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. 2022 Jun 28;119(26):e2120456119.
doi: 10.1073/pnas.2120456119. Epub 2022 Jun 21.

Affinity of disordered protein complexes is modulated by entropy-energy reinforcement

Milan Kumar Hazra  1 , Yaakov Levy  1
Affiliations

Affinity of disordered protein complexes is modulated by entropy-energy reinforcement

Milan Kumar Hazra et al. Proc Natl Acad Sci U S A. .

Abstract

The association between two intrinsically disordered proteins (IDPs) may produce a fuzzy complex characterized by a high binding affinity, similar to that found in the ultrastable complexes formed between two well-structured proteins. Here, using coarse-grained simulations, we quantified the biophysical forces driving the formation of such fuzzy complexes. We found that the high-affinity complex formed between the highly and oppositely charged H1 and ProTα proteins is sensitive to electrostatic interactions. We investigated 52 variants of the complex by swapping charges between the two oppositely charged proteins to produce sequences whose negatively or positively charged residue content was more homogeneous or heterogenous (i.e., polyelectrolytic or polyampholytic, having higher or lower absolute net charges, respectively) than the wild type. We also changed the distributions of oppositely charged residues within each participating sequence to produce variants in which the charges were segregated or well mixed. Both types of changes significantly affect binding affinity in fuzzy complexes, which is governed by both enthalpy and entropy. The formation of H1-ProTa is supported by an increase in configurational entropy and by entropy due to counterion release. The latter can be twice as large as the former, illustrating the dominance of counterion entropy in modulating the binding thermodynamics. Complexes formed between proteins with greater absolute net charges are more stable, both enthalpically and entropically, indicating that enthalpy and entropy have a mutually reinforcing effect. The sensitivity of the thermodynamics of the complex to net charge and the charge pattern within each of the binding constituents may provide a means to achieve binding specificity between IDPs.

Keywords: counterion entropy; high-affinity binding; intrinsically disordered proteins; polyelectrolytes; protein association.

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Conflict of interest statement

The authors declare no competing interest.

Figures

Fig. 1.
Fig. 1.
Biophysical characterization of protein–protein binding between pairs of IDPs and pairs of structured proteins. (A) Structures of the H1–ProTα (purple) complex involving two IDPs and of the barnase–barstar (orange) and DNase2–Im2 (green) complexes involving structured (folded) proteins. The structures of barnase–barstar and DNase2–Im2 complexes were plotted using PDB ID 1BRS and 3U43, respectively. No structure is available for the ProTα–H1 complex because it is fuzzy; therefore, the presented snapshot is from MD simulations undertaken for this study. The folded domain of H1 was modeled using PDB ID 6N89. (B) PMF profiles of the H1–ProTα, barnase–barstar, and DNase2–Im2 complexes plotted as free energy (F) versus the distance between the centers of mass of the two interacting proteins (RCOM), shown using the same color code as that of their corresponding conformations in A. The PMFs were determined at a salt concertation of 200 mM and a temperature of 300 K. (C) Dependence of the dissociation coefficient, KD, on salt concentration for the three complexes. The computationally estimated KD values (empty circles fitted with a straight line) are shown together with the available experimental values (filled triangles). (D) Change in free energy for binding (ΔF) at three different temperatures for the three complexes. (E) Change in configurational entropy (represented here as −TΔSCon) and enthalpy (ΔE) for the three complexes (obtained from simulating their bound and unbound states) at a temperature of 300 K and salt concentration of 200 mM (corresponding to Debye screening length of 0.9 nm).
Fig. 2.
Fig. 2.
Binding affinity of fuzzy complexes formed between variants of ProTα and H1. (A) PMF profiles for the binding of variants of ProTα and H1 that have different net charges plotted as a function of the distance between the centers of mass (RCOM) of the two constituent binding units. PMFs are shown for the association among variants A (low net charge, pink), C (medium net charge, purple), and E (high net charge, blue); see Table 1 for more details. For each of the variants, the PMF is simulated for ProTα and H1 having different patterning parameter, κ, values, where lower κ values indicate greater mixing of positively and negatively charged residues in the sequence, and higher κ values indicate greater segregation of charged residues into positively and negatively charged patches. It is evident that the PMF is affected by both the net charge and the charge pattern. (B) The dissociation constant (KD) of the 52 simulated complexes of variants of H1–ProTα charge (see also Table 1). The sequences of variants A–E (marked by different colors) are ordered by their κ values (where the lowest κ value is on the left). (C) The KD for binding between variants of ProTα and H1 plotted as a function of the net charge on H1 (note that for each variant, the net charge of the complex equals +1). The KD of each variant A–E is colored according to its net. The KD values of each variant are grouped based on their κ values: low κ (triangle), medium κ (square), and high κ (circle). The bars indicate SDs, which were calculated from all the sequences in each group. The KD values for each H1–ProTα complex were measured at a salt concentration of 66 mM (corresponding to Debye screening length of 1.6 nm) and temperature of 300 K. A linear line is added for clarity to indicate the dependence of KD on the net charge. (D) Enthalpy (ΔE; left y axis) and configurational entropy (TΔSCon, right y axis) as a function of the net charge on H1 for the five H1–ProTα variants examined (variants A–E; see Table 1). A linear dependence of ΔE and TΔSCon on net charge is observed that is much stronger for the enthalpy than for the entropy. For higher net charge, a lower value is seen for ΔE and a greater value for TΔS, which indicates greater stability. The charge pattern (as represented by the charge-patterning parameter, κ) affects the value of ΔE of each type of variant: the higher the value of κ, the lower the value of ΔE (i.e., the greater the stability of the fuzzy complex) but has minor effect on the configurational entropy.
Fig. 3.
Fig. 3.
Enthalpic and entropic analysis of the formation of fuzzy complexes. (A) Configuration entropy deference (−TΔSCon) plotted against the ΔE between the bound and unbound isolated states for all the variants of the H1–ProTα system. A linear correlation (solid black line) is evident between –TΔSCon and ΔE, illustrating the occurrence of enthalpy–entropy reinforcement. Dashed lines are plotted for variants (namely, A, D, and E), demonstrating instances when modulating κ produces an enthalpy–entropy correlation in the opposite direction to that shown by the solid black line, consistently with the compensation mechanism. (B) Like A, with the exception that the contribution of the counterion’s entropy is added to the configurational entropy. The counterion’s entropy is estimated by calculating the degree of counterion’s condensations to each variant of H1 and ProTα simulated in their unbound state with explicit counterions. (C) Plots of –TSCon versus E for bound proteins (Lower Left) and isolated unbound proteins (Upper Right) at a salt concentration of 66 mM at 300 K. Dashed lines are as for C. The bars indicate SDs, which were calculated from all the sequences in each group.
Fig. 4.
Fig. 4.
Conformational space of the fuzzy complexes formed between variants of ProTα and H1. The simulated conformational ensembles of the bound complexes projected onto the first two PCs (PC1 and PC2) of the covariance matrix illustrate the conformational space of the bound state. The conformational analysis is shown for low net-charge variant A (pink), medium net-charge variant C (purple), and high net-charge variant E (blue) of H1 and ProTα (see Table 1 for more details). (A–C) Simultaneous projections for all three variants having (A) low, (B) intermediate, and (C) high charge-patterning (κ) values, as indicated on each panel. A heterogeneous conformational ensemble is observed for the fuzzy protein complexes, which reduces in size when the sequences have a higher net charge or larger κ values.
Fig. 5.
Fig. 5.
Structural analysis of the fuzzy complexes formed between variants of ProTα and H1. (A) Sum of the Rg of ProTα and H1 in the bound state of their fuzzy complexes plotted against the net charge on H1 (corresponding to variants A–E; see Table 1 for more details). The different charge patterns on each of the simulated variants are grouped into three groups: low κ (triangle), medium κ (square), and high κ (circle). The bars indicate SDs, which were calculated from all the sequences in each group. Rg is linearly anticorrelated with the net charge, with the strongest anticorrelation for the sequences with lower κ values (i.e., the triangles). For the sequences with high κ, there is only a mild dependence of Rg on the net charge. (B) Representative snapshots of the bound complex formed among variants A, C, and E. Three sequences having low, medium, and high κ values are shown for complexes formed between pairs of each variant. The snapshots were selected to have Rg values close to the mean of the corresponding variant ensemble. In the snapshots, the H1 and ProTα sequences are shown in blue and red, respectively. The folded domain in H1 is shown as a surface. The exact κ value of the H1 and ProTα complex (being the average of the κ values of each of the two sequences) is indicated in each case.
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Comment in

  • Electrostatics tunes protein interactions to context.
    Fuxreiter M. Fuxreiter M. Proc Natl Acad Sci U S A. 2022 Aug 2;119(31):e2209201119. doi: 10.1073/pnas.2209201119. Epub 2022 Jul 15. Proc Natl Acad Sci U S A. 2022. PMID: 35858387 Free PMC article. No abstract available.

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