Cooperative mechanics of PR65 scaffold underlies the allosteric regulation of the phosphatase PP2A

Summary

PR65, a horseshoe-shaped scaffold composed of 15 HEAT repeats, forms, together with catalytic and regulatory subunits, the heterotrimeric protein phosphatase PP2A. We examined the role of PR65 in enabling PP2A enzymatic activity with computations at various levels of complexity, including hybrid approaches that combine full atomic and elastic network models. Our study points to the high flexibility of this scaffold allowing for end-to-end distance fluctuations of 40–50 Å between compact and extended conformations. Notably, the intrinsic dynamics of PR65 facilitates complexation with the catalytic subunit and is retained in the PP2A complex enabling PR65 to engage the two domains of the catalytic subunit and provide the mechanical framework for enzymatic activity, with support from the regulatory subunit. In particular, the intra-repeat coils at the C-terminal arm play an important role in allosterically mediating the collective dynamics of PP2A, pointing to target sites for modulating PR65 function.

eTOC blurb

Kaynak et al. shows that the repeat protein PR65 plays a critical role in mediating the catalytic activity and interactions of PP2A whose dysregulation is implicated in human cancers. The study demonstrates the unique ability of PR65 architecture to adapt to functional changes in conformation and to mechanical stress.

Graphical Abstract

Introduction

Around one third of human proteins contain units of varying size and secondary and tertiary structural composition, repeated in tandem ¹. Tandem-repeat proteins like ankyrin, tetratricopeptide and HEAT (observed in Huntingtin, elongation factor 3 (EF3), protein phosphatase 2A (PP2A), and the yeast kinase TOR1) repeats have highly versatile three-dimensional shapes arising from the stacking of small secondary-structure motifs of 20–40 amino acids into both quasi-one-dimensional arrays and circular forms.

Repeat proteins have been the subject of intensive study, as their simple architectures make them strikingly amenable to the dissection and redesign of their biophysical properties with potential for exploitation in biotechnology and medicine ^2–6. Helical repeat proteins look like springs and indeed are flexible molecules with spring-like properties ^7–18. Their flexibility is thought to be crucial to their function, though our understanding of how these structures direct functions is limited. Distantly located repeats fold cooperatively, even though the only contacts in these proteins are short-range ones ^19–21. Function may also be transmitted at a distance with allosteric effects, transferred through the repeat array.

Here we explore the conformational mechanics of the HEAT-repeat protein PR65, the elastic ‘connector’ subunit of PP2A. PP2A is a heterotrimeric Ser/Tyr phosphatase that regulates diverse cellular activities ²². PP2A dysregulation is associated with many types of cancer and other diseases ²³, hence the targeting of PP2A for developing therapeutics ²⁴. The PR65 scaffold (A) and catalytic (C) subunits form the core of the enzyme. Enzymatic activity is controlled by binding of different regulatory (B) subunits. Figure 1A displays the PP2A holoenzyme ²² where PR65 (Aα isoform; cyan surface) forms a scaffold for recruiting the catalytic (Cα isoform; yellow cartoon) and B56 regulatory (γ1; purple cartoon) subunits on the same side. PR65 in apo state ²⁵ (magenta) undergoes a significant conformational change during complexation (Figure 1B). PR65 consists of 15 HEAT-tandem repeats of two anti-parallel helices each (see Figure 1C). Here, the B56γ1 subunit is composed of eight pseudo-HEAT repeats.

Figure 1. PP2A complex and the PR65 scaffold.

(A) PP2A heterotrimer structure and its conformational flexibility. PP2A is composed of three subunits, PR65 (cyan), catalytic (yellow), and regulatory (purple) subunits, and PR65 is composed of 15 HEAT repeats, illustrated in panel C. The Protein Data Bank (PDB) structure (PDB id: 2iae) also contains a peptide (blue sticks) bound to the catalytic subunit. (B) Extended and compact conformations of the PR65 scaffold. The extended conformation is observed in the apo state of PR65 (PDB id: 1b3u). The distance between the 𝐶^α-atoms of N30 and Y577 (d_1–15) indicates an increase of > 25 Å (from 45.9 to 72.7 Å) as the repeats 13–15 move out in the extended structure relative to their position observed in PP2A complex. In contrast, the distance between inner repeats 5 and 11 (black dashed line, d_5–11) does not change significantly. (C) The HEAT motif: The N-terminal helix lines the inner surface of the PR65 horseshoe-like scaffold, and the C-terminal helix lies at the outer surface. A network of hydrophobic contacts stabilizes the motif.

In previous work by Grinthal et al. ¹¹, 2 ns molecular dynamics (MD) simulations were performed by applying a constant uniaxial tension or compression at the two ends of PR65. In the low force regime, application of a series of fixed forces up to 150 pN during tension experiments (or ≤ 70 pN during compression) led to gradual extension (or contraction) of the scaffold until it reached an equilibrium end-to-end distance dependent on the exerted force; and to return almost reversibly to its original state upon release of the force. At higher forces, on the other hand, the system could not recover its original shape, indicating that there were irreversible changes, e.g., disruptions at specific helix-helix interfaces or fractures at interhelix turns, which underlie the viscoelastic behavior of PR65.

In the first part of our study, we elucidate the intrinsic dynamics of PR65 and its complexes in solution (closer to in vivo conditions) without the application of any external forces. We performed simulations at various levels of complexity, including MD, elastic network model (ENM) analyses ²⁶, and a hybrid approach (ClustENMD) ^27,28 for conformational sampling. We demonstrate that the apo PR65 scaffold is extremely flexible with its arms opening/closing by 30–40Å multiple times during 200 ns runs. This intrinsic elasticity is also evident and consistent with the global modes of motion (the lowest frequency modes, also called soft modes) deduced from either ENM-based or full-atomic normal mode analyses (NMAs). We obtain a clear picture on the broadening of mode frequencies due the conformational variability of PR65 by performing ENM analyses on multiple MD snapshots. Our hybrid simulations elucidate how complexation with the catalytic and regulatory subunits alters the conformational dynamics of the scaffold. We further demonstrated that the global modes intrinsically accessible to PR65, predicted by ENM, facilitate the PR65 conformational changes occurring upon formation of the core enzyme (AC complex), and those accessible to AC favor its conformation selected in the PP2A trimer.

In the second part, we characterize the response of PR65 to stress toward understanding its mechanical behavior in the apo form and in the PP2A complex using our ENM-based tool MechStiff ²⁹. We identified the critical sites that endow those mechanical properties, and we point to the correlation between residue-based stiffness profile and evolutionary conservation across the scaffold. These findings underline the functional importance of the mechanical properties of the PR65 scaffold, and they reveal the critical sites that can be subjected to ligand binding for customized modulation of function.

Results

Large fluctuations in PR65 end-to-end distance mainly result from the reconfiguration of the HEAT repeats 1–4 and 12–15.

The end-to-end distance of the PR65 scaffold is a natural metric for analyzing its conformational dynamics and flexibility. However, the N-terminal helix, belonging to the first HEAT repeat unit, is unfolded in the PP2A complex considered in the present study, as indicated by the yellow arrow in Figure 1B. To avoid the variability resulting from this unstructured region, we monitor the distance (d_1–15) between the C^α-atoms of N30 and Y577, on the inward-facing helices of repeats 1 and 15, respectively. The PR65 arms extend more than 25 Å away as the scaffold reconfigures from compact (chain A in PP2A, d_1–15 = 45.9 Å) to extended (apo, d_1–15 = 72.7 Å) state, as shown in Figure 1B.

Figure 2A displays the time evolution of this distance d_1–15 during the four MD simulations, initiated from compact (C1 and C2) and extended (E1 and E2) conformers. Notably, the scaffold fluctuates between the compact and extended states multiple times during these runs (of 200 ns, each). The median for d_1–15 is 67.4 Å in C1, 54.9 Å in C2, 79.6 Å in E1 and 75.9 Å in E2, indicating that extended conformers are sampled more readily in all runs presumably due to an entropic effect in favor of the extended form. The d_1–15 distance can occasionally exceed 90 Å, which is appreciably larger than that observed in the apo crystal structure (72.7 Å).

Figure 2. Dynamics of PR65.

(A) Fluctuations in PR65 inter-repeat distances, d_1–15 and d_5–11, during MD simulations. The top panel refers to the runs C1 and C2 with the compact conformer of PR65 used as input (see the distances around 45Å at t = 0), and the bottom panel to those, E1 and E2, conducted using the extended conformer. d_1–15 shows large fluctuations in both cases. The compact form approaches the extended form within the time scale (200 ns) of simulations, whereas the extended form fluctuates in the range 60–90Å. The inner distance d_5–11 exhibits minimal fluctuations in both cases. (B) Global modes of motion predicted by the ANM. The slowest four modes are shown for the compact conformer by color-coded ribbon diagrams. Blue regions exhibit minimal displacements; yellow-green regions undergo large displacements along the directions indicated by the arrows. (C) Distribution of ANM eigenvalues based on 2,000 snapshots from MD run C2. Mode frequencies are spread/broadened due to the conformational fluctuations. The first four modes’ frequencies display well-separated Gaussian distributions. In contrast, the higher modes (see inset) display broader and partially overlapping distributions. Black vertical bars at the center of the histograms represent the corresponding medians. The labeled frequencies are obtained after rescaling ANM frequencies with respect to those from full-atomic NMA in panel E. (D) Overlap matrix (correlation cosines) between the first 10 modes from atomic NMA and those from ANM. (E) NMA vs ANM frequencies of the first 300 modes for compact PR65. Red line is fitted to the first 20 modes with R² > 0.99. See the counterpart of E for all four conformers in Supplementary Figure S2A.

The second distance plotted in Figure 2A is d_5–11 between the inward-facing helices on the respective repeats 5 and 11, specifically between M180 and R418 C^α-atoms. In contrast to d_1–15, d_5–11 fluctuates within a narrow band, consistent with the original d_5–11 of 44.7 Å and 48.4 Å by the compact and extended crystal structures, respectively. Thus, the central repeats between 5 and 11 tend to preserve their original curvature in all runs (see also Figure 1B). The overall picture that emerges from our MD simulations is that the central part of the scaffold (repeats 5–11) closely maintains its overall conformation, while the outer four repeats on both sides (repeats 1–4 and 12–15) are highly flexible and their cooperative reconfigurations underlie the opening and closing of the scaffold.

The ability of PR65 to undergo large end-to-end distance fluctuations is endowed by its global modes of motion uniquely defined by its tandem-repeat architecture

Previous studies have repeatedly shown the significance of low-frequency modes, also called global modes, predicted by anisotropic network model (ANM), in supporting biological function ^30,31. Figure 2B illustrates the first four global modes predicted for PR65 using its compact conformer in PP2A (PDB id: 2iae) ²², and Supplementary Movie S1 displays the first three modes of the compact and extended forms of PR65. The diagrams are color-coded by the displacements of the residues, from blue (most rigid) to yellow (most flexible), and the vectors indicate the direction and size of displacements for relatively mobile residues. The three repeats at the N- and C-termini constitute the most mobile regions of the horseshoe, as clearly observed in the first mode. The high mobility of the arms and the restrictions on the central part of PR65 are consistent with the large changes in d_1–15 and the relatively limited fluctuations in d_5–11 observed in MD runs.

Each of the first four modes illustrated in Figure 2B describes a cooperative mechanism of motion: in-plane stretching/compression that induces an overall extension/contraction (mode 1), opposite direction out-of-plane up and down movements of the arms accompanied by slight rotations (mode 2) as best viewed from the side, smaller amplitude in-plane undulating/twisting motions of subsets of repeats (mode 3), and concerted rolling of the ends (mode 4). Previously, Grinthal et al. ¹¹ have performed classical NMA on the extended, apo conformer of PR65 (PDB id: 1b3u) ²⁵. They defined the first two modes as ‘uniform, in-plane increase and decrease in the overall curvature’ and ‘overall twisting motion distributed uniformly along the length of the structure’, respectively, consistent with the present predictions based on the compact form. Corresponding mode frequencies were reported as 11.1 and 24.3 GHz. They also showed that these two modes cumulatively accounted for a large extent of the conformational changes between the extended and compact conformers. The contributions of the individual ANM modes (1 ≤ k ≤ 10) to the overall dynamics computed here are presented in the Supplementary Figure S1. The bar plot shows that the first mode accounts for 34% of the PR65 dynamics in the compact form, and 38% in the extended form; and the 2^nd mode 13.2 and 10.3%, respectively, and the cumulative contribution of the first three modes is above 50% in both forms.

Our analysis therefore shows that the ability of PR65 to undergo large (~30Å) distance fluctuations between its ends is encoded in its architecture that favors (as the softest or lowest frequency modes) such coupled opening/closing of the two ends, and especially 3–4 repeat units at both ends. These regions are distinguished by their high mobility in global modes 1–4, which assist in the cooperative rearrangements that are apparently used for stabilizing the trimeric phosphatase. Thus, the global movements are not uniformly distributed over all repeats but affect the terminal repeats more strongly than the inner ones.

MD snapshots combined with ANM analysis permit us to evaluate the broadening of the dispersion of collective modes’ frequencies

We performed classical NMA, using as input snapshots selected from the MD runs C1, C2, E1 and E2. Supplementary Table S1 lists the frequencies of the first four normal modes computed for each case. The frequencies of the extended conformers are higher than those of the compact conformers in general, indicating that the structure is more strained/relaxed in the extended/compact form. Given that the mode frequencies may be sensitive to variations in conformations, which presumably underlie the broadening effect in experimentally observed histograms of vibrational frequencies, we performed an ANM analysis for a large ensemble of conformers sampled during the four MD simulations. Such an extensive analysis is supported by the computational efficiency of ANM, as ANM analysis does not require any energy minimization prior to spectral decomposition and yields a unique analytical solution for each conformer. Figure 2C overlays the resulting histograms for the global modes sampled in run C2. Even though this run starts from the compact conformer, it also visits the extended state several times during 200 ns (blue curve in Figure 2A upper panel). Thus, the conformational variability of the scaffold results in the broadening of the ANM frequencies. This broadening effect becomes more pronounced as the mode index increases. While the distributions for the first four modes are well-separated distributions of those of the higher modes are not. The increasingly higher overlaps between the frequency ranges of modes 5–8 can be seen in the inset.

PR65 cooperative mechanisms of motions and their frequency dispersion captured by elastic network models show agreement with those inferred from full atomic NMA

Next, we examined to what extent the shapes of the ANM global modes were similar to those obtained by classical NMA. These mode-mode similarities were assessed by generating the correlation cosines between the top 10 modes, presented in Figure 2D for the compact conformer. The first four modes are robustly maintained (correlation cosine > 0.90) and modes 6–10 exhibit high correlation (while the orders of modes 8 and 9 are swapped). ANM mode 5 shows a moderate correlation with its NMA counterpart; however, its correlation cosine (of 0.6 with NMA mode 5) is significantly enhanced by the contributions of NMA modes 6–7 suggesting that this normal mode is represented by the partial contribution of these three modes. This analysis consistently reveals that the same global modes are reproduced, irrespective of the resolution of the spectral analysis.

As a further analysis, we examined the frequencies of global modes obtained by ANM and classical NMA. Figure 2E displays the comparison for the top-ranking 300 modes (each represented by a dot). It is important to note that the higher resolution (and the use of full-fledge force field) of atomic NMA does not affect the low frequency end of the mode spectrum, e.g., the top ranking 20 modes, which, in principle, refer to collective movements of substructures are insensitive to atomic details and precise interactions. This permits us to deduce from the fixed slope of this plot in this regime the proportionality constant to evaluate the ANM frequencies (proportional to λ_k^1/2 for mode k) in GHz. The inset shows this linear relationship which yields a value of γ = 0.31 kcal/(mol. Ų) = 0.22 N/m for the ANM inter-residue spring constant, using Eq. 4 in Supplementary Methods. The median frequencies written in Figure 2C for modes 1–4 are obtained using this force constant in the ANM.

Note that γ is a local property dependent on the tightness of associations between residue pairs in the folded protein, and as such, it is expected to show little dependence on the global conformation, hence the minimal differences in the slopes of the curves for compact and extended conformers as illustrated in Figure S2A. In fact, rescaling of γ based on the NMA frequencies obtained for the conformers C1, C2, E1 and E2 yield the value of γ = 0.312 ± 0.019 kcal/(mol. Ų) for PR65 (see Figure S2A and Supplemental Information). The value of γ is often predicted by comparison with experimental B-factors using Eq. 3. If we use the experimental data for extended apo structure of PR65, we obtain γ = 0.915 kcal/(mol.Ų); whereas using 14 experimentally measured B-factors extracted from the PDB files including complexes yields γ = 0.456 ± 0.139 kcal/(mol.Ų).

While the force constant is a material property independent of the overall conformation, the frequencies of the global modes (i.e. eigenvalues of the ANM Hessian) as well as the mode shapes (eigenvectors) depend on the overall conformation. Supplementary Figure S2 panel B-E displays the frequencies of ANM global modes (1 ≤ k ≤ 20) for the two extended and two compact conformers, showing (i) the close reproducibility of the results between the two extended forms (in accord with full atomic NMA), as well as that between the two compact forms; and (ii) the differences between the operating frequencies in the extended and compact forms (see also Table S1), the frequencies of the extended (more strained) conformers being higher in general. Likewise, the mode-mode overlap heat map in Supplementary Figure S3 panel A shows that the shapes of the modes accessible to the two forms gradually differentiate as higher modes are considered; whereas the lowest frequency three modes are robustly shared between the two forms (see also Supplementary Movie S1). Overall, this analysis confirms the robustness of global modes of motion intrinsically accessible to PR65 scaffold, the functional significance of which will be clear in the context of the dynamics of PP2A.

Binding of the catalytic subunit reinstates the regular dynamics of C-terminal HEAT repeats of PR65, whereas binding of the regulatory subunit enhances the cooperativity across PR65

To compare the global dynamics of PR65 in its isolated unbound form and in complex with regulatory subunit B and catalytic subunit C, we performed ClustENMD runs for PP2A heterotrimer (PDB id: 2iae, chains A, B and C), isolated PR65 (chain A) and the dimer of PR65 and the catalytic subunit (chains A and C, extracted from trimer). These hybrid simulations are highly efficient, e.g., ClustENMD run takes 20 min compared to 8 days for a 100 ns MD simulation of PR65. The conformational space predicted by ClustENMD shows a high correlation with experiments (for molecular systems resolved in multiple conformational states)³².

The mean-square fluctuation (MSF) profiles of amino acids of the three systems (referred to as A, AC and ABC) are plotted in Figure 3 (top panel) based on 600 conformers generated by ClustENMD for each system. In all cases, the mobility increases towards the ends of the PR65 scaffold. The oscillatory behavior of PR65 reflects the 15 HEAT-repeat architecture of PR65: peaks occur at the inter-repeat loops, and minima at the intra-repeat turns and C-terminal helices of the helix-turn-helix repeats which face the horseshoe interior. The fluctuations at the N-terminus are highly consistent with the unwinding of the terminal helix. The high fluctuations at the C-terminal arm, on the other hand, originate from an inherent conformational variability intrinsic to repeats 12–15. The fluctuation behavior of these repeats (highlighted in the semi-transparent green box) is distinguished from all others as the regular pattern of minima and maxima is disrupted. Notably, binding of the catalytic subunit near repeats 12–15 (see Fig 1A) restores the regular pattern, as the comparison of the blue (A) and cyan (AC complex) curves reveals (PR65 makes close contacts with the catalytic subunit at repeat 12). This regular pattern persists in the trimer also (ABC, red curve), where the binding of the regulatory subunit (B) does not alter the dynamics of the C-terminal arm but induces an increased mobility at the central part of the scaffold (enclosed in the yellow box in the figure) especially at the outer helices of repeats 9 and 10 and overall strengthens the communication (that propagates via fluctuations) across neighboring repeats. The bottom panel shows the ribbon diagrams for the three cases, color-coded by residue MSFs. The diagrams clearly show the most mobile regions (red), and the higher mobility of the outer helices of the repeats compared to their inner helices.

Figure 3. Comparison of residue mobilities in PR65 and its complexes based on ClustENMD simulations.

Panel A shows the residue MSFs in the runs performed for unbound PR65 (blue curve), the dimer AC (PR65 and catalytic C subunit; cyan), and the heterotrimer ABC (red). HEAT repeat numbers are indicated for some of the repeats in PR65. Panel B presents each structure as color-coded diagrams based on MSFs. Binding of the regulatory subunit (chain B in ABC complex) increases the fluctuations in the middle of the PR65 scaffold (yellow box in the top panel, while repeats 12–16 gets ordered upon binding the catalytic subunit (see the light-green box).

The regulatory subunit of PP2A allosterically couples the PR65 C- and N-terminal arms to the catalytic subunit domains 1 and 2 to support enzymatic mechanics

Results from further analysis of PR65 global dynamics in the isolated form (A), in the complex with the catalytic subunit (AC) and in the trimeric PP2A are presented in Figure 4. Heat maps in panels A-C show the orientational cross-correlation between residue motions, computed for the PR65 alone, PR65 in the dimer with the catalytic subunit, and PR65 in the trimer, respectively. Panels D and E display the cross-correlations for the entire dimer and trimer, respectively. The black lines separate the individual subunits, and the chain identifiers and residue numbers are provided along the abscissa and ordinate.

Figure 4. Residue cross-correlations based on ClustENMD conformers.

A-C Cross-correlation maps for PR65 along (A), PR65 in the dimer AC (B) and PR65 in ABC (C). D and E display the cross-correlations for AC and ABC, respectively. Subunits are separated by black lines. Cross-correlations are based on all conformers/simulations also reported in Figure 3. Panel F shows the two domains (orange and lime, surface representation) of the catalytic subunit bound to the PR65 scaffold (cyan) and regulatory subunit (purple). A peptide (blue sticks) and metal ions (red sphere) are located at the catalytic cleft between the two domains.

In the isolated PR65 (panel A), there are two equally sized (red) blocks at the N- and C-termini, both corresponding to four repeat units. These positively correlated blocks along the diagonal reflect the concerted internal movements of the subsets of four repeat units at each end, and the off-diagonal blue blocks show that the two subsets correlate but fluctuate in opposite directions (they are anticorrelated). The anticorrelated movements are consistent with the stretching/contraction observed in mode 1 in Figure 2B - indicating the dominant effect of mode 1. The middle part presents a narrower band of positive correlations compared to the two terminal blocks of four repeats.

Comparison of Figure 4 panels A and B shows that the repetitive pattern of the repeat units, especially that of C-terminal units, becomes more pronounced upon binding the catalytic subunit. We also note that PR65 in this dimeric form (AC) exhibits anticorrelated movements between consecutive blocks of 3–4 repeats. These observations are consistent with the coupled movements predicted in in mode 3 (Figure 2B). In the heterotrimer (panel C), there is an overall strengthening in the cooperativity of the adjacent HEAT repeats across the scaffold (evidenced by the widened red band along the diagonal). This may facilitate the allosteric signal transduction across the scaffold. The concerted motions of the N-terminal repeats 1–4 propagate to the near neighbors in the N-terminal half of PR65, up to repeat 10, while the C-terminal repeats 12–15 are distinguished by accentuated anticorrelated (blue) movements with respect to the rest of the scaffold. Thus, binding of the regulatory subunit significantly impacts the cross-correlations between the residues of the scaffold, increasing the overall correlations along the scaffold, and engaging the central repeats to coherently propagate signals, as also hinted by Figure 5A.

Figure 5. The conformational transitions of the scaffold A and of the core enzyme AC are enabled by the global modes of motion.

(A) Superposition of A in the extended apo PR65 (grey; PDB ID: 1b3u) and PR65 in the complex AC (blue; PDB ID: 2ie3). Red lines indicate the deformation vector between the two conformers (B) The overlap (correlation cosine) between the first 20 ANM modes of apo PR65 with the deformation vector in (A). (C-D) Same as A-B, for the deformation of AC from the core enzyme (PR65 in blue and catalytic subunit C in yellow; PDB ID: 2ie3) to AC in the PP2A trimer (PR65 in grey and catalytic subunit C in orange; PDB ID: 2iae). The cumulative overlap in (B) and (D) is shown by the blue line with dots.

Notably, in the dimeric complex (Fig 4D), the catalytic subunit is divided into two internally correlated domains, dom1 and dom2, illustrated in panel F; dom1 binds to the C-terminal arm of PR65 and its movements are correlated with those of the C-terminal arm and anticorrelated with the N-terminal arm. Upon binding of the regulatory subunit (panel E), the anticorrelated movements of the N-terminal arm with respect to dom1 spread to a larger portion (up to repeat 10) of the scaffold. Thus, a strong cooperativity is induced which encompasses repeats 1–10, and the N-terminal arm moves in concert with dom2 of the catalytic subunit even though it does not make direct contacts. The regulatory subunit thus serves as an allosteric agent strengthening the cooperativity of almost the entire scaffold, with repeat unit 11 acting as a hinge site. Notably, dom1 continues to be coupled to the C-terminal arm with which it makes direct contacts.

Overall, this analysis highlights the importance of the regulatory subunit for inducing a high cooperativity across HEAT repeats 1–10 of PR65, accentuating the anticorrelated movements of C-terminal repeats 12–15 with respect to the rest of the scaffold, and enhancing the correlated movements of the C-terminal repeats with dom1 and the N-terminal repeats with dom2. This type of allosteric coupling of both ends of PR65 to the two domains of the catalytic subunit, mediated by the regulatory subunit, may be essential to facilitating the opening/closing of the catalytic cleft in tandem with the stretching/contraction of PR65 in its intrinsically accessible (global) mode 1.

Further investigation of the collective dynamics of PP2A verified that the global stretching/contraction mode of PR65 is retained as the softest mode of the trimer (see Supplementary Figure S3B). Notably, the same mode operates almost invariably in both the compact and extended forms of PR65, indeed providing a path for the passage between these two forms (Figure S3, panel A). Furthermore, Figure S3B shows that the first five modes intrinsically accessible to PR65 are operational in the trimer (the fourth being represented by a combination of a few slow modes of the trimer). In particular, the global modes 2 and 5 closely retain their identity in the trimer (with a correlation cosine > 0.77). Note that in the 3N-dimensional space of modes, this is an enrichment of several orders of magnitude compared to the random correlation cosine of (3N)^−1/2, where N is the number of residues/nodes in the ANM.

Supplementary Movie S2 illustrates the first (lowest frequency) mode accessible to the trimer, where the scaffold retains its intrinsically accessible stretching/contraction (mode 1 in Figure 2B) now engaging the catalytic subunit, supported by the regulatory subunit.

Global modes enable the conformational transition of PR65 to form the core enzyme AC, and that of AC to bind the regulatory subunit B to form the full ABC complex

As the flexible scaffold undergoes complexation with different partners, we examined whether the global modes facilitate its conformational transitions. First, we investigated the transition of the apo PR65 (1b3u) upon binding the catalytic subunit to form the so-called core enzyme or the AC complex (Figure 5A). The RMSD undergone by PR65 is 2.7 Å during this transition. We concentrated on the deformation vector between PR65 conformation in the extended apo structure and that in the crystal structure of the AC complex (PDB id: 2ie3) ³³, which is shown by the red lines connecting the same residues on both structures. Our aim is to gauge the propensity of PR65 collective motions for driving it towards the specific conformation in the AC complex. Figure 5B displays the correlation cosine (overlap) between this deformation vector and each global ANM mode. The first mode with a remarkably high overlap value of 0.77 effectively drives the transition between the PR65 conformers in the apo form and in the AC complex. The cumulative overlap of first three modes is 0.89, which collectively account for more than half of the total variance (see Figure S4).

Next, we concentrate on the transitions undergone by the core enzyme (AC complex, PDB id: 2ie3). In crystal structure of this dimeric complex bound to an inhibitor, the position of the catalytic subunit is quite different from that in the ABC complex (Figure 5C). The RMSD is 6.7 Å for this AC transition between the core enzyme and its counterpart in the ABC trimer (PDB id: 2iae). We examined whether the global modes of AC enable the conformational transition taking place during complexation with the regulatory B subunit B56. The 1^st mode shows a strong correlation (overlap > 0.75) with the deformation vector (Figure 5D), and the cumulative overlap of the first two modes is above 0.9. The first mode of AC is in fact a twisting motion, rather than a stretching-contraction, as illustrated in Supplementary Movie S3 (A in blue and C in yellow). It is evident that the twisting motion repositions the AC dimer for complexation with the regulatory subunit in PP2A (A in grey and C in orange).

Another interesting complexation event for the core enzyme has been observed in a dual-enzyme complex, namely the Integrator-PP2A complex (INTAC) (PDB id:7cun) ³⁴. The 12-mer INTAC is a platform that combines an RNA endonuclease with the dephosphorylation activity provided by the PP2A core enzyme. Interestingly, the positioning of the catalytic subunit is similar to that found in PP2A (ABC complex). In the supplementary Figure S5, we present the high correlations of the first and second modes of the AC core with this conformational transition experienced upon complexation with the integrator INTAC.

Mechanical resistance of PR65 to uniaxial deformation depends on the application site of the force and is enhanced in the trimeric complex

Next, we present a detailed analysis of the effect of complexation and conformational state on the mechanical response of PR65 to uniaxial tension/compression as examined in atomic force microscopy (AFM) or optical tweezer experiments. Using the MechStiff module ²⁹ of ProDy ³⁵, we analyzed the following systems: (i) intact PP2A holoenzyme (PDB id: 2iae, trimer ABC), in compact form, (ii) compact PR65 conformer extracted from this trimer, and (iii) extended PR65 conformer resolved in apo state (PDB id: 1b3u, chain A). Comparative analysis of systems (i) and (ii) reveals the effect of complexation on the mechanical properties of PR65; whereas (ii) and (iii) provides information on the effect of the PR65 conformational change (extended to compact).

The heatmap in Figure 6A displays the mechanical resistance map for PP2A, where the color-coded ij^th entry represents the effective force constant, also called resistance or stiffness, < κ_ij >, of the overall molecule in response to a uniaxial deformation applied to residues i and j (see the color-coded bar on the right). The catalytic subunit is distinguished by high resistance to deformation, (see the abundance of green to blue entries at the upper right block of the map). In contrast, PR65 exhibits strong resistance around the main diagonal only (enclosed in ellipse), i.e., sequentially close pairs exhibit a high resistance to deformation. This reflects the smaller number of ways (or degrees of freedom) sequentially close pairs can accommodate the deformation due to restrictions imposed by connectivity and bonded interactions. The regulatory subunit (middle box) exhibits an intermediate behavior.

Figure 6. Mechanical properties of PR65.

The resistance to uniaxial deformation is shown for PR65 in PP2A. (A) Heat map displaying the effective resistance <κ_ij> of PP2A to deformation upon application of a uniaxial deformation to any pair of residues i and j. Residue numbers along the axes refer to those of the three subunits resolved in the examined structure (PDB id: 2iae). Strongest resistance is observed at the catalytic domain. (B) <κ_i> for each residue i, averaged over all pairs (i, j). The N-terminus is highly yielding (enclosed in black ellipse), while the dom1 of the catalytic subunit (red ellipse) shows high resistance to deformation. (C) distribution of <κ_i> in kcal/(mol.Ų). (D) dependency of <κ_i> on position i. See also Supplementary Figure S6A. (E) Mechanical resistance of PR65 to uniaxial deformation and its stiffening in PP2A. (Top) Results are presented for PR65 compact and extended forms (in isolation, respective green and blue curves) and PR65 (compact) in the trimer (red curve). (E) changes in stiffness between different forms, as indicated in the legend.

Panels B and C display the residue-averaged resistances, <κ_i> = ∑_j κ_ij /N. These usually lie in the range 3–5.5 in kcal/(mol.Ų), with the stiffest residues belonging to the catalytic subunit and the softest at PR65 N-terminus. The stiffness of the catalytic subunit originates from its overall tightest packing consistent with the requirement of high stability and precision near the catalytic site to enable the specific chemical reaction. The color-coded diagram in panel D shows that the inter-repeat loops are more flexible (gray/white) than intra-repeat loops (blue), and that inner residues in the horseshoe-like architecture are stiffer than others. Supplementary Figure S6A provides additional color-coded diagrams shown from different perspectives.

Further examination of PR65 (alone) in comparison to its behavior in the trimer, showed that trimerization induces an increase in the resistance to tension exerted at spatially (and sequentially) distant pairs, as can be seen in Supplementary Figure S6 panel B. Therein the two boxes show that the ‘yielding pairs’ are more populated in the isolated PR65 compared to the trimer, i.e., trimerization spatially restricts the PR65 N- and C-arms, consistent with the coupling of the C-terminal repeats to the catalytic subunit, and N-terminal repeats to the regulatory subunit during the PP2A collective dynamics as presented above.

Complexation significantly stiffens the intra-repeat loops of PR65 while having minimal effect on the inter-repeat loops

Next, we compared the profiles of PR65 scaffold within the complex (compact in trimer) to its isolated counterpart extracted from the complex (compact conformer; PDB: 2iae, only chain A) and the apo form (extended conformer; PDB: 1b3u). The profiles in Figure 6E show that the mechanical behavior of PR65 in isolation is retained with minimal change (correlation coefficient of 0.92) between the extended and compact forms. Note that this reflects the intrinsic response of this architecture to uniaxial deformation, tension or compression, i.e., one or the other form is not necessarily more ‘stressed’ in this type of evaluation. In the trimeric complex, on the other hand, the resistance of PR65 is enhanced due coupling to catalytic and regulatory subunits. For better visualization, we listed along the upper abscissa the positions of the repeat units and indicated the central part of each intra-repeat loop with a dashed vertical line. As expected, these loops (as well as the inter-repeat loops) show sharp minima consistent with their conformational malleability.

The lower plot shows the change in stiffening induced upon trimerization. Strikingly, intra-repeat loop regions are distinguished by their maximal stiffening (peaks). We note that complexation induces significant stiffening at the C-terminal repeats’ intra-repeat loops. These regions directly interact with the catalytic subunit. The increase in <κ_i> is indicative of the induction of a stronger cooperativity across the scaffold in the trimer. The N-terminal repeats also experience a stiffening upon complexation, presumably due to their interaction with the regulatory subunit (see Supplementary Figure S7).

Overall, while the mechanical character of the PR65 scaffold is maintained (as evidenced by the correlation coefficient of R = 0.85 between the compact PR65 in isolation and that in the trimer, and even R = 0.73 with the extended PR65 in isolation and the compact form in the trimer), the complexation with the catalytic and regulatory subunits endows PR65 with strong allosteric properties, and this effect is most pronounced at the N- and C-terminal repeats 3 and 13–15 respectively. Repeat 12 exhibits a peculiar behavior where there is a softening rather than stiffening upon trimerization at its first helix. This region (containing inter-repeat residues G432-G436) emerges as a potential site for modulating the overall mechanics of the phosphatase, e.g., by small molecule ligand binding, due to its local flexibility as well as interfacial/hinge position between the relatively rigid central part of the scaffold and the relatively flexible C-terminal arm composed of repeats 13–15.

The intrinsic mechanical properties of PR65 are evolutionarily conserved

Previous work has pointed to the significance of mechanical properties for enabling biological function, the regions distinguished by important mechanical roles also being evolutionarily conserved ^36,37. Figure 7 depicts PR65 compact structure color-coded by the conservation score of amino acids, evaluated by ConSurf ^38,39. Interestingly, the conservation pattern is generally in accord with the stiffness pattern depicted in Figures 6D and S6A, as well as its further differentiation upon complexation (Fig 7A–B), including the different characters of the top and bottom parts of the scaffold. Residues facing the top part (when the N-terminus is placed on the left, panel A and C of Figure 7) are evolutionarily more conserved. These correspond to the intra-repeat loops. In contrast, residues in the bottom corresponding to inter-repeat loops are less conserved. The regulatory and catalytic subunits both bind to the conserved side of the horseshoe, which harbors the intra-repeat coils (see Supplementary Figure S6A).

Figure 7. Evolutionary conservation of key mechanical regions of PR65.

Panels A-B display the top and bottom views of the PR65 scaffold color-coded by the changes in stiffness undergone in the compact form upon complexation (using the red curve in Figure 6E bottom panel). Panels C-D display the PR65 structure (in surface representation) from the same perspectives, color-coded by the conservation of amino acids, as predicted by ConSurf (color code in the center).

Discussion

The structures of repeat proteins underline their spring-like characteristics. Strikingly, in the case of PR65, the multiple snapshots provided by the protein both in uncomplexed and in different complexed forms hint at just how flexible a molecule it is. Notably, this high flexibility is also accompanied by a robust mechanical behaviour and stiffening upon participation in the trimeric PP2A. Our findings highlight the unique mechanical properties of the PR65 scaffold endowed by its tandem-repeat architecture and how the structure-encoded intrinsic dynamics of this subunit, complemented by the regulatory subunit, provides a framework for establishing allosteric communication and assisting in the catalytic activity of PP2A. The high mobility of repeats 12–15 may be a prerequisite for facilitating the binding of the catalytic subunit. Upon further complexation with the regulatory subunit, PR65 retains its softest modes of motion - expansion/contraction of the overall structure permitting distance changes of about 40Å between its two ends. Trimerization induces, on the other hand, an enhanced cooperativity across the scaffold. Notably, in the trimeric PP2A, the catalytic subunit is sequestered between the C-terminal arm of PR65 and the C-terminal repeats of the regulatory subunit, both of which may concertedly assist in the catalytic interdomain cleft opening/closure for enzymatic activity.

The effective resistance <κ_ij> of PR65 to uniaxial deformation lies in the range 2.0 ≤ κ_ij ≤ 4.5 N/m (or 325±125 pN/Å), depending on the pairs of residues (i, j) on which the stress is applied. Note that our previous study ²⁹ for a series of proteins (tandem spectrin repeats ^40,41, enhanced yellow fluorescent protein ⁴², fibronectin repeat domain 10, titin ⁴³ and protein L ⁴⁴) showed that the resistance <κ_1N> to tension exerted at the ends (i = 1 and j = N) scaled linearly with unfolding force (in pulling experiments applied to N- and C-termini), with an increase in <κ_1N> from 1.0 to 2.0 N/m accompanying an unfolding force increase from 30 to 160 pN, approximately. Furthermore, the response is anisotropic: it depends on the pairs of residues on which the forces are exerted. For example, GFP shows a variation from 116 to 548 pN ⁴⁵. Theoretically predicted <κ_ij> values for five different pairs in GFP yielded a correlation of 0.94 with the unfolding forces measured by AFM ²⁹. Notably, the ANM force constant used therein was γ = 0.25 kcal/(mol Ų), which is comparable to that determined for PR65 here upon comparing the ANM mode spectrum with full-atomic NMA spectrum.

In the previous work of Grinthal et al. ¹¹, 2 ns-long MD simulations were performed by applying a constant force at the two ends of the PR65, either in tension or compression mode. The scaffold behaved like an elastic medium under low force, whereas viscoelastic behavior prevailed under higher forces due to disruption of certain helix-helix interfaces. In contrast to these simulations, our aim was to observe the conformational behavior of PR65 scaffold in solution, closer to in vivo conditions. Our unbiased MD simulations as well as ClustENMD sampling pointed to the highly elastic character of this horseshoe-shaped scaffold with its highly variable end-to-end distance for the first time. These findings are consistent with the global modes of motions intrinsically accessible to the scaffold, as predicted by the ANM. Such global modes also underlie the allosteric dynamics of multimeric proteins ³⁶. In the present system, they mediate the cooperative action of the three subunits in PP2A. Global modes also facilitate the conformational transitions of the scaffold and the core enzyme during complexation. Specifically, the structural transitions undergone by the core enzyme (AC complex) during its binding to either the regulatory subunit or multiple subunits in the formation of the 12-meric INTAC are facilitated by the first two global modes.

The regions subject to mechanical constraints are also verified here to be evolutionarily conserved. In particular, the intra-repeat coil regions stiffen at the C-terminal arm of PR65 more than any other regions upon complexation with the regulatory and catalytic subunits, suggesting that they play a key role in establishing the allosteric communication across PR65. Not surprisingly, the intra-repeat coils are verified to be more conserved evolutionarily than the inter-repeat loops. Given their importance in establishing communication or substrate binding, as well as their adaptability (by virtue of their coiled structure), the intra-repeat regions appear to be strong candidates for amino acid substitutions or ligand binding toward redesigning PR65 or similar tandem-repeat proteins for customized functionalities. Of interest is a ‘vulnerable’ region occupying a hinge-like site at the interface between repeats 11 and 12, which exhibited unusual changes (a softening) upon complexation in the trimeric PP2A. This region may be explored as a target site for modulating the dynamics, and thereby function, of PR65.

STAR*Methods

RESOURCE AVAILABILITY

Lead contact:

All requests should be directed to and will be fulfilled by the Lead Contact, Ivet Bahar (bahar@laufercenter.org).

Materials availability:

This study did not generate new unique reagents.

Data and code availability

• This paper analyzes existing, publicly available data. These accession numbers for the datasets are listed in the key resources table.

• All data reported in this paper will be shared by the lead contact upon request.

• The source code for all computations and input/output data are available upon request. ANM, Mechanical Stiffness, ClustENMD analysis have been conducted using ProDy, an open-source API freely available on the web via http://prody.csb.pitt.edu/. MD analysis have been performed using NAMD and NMA analysis have been performed using VIBRAN module of CHARMM.

• MD trajectories will be provided on request.

• Any additional information required to reanalyze the data reported in this paper is available from the lead contact upon request. (bahar@laufercenter.org).

KEY RESOURCES TABLE.

REAGENT or RESOURCE	SOURCE	IDENTIFIER
Deposited data
Apo structure of PR65	25	PDB: 1B3U
Structure of hetero-trimeric complex PP2A	22	PDB: 2IAE
Structure of the Protein Phosphatase 2A Core Enzyme	33	PDB: 2IE3
Structure of Integrator-PP2A complex (INTAC)	34	PDB: 7CUN
Software and algorithms
NAMD 2.13	46	http://www.ks.uiuc.edu/Research/namd/
VIBRAN module of CHARMM-GUI	47	https://www.charmm-gui.org/charmmdoc/vibran.html
ANM module in ProDy 2.0	35,48	http://prody.csb.pitt.edu/
MechStiff module in ProDy 2.0	35,48	http://prody.csb.pitt.edu/
ClustENMD	28	http://prody.csb.pitt.edu/clustenmd/
ConSurf	38,39	https://consurf.tau.ac.il/consurf_index.php

METHOD DETAILS

MD simulations.

Four independent runs, each of 200 ns duration, were performed using NAMD ⁴⁶ for PR65 scaffold in explicit solvent. NPT simulations were carried out at 303.15 K and 1 atm (2 fs time step) using the additive c36m force field ^49,50. Two of the runs (named as E1 and E2) were initiated from the apo structure of PR65 (PDB id: 1b3u), which is in an extended conformation. The remaining two runs (C1 and C2) were based on a more compact conformer of PR65, which is extracted from the hetero-trimeric complex PP2A (PDB id: 2iae). Extended and compact structures correspond to magenta and cyan conformers aligned in Figure 1B. The initial systems were prepared in explicit solvent using the default procedure of system preparation on CHARMM-GUI server ⁵¹.

Classical normal mode analysis (NMA).

All-atom normal modes were calculated using the VIBRAN module of CHARMM software ⁴⁷. To compare the vibrational frequencies of PR65 extended and compact states, a representative conformer was chosen from the initial stage (between 1–5 ns) of each independent MD run, leading to four conformers in total (E1, E2, C1, C2). Prior to NMA, extensive energy minimization was performed on each conformer in vacuum after extracting the protein from the periodic box. The potential energy was minimized till an energy RMS gradient of 10⁻⁵ kcal/mol/Å was reached. Then, normal modes were calculated using the VIBRAN module with the additive c36m force field ^49,50.

Anisotropic network model (ANM).

To observe the effect of conformational flexibility on global dynamics, we used the widely used elastic network model ANM ^26,52. ANM analysis implemented in ProDy API ^35,48 was adopted with the default cutoff radius of 15 Å between α-carbons. Calculations were repeated for a series of MD snapshots to allow for a broader distribution of accessible motions. In the ANM analysis, the Hessian matrix of the 2^nd derivatives of the overall potential with respect to displacements is a 3N × 3N matrix (for a structure of N residues), is constructed based on harmonic potentials with uniform force constant γ between all residue pairs connected by a spring (i.e., within the cutoff-distance) ^26,30,31,52. The Hessian can thus be written as γH after factoring out the uniform force constant. As in classical NMA, the frequencies and shapes of collective modes are determined by eigenvalue decomposition of H. The absolute value of γ does not affect the relative frequencies (obtained from the eigenvalues of H) nor the relative distribution of residue motions (represented by the eigenvectors of H), but uniformly rescales their size ^26,29. The cross-correlation $<\mathrm{\Delta }{\mathbf{R}}_i\cdot \mathrm{\Delta }{\mathbf{R}}_j{>}_{ANM}$ between the fluctuations $\mathrm{\Delta }{\mathbf{R}}_i$ and $\mathrm{\Delta }{\mathbf{R}}_j$ of residues i and j is given by

$$<\mathrm{\Delta }{\mathbf{R}}_i•\mathrm{\Delta }{\mathbf{R}}_j>ANM=(k_B\text{T}/\gamma )tr{\left[{\mathbf{H}}^{-\mathbf{1}}\right]}_{ij}=(k_B\text{T}/\gamma )\sum _{k=1}^{3N-6}\left(1/{\lambda }_k\right)tr{\left[{\mathit{u}}_i^{(k)}{\mathit{u}}_j^{{(k)}^T}\right]}_{ij}$$ (1)

where $\mathrm{tr}{\left[{\mathbf{H}}^{-\mathbf{1}}\right]}_{ij}$ is the trace of the ij^th 3×3 submatrix of the pseudoinverse of H, ${\lambda }_k$ and ${\mathit{u}}^{(k)}$ are the k^th eigenvalue and eigenvector of H, ${\mathit{u}}_i^{(k)}$ is the i^th super-element (a 3D vector) of ${\mathit{u}}^{(k)}$ describing the i^th residue/node motion in 3D along mode k, k_B is the Boltzmann constant, T is the absolute temperature, and the summation is carried out over all 3N-6 modes. The mean-square fluctuations (MSFs) of residues, $<{\left(\mathrm{\Delta }{\text{R}}_i\right)}^2{>}_{ANM}$, are given by the same equation, with i = j. A common practice has been to evaluate γ upon comparison of the $<{(\mathrm{\Delta }{\text{R}}_i)}^2{>}_{ANM}$ profile with that inferred from X-ray crystallographic B-factors ⁵³ using

$$B_i=8{\pi }^2/3<{\left(\mathrm{\Delta }{\text{R}}_{\text{i}}\right)}^2{>}_{exp}$$ (2)

which upon comparison with Eq. 1 yields the average force constant adopted in the ANM

$$\gamma =\left(\frac{k_B\text{T}}{N}\right){\sum }_{i=1}^N\left(8{\pi }^2/3\right)tr{\left[{\mathbf{H}}^{-\mathbf{1}}\right]}_{\text{ii}}/B_i$$ (3)

Here $B_i$ is the B-factor reported in the PDB for the i^th α-carbon. However, the use of B factors for calibration has limitations, ^{54, 55} as they refer to crystallographic conditions, i.e., they depend on the crystallization conditions as well as intermolecular contacts that are artifacts of the crystal lattice environment. Instead, we adopt here an alternative route for evaluating γ. ANM-predicted eigenvalues (λ_k) are related to the mode frequencies ${\omega }_k$ obtained by classical full-atomic NMA as

$${\omega }_k=(1/2\pi ){\left(\gamma {\lambda }_k/m\right)}^{1/2}$$ (4)

where m is the mass of ANM nodes, each representing a residue. Here we use the average (<m> = 150.7 g/mol) over all twenty types of amino acids. The above relationship permits us to evaluate the force constant γ consistent with the frequencies of the global modes computed by full-atomic NMA, using for example the slope of the plot of ω_k against λ_k^1/2, and use γ for calculating material properties such as resistance to deformation, as explained next. As to the mode shapes predicted by ANM and NMA, we simply evaluate the correlation cosine, also called overlap, between the two sets of eigenvectors, as the eigenvectors are, by definition, normalized.

Mechanical stiffness (Mechstiff).

The mechanical stiffness, or the resistance to deformation in response to uniaxial tension was computed using the Mechstiff module of ProDy implemented ⁵⁶ after the theory introduced by Eyal and Bahar ^29,30. The approach allows for generating an N × N heat map for the effective stiffness (or effective resistance or force constant, < κ_ij >) for each residue pair in response to uniaxial tension applied at those particular pair (i, j) for a protein of N residues, using

$$<{\mathrm{\kappa }}_{ij}>=\sum (\text{k})d_{ij}^{(k)}\gamma {\lambda }_{\text{k}}/\sum (\text{k})d_{ij}^{(k)}$$ (5)

where $d_{ij}^{(k)}$ is the contribution of the k^th mode to the deformation imposed by the exerted force, given by

$$d_{ij}^{(k)}={\left(k_{B}T/\gamma {\lambda }_k\right)}^{\frac{1}{2}}cos{\alpha }_{ij}{}^{(k)}\left|{\mathit{u}}_i^{(k)}-{\mathit{u}}_j^{(k)}\right|$$ (6)

Here ${{\alpha }_{ij}}^{(k)}$ is the angle between the direction of the external force and that of the change $\mathrm{\Delta }{\mathbf{R}}_{ij}^{(k)}$ in inter-residue distance induced by mode k. As may be seen from Eq. 5, the value of effective stiffness is lower if the deformation is accommodated by soft modes and vice versa.

Hybrid simulations.

We used ClustENMD ²⁸ for sampling the ensemble of conformers accessible to (a) the heterotrimeric PP2A, (b) the dimer formed by the PR65 and catalytic subunits, and (c) PR65, all using structural data from the crystal structure of PP2A (PDB id: 2iae). ClustENMD is a hybrid technique that allows for sampling the conformational space of the examined biomolecular system, guided by ANM, and complemented by clustering of conformers to identify representatives using MD simulations at 303.15 K in implicit solvent. It is particularly suitable for exploring the conformational space of multimeric proteins, as shown in a recent comparative study ³². We performed two independent ClustENMD runs for each of the three systems a-c and generated 600 conformers for each system. Each run was composed of 5 generations of conformational sampling with 1 Å average deformation each, using random combinations of the three lowest frequency ANM modes. Short MD simulations were performed for relaxation of each representative conformer.

QUANTIFICATION AND STATISTICAL ANALYSIS

We carried out four independent MD simulation runs, each of 200 ns duration, using NAMD for the PR65 scaffold in explicit solvent. The fluctuations in PR65 inter-repeat distances, d_1–15 and d_5–11, during these MD simulations are provided in Figure 2. We further carried out ANM analysis on all MD snapshots and reported distributions of global mode frequencies (Figure 2). We carried out normal mode analysis on four representative conformations chosen between 1–5 ns of each independent MD run to report global mode frequencies. We performed two independent ClustENMD runs for each of the following systems- (a) the heterotrimeric PP2A, (b) the dimer formed by the PR65 and catalytic subunits, and (c) PR65, all using structural data from the crystal structure of PP2A, and generated 600 conformers for further analysis of dynamics features (Figures 3 and 4). The Mechstiff module of ProDy was used to compute the mechanical stiffness for different crystal structures of PR65 and PP2A (Figure 6).

Supplementary Material

2

Supplementary Movie S1. Global modes of motion of PR65 (related to Figure 2). ANM fluctuations along modes 1–3 for PR65 in compact and extended forms.

3

Supplementary Movie S2. Lowest frequency modes of motion accessible to PP2A (related to Figure 4). Fluctuation along ANM mode 1 of PP2A trimer where the PR65 scaffold retains its intrinsically accessible stretching/contraction now engaging the catalytic subunit, supported by the regulatory subunit.

4

Supplementary Movie S3. ANM first mode in the AC complex undergoes a twisting motion (related to Figure 5). PR65 is shown in blue and the catalytic subunit in yellow (PDB id: 2ie3). The twisting motion predisposes the complexation of the AC dimer with the regulatory subunit in PP2A (PR65 in grey and the catalytic subunit in orange) (PDB id: 2iae).

Highlights:

• PR65 is a highly elastic scaffold facilitating the allosteric events within PP2A.

• PR65 intra-repeat coils stiffen upon participation in the PP2A trimer.

• The intrinsic dynamics of PR65 predisposes it to binding the catalytic subunit C.

• Global modes of the core enzyme AC facilitate its complexation events.