Dissecting the Energetics of Intrinsically Disordered Proteins via a Hybrid Experimental and Computational Approach

Abstract

Intrinsically disordered proteins (IDPs) play important roles in biology, but little is known about the energetics of their inter-residue interactions. Methods that have been successfully applied to analyze the energetics of globular proteins are not applicable to the fluctuating partially ordered ensembles populated by IDPs. A combined computational experimental strategy is introduced for analyzing the energetic role of individual residues in the free state of IDPs. The approach combines experimental measurements of the binding of wild-type and mutant IDPs to their partners with alchemical free energy calculations of the structured complexes. This data allows quantitative information to be deduced about the free state via a thermodynamic cycle. The approach is validated by the analysis of the effects of mutations upon the binding free energy of the ovomucoid inhibitor third binding domain to its partners and is applied to the C-terminal domain of the measles virus nucleoprotein, a 125-residue IDP involved in the RNA transcription and replication of measles virus. The analysis reveals significant inter-residue interactions in the unbound IDP and suggests a biological role for them. The work demonstrates that advances in force fields and computational hardware have now led to the point where it is possible to develop methods which integrate experimental and computational techniques to reveal insights that cannot be studied using either technique alone.

Graphical Abstract

Introduction

Intrinsically disordered proteins (IDPs) lack stable secondary and tertiary structure due to their low content of bulky hydrophobic residues and their high content of polar and charged residues^1–2. While they do not fold into well-defined globular structures in isolation^3–4, IDPs populate ensembles ranging from expanded states with little residual structure to ensembles which are more compact and contain residual secondary and tertiary interactions and they often fold upon binding to their partners ^5–10. IDPs play important roles in biology. Structural characterization of IDPs in their uncomplexed state and of the denatured state of globular proteins show that neither are true random-coils, instead, they often contain transient secondary structure and long-range interactions^11–20. Inter-residue interactions in the unbound state of IDPs could modulate their binding affinity and other interactions, and thus modulate their biological activity. Moreover, long-range interactions in IDPs and in unfolded proteins may play an important role in controlling the propensity to aggregate and thus preventing protein misfolding diseases^{12–13, 21,22}. In general, conservation of IDP sequences is believed to be lower than for the sequences of globular proteins, suggesting that there may be an overall lower free-energy cost to mutations in the free state of IDPs²³. Progress has been made in characterizing the structural properties of IDPs and in defining relationships between sequence and conformational properties, but much less is known about the energetics of inter-residue interactions in IDPs^{2, 24–26}, and quantitative analysis of the inter-residue energetics of IDPs is still absent.

The contribution of a residue to the energetics of the folded state of a protein is traditionally obtained by mutagenesis and unfolding free energy measurements, but such a strategy cannot be applied to IDPs. In principle, it is also possible to estimate the energetics of a residue in a globular protein via molecular modelling if the structure of the protein is resolved in atomic level^27–28. Structural ensembles of IDPs can be obtained from ensemble fitting using experimental observables such as Rg and NMR as constraints and the ensembles used as input to potential energy functions to estimate energies. However, the ensembles derived are not fully deterministic as the experimental observables are not sufficient to uniquely define highly conformationally heterogeneous IDPs and the energetics obtained are not always reliable. Molecular dynamics (MD) simulations are becoming popular for studying the structural propensities of IDPs as newly developed force fields are being trained not only for globular proteins, but also for IDPs^29–31. While many current force fields have shown good performance at folding proteins^32–34, their accuracy for IDPs are still not as well established and many force fields have had difficulty reproducing global properties of protein unfolded states³⁵. Simulations of IDPs also require considerably more sampling than simulations of folded proteins because of their flat free energy landscape, increasing computational cost. Larger IDPs are currently not suitable for MD simulations in explicit solvent so implicit solvent models must be used, which can be less accurate. This inability to accurately model the disordered state of IDPs has hampered the application of MD to study IDP energetics.

Here, we describe a strategy to quantitatively analyze the energetic effects of mutations upon the free state of IDPs and to define the energetic contribution made by individual residues in the free state. The approach combines experimental structural and energetic information on complexes of IDPs with their binding partners and alchemical free energy calculations of the bound state to deduce the properties of the unbound state via a thermodynamic cycle. The strategy is validated using mutants of the turkey ovomucoid inhibitor third binding domain (OMTKY3) and its binding partners and is then applied to the C-terminal domain of the measles virus nucleoprotein (NTAIL), a 125-residue IDP involved in the RNA transcription and replication of measles virus. NTAIL undergoes binding and folding upon encounter with the X domain (XD) of its phosphoprotein binding partner³⁶. Residues 486 to 502 of NTAIL form a so-called α-helical Molecular Recognition Element (αMoRE) and fold into a stable helix upon binding to XD. SAXS studies have shown that NTAIL has a radius of gyration, Rg, of 27.5 ± 0.7 Å which is significantly less than the predicted Rg for a random coil with the same length as NTAIL, 35 – 38 ų⁷, suggesting inter-residue interactions lead to compaction in the free state. A recent study of the effect of the truncation of the disordered N-terminal region of NTAIL on the binding energetics support this hypothesis. A non-monotonic dependence of binding strength on truncation length was observed³⁸, indicating that residues in the disordered N-terminal region of NTAIL contribute to the binding affinity of NTAIL and XD. This work also suggested that the folding of NTAIL upon binding is impeded by the disordered regions flanking the αMoRE. However, the molecular basis of these effects is unclear and the mechanisms behind these unexplained observations cannot be determined using conventional methods. We quantify the effect of three mutations in the unbound state of NTAIL and show that the residues participate in long-range interactions in the unbound state and that these interactions can modulate the binding of NTAIL to its partner. Interactions in the free state are predicted to reduce the affinity of NTAIL for XD, thereby providing a mechanism for tuning binding affinity and biological function. Our approach allows quantitative analysis of these interactions without the need to fully model the IDP ensemble.

This work illustrates that, as computational results become more and more reliable due to advances in force fields and computing hardware, it is possible to develop accurate and precise hybrid methods which rely on experiments and calculations simultaneously to reveal insights that cannot be studied by conventional methods.

Methods

Free energy calculations were performed using non-softcore thermodynamic integration (TI) implemented in Amber as described in detail in the supporting information (see SI). Minimization and equilibration under constant pressure were conducted to heat up and relax the X-ray structures. Production runs were conducted using the implementation of GPU-accelerated thermodynamic integration, pmemdGTI^39–43, under constant volume (see SI). Details of the calculations, including the methods used to account for any changes in protonation state involving mutation of charged residues and details of the analysis of the data are provided in the supporting information.

Results

A Thermodynamic Cycle for Analyzing the Energetics of the Free State of IDPs

We calculate the free energy changes caused by mutations in IDPs by taking a detour through a thermodynamic cycle (Fig. 1). The measurable binding free energy of the wild-type and mutant IDP are combined with high-level TI calculations on the folded complexes to define the energetics of the free state of the IDP. The approach relies on a thermodynamic cycle, in which the values of three branches of the cycle define the value of the fourth (Fig. 1). For example, the effect of changing an alanine to a glycine in the unbound state of an IDP, ΔG_free, can be obtained by ΔG_free = ΔG_bind - ΔG’_bind + ΔG_com. ΔG_bind and ΔG’_bind are the experimental binding free energies of the mutant and wildtype respectively. ΔG_com is the free energy change caused by mutation of Ala to Gly in the complex and is calculated using alchemical free energy calculations. The effect of the mutation in a capped tripeptide or a small fragment, in which the mutated residue is in the middle of the fragment and flanked by the same amino acids found next to the site in the full-length IDP, also needs to be calculated to provide a reference state and is denoted as ΔG_frag. The capped tripeptide is not meant to represent the unbound state of IDP as it ignores secondary structure and long-range interactions. Rather the capped tripeptide is just a necessarily bookkeeping device that accounts for purely local interactions and for the fact that the different sized side chains will make different interactions with water. It is important to reiterate that the capped tripeptide is not used as a model of the IDP, rather the differences in the values of ΔG_free and ΔG_frag denoted as ΔΔG_inter, quantitatively defines the energetic effect of nonlocal interactions that are not present in the peptide model.

Figure 1.

Illustration of the approach used to deduce the energetics of the free IDP. The thermodynamic cycle describes the binding of a wild-type IDP and a mutant IDP to its partner. The capped tripeptide has the same residues adjacent to the mutation site as found in the full protein. ΔG_bind and ΔG’_bind are the binding free energies measured by experiment for wildtype and mutant respectively (red text). ΔG_com and ΔG_frag are calculated using alchemical free energy calculations (blue text). The value for ΔG_free is obtained from ΔG_free = ΔG_bind - ΔG’_bind + ΔG_com. The effect of secondary structure and long-range interactions on the mutations is obtained from ΔΔG_inter = ΔG_free - ΔG_frg. ΔΔG_inter and ΔG_free (green text) cannot be measured by either experiments or calculations alone but can be obtained by combining the experimental and computational measurements.

In principle, the effect of mutations on interactions in the unbound state of IDPs could be directly calculated using alchemical free energy calculations, but such calculations are practically impossible due to the dynamic nature of the free state which leads to insufficient sampling. The approach developed here circumvents this issue by bridging the complex state and the free state using the binding free energies measured by experiments such as isothermal titration calorimetry (ITC), differential scanning calorimetry (DSC), binding kinetic experiments and others. The experimental binding free energies (ΔG_bind and ΔG’_bind) provide relationships between the phase space of the bound and free state of the IDP. This allows the calculated free energy change in the complex state (ΔG_com) to be combined with experimental binding data to deduce the free energy changes in the free state (ΔG_free)

Another Interpretation of the Approach

From another perspective, this approach can be interpreted as a method which obtains the effects of mutations on the free state of IDPs by deconvoluting the experimentally measured binding free energy changes. The values of ΔG_bind and ΔG’_bind are the binding affinities of the wild-type and mutant measured experimentally using techniques such as ITC, DSC, binding kinetic experiments and others. The value of ΔG_bind - ΔG’_bind represents the effect of the mutation on the binding affinity of the IDP and its binding partner. However, ΔG_bind - ΔG’_bind is a convolution of the effect of the mutation on both the complex and free state of the IDP. This is analogous to protein folding where ΔG_mutation contains contributions from the folded and unfolded states. If the effect of the mutation on the free state is to be quantified, ΔG_bind - ΔG’_bind must be deconvoluted. In our approach, ΔG_bind - ΔG’_bind is deconvoluted by calculating the effect of mutation on the complex state (ΔG_com) using free energy calculations. The deconvolution leads to the effect of the mutation on the free state (ΔG_free) of the IDP via a thermodynamic cycle. The resulting value of ΔG_free is another convolution of the purely local and long-range interactions disrupted by the mutation. The calculation using the capped tripeptide (ΔG_frag), which only describes the local interactions, allows further deconvolution of ΔG_free so that the long-range interactions disrupted by the mutation (ΔΔG_inter) can be quantified. One practical consideration is that some IDPs retain disordered tails in the bound state. If necessary, the disordered regions in the bound state can be truncated during the calculation of ΔG_com to increase computational efficiency provided that the disordered regions do not alter the conformation or energetics of the structured regions under investigation in the complex. This is likely to be valid for residues which are buried in the binding interface and sequestered from solvent since they are protected from transient contacts with any disordered segments.

IDP Complexes and Mutation Sites that are Suitable for the Approach

Many IDPs retain a certain degree of so-called “fuzziness” upon binding to their partners and are relatively dynamic even in the bound state. These IDPs may remain partially or even fully flexible upon binding and they can adopt multiple binding conformations^44–48. Similar to the free state of IDPs, calculations of ΔG_com for this type of IDPs are challenging due to the vast conformational ensembles that need to be sampled. However, some IDPs that form a “fuzzy” complex with one of their partners may form a rigid complex with a different partner⁴⁸. Since the energetics of the free state of IDPs are independent of their binding partners and their structures in the complex state, our approach can be applied to any IDP as long as it forms a rigid complex with one of its natural binding partners or an engineered binding partner and the binding free energies can be measured experimentally.

For IDPs that form both structured and disordered regions upon binding, it is easiest to study the residues that belong to the structured regions since large segments of disordered regions are too computationally expensive to model directly. Thus, truncated IDP complexes, with only the structured region, may be used during the calculation of ΔG_com provided certain conditions are met. This approximation requires that the disordered regions do not form strong interactions with the structured regions and do not alter the conformations of the structured regions of the complexes. Moreover, analysis of surface mutations should be avoided if using truncated IDP complexes as they may form transient contacts with the disordered regions in experiments that will be missing during the calculations of ΔG_com using truncated models. There is a significantly smaller possibility of forming direct contacts between buried residues and residues in the disordered regions, so the effect of transient interactions with the disordered regions on these buried residues can be more safely ignored. For the example of the NTAIL/XD complex studied here, residues 486 to 502 of NTAIL form the αMoRE and fold into a stable helix upon binding to XD, but the regions preceding (401–485) and following (503–525) the αMoRE remain disordered upon binding, do not contact the structured region and make at most a small contribution to binding enerergetics^{5, 36, 49–54}.

Ovomucoid Inhibitor Protease Interactions Provide an Excellent System to Validate the Approach

The accurate estimation of ΔG_inter depends on precise and accurate free energy calculations since they are combined with experimental binding affinities to make predictions about the free state. Thus, it is necessary to evaluate critically the accuracy of alchemical free energy calculations and define their limitations. In a previous study, we successfully reproduced the experimentally measured effects of Gly-to-D-Ala substitutions on the unfolding free energy changes in eight proteins using TI calculations with a root-mean-square error of 0.23 kcal/mol²⁸. In this study, using the same force field and solvent model, we further validated the accuracy of our free energy calculations on a more relevant system involving calculations of protein-protein binding energetics. We tested the ability of our protocol to reproduce the experimental binding free energy of OMTKY3 to its target proteases using TI calculations (Fig. 2). This is an excellent model system: high-resolution structures of the free and bound states are available and precise thermodynamic binding data has been reported for multiple mutations^55–57. For the complexes between OMTKY3 and Streptomyces griseus proteinase B (SGPB) (Fig. 2), high-resolution crystal structures for all substitutions at position 18 of OMTKY3 have been reported except Met18 and Cys18^56–57. The perturbations to the structures of the complexes caused by mutation at position 18 of OMTKY3 are minimal. For the 10 variants studied here (OMTKY3/Leu18, Ala18, Gly18, Asn18, Asp18, Val18, Thr18, Ser18, Phe18 and Tyr18), the root-mean-square deviations for the backbone coordinates are at most 0.158 Å (PDB codes listed in SI). The small differences in structures minimize the complexity of the free energy calculations on the bound state of the SGPB/OMTKY3 complex. Furthermore, the mutation site is only partially buried in the complex interface which allows the efficient exchange of water around the side chain during the free energy calculations of complexes. This avoids any complications that might arise from having different numbers of waters in the interface for different side chains. In the unbound state, OMTKY3 is highly stable and the mutation site is located in a short loop with the side chain fully exposed to solvent. These factors make SGPB/OMTKY3 an ideal system for testing the accuracy of free energy calculations. Calculations were also conducted on a Leu-to-Ala mutation in the complex of a different protease, subtilisin Carlsberg (CARL), with OMTKY3 to check if the calculation is sensitive enough to reproduce context-dependent ΔΔG values (reported experimental values of 2.95 kcal/mol for SGPB/OMTKY3 and 0.33 kcal/mol for CARL/OMTKY3) for Leu-to-Ala mutations⁵⁸. This is important because it provides a significant test of context depend effects and because free energy changes for two Leu-to-Ala mutations in NTAIL are studied later. The difference between ΔΔG_exp = (ΔG_bind - ΔG’_bind) and ΔΔG_calc = (ΔG_free - ΔG_com), see free energy cycle in Fig. 2, provides a rigorous test of the accuracy of the free energy calculations.

Figure 2.

Free energy cycle of L-to-A mutations in the binding of SGPB and OMTKY3. Ribbon structures represent SGPB (pink), OMTKY3 (blue) and the SGPB/OMTKY3 complex. Leu18 (top) and Ala18 (bottom) of OMTKY3 are shown in stick format. ΔG values in red are binding free energies measured by experiment⁵⁵. ΔG values in blue are free energies calculated using TI.

The Amber force field ff14SB⁵⁹ and the TIP3P⁶⁰ water model were used for the TI calculations^61–62, with the implementation of GPU-accelerated thermodynamic integration, using pmemdGTI³⁹. In order to test the convergence of the TI calculations, two independent TI calculations were carried out for each X-to-Y substitution in the SGPB/OMTKY3 complex. One calculation started with the structure of SGPB/OMTKY3-X18, and the other calculation started with the structure of SGPB/OMTKY3-Y18. A total of 22 independent TI calculations were carried out.

The calculations show excellent agreement with experiments. All numerical values are provided in Table S2. The mutation involving Asp18 require proper accounting of any changes in the pKa of Asp18 in the complex and free states. The free state pKa is available from NMR measurements⁴³ and the bound state pKa has been estimated from experimental pKa dependent binding free energies⁶³. Details are provided in the SI. The root-mean-square error between ΔΔG_calc and ΔΔG_exp for all mutations was 0.86 kcal/mol (Fig. 3). V-to-A, Y-to-F and S-to-C have more significant errors, with deviations of 1.30 ~ 2.11 kcal/mol respectively from the experimental results, while all other mutations have errors below 0.45 kcal/mol. The probable causes of the larger errors in V-to-A, S-to-C and Y-to-F mutations are discussed in detail in the SI. Briefly, the issue with the S-to-C mutation is likely due to the Lennard-Jones parameters used for sulfur in Amber ff14SB force field. The issue with Y-to-F mutation may be due to a bound water. The V-to-A mutation is an example of a β-branched residue being changed to a non β-branched residue. We have observed problems with other substitutions of this type and believe it may reflect poor transferability between β-branched residue and non β-branched residue in the force field. Excluding these three apparent outliers reduces the root-mean-square error to only 0.27 kcal/mol and gives an even stronger correlation between ΔΔG_calc and ΔΔG_exp with slope = 1.00 and R² = 0.98, p < 10^-13.

Figure 3.

Scatter plot of experimental (ΔΔG_exp) and calculated (ΔΔG_calc) ΔΔG values for the binding of SGPB with different OMTKY3 variants. ΔΔG_exp = ΔG_bind -ΔG’_bind. ΔΔG_calc = ΔG_free - ΔG_com. The point labeled CARL is for the binding of subtilisin Carlsberg with OMTKY3 variants. Blue and orange dots indicate calculated ΔΔG values calculated using different starting structures. For example, the value for the blue dot for A to G was calculated using the structure of SGPB/OMTKY3-Ala18 (PDB code 1SGP) and the value for the orange dot for A to G was calculated using the structure of SGPB/OMTKY3-Gly18 (PDB code 1SGQ). There is no structure for subtilisin Carlsberg/OMTKY3-Ala18 so only one ΔΔG values using the structure of subtilisin Carlsberg/OMTKY3-Leu18 (PDB code 1R0R) was calculated. Similarly, only one ΔΔG value for S-to-C mutation in SGPB/OMTKY3 was calculated. Three outliers, V-to-A, S-to-C and Y-to-F are labeled as crosses. The solid line represents ΔΔG_exp = ΔΔG_calc. The dashed red line indicates the results of the linear regression of the data (y=0.86x+0.31, R²=0.82 p<10⁻⁹).

The precision of the method was tested by carrying out two independent calculations using different starting structures for each mutation (except L-to-A in CARL/OMTKY3 and C-to-S in SGPB/OMTKY3, see caption of Fig. 3). ΔΔG_calc values were essentially identical with an average absolute difference of 0.25 kcal/mol, indicating high precision and good convergence of the calculations. The ΔG_free values estimated by ΔG_free = ΔG_bind - ΔG’_bind + ΔG_com and the ΔG_free values directly calculated by TI calculations are compared in Table S3. Overall, the results demonstrate that the TI calculations are accurate and precise enough to be combined with experimental binding free energies as outlined in Fig. 1 with the exception of the mutations which lead to the outliers.

Application to the NTAIL Domain: Identification of Long-range Interactions

Having validated the approach, we next applied the strategy to the NTAIL domain. Residues 486 to 502 of NTAIL, form the so called α-helical Molecular Recognition Element (αMoRE), and fold into a stable helix upon binding to the XD, thereby forming an intermolecular four-helix bundle complex (Fig. 4)^{36, 49–50}. The αMoRE of NTAIL has residual helicity in the unbound state, but the regions preceding (401–485) and following (503–525) αMoRE have much less residual structure^{5, 49, 51–54}. The regions preceding (401–485) and following (503–525) the αMoRE remain disordered in the bound state and experimental data indicates that they do not form direct contacts with XD in the complex ^{5, 36, 49–54}. In addition, ITC and surface plasmon resonance experiments indicate that the regions following the αMoRE of NTAIL make only minimal contributions to the binding between NTAIL and XD^64–65. This data suggests that the disordered regions of NTAIL/XD complex do not alter the conformations of the structured region formed by the αMoRE and XD. Mutations of three residues which are buried in the complex, A494G, L495A and L498A, are examined in this study. A494, L495 and L498 are within the αMoRE region of NTAIL and located in the interface of NTAIL/XD complex (Fig. 4). Since A494, L495 and L498 are buried in the interface of NTAIL/XD complex, it is unlikely that the truncated disordered regions make contact with these residues in the complex.

Figure 4.

Ribbon representation of the NTAIL (486–504)/XD (458–506) complex from the X-ray structure (PDB code 1T6O). The X-ray structure includes the region shown in ribbons, and an artificial linker which was deleted in simulations and is not shown in this figure. Residue A494, L495 and L498 are shown in stick format. The disordered N and C-terminal regions of NTAIL were not included in the X-ray structure and MD simulations and are depicted schematically as thin lines.

The binding free energy changes (ΔG_bind - ΔG’_bind) caused by the A494G, L495A and L498A mutations have been reported⁶⁶. The free energy changes caused by the mutations (ΔG_com) in the NTAIL/XD complex were calculated using the X-ray structure (PDB code 1T6O) and the protocol that we validated with the SGPB/OMTKY3 complexes. In order to check the convergence of the calculations of ΔG_com, two independent TI calculations for each mutation were conducted. One started with the X-ray structure which is the structure of the wild-type NTAIL/XD complex and proceeded toward the mutant. Only the structure of the wild-type NTAIL/XD complex is available, so the second starting structure was a model of the mutant complex. In silico mutations of A494G, L495A and L498A were applied to the X-ray structure of NTAIL/XD complex and a 100ns MD simulation for each mutant was conducted to relax any perturbation caused by the mutations. The TI calculations were performed starting with the structure from the last frame of the MD simulation of the mutant complex and proceeded in reverse to the wild-type complex. The forward and reverse calculations were in excellent agreement with differences ranging from only 0.06 to 0.36 kcal/mol (Table 1).

Table 1.

Free energy changes (kcal/mol) calculated for A494G, L495A and L498A mutations in the complex, free, capped tripeptide fragment and fully helical state of NTAIL. The calculated ΔG values are referenced to the values of their corresponding ΔG_frag. The original values are listed in the parenthesis. The original ΔG values have no physical meaning because they contain a force field dependent baseline. The referenced ΔG does have physical meanings as the force field dependent baseline effect is canceled.

	Forward ΔGcom	Backward ΔGcom	ΔGinter 1	ΔGfrag 2	ΔGhelix 2
A494G	2.36 (−6.87)	2.22 (−7.01)	1.59±0.13 (−7.64±0.12)	0 (−9.23±0.04)	1.22±0.08 (−8.01±0.07)
L495A	5.09 (23.75)	4.73 (23.39)	3.81±0.21 (22.47±0.21)	0 (18.66±0.04)	0.81±0.16 (19.47±0.15)
L498A	2.26 (20.05)	2.09 (19.87)	0.77±0.16 (18.56±0.13)	0 (17.79±0.09)	0.42±0.10 (18.21±0.05)

^1.The uncertainties are calculated by combining the standard deviation of ΔG_com with the published standard deviation of (ΔG_bind - ΔG’_bind)⁶⁶.

^2.The uncertainties are the standard deviation of three independent runs of MD simulations with different starting velocities.

The free energy changes caused by the mutations in the free state of NTAIL (ΔG_free) are all significantly higher than the free energy changes in the capped tripeptide reference state (ΔG_frag) with differences ranging from 0.8 to 3.8 kcal/mol (Table 1). This indicates that the residues are involved in interactions in the free state which are not captured by the capped tripeptide reference state. In other words, these residues are involved in secondary structure or long-range interactions, or both in the free state.

Because the αMoREs region was experimentally found to have residual helicity in the free state of NTAIL^{5, 49, 51–54}, we also examined whether the difference between ΔG_free and ΔG_frag could be explained by helicity rather than long-range interactions in the unbound (IDP) state. TI calculations were repeated using a fully helical conformation of unbound NTAIL (486–504) monomer (ΔG_helix). The structure was adopted from the PDB code 1T6O by deleting the XD domain and the artificial linker. If the contributions from the long-range interactions are negligible, then the free energy changes caused by the mutations in the free state of NTAIL (ΔG_free) should be between those of ΔG_frag and ΔG_helix depending on the fraction of helicity adopted in the free IDP. However, we found that ΔG_free values are still higher than the ΔG_helix values, especially for the L495A mutations. This argues that any propensity to adopt helical structure cannot explain the ΔG_free values, and that A494, L495 and L498 are all involved in favorable long-range interactions in the free state of NTAIL. This is especially notable at position 495, where the long-range interactions favor leucine over alanine.

Discussion

In this work, we have validated a hybrid strategy to measure quantitatively the free energy changes caused by mutations in the free state of IDPs, which cannot be measured directly using conventional experimental or computational techniques. A possible limitation of the strategy is that the IDP must form a structured complex with its receptor and many IDPs remain “fuzzy” upon binding^44–48. However, since the energetics of the free state of an IDP are independent of its binding partner, this approach can still be applied to the IDP if it folds upon binding to one a different natural binding partner or an engineered molecule. Another potential limitation is that for IDPs that remain partly disordered upon binding, the truncation of the disordered regions, which is ideal for the calculations of ΔG_com, is only rigorous if the disordered regions have minimal interactions with the structured regions. Ideally, the residues of interest will be buried in the complex to avoid transient long-range interactions with disordered regions of the bound complex that complicate the modeling. Fortunately, residues in the binding interface are usually buried and these are often of major interest since residues in the interface normally contribute the most to the binding affinity of a complex. Studying their interactions in the unbound IDP can provide quantitative information about the properties at the free state and about the possible roles of any free state interactions in the regulation of biological activity.

Our free energy calculations on SGPB/OMTKY3 complexes show that the free energy changes caused by most mutations can be reproduced with high precession and within a small error. Although the outliers V-to-A, C-to-S and Y-to-F were identified in our calculations, the validation included L, I, F, and A, which are the four most commonly observed amino acids in the binding interface between IDPs and their binding partners^67–69. On average, about 40% of the residues in the binding interface are one of these four residues⁶⁹. This indicates that the approach should be broadly applicable to folding upon binding IDPs. Since the approach relies on accurate calculations of free energy, the sampling convergence of the free energy calculations must be considered carefully⁷⁰. For example, buried mutations may cause displacement of interior water which usually has a slow relaxation beyond the timescale of MD simulations⁷¹. However, new algorithms have been developed to address the limitations of sampling in free energy calculations^72–74. We believe that as the reliability of these calculations continues to improve, the impact of our approach will increase.

Our analysis shows that A494, L495 and L498, which form part of the binding interface of NTAIL and XD, participate in favorable long-range interactions in the free state of NTAIL that modulate the binding affinity of NTAIL to XD. The strength of the long-range interactions made by A494 and L498 in the free state of NTAIL range from 0.3 to 1.6 kcal/mol depending on the helicity of A494 and L498. If NTAIL were to exist as a true random coil in its free state, then L495 would be 4.9 kcal/mol more favorable than A495 in the complex of NTAIL/XD. Even if L495 is in a fully helical structure in the free state of NTAIL, L495 is predicted to be > 4.1 kcal/mol more favorable than A495 in the complex state. However, the experimentally measured binding free energy change indicates that L495 is only 1.1 kcal/mol more favored than A495 in the complex. The difference can be explained by favorable long-range interactions experienced by L495 in the free state of NTAIL, which compete with the binding interactions involving L495. Stated differently, the interactions in the free state modulate the binding energetics and are predicted to reduce affinity. This provides an important mechanism for tuning binding affinity. The insights revealed by our approach correlate well with prior observations on NTAIL and illustrate that long-range interactions between the flanking disordered regions and the αMoRE can modulate the overall dimensions of NTAIL and the NTAIL/XD binding free energy.

It may be surprising that the interactions in NTAIL appear to favor L495 more than A495 by as much as 3.0 ~ 3.8 kcal/mol. However, if such interactions are responsible for inhibiting the aggregation of proteins^{22, 75}, then they should be reasonably strong. In addition, the full free energy contribution is very unlikely to arise from a pairwise interaction, instead it is highly likely that the residue in question makes interactions with more than one other residue in the free state, or that the mutation alters the unfolded state and thereby modulates multiple other interactions.

The identified long-range interactions identified in NTAIL may play a biological role. Dynamic binding and breaking of the nucleocapsid and polymerase are necessary to ensure the transcription and replication of the RNA encapsulated by nucleocapsids and the affinity needs to be tuned for optimal activity. Increasing and decreasing the binding affinity of NTAIL/XD both lead to a reduction in transcription activity and viral growth^76–77, so a balanced interaction between NTAIL and XD is crucial. The long-range interactions involving A494, L495 and L498 in the free state attenuate the binding affinity to reach an optimal efficiency of transcription and replication. This provides a clear example of how interactions within the free state of an IDP can tune biological activities.

Conclusions

This work offers a general methodology for assessing the energetic contributions of individual residues in IDPs to the energetics of the free state of IDPs. The approach allows the identification of residues that participate in long-range interactions and thus may modulate binding affinity, but avoids the difficulties associated with MD simulations of free IDPs. The approach described here is complimentary to methods that generate ensemble level descriptions of residual structure and transient contacts in the free state of IDPs as it provides information about the energetics of specific residues in the free state. Combining energetic information with structural descriptions will provide more insight into the properties of IDPs.

Many IDPs become structured upon binding^78–79, thus the strategy is expected to be broadly applicable and will become even easier to apply as computing power continues to increase. The work with the OMTKY3 and its binding partners also provides a rigorous evaluation of the accuracy and precision of TI calculations performed using the Amber ff14SB force field. The work also illustrates how IT calculations can be used to help validate force fields. This work demonstrates that advances in force fields and computing hardware have now led to the point where it is possible to develop novel methods which integrate experimental and computational techniques to reveal insights that cannot be studied by using either technique alone. The interactions and effects revealed by the analysis presented here could not be deduced from experiment and computation in isolation.