Intrinsic disorder as a mechanism to optimize allosteric coupling in proteins

Abstract

Transcription factors and other allosteric cell signaling proteins contain a disproportionate number of domains or segments that are intrinsically disordered (ID) under native conditions. In many cases folding of these segments is coupled to binding with one or more of their interaction partners, suggesting that intrinsic disorder plays an important functional role. Despite numerous hypotheses for the role of ID domains in regulation, a mechanistic model has yet to be established that can quantitatively assess the importance of intrinsic disorder for intramolecular site-to-site communication, the hallmark property of allosteric proteins. Here, we present such a model and show that site-to-site allosteric coupling is maximized when intrinsic disorder is present in the domains or segments containing one or both of the coupled binding sites. This result not only explains the prevalence of ID domains in regulatory proteins, it also calls into question the classical mechanical view of energy propagation in proteins, which predicts that site-to-site coupling would be maximized when a well defined pathway of folded structure connects the two sites. Furthermore, in showing that the coupling mechanism conferred by intrinsic disorder is robust and independent of the network of interactions that physically link the coupled sites, unique insights are gained into the energetic ground rules that govern site-to-site communication in all proteins.

Fig. 1.

Model for allosteric coupling. (A) Schematic representation of a test model for allosteric coupling. Shown is a hypothetical two-domain protein that can bind two different ligands (A and B), one in each domain. Each domain can be folded or unfolded, resulting in four possible states (i.e., N, 1, 2, and U). (B) Site-to-site coupling is evaluated through the addition of ligand A, which binds to only domain I. Because ligand A stabilizes those states that bind A (blue arrows), the ensemble probabilities are redistributed. Depending on the relative probabilities of each state before the addition of ligand A, those states that can bind ligand B will either be: (i) stabilized, (ii) destabilized, or (iii) not affected by the binding of ligand A. The effect can be quantified through a parameter called the CR [CR = Δ(P_N + P₂)/ΔlnZ_Lig,A], which is the change in the probability of states that can bind ligand B (i.e., P_B,Folded = P_N + P₂) as a result of binding ligand A. For this model, values for the intrinsic stabilities of each domain (i.e., ΔG_I and ΔG_II) are relative to the folded conformation; positive values mean that the folded conformation of each domain is more stable, and negative values mean that the unfolded form is more stable. The interaction energy (i.e., Δg_int) is referenced to the interacting (i.e., N) state; positive values mean that it is more energetically favorable for the interaction to be formed than to have the domains interact with solvent, and negative values mean that it is more favorable to have the domains interact with solvent. The parameters used, ΔG_I = −2.3 kcal/mol, ΔG_II = −0.7 kcal/mol, Δg_int = 1.6 cal/mol, and Δg_Lig,A = −3.0 kcal/mol, result in a significant CR and is part of the positively coupled node of parameters in Fig. 2A. (Upper) Without ligand A. (Lower) With ligand A.

Fig. 2.

Proteins with ID domains are optimized for allosteric coupling. (A) 3D plot showing all parameter combinations that generate a CR ≥ 0.10. A wide range of parameter combinations is sufficient to elicit a high response. The absence of points in the region marked minimal coupling indicates that although a wide range of parameter values can combine to produce a high CR, significant interaction energy (i.e., for this case, |Δg_int| > ≈1.0 kcal/mol) is a prerequisite to coupling. All energies are in kcal/mol. The star and dashed red lines indicate those parameter values used to generate Fig. 1B, and solid red axes denote the origin. (B) Plot of the folding probability of the ligand A site (i.e., P_N + P₁) vs. the folding probability of the ligand B site (i.e., P_N + P₂) showing only those parameter combinations where the CR exceeds a specified response threshold. Three different response thresholds are shown: 0.07 (yellow), 0.10 (orange), and 0.15 (red). The maximum responses (dashed boxes) are observed in two regions. In region 1, domain I is unfolded and domain II is folded. Binding of ligand A folds domain I, but because of unfavorable domain coupling, domain II unfolds. In region II, both domains are unfolded. Binding of ligand A folds domain I, and as a result of favorable domain coupling, domain II folds.

Fig. 3.

Extension of the allosteric model to three domains. 3D plot of probability space for the three-domain protein (analogous to the 2D plot shown in Fig. 2B for the two-domain protein). Shown are those parameters that result in a CR ≥0.07 (purple points). Arrows denote which is the dominant state for each one of the four nodes (groups of points) observed.

Fig. 4.

The effect of binding energy on the optimum distribution for allosteric coupling. Plot of the folding probability of the ligand A site (i.e., P_N + P₁) vs. the folding probability of the ligand B site (i.e., P_N + P₂) showing only those parameter combinations where the CR exceeds a specified response threshold. Shown is the dependence of the optimum distribution on the binding free energy available to induce the allosteric transition. For binding energies of −0.01, −1.0, and −3.0 kcal/mol the corresponding values of K_a[A] (from Eq. 4) are 0.02, 4.4, and 157, respectively. For clarity, response thresholds of 0.23, 0.21, and 0.15 were used to show the maxima for Δg_Lig,A = −0.01, −1.0, and −3.0 kcal/mol, respectively.