to-nanosecond and microsecond-to-millisecond dynamics than FFpSPR did. To see whether the reduced allosteric action is mediated by weakened intermicrodomain coupling, here we carried out an MD simulation of Pin1 with the Cdc25C peptide bound at the WW site. Compared to FFpSPR, the Cdc25C peptide has more extensive interactions with microdomain 1 but minimal interactions with microdomain 3 (Fig. 1 B and Fig. S1 A in the Supporting Material). The catalytic loop and neighboring residues do not become rigidified (Fig. S1 B), indicating reduced allosteric action. A community network analysis confirms that the intermicrodomain coupling is not as strong as in the case with FFpSPR bound (Fig. S1 A).

The disparate responses for fast and slow motions predicted by our model are also observed in many other proteins that involve a strong dynamic component in allosteric regulation. When thrombomodulin (specifically TM456) is bound to the anion binding exosite 1 (ABE1) of thrombin, MD simulations of Gasper et al. (8) showed that the picosecond-to-nanosecond dynamics of the 30_CT loop (part of the ABE1) and the neighboring 60_CT insertion is quenched but microsecond-to-millisecond dynamics of the loops around the active site is initiated (Fig. S2 A). In agreement with model prediction, the motions of these loops are strongly correlated. Community analysis showed that the ligand (i.e., TM456), the distal binding site (i.e., ABE1), and active-site loops form strongly connected communities, similar to what we found for Pin1.

Srivastava et al. (10) studied the dynamic effects of a mutation, Y204A, in the catalytic subunit of the cAMP-dependent protein kinase. The mutation is far away from the active site (Fig. S2 B) but still renders cAMP-dependent protein kinase catalytically inefficient. The mutant can be viewed as an apo protein whereas the wild-type protein is bound with an allosteric ligand. Tyr²⁰⁴ forms a hydrogen bond with Glu²³⁰ on the F helix and also van der Waals contacts with the F helix. The wild-type protein undergoes synchronous slow (millisecond) motions (possible opening and closing between the small and large lobes separated by the active-site cleft). In contrast, in the mutant, motions are faster and uncorrelated. Community analysis showed that the structural elements around Tyr²⁰⁴, the rest of the large lobe, and the small lobe, form tightly coupled communities, but the coupling is significantly weakened in the mutant. The mediation of the allosteric action of Tyr²⁰⁴ through strengthening intermicrodomain coupling is reminiscent of the situations with Pin1 and thrombin.

Popovych et al. (4) studied the conformational and dynamic effects of sequential cAMP binding to the two distant sites in the catabolite activation protein N-terminal domain dimer. In the singly-liganded species, the subunit with the bound ligand undergoes significant conformational perturbation but the conformation of the unliganded subunit is minimally affected. On the other hand, correlated microsecond-to-millisecond motions are initiated throughout the whole dimer while picosecond-to-nanosecond motions of some residues are dampened, consistent with our model prediction. Further support of the dynamic model is provided by experimental observations on other proteins, including quenching of picosecond-to-nanosecond dynamics by a distal helix appendage in a PDZ domain (5); enhancement of millisecond motions by the binding of an allosteric activator to imidazole glycerol phosphate synthase (6); appearance of microsecond-to-millisecond dynamics at the Flim binding interface of CheY upon phosphorylation of Asp⁵⁷ (9); and the initiation of concerted microsecond-to-millisecond motions by an N-terminal sequence in the catalytic domain of CheA (11). (An allosteric inhibitor could weaken intermodule coupling by, e.g., wedging into tightly interacting structural elements (20).) Interestingly, in a case where allostery is apparently mediated by significant conformational transition, microsecond-to-millisecond dynamics is suppressed upon allosteric activation (21).

In conclusion, the dynamic model and the many supporting examples suggest that dynamically driven allostery has generic features. This type of allosteric action is manifested by quenching of fast (e.g., picosecond-to-nanosecond) motions but initiation of slow (e.g., microsecond-to-millisecond) motions. Such slow dynamics has often been suggested to be functionally important ((6,8,10); see the Supporting Material for further discussion of this and other pertinent issues). The disparate responses of fast and slow dynamics come about due to strengthening of intermicrodomain coupling by allosteric activators, and may represent a defining departure from traditional conformationally driven allostery.

Author Contributions

J.G. and H.-X.Z. designed and performed research; H.-X.Z. wrote the article.

Editor: Nathan Baker.