Multi-state recognition pathway of the intrinsically disordered protein kinase inhibitor by protein kinase A.

In the nucleus, the spatiotemporal regulation of the catalytic subunit of cAMP-dependent protein kinase A (PKA-C) is orchestrated by an intrinsically disordered protein kinase inhibitor, PKI, which recruits the CRM1/RanGTP nuclear exporting complex. How the PKA-C/PKI complex assembles and recognizes CRM1/RanGTP is not well understood. Using NMR, SAXS, fluorescence, metadynamics, and Markov model analysis, we determined the multi-state recognition pathway for PKI. After a fast binding step in which PKA-C selects PKI's most competent conformations, PKI folds upon binding through a slow conformational rearrangement within the enzyme's binding pocket. The high-affinity and pseudo-substrate regions of PKI become more structured and the transient interactions with the kinase augment the helical content of the nuclear export sequence, which is then poised to recruit the CRM1/RanGTP complex for nuclear translocation. The multistate binding mechanism featured by PKA-C/PKI complex represents a paradigm on how disordered, ancillary proteins (or protein domains) are able to operate multiple functions such as inhibiting the kinase while recruiting other regulatory proteins for nuclear export.


Introduction
The cAMP-dependent protein kinase A (PKA) is a ubiquitous phosphoryl transferase that regulates numerous cellular signaling pathways (Taylor et al., 2012). As for other eukaryotic protein kinases, PKA regulatome comprises globular domains as well as extensive disordered regions, which are essential for protein-protein interactions and signaling (Akimoto et al., 2013;Gó gl et al., 2019;Pellicena and Kuriyan, 2006). In fact, the activity and localization of PKA-C within different cellular compartments are finely regulated by ancillary proteins such as the regulatory subunits (R), A-kinaseanchoring proteins (AKAPs) (Bauman and Scott, 2002;Johnson and Lewis, 2001), and the heat-stable protein kinase A inhibitor (PKI) (Dalton and Dewey, 2006). While R-subunits are primarily responsible for the regulation and localization of PKA-C in the cytoplasm through interaction with Figure 1. PKIa primary sequence, homology, and complex with PKA-C. (A) Primary sequence of PKIa, featuring the high affinity region (HAR), the pseudo-substrate region (PSS), and the nuclear export signal (NES). (B) X-ray structure of the PKA-C/ATP/PKI 5-24 ternary complex featuring only part of the HAR sequence and the PSS motif (PDB ID: 1ATP; Knighton et al., 1991a). PKA-C secondary structure elements are color-coded using Hanks and Hunter definition (Hanks et al., 1988). (C) Comparison of the substrate recognition sequences (SRS) for different PKA-C substrates, including PKIa, Kemptide, phospholamban (PLN), and the regulatory subunit RIa and RIIb. D. NES sequences from different proteins (Fung et al., 2015;Fung et al., 2017). expression in various tissues and the highest inhibitory potency [K i~0 .22 nM, (Collins and Uhler, 1997;Gamm and Uhler, 1995). The initial crystal structures of PKA-C were obtained with truncated variants of PKIa, encompassing either residues 5-22 or 5-24 with part of the HAR and PSS sequences, lacking the NES as well as the C-terminal regions. ( Figure 1B; Knighton et al., 1991a;Knighton et al., 1991b). More importantly, there are no reports on how PKI is recognized by the kinase and its binding mechanism.
Using a combination of NMR spectroscopy, small angle X-ray scattering (SAXS), stopped-flow fluorescence, replica-averaged metadynamics (RAM), and Markov model analysis, here we provide a comprehensive view of the molecular mechanism for recognition of PKIa by PKA-C. We found that free PKIa is intrinsically disordered, with incipient a-helical segments spanning the HAR and NES regions. PKA-C recognizes and binds extended PKIa conformations, rigidifying the PSS region and increasing the helicity of the HAR and NES motifs. Transient binding kinetics show that the recognition occurs via a multi-state pathway, with an initial fast binding step followed by a slow phase in which PKIa undergoes a conformational rearrangement within the binding site. Although the C-terminal tail of PKIa interacts transiently with the kinase's C-lobe, it remains essentially disordered facilitating the recruitment by the CRM1/RanGTP complex for nuclear export. We propose that the multistate pathway for PKIa recognition by PKA-C is preparatory for the recruitment by CRM1/ RanGTP for nuclear export and regulation of gene expression.

PKIa is an intrinsically disordered protein with transient secondary and short-lived tertiary interactions
In agreement with Hauer et al. (Hauer et al., 1999a;Thomas et al., 1991), we found that the dichroic profile, the NMR fingerprint, and the dynamic NMR parameters display the typical signature of mixed a-helix and random-coil structure for PKIa ( Felitsky et al., 2008;Marsh et al., 2007). We also probed the presence of long-range contacts using 1 H N paramagnetic relaxation enhancement ( 1 H N PRE-G 2 ) experiments (Clore and Iwahara, 2009;Figure 2E-G). For these experiments, we conjugated a nitroxide spin label (MTSL) on engineered cysteine residues at three different positions: PKIa V3C , PKIa S28C , and PKIa S59C in analogy to earlier fluorescence studies (Hauer et al., 1999b). We then measured the peak intensities in the presence of paramagnetic (I para ) and diamagnetic (I dia ) labels to estimate the G 2 relaxation rates (Clore and Iwahara, 2009). When the spin label was engineered at the N-terminus (PKIa V3C ), we observed a reduction of the resonance intensities near the N-terminal region and gradual effects that culminate in the middle of the linker between the PSS and NES motifs and decrease toward the C-terminus (PRE values less than two standard deviations, 2s). The C-terminal residues remained essentially unperturbed ( Figure 2E). On the other hand, when the spin label was positioned between the PSS and NES motifs (PKIa S28C ), we detected strong PREs near the spin label position (PRE greater than 3s), at the N-terminus, and within the NES motif ( Figure 2F). Finally, for the spin label at position 59, we found that approximately 75% of the residues display a reduced signal intensity, with marked effects in the PSS, linker region, NES, and C-terminus. In this case, we observed only marginal effects for the N-terminal residues ( Figure 2G). Altogether, the CD and NMR data reveal that in absence of a binding partner PKIa samples transient secondary structures encompassing the HAR and NES motifs with short-lived tertiary conformations.

PKA-C binding rigidifies the PSS motif and stabilizes HAR and NES helices of PKIa
To map the fingerprints of both PKA-C and PKIa in the PKA-C/ATPgN/PKIa complex, we used our previously developed method in which we combine asymmetric isotopic labeling for each binding partner with a spin-echo filter for 13 C-linked amide protons in the heteronuclear single quantum coherence experiment (HSQC), [ 1 H, 15 N]-carbonyl carbon label selective-HSQC or [ 1 H, 15 N]-CCLS-HSQC (Tonelli et al., 2007;Larsen et al., 2018;  However, the HAR and PSS resonances display significant chemical shift changes ( Figure 3A,B,E), suggesting that these regions of PKI undergo drastic structural rearrangements upon binding the kinase. This finding is also supported by the dD2 analysis (Camilloni et al., 2012) of the Ca and Cb chemical shifts showing an increase in helical content of the HAR and rigidification of the PSS motif; while the rest of the peptide remain unaffected by the interaction with PKA-C ( Figure 3B, Figure 3figure supplement 2A). The analysis of the chemical shift difference between the ATPgN-bound form and the ternary complex mapped on PKA-C are reported in Figure 3 (panel C-D). As previously reported (Masterson et al., 2010;Masterson et al., 2008), the amide fingerprint of the kinase changes significantly upon nucleotide binding ( Figure 3C). Additional changes are observed upon  (Wicky et al., 2017;Chemes et al., 2012;Silvers et al., 2012). (B) Secondary structure content for free PKIa as determined from NMR chemical shifts using d2D program (Camilloni et al., 2012). Note that the program neglects to calculate values for the first and last residues. (C) Plots of the [ 1 H, 1 H] NOEs derived from the analysis of [ 1 H, 15 N] NOESY-HSQC experiment. (E) Residual dipolar couplings (RDCs) for PKIa aligned in stretched polyacrylamide gels and 5% bicelles (q = 3.5). The oscillations around zero of the 1 D NH values confirm the absence of a defined structure. (E-F) Intra-molecular 1 H-G 2 -PRE measurements of the three cysteine mutants of PKIa (Iwahara et al., 2007). For these experiments, a delay of 10 ms was used to calculate the intra-molecular 1 H-G 2 -PRE effects. The yellow spheres on the schematic of PKIa (B panel) indicate the location of the cysteine mutations. The yellow dots in each graph indicate those residues broadened beyond detection. The horizontal lines indicate one (blue), two (green), and three (red) standard deviations (s) from the mean PRE. The online version of this article includes the following figure supplement(s) for figure 2:   (Williamson, 2013). The residues of PKIa that undergo significant CSPs are localized in the HAR and PSS, which are involved in strong electrostatic interaction within the binding site of PKA-C. (B) Chemical shift index (CSI) for Ca and Cb of free (red) and bound (blue) PKIa. The PSS motif becomes more rigid upon interaction with PKA-C. The HAR and the NES adopt a transient a-helical conformation, which is enhanced upon binding the kinase. (C) CSP of PKA-C amide fingerprint upon binding ATPgN. (D) CSP of the PKA-C/ATPgN binary complex upon binding PKIa. The red lines in the histograms indicate one standard deviation from the average CSP: 0.38 ppm, 0.11 ppm, and 0.10 ppm for (A), (C and D), respectively. (E) CSPs for PKA-C and PKIa amide resonances mapped onto a selected conformer from the ensemble of the PKA-C/ATP/PKIa structures calculated from MD simulations (see Materials and methods). The online version of this article includes the following figure supplement(s) for figure 3:  binding PKIa, especially for aC, aF, aG helices as well as b6 loop. The map of the chemical shift changes on the PKA-C/ATPgN/PKIa complex for the two proteins is reported in Figure 3E. Interestingly, smaller changes are present for the NES region of PKIa, which are mirrored by higher values of heteronuclear nuclear Overhauser effects (NOE), indicating reduced motions of the backbone amides in the pico-to-nanosecond time scale ( Figure 4A, Figure 3-figure supplement 2B; Dyson and Wright, 2004;Bah et al., 2015). The formation of the PKA-C/ATPgN/PKIa (ternary) complex is also reflected by the differences of longitudinal and transverse relaxation rates (DR 1 and DR 2 ) for both the HAR and PSS motifs upon forming the complex, which define a local rigidification of the PKIa backbone upon binding PKA-C, with the C-terminal portion (residues 47-75) remaining essentially unstructured ( Figure 4B,C).
The T 1 /T 2 ratios can be used as an estimate of the global correlation time for the PKA-C/PKI complex Cavanagh et al., 2007a;Cavanagh et al., 2007b;Gaspari and Perczel, 2010). The PSS and HAR regions of PKIa, which show the most prominent chemical shift changes, adopt the overall correlation time of the kinase in agreement with previous fluorescence anisotropy measurements (Figure 3-figure supplement 2C; Hauer et al., 1999b). Interestingly, the DR ex values obtained from the Carr-Purcell-Meiboom-Gill (CPMG) relaxation dispersion experiments show the presence of ms-ms motions for residues in the HAR and PSS motifs, which gradually decrease toward the NES motif, suggesting the presence of conformational interconversion of these regions upon binding ( Figure 4D, Figure 3-figure supplement 2D). Next, we analyzed the large amplitude motions of the kinase-bound PKIa by conjugating MTSL to cysteine 59 in the C-terminal region (PKIa S59C ) and used the [ 1 H, 15 N]-CCLS pulse sequence to simultaneously measure the PREs on both PKIa and PKA-C  Figure 5A,B). The most significant PREs for PKIa were detected for resonances of residues proximal to the MTSL label, with a gradual reduction moving away from residue 59. Interestingly, we detected some long-range effects for specific residues located in the HAR and PSS motifs and the intervening linker. This implies that the C-terminal   domain of PKIa undergoes large amplitude motions and transiently interacts with the N-terminus, N-lobe (b 1 -b 2 loop), C-lobe (G-, and H-helices) as well as the peptide-positioning loop of PKA-C. Taken together, the relaxation data show that PKA-C binding to PKIa causes differential effects on the various regions of the inhibitor. While disorder-to-order transitions occur for the HAR, PSS, and NES motifs, the C-terminal tail of the PKIa remains disordered. ( Figure 5C).
The PKA-C/PKIa complex relaxes through two structurally and kinetically distinct states to form the complex To determine the mechanism of binding PKA-C and PKIa, we utilized stopped-flow rapid mixing fluorescence resonance energy transfer (FRET) and analyzed transient and total changes in donor fluorescence during the binding reaction. This procedure enables the interpretation of the kinetic mechanism and structural changes occurring during a binding reaction (Muretta et al., 2015;Nesmelov et al., 2011). To determine the kinetics of binding, we engineered a double mutant of PKA-C (PKA-C C199A,S325C ) and labeled the single reactive S325C with Alexa Fluor 488 (PKA-C DONOR ). We also expressed and purified three different mutants of PKIa (PKI V3C , PKI S28C , and PKI S59C ) and labeled each cysteine with tetramethylrhodamine-5-maleimide (PKI ACCEPTOR-3 , PKI ACCEPTOR-28 , and PKI ACCEPTOR-59 ). For the first set of experiments, we mixed PKA-C DONOR with increasing concentrations of each acceptor (PKI ACCEPTOR-3 , PKI ACCEPTOR-28 , PKI ACCEPTOR-59 , ( Figure 6A-D). As expected indicate those resonances that broaden out beyond detection mainly in the sample with the spin-label active (paramagnetic sample). The horizontal lines indicate one (blue), two (green), and three (red) standard deviations from the mean (s) of the observed PRE values. We refer as strong PRE effects values greater than 3s, medium between 1 and 2s, and weak less than 1s.
for the formation of the PKA-C/PKIa complex, we observed a gradual decrease in the total fluorescence of the donor probe. In a second set of experiments, we tested the time-dependence of longrange rearrangements of PKIa as suggested by PRE measurements ( Figure 6A, Figure 6-figure supplement 1A). To this extent, we utilized the PKA-C C199A,S325C mutant without fluorescent label and engineered a double mutant of PKIa with two cysteines at residue 3 and 59 (PKI V3C,S59C ). the PKI V3C,S59C mutant was then labeled with both Alexa-488 (donor) and TMR (acceptor) at positions 3 and 59, respectively (PKI DONOR-ACCEPTOR ). When a fixed concentration of PKI DONOR-ACCEPTOR was titrated with increasing concentrations of unlabeled PKA-C C199A,S325C , we detected an increase of the total fluorescence ( Figure 6E, Figure 6-figure supplement 1B), indicating that the distance between the two probes of PKIa increases upon formation of the complex, that is the conformational ensemble of PKIa becomes on average more extended during the binding reaction in agreement with the PRE data. From an initial analysis of the binding curve, we found that the total fluorescence of the Alexa-488 donor emission from the PKA-C DONOR /PKI ACCEPTOR changed bi-exponentially through the course of the binding reactions ( Figure 6A-D). The bi-exponential behavior suggests the presence of an initial fast binding step followed by a slow structural rearrangement ( Table 1; Gianni et al., 2014).
These two phases can be identified for all the PKI labeled species, irrespective of the fluorescence acceptor position. The rate constants for the fast phase increases linearly with PKIa concentration, with an average second-order rate constant of 1.63 Â 10 7 M À1 s À1 and an extrapolated average dissociation rate constant of 7.0 s À1 . Comparatively, the observed rate constant for the slow phase increased hyperbolically with an average K 0.5 of 3.1 mM and a maximum value (k slow ) of 24 ± 1.8 s À1 . We also observed two distinct binding phases for the second set of experiments with unlabeled PKA-C C199A,S325C and PKI DONOR-ACCEPTOR . Indeed, the kinetic constants obtained for these experiments are very similar to those found in the first set of the experiments, underscoring the same binding mechanisms. The pre-exponential amplitudes for the fast phases increased hyperbolically, while the slow phase decreased hyperbolically ( Figure 6D-H). Taken together, the behavior of the rate constants and the pre-exponential amplitudes for the fast and slow phases are consistent with a multi-pathway mechanism in which there is a fast binding phase of PKIa ensembles competent for binding and a subsequent structural rearrangement of these conformers upon binding Gianni et al., 2014).

Conformational landscape and kinetics of conformational transitions of PKIa
Using chemical shift (CS) and residual dipolar couplings (RDC) ( Figure 2D) as structural restraints, we performed replica-averaged metadynamics (RAM) to define the energy landscapes of free and kinase-bound PKIa. During the simulations, the HAR and NES motifs of free PKIa undergo multiple coil-to-helix transitions ( Figure 8). We identified two major basins, featuring a compact ensemble (R g <1.5 nm), with three relative minima with helical structures for the HAR and NES motifs; and a more extended ensemble (R g >3.0 nm), where the protein is essentially disordered. The HAR motif populates mostly a random coil conformation, with a sparsely populated helical conformation, whereas the NES motif populates both helical and coil conformations ( Figure 7A,B). To validate the RAM-generated ensembles, we carried out small angle X-ray scattering (SAXS) experiments and back-calculated the SAXS profiles from the conformers sampled in the RAM trajectories. Figure 7C shows the scattering intensity plots (log I(q) vs q) and the corresponding Kratky plot for free PKIa. These profiles show the typical signatures of intrinsically disordered proteins, with the Kratky plot featuring a plateau at high q values as well as the absence of a bell-shaped curve ( Figure 7C, bottom panel). In addition, the P(r) curve shows that PKIa adopts a highly extended conformational ensemble, with an abnormally large D max (~110 Å ) and R g (~30 Å ) values for a protein of its size, both parameters are indicative of an extended, intrinsically disordered protein (Kikhney and Svergun, 2015; Figure 8D). In fact, the back-calculated SAXS profiles from the RAM-generated ensembles are in excellent agreement with the experimental SAXS scattering profiles (c = 0.86 for q < 0.2) ( Figure 7C). In the bound state, the HAR motif of PKIa is more ordered and adopts a more stable helical conformation; whereas the NES motif is considerably more dynamic and adopts a transient helical conformation ( Figure 7E).
In this case, the SAXS data are less informative as the Kratky plot for the PKA-C/ATPgN/PKIa complex is dominated by the bell-shaped curve of the globular enzyme, with a well-defined maximum in the low q region (~0.08 Å À1 ) that decays to near zero at high q values. To determine the rates of conformational exchange and the populations of PKIa free and bound, we performed unbiased molecular dynamics (MD) simulations and analyzed the conformational transitions building a Markov model. To simplify and visualize the conformational space of PKIa, we reduced the highdimensionality space of the residue-residue contacts into a 6-dimensional space using time-lagged Table 1. Rate constants obtained from the fluorescence decay of PKI ACCEPTOR-3 , PKI ACCEPTOR-28 , and PKI ACCEPTOR-59 upon mixing with Alexa-labeled PKA-C C199A,S325C or the fluorescence buildup of PKI DONOR-ACCEPTOR upon mixing with unlabeled PKA-C C199A,S325C at 25˚C.
Olivieri et al. eLife 2020;9:e55607. DOI: https://doi.org/10.7554/eLife.55607 independent component analysis (tICA). We then projected the free energy landscape along the main components, tlC1 and tlC2. In this reference frame, free PKIa occupies six local minima (DDG < 1 kcal/mol) and a higher energy state (DDG~2.5 kcal/mol) ( Figure 8). We then clustered the conformers into four major ensembles based on the secondary structure content of the HAR, PSS, and NES motifs: HLH (helix-loop-helix), CLC (coil-loop-coil), HLC (helix-loop-coil), and CLH (coilloop-helix) (Figure 8-figure supplement 1). For free PKIa, the CLH ensemble is dominant, with a mean population of 51%, followed by CLC (32%), HLC (15%), and HLH (~2%) ( Figure 8A). The kinetics of the conformational transitions were calculated using the mean-first-passage-time (MFPT) among these states. We found that all the conformational transitions take place on a ms time scale, with the slowest transitions from the HLC, CLH, and CLC ensembles to the HLH ensemble; while the transitions from CLC, HLH, and HLC to the CLH ensemble are more rapid ( For PKIa bound to PKA-C, the conformational space spanned becomes more restricted ( Figure 8D). Specifically, the HLC, CLC, and HLH minima become more populated, with 72, 22, and 6% ( Figure 8B). In addition, the transition kinetics from CLC and HLC to the HLH ensemble is estimated to occur approximately 10 times faster (  The blue (complex) and red (free PKIa) traces are the best-fit curves obtained by fitting predicted scattering data from the conformation ensembles from RAM simulations. (D) Conformational ensemble of free PKIa that best fits the SAXS profile. E. PKIa ensemble bound to PKA-C that best fits the SAXS profile.

Proposed mechanistic model
Based on NMR, SAXS, fluorescence, RAM simulations as well as Markov model analysis, we propose that PKIa binding to PKA-C occurs via a multistate recognition pathway. We envision that free PKIa spans a broad conformational space with incipient helical elements for the HAR and NES motifs. These conformations are in fast exchange in the NMR time scale. We propose that the initial step (fast) of recognition by PKA-C is driven by electrostatic interactions between the conformations of PKIa featuring an exposed PSS motif (CLC and HLC) and PKA-C (Tsigelny et al., 1996). These encounter complexes undergo slower conformational rearrangements in which a) the HAR motif folds upon binding in a helical conformation, b) the PSS motif binds within the active cleft in an extended conformation, and c) the transient helix of the NES motif adopts a more defined conformation. To validate our hypothesized mechanism, we fitted the fluorescence curves using a set of equations detailed in the supporting information (Scheme 1 and Scheme 2). Under these constraints, we obtained a kinetic constant of 1.5 Â 10 7 M À1 s À1 for the formation of the PKA-C*/PKI* encounter complex and a slow relaxation of the complex with a constant of 2400 s À1 . These kinetics parameters are in the same order of magnitude of the association rates measured for binding of other intrinsically disordered proteins (Mollica et al., 2016).

Discussion
When unleashed from the R-subunit, the C-subunit of PKA is in a constitutively active state, where binding of nucleotide engages the N-and C-lobes priming the kinase for substrate recognition and catalysis. R-subunits and PKI share small linear motifs (SLiMs) that bind the substrate binding site with high affinity and trap PKA-C in an inactive state. SLiMs are intrinsically disordered regions that are part of the allosteric machinery of kinases and control the cross-talk between different kinase signaling pathways (Akimoto et al., 2014;Akimoto et al., 2013;Delaforge et al., 2018;Gó gl et al., 2019;Kragelj et al., 2015;Wang et al., 2011;Wright and Dyson, 2015;Guiley et al., 2019). PKI can be portrayed as a prototypical SLiM that is able to bind and inhibit the kinase and recruit the CRM1/RanGTP complex to export the enzyme out of the nucleus, thereby regulating cell proliferation. Previous structural studies focused on the 5-24 region of PKIa that encompasses both the HAR and PSS motifs, which has been instrumental in trapping the ternary complex of the kinase and obtain the first crystal structure of a kinase (Knighton et al., 1991a). Subsequent spectroscopic studies provided evidence for the dynamic nature of the PKIa peptide, suggesting the presence of minimal secondary structural elements such as the HAR and NES regions, with a C-terminal tail completely disordered (Padilla et al., 1997;Hauer et al., 1999a). The HAR is extremely important for binding/anchoring to the catalytic subunit as well as positioning the PSS within the catalytic cleft of the enzyme (Walsh et al., 1971;Cheng et al., 1986). However, most PKA target substrates do not possess this motif and the only substrate recognition requirement is the highly positively charged consensus sequence in the linear PSS motif. In fact, in most cases this recognition motif is located in highly dynamic or intrinsically disordered regions as it molds into the binding groove of the kinase situated at the interface between the small and large lobes. Our studies bring new insights into the dynamic nature of the PKIa recognition mechanism. After the initial binding of ATP in the pocket between the two lobes that primes the substrate binding site (Chu et al., 2017;Hyeon et al., 2009;Masterson et al., 2010), this highly disordered polypeptide, with incipient helices at both the HAR and NES motifs, is driven toward the kinase via positively charged Arg residues in the PSS sequence. Deletion of one of the Arg residues in the PSS provokes a dramatic reduction of the phosphorylation kinetics and has been linked to the progression of dilated cardiomyopathy (Kim et al., 2015;Haghighi et al., 2006). On the other hand, mutations in the active site of the kinase that change electrostatic interactions such as L205R dramatically influence the thermodynamics and kinetics of substrate binding, leading to the development of adrenocortical adenomas and the resultant Cushing's syndrome (Calebiro et al., 2014;Cheung et al., 2015;Walker et al., 2019). More importantly, our studies reveal a significant ordering of the PKIa structure upon interaction with the kinase, particularly for the HAR, PSS, and NES motifs. This ordering occurs in the second, slower binding step as revealed by FRET measurements, while the C-terminal tail of PKIa remains essentially disordered, undergoing large amplitude motions with transient interactions with the C-lobe of the kinase. Interestingly, when PKIa is bound to PKA-C, the NES region undergoes a structural rearrangement, showing a higher degree of helicity as supported by NMR and MD simulations. The NES motif comprises Leu 37, Leu 41, and Leu 44 that are essential for high binding affinity to the nuclear export machinery CRM1/RanGTP (Güttler et al., 2010;Fu et al., 2018). The CRM1 binding pocket is a relatively rigid cavity and NES sequences must possess significant plasticity to mold into the binding pocket (Güttler et al., 2010;Fu et al., 2018). This observation could explain why the NES assumes a defined conformation only upon interaction with CRM1. Based on our data, it is possible to speculate that the interactions of PKIa with PKA-C preambles the formation of the complex and that the helix-coil equilibrium of the NES domain is critical for recruiting the CRM1/RanGTP nuclear export complex (Fu et al., 2018;Fung et al., 2017;Güttler et al., 2010). This complex binding mechanism shows how SLiMs can orchestrate multiple functions and regulate kinases through disordered ancillary proteins or protein domains.

Expression and purification of Full-length PKIa
Gene coding for full-length PKIa (Oryctolagus cuniculus, PKIA PRKACN1) subcloned into pT7-7 vector was a gift to us by Dr. Friedrich Herberg (Universitä t Kassel, Germany). For the fluorescence and PRE-experiments, three different single-site (PKIa V3C , PKIa S28C and PKIa S59C ) and a double-site (PKIa V3C, S59C ) mutants were generated by QuikChange Lightning mutagenesis kit (Agilent genomics) using PKIa as template. The choice of the sites of mutation was based on previous work (Hauer et al., 1999b). Recombinant full-length PKIa was expressed in E. coli BL21 (DE3) cells at 30C and the purification was performed as previously reported (Hauer et al., 1999a). Briefly, transformed cells were grown in Luria-Bertani (LB) medium for fluorescence while uniformly labeled 15 N, 13 C/ 15 N, and 2 H/ 13 C/ 15 N PKIa was expressed in minimal medium (M9) for NMR experiments. Protein expression was induced by the addition of 0.4 mM of IPTG to a culture with optical density of~1.3-1.4 at 30˚C and was performed for 5 hr. The cell pellet was resuspended in 20 mM MOPS (pH 7.5) and lysed through sonication. The lysate was then centrifuged at 20,000 rpm for 30 min. The supernatant was then heated in a boiling water bath at 95˚C for 5 min to precipitate out most of the undesired proteins. The protein suspension was centrifuged a second time at 20,000 rpm for 30 min. The resulting supernatant was dialyzed against 20 mM TRIS-HCl (pH 7.0) buffer overnight. A second purification step with anion exchange chromatography was carried out using HiTrap Q HP column (GE Healthcare Biosciences Corp) in 20 mM TRIS at pH 7.0 where a NaCl gradient was used to elute the protein. A reversed phase HPLC purification step was also performed to obtain a higher grade of purity using C18 column (HiCHROM, UK) using water as buffer A and isopropanol as buffer B with 0.1% trifluoroacetic acid in both buffers. The purified peptide was concentrated, lyophilized, and stored at À20˚C. The final product was accessed using SDS-PAGE with a final purity of >97%. The molecular weight and the quantity of the peptide were verified by amino acid analysis (Protein chemistry laboratory at Texas A and M University, TX, USA). All the cysteine mutants of PKIa were purified following the same protocol used for the wild-type protein with additional supplement of reducing agent (5 mM b-mercaptoethanol) in all the dialysis buffers.
Expression and purification of PKA-C Recombinant catalytic subunit of PKA-C (Mus musculus gene) was expressed in E. coli BL21 (DE3) cells at 24˚C in M9 minimal medium. The purification was performed using the His6-RIIa(R213K) subunit as described previously (Hemmer et al., 1997). A subsequent second purification step was performed using a HiTrap SP HP cation exchange column (GE Healthcare Biosciences Corp) to separate out the three isoforms of PKA-C that differ in their phosphorylation profiles (Yonemoto et al., 1993). The purified protein was then stored in phosphate buffer supplied of 10 mM DTT, 10 mM MgCl 2 , and 1.0 mM NaN 3 , at 4˚C. For isotopically 2 H-labeled protein, the cells were growth 80% D 2 O M9 minimal medium in a bench fermenter (2.0 L). The most abundant isoform of PKA-C, corresponding to phosphorylation at S338, T197, and S10 residues (isoform II) (Walsh and Ashby, 1973), was used for all experiments. The purity was assessed using SDS-PAGE electrophoresis and the final purity was >97%. The kinase activity was tested with a gel-shift assay from Promega (Fitchburg, Wisconsin) and quantified using A 280 = 52,060 M À1 cm À1 .
The C199A S325C mutant of the catalytic subunit of PKA (PKA-C C199A, S325C ) was recombinantly expressed by growing transformed E. coli BL21(DE3) cells in LB medium and induced by addition of IPTG at 24˚C as described previously. The mutant PKA-C was purified using the previously described protocol (Masterson et al., 2009). Briefly, cells were resuspended in lysis buffer (30 mM MES, 1 mM EDTA, 50 mM KCl, 5 mM b-mercaptoethanol, 0.15 mg/mL lysozyme, 1 mM PMSF, pH 6.5), and lysed using French press at 1000 psi. The supernatant after pelleting the cell debris was batch-bound with P11 phosphocellulose resin in lysis buffer at pH 6.5. PKA-C was purified by eluting over a gradient of 0-500 mM KH 2 PO 4 . The different isoforms of PKA-C were further separated by cation exchange chromatography with a HiTrap SP column using a KCl gradient in 20 mM KH 2 PO 4 at pH 6.5. Upon purification, wild-type or mutant proteins were supplied with 10 mM MgCl 2 , 10 mM DTT and 1 mM NaN 3 and stored at 4˚C.

Spin labeling of proteins
Lyophilized single site 15 N PKIa mutants were first dissolved in 1 mL of buffer containing 20 mM KH 2 PO 4 , pH 7.0, and incubated for about an hour in the presence of 1 mM TCEP. The sample was concentrated to 0.6 mM. The protein solution was then buffer exchanged into 20 mM KH 2 PO 4 , 90 mM KCl, 10 mM MgCl 2 , 1 mM NaN 3 pH 7.0. The sample was concentrated and divided into two equal aliquots to perform two separate spin labeling reactions in parallel: one using the paramagnetic spin label MTSL (1-oxyl-2,2,5,5-tetramethyl-dÀ3-pyrroline-3-methyl)methanethiosulfonate, Toronto Research Chemicals, Inc), and the second using the diamagnetic form, dMTSL (1-acetyl-2,2,5,5tetramethyl-dÀ3-pyrroline-3-methyl)methanethiosulfonate, Toronto Research Chemicals, Inc). The reactions were carried out at 4˚C overnight with ten-fold excess of labeling compounds that was then removed by passing the reaction solution through a 5 mL HiTrap Desalting column (GE Healthcare Biosciences Corp.) equilibrated with 20 mM KH 2 PO 4 , 90 mM KCl, 10 mM MgCl 2 , 1 mM NaN 3 , pH 6.5. The extent of labeling was assessed by ESI TOF mass spectrometry (Mass Spectrometry Laboratory, Department of Chemistry, University of Minnesota), and was found to be >99%.

NMR sample preparation
The NMR samples used to study the free form of PKIa were composed primarily by 15 N and 13 C/ 15 N labeled protein expressed in M9 media. The final concentration of samples ranged from 0.5 mM to 0.8 mM in 20 mM KH 2 PO 4 , 90 mM KCl, 10 mM DTT, 10 mM MgCl 2 , 1 mM NaN 3 at pH 6.5. Samples for the assignment of the PKIa in complex with PKA-C were performed using uniformly 2 H/ 13 C/ 15 N and 2 H/ 15 N labeled PKIa and uniformly 2 H/ 15 N PKA-C. The ternary complex between PKIa and PKA-C and ATP-analogues (AMP-PNP) were reconstituted in 20 mM KH 2 PO 4 , 90 mM KCl, 12 mM of ATPgN, 10 mM DTT, 10 mM MgCl 2 , 1 mM NaN 3 at pH 6.5. A molar ratio of 1:1.2 (PKIa:PKA-C) to saturate the complex with a concentration of 0.150 mM of PKIa. All experiments were performed at 27˚C. The denaturation experiments were carried out on 0.3 mM sample of uniformly 15 N PKIa resuspended in 20 mM KH 2 PO 4 , 90 mM KCl, 10 mM DTT, 10 mM MgCl 2 , 1 mM NaN 3 , 8 M Urea at pH 6.5. The 1 H N -G2 relaxation experiments were performed on 0.25 mM 15 N labeled single mutants of PKIa for the free form and uniformly 2 H/ 13 C/ 15 N protein for the bound form. In both preparations the buffer used for the analysis was 20 mM KH 2 PO 4 , 90 mM KCl, 10 mM MgCl 2 , 1 mM NaN 3 at pH 6.5. For all the NMR experiment carried out on the PKA-C/ATPg/PKIa complex, a low protein concentration sample was prepared to due to the high tendency to aggregate.

Preparation of fluorescent labeled proteins
Lyophilized single-site PKIa mutants were first dissolved in 1 mL of buffer containing 20 mM KH 2 PO 4 , pH 7.0, and incubated for about an hour in the presence of 1 mM TCEP. About four-fold excess of fluorescent dye (tetramethylrhodamine-5-maleimide, TMR) was added to the sample and incubated for about an hour at room temperature with stirring and protected from light. The reaction mixture was then passed through two 5 mL HiTrap Desalting columns (GE Healthcare Biosciences Corp.) equilibrated with 20 mM KH 2 PO 4 , 90 mM KCl, 10 mM MgCl 2 , 1 mM NaN 3 pH 6.5 to remove the unreacted dye. The extent of labeling was also verified using mass spectrometry. For the double-mutant PKIa, the procedure described above was used. In this case, Alexa-488 was added to the solution in 1:1 stoichiometric ratio with PKIa and the reaction was allowed to proceed for one hour at room temperature with stirring and protected from light. Since Alexa Fluor 488 carries a charge, the single-labeled PKIa was separated using anion exchange chromatography with HiTrap Q HP column using an NaCl gradient in 20 mM TRIS pH 7.0. The fraction containing the single Alexalabeled PKIa was buffer exchanged using a PD-10 MidiTrap column equilibrated with 20 mM KH 2 PO 4 , 90 mM KCl, 10 mM MgCl 2 , 1 mM NaN 3 , pH 7.0. Five-fold excess of tetramethylrhodamine-5-maleimide (TMR) was added and the reaction mixture was incubated for about an hour with stirring and protected from light. The asymmetrically double-labeled PKIa was separated from the unreacted dye by passing the reaction through two 5 mL HiTrap Desalting columns (GE Healthcare Biosciences Corp.) equilibrated with 20 mM KH 2 PO 4 , 90 mM KCl, 10 mM MgCl 2 , 1 mM NaN 3 pH 6.5. The extent of labeling in each step was determined using mass spectrometry. For the labeling of PKA-C C199A, S325C mutant, the protein was buffer-exchanged by passing through a PD-10 Midi-Trap column (GE Healthcare Bio-Sciences Corp.) equilibrated with 20 mM KH 2 PO 4 , 90 mM KCl, 10 mM MgCl 2 , 1 mM NaN 3 , pH 7.0 at room temperature. The fractions containing PKA-C were pooled and the concentration was adjusted to~5-6 mM. ATP at a final concentration of 8 mM was added to protect the C343 site from being labeled as shown previously (Nelson and Taylor, 1981). The reaction was initiated by adding a five-fold molar excess of Alexa Fluor 488 and allowed to proceed for about one hour at room temperature with stirring and protected from light. The sample was then buffer-exchanged with the same buffer composition as before, but with 10 mM DTT and pH 6.5. The extent of labeling was assessed using mass spectrometry. The protein sample was then concentrated to~20 mM.
All experiments for the backbone assignment of the PKA-C/ATPgN/PKIa ternary complex were performed on a Bruker Avance III 850 MHz spectrometer with a TCI cryoprobe. TROSY-based (Salzmann et al., 1998;Salzmann et al., 1999) HNCA and HN(CO)CA (Kay et al., 2011) experiments were collected with a minimum of 32 scans, 1024 ( 1 H), 32 ( 15 N), and 64 ( 13 C) complex points. The TROSY-based HNCACB experiment was collected with 32 scans, 1024 ( 1 H), 35 ( 15 N) and 50 ( 13 C) complex points were performed to measure the 13 Ca and 13 Cb correlations. The HNCO experiments were acquired with a minimum of 16 scans, 1024 ( 1 H), 30 ( 15 N), and 40 ( 13 C) complex points. Before and after each triple resonance experiments a 1 H-15 N CLEAN-TROSY-HSQC (Schulte-Herbrüggen and Sorensen, 2000) spectrum was acquired with 1024 ( 1 H) and a minimum of 64 ( 15 N) complex points. All data were processed using NMRPipe (Delaglio et al., 1995) and visualized using Sparky (Lee et al., 2015;Goddard and Kneller, 2004). The CSI for Ca, Cb, C' and Ha were derived with respect to the reference calculated by Schwarzinger et al. (Schwarzinger et al., 2000;Schwarzinger et al., 2001) and plotted using the GraphPad Prism six software package (GraphPad Software, Inc). The CSP plot (Williamson, 2013) was calculated using the amide chemical shifts according to the following equation: Where Dd is the compounded chemical shift perturbation, Dd HN is the chemical shift perturbation of the amide proton, Dd N is the chemical shift perturbation of nitrogen, and 0.154 is the scaling factor for nitrogen (Mulder et al., 1999).

NMR relaxation experiments
The heteronuclear [ 1 H, 15 N]-NOE spectra were acquired using standard pulse sequences (Farrow et al., 1994a) on a Bruker 850 MHz and 900 MHz Advance spectrometer III equipped with TCI cryoprobes at 27˚C. The heteronuclear [ 1 H, 15 N]-NOE values were calculated from the ratio of the peak intensities with and without proton saturation. The errors were estimated by evaluating the standard deviation of the NOE values (s NOE ): where s Isat and s Iunsat are the root-mean-square noise of the spectra and I sat and I unsat are the intensities of the resonance with and without proton saturation (Farrow et al., 1994b). The 15 N spin relaxation rates (T 1 and T 2 ) for PKIa free and bound to PKA-C/ATPgN complex were measured as reported by Barbato et al. (1992) by acquiring a series of 2D [ 1 H, 15 N]-HQCS spectra at different relaxation delays. The relaxation rates for each resided were obtained by fitting the intensities of each peaks with an exponential decay function. 16 scans, 1024 ( 1 H), 60 ( 15 N) complex points were used to record T 1 -relaxation experiment. The T 2 measurements were recorded using 32 scans, 1024 ( 1 H), 64 ( 15 N) complex points for both PKIa free and bound. For T 1 , the relaxation delays were: (20), 100, 200, 300, 400, 600, 800, and 1000 ms. For T 2 , the relaxation delays were (16.6), 83.1, 166, 249, (332), 498, 664, 830 ms. The numbers in parenthesis indicate the experiments that were repeated for error estimation. All the experiments were recorded using a Bruker 900 MHz Advance spectrometer III equipped with TCI cryoprobes at 27˚C. All experiments on the free form of PKIa was performed using a 0.2 mM sample of uniformly 2 H/ 15 N labeled protein. To measure PKIa relaxation in the ternary complex, the final sample concentration was 0.180 mM 2 H/ 15 N labeled PKIa and 0.220 mM of U-2 H labeled PKA-C. All samples were prepared in aqueous buffer consisting of 20 mM KH 2 PO 4 , 90 mM KCl, 60 mM MgCl 2 , 10 mM DTT, and 1 mM NaN 3 at pH 6.5.
The ms-ms timescale conformational dynamics of backbone amides in PKIa free form and the PKA-C/ATPgN/PKIa complex were measured using the relaxation-compensated version of the Carr-Purcell-Meiboom Gill (CPMG) relaxation dispersion experiments (Baldwin and Kay, 2009;Long et al., 2008;Palmer et al., 2001). The experiments were performed in an interleaved mode with a n CPMG values of 0, 12.5 and 1000 Hz. Effective transverse relaxation rate constant, R 2; eff , were determined at each n CPMG value using the peak intensities with and without relaxation period according to the equation (Mulder et al., 2001): where I 0 and I are the peak intensities of the resonances in the 2D spectra acquired in the absence and presence of a relaxation period, respectively, and T is the total CPMG time (Mulder et al., 2001) which was 40 ms. All the experiments were acquired on Bruker 900 MHz spectrometer using 16 scans with 1024 ( 1 H) and 64 ( 15 N) complex points with a recycle delay of 4.5 seconds.

Paramagnetic relaxation measurements
The intra-molecular 1 H PRE-G 2 relaxation measurements on the free form of PKIa mutants were carried out using the pulse sequence by Iwahara et al. (2007) on a Bruker Advance 700 MHz spectrometer at 27˚C. All experiments were performed using 160 scans with 2048 ( 1 H) and 128 ( 15 N) complex points. A two-time point measurement was performed using a relaxation time of 4 and 14 ms in an interleaved fashion. The 1 H PRE-G 2 values were calculated using the equation (Iwahara et al., 2007): where G2 is the PRE-relaxation rate, the time points are T a and T b , I para is the corresponding intensity with a spin label and I dia is the corresponding intensity with a reduced spin label: Where s dia and s para are the roots mean square noise of the respective spectra. For the simultaneous detection of inter-and intra-molecular PREs of PKIa bound to PKA-C/ATPgN, we used a TROSY-based CCLS variation of the standard PRE pulse sequence . For both paramagnetic and diamagnetic experiment, the complex sample was prepared with a total protein concentration of 140 mM using a 1:1 PKA-C/PKIa molar ratio.

Residual dipolar coupling measurements
Backbone amide 1 D NH RDCs of 15 N PKIa were measured at 27˚C by taking the difference in 1 J NH scalar coupling in aligned and isotropic media (Tjandra and Bax, 1997). The aligned medium was constituted by DMPC/D7PC bicelles (q = 3.5) and 1 J NH couplings were measured using the in-phase anti-phase [ 1 H-15 N] HSQC sequence (Ottiger et al., 1998). To get an orthogonal set of 1 D NH RDCs values, we used stretched polyacrylamide gel (Ishii et al., 2001). All the experiments were carried out on a Bruker 850 MHz Avance III spectrometer equipped with a 5 mm triple resonance cryoprobe, using 320 scans with 1024 ( 1 H dimension) and 60 ( 15 N dimension) complex points.

Circular dichroism (CD) spectra acquisition and data analysis
The CD spectra in the far-UV of free PKIa in native conditions were recorded using a JASCO J-815 spectropolarimeter (Chemes et al., 2012). The spectra were acquired at 25˚C scanning from 180 to 260 nm and recording at 20 nm/min scan speed with a bandwidth of 5 nm and a pitch of 0.1 nm. 100 mM PKIa was solubilized in 20 mM PIPES buffer (pH 7.0) with 150 mM NaCl. To record the baseline, a blank sample with buffer alone was used. The data were analyzed using the BeSTSel web server (http://bestsel.elte.hu/; Micsonai et al., 2018).
Small angle X-ray scattering (SAXS) experiment and data analysis SAXS data were collected at the University of Utah using an Anton Paar SAXess instrument with line collimation and solid-state detector. In both PKIa free and the PKA-C/PKIa complex, the proteins were equilibrated by dialysis in buffer containing 20 mM MOPS, 90 mM KCl, 60 mM MgCl 2 , 10 mM DTT, 1 mM NaN 3 (pH 6.5), and 12 mM of ATPgN. For measurements of the PKIa free form, a protein concentration of 1 mM was used, and for the PKA-C/PKIa complex sample, a final protein concentration 0.2 mM protein with PKA-C/PKIa in 1:1 molar ratio. SAXS data were reduced and desmeared using the SAXSQuant (Anton Paar) software suite and further analyzed using PRIMUS in the ATSAS 2.8.3 software suite (Franke et al., 2017). The fitting of the MD structural ensembles to the experimental scattering data was performed using the MultiFoXS server (Schneidman-Duhovny et al., 2013). 100 random snapshots from MD simulations with different radius of gyration (R g ) were chosen as the conformational ensembles, and the fitting was done for the q range (0.01 to approximately 0.18 Å À1 ). The top 10 structures with the lowest c values were selected as the final structure ensembles.

Modeling of PKIa ensembles using replica-averaged metadynamics (RAM) simulations
For the free form, we used the extended conformation of the full-length PKIa as a template. The protein was solvated in a rhombic dodecahedron solvent box with TIP3P water molecule layer extended approximately 10 Å away from the protein's surface. Counter ions (K + and Cl -) were added to ensure electrostatic neutrality corresponding to an ionic concentration of~150 mM. All protein covalent bonds were constrained with the LINCS (Hess et al., 1997) algorithm and long-range electrostatic interactions were calculated using the particle-mesh Ewald method with a real-space cutoff of 10 Å (Best et al., 2012;Darden et al., 1993). Parallel simulations of 130 ns were performed simultaneously using GROMACS 4.6 (Hess et al., 2008) with CHARMM36a1 force field (Best et al., 2012). As a starting configuration for the bound form, we used the ternary complex of PKA-C/ATP/ PKI 5-24 (PDB: 1ATP) and built the reminder amino acids of PKIa using PyMOL (pymol.com). The remaining parameters were set using the same protocol for the free form.
The subsequent RAM simulations were started from the random snapshots of the production trajectory (the last 100 ns). As for previous RAM simulations (Roux and Weare, 2013), we chose 10 replicas: five replicas initiated from partially folded conformers, and the others from extended conformers. We set two protocols imposing different restraints: a) RAM with CS restraints (RAM_CS) for both free and bound forms in which the predicted backbone chemical shifts were back-calculated by Camshift method implemented in ALMOST 2.1 (Fu et al., 2014); and b) RAM with CS and RDC restraints (RAM_CSRDC) for the free form only in which the predicted RDCs were back-calculated using the tensor-free method (Camilloni and Vendruscolo, 2015) implemented in PLUMED 2.1 (Bonomi et al., 2009). Four collective variables (CVs) were chosen to monitor the conformational plasticity and secondary structure of PKIa: a) psi angles for all residues (backbone and dihedral); b) radius of gyration for all backbone Ca atoms (radius of gyration); c) helical content of residues 4-22 (helical content of the N-terminus); and d) helical content of residue 32-50 (helical content of the NES motif). Gaussian deposition rate was performed with an initial rate of 0.125 kJ/mol/ps, where the s values were set to 0.5, 0.02 nm, 0.1, and 0.1 for the four CVs. Of the 10 replicas, each of the four CVs were imposed on two replicas, and the remaining two replicas were left neutral. The RAM simulations were carried out using GROMACS 4.6 in conjunction with PLUMED 2.1 (Bonomi et al., 2009) and ALMOST 2.1 (Fu et al., 2014), and continued for~250 ns for each replica with exchange trails every 0.5 ps. The free energy along the four CVs converged after 150 ns, with the standard deviation below one kcal/mol. The last 100 ns of each replica constituted the production trajectory for a total simulation time of 1.0 ms and used for analysis.

Adaptive sampling of pkia in free and bound forms and Markov model analysis
For the free form, the adaptive sampling was started from randomly chosen 320 snapshots of PKIa from the RAM simulations. The initial velocities were randomly generated to satisfy the Maxwell distribution at 300K. A~200 ns simulation was initiated from each starting configuration. Therefore, a total of 60 ms trajectories and 240,000 snapshots (250 ps per frame) were collected for subsequent analysis. For the bound form, the adaptive sampling was started from 50 snapshots of the RAM simulations, and~20 ms trajectories have been collected. More samplings are undertaken.

Markov model and time-lagged independent component analyses (tICA)
The Markov model analysis was carried out using MSMBuilder 3.5 (Harrigan et al., 2017). The contact distances between residue pairs that are separated by at least four residues, were chosen as the metrics to characterize the conformational transition of PKIa. The representation in this metric space was further reduced to 6-dimension vectors using time-lagged independent component analysis (tICA) at a lag time of 15 ns. The 240000 snapshots were clustered into 50 microstates with minibatch K-Mean clustering and Markov model was built upon the transition counts between these microstates. The same tICA analysis was applied to both free and bound forms.

Statistical analysis of equilibrium population and MFPT
To obtain the statistical distribution and errors on the equilibrium population and MFPT along the given tICA projections, 150 rounds of bootstrapping with replacement were performed. Specifically, for each round, new clustering and Markov model is built, and the microstates are categorized into four major states based on the tICA projections. The equilibrium population and MFPT are subsequently computed. The same MFPT analysis was applied to both free and bound forms.

Stopped-flow TR-FRET experiments and kinetic binding model
The kinetics of binding between PKA-C and PKIa were measured using home-built stopped-flow spectrofluorometer (Muretta et al., 2015). Equal volumes of each component were mixed, the samples were then excited at 475 nm, and fluorescence emission was measured using a 520 nm filter. For Alexa-labeled PKA-C C199A, S325C and TMR-labeled PKIa, the final concentration of the kinase was fixed at 100 nM, while the concentration of PKIa was varied from 0 to 250 times the concentration of PKA-C. For the doubly-labeled PKIa V3C, S59C and unlabeled PKA-C, the concentration of the peptide was fixed at 100 nM final concentration while the concentration of the kinase was varied from 0 to 800 times the concentration of PKIa V3C, S59C . The buffer used in both setups contains 20 mM KH 2 PO 4 , 90 mM KCl, 10 mM MgCl 2 , 16 mM ATP, 10 mM DTT, 1 mM NaN 3 , pH 6.5 at 25˚C. The total fluorescence was fit into equations describing either single, double or triple exponential decays. Data analyses were done using Origin (OriginLab) software.
Since we saturated PKA-C with an excess of nucleotide, we neglected the equilibrium between open (apo PKA-C) and intermediate (ATP-bound, PKA-C*) state in the fitting procedure. In the model, PKI* represents the ensemble of conformations that is recognized by PKA-C*. The proposed model of binding is reported in Scheme 1.
The differential equations describing the kinetic model of Scheme 1 are: For simplicity, PKA-C is denoted as P and PKI as I. The instantaneous fluorescence intensity FI was calculated using the formula, Where c PKA C Ã PKI Ã ½ þc Ã PKA C PKI ð Þ Ã ½ ð Þ c PKA C Ã PKI Ã ½ eqþc Ã PKA C PKI ð Þ Ã ½ eq ð Þ is the normalized intensity, 'SC' is a scaling factor, 'Baseline' is the basal fluorescence, c and c* are the FRET efficiency parameters. The differential equations 1-5 were solved numerically using MATLAB ode solver 'ode23s', which was incorporated in an optimization protocol to evaluate the kinetic parameters. The optimization protocol included an initial minimization using MATLAB's nonlinear programming solver (fminsearch), which was ran for 10 4 steps and followed by Genetic Algorithm optimization with a population size of 50 and 10 4 generations. All the six rate constants (k 1 , k -1 , k b , k -b , k r , k -r ) were collectively fit for all data points. The FRET efficiency parameters (c and c*) were fit for each specific labelling scheme. The parameters 'SC' and 'Baseline' were fit for each FRET experiment to correct for the experimental errors.
The fitting resulted in an on rate binding constant (k b ) of 1.5 Â 10 7 M À1 s À1 and a dissociation rate constant (k -b ) of 0.5 s À1 . For the slow phase, we found a forward rate of 2400 s À1 and reverse rate of 720 s À1 . The 'on' and 'off' conformational exchange rates (k 1 and k -1 ) of free PKIa were 1.9 Â 10 4 s À1 and 1.5 Â 10 4 s À1 .