Extent of N-terminus exposure by altered long-range interactions of monomeric alpha-synuclein determines its aggregation propensity

As an intrinsically disordered protein, monomeric alpha synuclein (aSyn) constantly reconfigures and probes the conformational space. Long-range interactions across the protein maintain its solubility and mediate this dynamic flexibility, but also provide residual structure. Certain conformations lead to aggregation prone and non-aggregation prone intermediates, but identifying these within the dynamic ensemble of monomeric conformations is difficult. Herein, we used the biologically relevant calcium ion to investigate the conformation of monomeric aSyn in relation to its aggregation propensity. By using calcium to perturb the conformational ensemble, we observe differences in structure and intra-molecular dynamics between two aSyn C-terminal variants, D121A and pS129, and the aSyn familial disease mutants, A30P, E46K, H50Q, G51D, A53T and A53E, compared to wild-type (WT) aSyn. We observe that the more exposed the N-terminus and the beginning of the NAC region are, the more aggregation prone monomeric aSyn conformations become. N-terminus exposure occurs upon release of C-terminus interactions when calcium binds, but the level of exposure is specific to the aSyn mutation present. There was no correlation between single charge alterations, calcium affinity, or the number of ions bound on aSyn’s aggregation propensity, indicating that sequence or post-translation modification (PTM)-specific conformational differences between the N- and C-termini and the specific local environment mediate aggregation propensity instead. Understanding aggregation prone conformations of monomeric aSyn and the environmental conditions they form under will allow us to design new therapeutics targeted to the monomeric protein, to stabilise aSyn in non-aggregation prone conformations, by either preserving long-range interactions between the N- and C-termini or by protecting the N-terminus from exposure.


Introduction 43
In Parkinson's disease (PD) and other synucleinopathies, the monomeric protein alpha synuclein 44 (aSyn) becomes destabilised, misfolds and aggregates into insoluble, highly structured and β-sheet 45 containing fibrils which form part of Lewy bodies (LB) and Lewy neurites (LN) 1,2 . In its monomeric 46 form, aSyn is a soluble, intrinsically disordered protein (IDP) that is highly flexible and thereby enables 47 been shown to be altered upon phosphorylation 41  presence of calcium are located at the C terminus (arrows with assigned amino acid residues) in both 175 pS129 and D121A aSyn. 176 In order to determine whether the above structural changes we observed in the presence of calcium 177 were simply due to changes in the affinity for calcium of the different aSyn variants, we performed 178 calcium titrations experiments. We applied two different fitting algorithms to determine the 179 dissociation constant. Using a previously applied model 43 , but this time using a fixed ligand (calcium) 180 number of 3 (which relates to the number of calcium ions bound as determined by MS with the same 181 aSyn to calcium ratio), we obtained a KD of 95 (± 16) μM, 91 (± 16) μM and 69 (± 8) μM for WT, pS129 182 and D121A aSyn, respectively. Using the Hill equation, which also takes into account the level of 183 cooperativity, we obtain a KD of 670 (± 51) μM, 670 (± 33) μM and 460 (± 27) μM for WT, pS129 and 184 D121A aSyn, respectively. For all fittings, we get an n >1, indicating that calcium binds cooperatively 185 to aSyn ( Figure S7). 186 We next performed ThT-based kinetic assays to investigate whether the above observed 187 conformational differences or calcium binding capacities of aSyn influenced the aggregation 188 propensity of the three aSyn variants. The results of the assay showed that although D121A and pS129 189 aSyn had different charges at the C-terminus, both had a lower aggregation propensity than WT aSyn,190 particularly in the absence of calcium ( Figure S8). The presence of calcium did increase the aggregation 191 rate of D121A and pS129 aSyn in comparison to aggregation rates without calcium, however not to 192 the same extent as the rate of WT aSyn. This was also reflected in the concentration of remaining 193 monomer determined by size-exclusion chromatography high-pressure liquid chromatography (SEC-194 HPLC) ( Figure S8 and S9). It thus appears that the affinity of aSyn to calcium does not influence 195 aggregation rate per se as the affinity of D121A aSyn for calcium is higher than of WT and pS129 aSyn. 196 197 D121A and pS129 aSyn are less exposed at the N-terminus compared to WT aSyn upon calcium 198 addition 199 D121A and pS129 aSyn monomers using HDX-MS. This technique probes the submolecular structure 201 and dynamics of proteins by employing hydrogen-deuterium exchange, and thus permit the 202 identification of protein sequences that are more exposed to the solvent and/or less strongly 203 hydrogen-bonded (deprotected). Binary comparison of the deuterium uptake profile between WT and 204 D121A aSyn and WT and pS129 aSyn showed that both variants are not significantly different to WT 205 aSyn (Figure 3a and b). 206 We again used calcium to perturb the ensemble of conformations to compare alterations of long-207 range interactions between the three aSyn variants. Binary comparison of the deuterium uptake 208 profile of monomeric WT aSyn revealed solvent protection at the C-terminus and significant 209 deprotection at the NAC and the N-terminus region of aSyn in the presence of calcium compared to 210 the absence of calcium ( Figure 3c). This indicates that, when calcium is bound to aSyn, there is reduced 211 exposure to the solvent or increased hydrogen bonding at the C-terminus of aSyn, where calcium 212 binds, and deprotection of the N-terminus, as observed by CSPs using NMR. A similar behaviour was 213 also observed for D121A and pS129 aSyn as, upon calcium binding, solvent protection is observed at 214 the C-terminus and deprotection at the NAC region of aSyn (Figures 3d,e). However, while D121A aSyn 215 has a more solvent exposed N-terminus, pS129 aSyn displays little difference in protection levels at 216 the N-terminus. Despite both of these averaging structures being deprotected upon the addition of 217 calcium, they are still more protected/less exposed compared to WT aSyn in the calcium-bound state 218 (Figure 3c-e). Both NMR and HDX-MS indicate that D121A and pS129 aSyn have different ensembles 219 of conformations compared to WT aSyn. Upon perturbation of the conformational ensemble by 220 calcium binding, the degree of exposure of the N-terminus is much less pronounced in D121A and 221 pS129 aSyn than in WT aSyn. This correlates with the reduced aggregation propensity in the calcium-222 bound state of D121A and pS129 aSyn, as determined by the ThT fluorescence kinetic assay. compared to WT aSyn. Bars represent differences in deuterium uptake along the sequence of 226 differently compared aSyn variants (e.g. WT vs D121A aSyn) with the N-terminus labelled in blue, the 227 NAC region in yellow, and the C-terminus of aSyn in red. Negative values represent increased 228 deuterium uptake in the mutant (a,b) or in the calcium bound state (c-e), more solvent exposure, and 229 less hydrogen bonding. Peptides containing the mutation were not comparable to WT aSyn and were 230 removed from the data set, indicated by blank regions. Comparison of the deuterium uptake (in Dalton 231 -Da) between (a) WT and D121A aSyn and (b) WT and pS129 aSyn showed that both were not 232 significantly different to WT aSyn. (c) In the presence of calcium, WT aSyn becomes significantly more 233 deprotected (more solvent exposed/less hydrogen bonded) at the N-terminus and the NAC region, 234 and at the same time becomes solvent protected at the C-terminus. (d) D121A aSyn is significantly 235 more deprotected at the N-terminus and the NAC region upon calcium addition and solvent protected 236 at the C-terminus. (e) pS129 aSyn is deprotected at the NAC region upon calcium addition and solvent 237 protected at the C-terminus. The grey trace signifies the error (1 s.d.) of six replicates collected per 238 condition. Data acquired at each peptide were subjected to a Student's t-test with a p-value ≤ 0.05 239 and significant differences are presented by a *. 240 241 Familial aSyn mutants display differences in aggregation propensity and N-terminus solvent 242 exposure compared to WT aSyn 243 To further investigate whether differences in the sub-molecular structure are apparent in the familial 244 aSyn mutants A30P, E46K, A53T, A53E, H50Q, and G51D and whether this can influence aggregation 245 rates, we first studied their aggregation kinetics in the presence and absence of calcium using ThT-246 based kinetic assays. Comparison of the fibrillisation rates of the familial mutants with WT aSyn in the 247 absence of calcium shows that the aSyn mutants E46K, A53T, and H50Q aggregate faster than WT 248 aSyn while the familial aSyn mutants A30P, A53E, and G51D aggregate more slowly than WT aSyn 249 ( Figure S10). Upon the addition of calcium, WT aSyn nucleation and elongation is enhanced, as 250 previously shown 39 , and for the fast aggregating aSyn mutants, A53T, E46K, and H50Q the aggregation 251 rate is also enhanced upon the addition of calcium, similarly to WT aSyn. However, the slow 252 aggregating aSyn mutants A30P, A53E, and G51D are either insensitive to calcium addition or 253 aggregate more slowly. In order to determine whether the difference in aggregation was due to 254 structural differences of the monomer, we again employed FTIR spectroscopy. The monomeric familial 255 aSyn mutants all had an increased beta-sheet content, particularly A30P, E46K and A53T aSyn which 256 were significantly different ( Figure S11). 257

258
To gain more detailed and localised structural information than obtained by FTIR, we employed HDX-259 MS. The familial aSyn mutants A53T and A53E were selected from the familial mutants' panel for this 260 analysis, as they displayed different aggregation behaviour, even though the point mutations were 261 localised on the same residue. Binary comparison of WT and A53T aSyn in the absence of calcium 262 showed that there was no significant difference in deuterium uptake between the two protein states 263 (Figure 4a), as observed for comparisons between WT and A53E aSyn (Figure 4b), and also A53T and 264 A53E aSyn in the absence of calcium (Figure 4c). Upon the addition of calcium, solvent protection is 265 observed at the C-terminus of A53T and A53E aSyn similar to WT and the other aSyn variants (see 266 D121A and pS129 aSyn), indicating that the protection at this region is primarily due to calcium 267 binding. At the same time, A53T aSyn is significantly deprotected at the N-terminus, at a similar level 268 the NAC region nor at the N-terminus, upon calcium binding. Thus, the extent to which structural 271 dynamics are perturbed in the N-terminal region in response to binding of calcium at the C-terminus 272 correlates with an increase in the aggregation propensity of aSyn and its variants.  Table S1 and S2). 313 conformation C, as indicated by more populated low CCS values (Figure 5a, +2Ca 2+ ). Furthermore, 315 analysis of the mass spectra showed that there were no significant differences in the distribution and 316 maximum number of calcium ions bound to any of the aSyn variants, with, on average, two to three 317 Ca 2+ ions bound at a 1:10 protein to calcium ratio ( Figure S14, S15). to detect using ensemble measurement techniques. Furthermore, it is difficult to discern differences 344 in overall conformations when comparing mutant to WT aSyn. In this study, we used the biologically 345 relevant ion, calcium, to perturb the conformational ensemble of aSyn structures and compared the 346 differences in CSPs, hydrogen bonding/solvent exposure and distribution of conformations between 347 aSyn and its mutants. In general, calcium has been shown to enhance the aggregation rate of aSyn 348 39,47 , likely by a similar mechanism as low pH, whereby the reduction of the negative charge at the C-349 terminus leads to C-terminal collapse, altered long-range electrostatic interactions and enhanced 350 hydrophobic interaction between the C-terminus and the NAC region which drives aggregation 22,48-351 51 . We observed mutant specific differences in long-range interactions, compaction and solvent 352 exposure compared to WT aSyn which will be discussed individually. 353 354

Mutation and phosphorylation at the C-terminus alter long-range interactions 355
We first investigated the role of charge and long range interactions at the C-terminus by comparing 356 two aSyn variants with reduced (D121A) and added (pS129) negative charge. We observed that both, 357 D121A and pS129 aSyn displayed reduced aggregation rates in comparison to WT aSyn, indicating that 358 increasing or decreasing charge by one residue at the C-terminus does not decrease or increase 359 aggregation rates, respectively, as may have been expected. Many studies investigating the effect of 360 charge on aSyn aggregation rates use C-terminus truncations which heavily disrupt and remove long-361 phosphorylation at S129 of these truncated aSyn reduces the aggregation rate, suggesting 363 phosphorylation at S129 does have an inhibitory effect on aggregation 52 . Furthermore, calcium 364 binding affinity does not correlate with aggregation rates, suggesting that altered residual monomeric 365 structure at specific regions and not calcium binding or alteration of single charges per se influences 366 aggregation rates. We observed only small differences in the conformational properties of the 367 monomeric aSyn, as revealed by changes in CSPs and solvent exposure for D121A or pS129 compared 368 to WT aSyn in the absence of calcium. This is likely due to the vast array of conformations sampled by 369 the protein leading to minimal structural changes using protein ensemble measurement techniques 370 such as NMR and HDX-MS. However, by perturbing the ensemble of conformations, as seen upon the 371 addition of calcium, we could observe differences in CSPs and deuterium uptake upon calcium binding. 372 pS129 aSyn has a different calcium-binding region and displays no broadening in the NAC region 373 compared to WT aSyn, while D121A has a higher degree of CSPs across the sequence, but also no NAC 374 region broadening, suggesting long-range interactions with the NAC region in both these mutants are 375 altered before calcium binds. Broadening in the NAC region has been observed for WT aSyn when 376 bound to calcium 39 and at low pH, suggesting enhanced interactions the between calcium binding 377 region, namely the charge neutralised C-terminus, and the NAC region 22 . Regarding aSyn's propensity 378 to aggregate, we observe, using HDX-MS, that the N-terminus of pS129 aSyn is not solvent exposed 379 upon calcium binding, whereas for D121A aSyn, although the N-terminus is slightly exposed, is 380 significantly less exposed compared to WT aSyn upon calcium binding, correlating to the decreased 381 aggregation propensity of D121A and pS129 aSyn. Previous HDX-MS studies have suggested that the 382 N-terminus of aSyn may be involved in aggregation as there is heterogeneity in its solvent exposure 383 during aggregation which is also linked to fibril morphology, while the C-terminus remains completely 384 solvent exposed 53-55 . Here, we show that the extent of N-terminus (aar 1-60) and NAC region (aar 61-385 95) exposure, based on the amount of deuterium exchange which is determined by ease of 386 accessibility, is correlated to the aggregation propensity of aSyn, where WT>D121A>pS129 in terms 387 of N-terminus exposure, but the opposite is observed for aggregation propensity. Importantly, we only 388 observe N-terminus exposure upon the disruption of long-range interactions with the C-terminus 389 upon calcium binding. The C-terminus thus greatly influences aggregation propensity, as it is 390 important in maintaining long range interactions and solubility of monomeric aSyn 56,57 . Mutation of 391 proline 58 , or glutamate 57 residues to alanine at the C-terminus increases aSyn aggregation propensity, 392 yet mutation of tyrosine 27 residues to alanine decreases aSyn aggregation propensity. This suggests 393 that mutations of specific residues alter specific long-range interactions which subsequently influence 394 the distributions of conformations within the dynamic ensemble and thus the aggregation propensity 395 to differences in aggregation rates, as pY125 does not influence the aggregation rate compared to WT 397 aSyn 59 , neither the binding capacity of aSyn to nanobodies nor the alteration of metal binding sites, 398 indicating very site-specific functions and interactions are present at the C-terminus 41,59 . Although 399 D121A aSyn is not a naturally occurring mutation, by comparing it to pS129, we can explore how

Familial aSyn mutants display different long-range interactions 409
While all familial aSyn point mutations reside at the N-terminus, the putative calcium binding site is 410 at the C-terminus 60 . Certainly, the presence of a familial aSyn mutation has been shown to alter 411 interactions between the mutation site and the C-terminus by NMR compared to WT aSyn, with 412 regional differences apparent for each aSyn mutant in physiological and mildly acidic conditions 23,35 . 413 In the present study, we observe that the familial aSyn mutants have different aggregation kinetics in 414 response to calcium, which is understandable considering the mutation regions interact with the 415 calcium binding regions at the C-terminus. Using HDX-MS, we observe a difference in the level of 416 solvent protection at the N-terminus of A53T and A53E aSyn upon binding of calcium suggesting that 417 indeed different long-range interactions are present. A local unfolding event (deprotection) at the N-418 terminus and the NAC region of WT and A53T aSyn correlates with their increased aggregation 419 propensity upon calcium addition. No such deprotection was observed for the aSyn mutant A53E, 420 whose aggregation kinetics were similar in the presence and absence of calcium. We expect that the 421 release of long-range contacts with the C-terminus leads to exposure of the N-terminus and the NAC 422 region, which is observed in WT and A53T aSyn, to be a major factor influencing aSyn aggregation 423 kinetics. Several experiments have shown the importance of the N-terminus in modulating aSyn 424 aggregation. The presence of repeating units, KTKE, across the N-terminus seems to have an important 425 role because addition, deletion, swapping and their spacing lead to differential aggregation rates 61,62 . 426 Furthermore, cross linking G41C and V48C leads to inhibition of aggregation 63 , and targeting proteins 427 that bind to aar 37-54 prevents aggregation 64,65 . It must be noted that all the familial aSyn mutations 428 stability combined with a lower propensity to form an α-helix, as observed by FTIR, at the N-terminus 431 compared to WT aSyn, may skew the distribution of the conformational ensemble leading to 432 conformations with high propensity to form oligomers and fibrils 67,68,71,72 . We observe increased N-433 terminus solvent exposure for the 'fast aggregating' mutant A53T compared to the 'slow aggregating' 434 mutant A53E. In another study, the 'fast aggregating' mutant, E46K, also displays an increased solvent 435 exposure across its sequence, and, in addition, N-terminus residues are involved in oligomerisation 35 . 436 The fact that such differences in aSyn long-range contacts and an increase in N-terminus solvent 437 exposure can be identified as early as the monomer level, and correlate to the propensity to fibrillise 438 is important, and a step towards understanding early events in the misfolding pathway and how 439 structure and environmental factors may influence aggregation propensity of the monomer. aSyn mutants as the C-terminus collapses due to charge neutralisation upon binding to calcium, which 448 has also been previously observed when Mn 2+ and Co 2+ bind WT aSyn 44 . Divalent cation binding is 449 specific to the C-terminus, leading to compaction of aSyn conformations, non-specific binding of 450 monovalent ions (e.g. K + , Na + ) leads to extended structures being favoured due to charge shielding of 451 the N-and C-termini (A.D. Stephens, et. al., in preparation). Of note, the CCS values most favoured in 452 the calcium-bound state in region C are also present in the non-calcium bound state, but to a lesser 453 extent, it is thus possible that calcium binding leads to a bias towards structures that are already 454 available to the monomer in the calcium-free state. The increase in aggregation propensity of WT aSyn 455 upon calcium binding cannot only be explained by charge neutralisation at the C-terminus as all 456 familial aSyn mutants should have responded in the same way to calcium which was not the case. It is 457 more likely that the difference in aggregation propensity is a result of perturbed long-range 458 interactions between the C-terminus, and thus the sequence and its interaction with the local 459 environment, which skew the population towards more aggregation prone structures. Multiple As an IDP, aSyn samples many different conformations making it difficult to identify specific 466 aggregation prone conformations, particularly using ensemble measurement techniques. By 467 comparing the submolecular structure of calcium-bound aSyn variants, we instead sampled a skewed 468 population and inferred differences in structure and aggregation propensity as part of a response to 469 calcium binding at the monomer level. We attribute the increase in aggregation propensity upon 470 calcium binding to structural perturbation, as we observe no correlation in aSyn's aggregation 471 propensity to its affinity to calcium, the number of calcium ions bound or charge neutralisation at the 472 C-terminus. Instead, we observe different responses to calcium based on the presence of different 473 long-range interactions which are likely already altered in non-calcium bound forms of the familial 474 mutants and upon the addition of PO 4at S129 ( Figure 5). Calcium binding leads to further disruption 475 of intramolecular interactions with the C-terminus leading to unfolding and solvent exposure of the 476 N-terminus. 477 The extent of N-terminus solvent exposure upon C-terminal binding of calcium correlates with the 478 aggregation propensity of aSyn; pS129, A53E, and to some extent D121A aSyn were less solvent 479 exposed at the N-terminus and had a reduced aggregation propensity compared to WT and A53T aSyn 480 which were more aggregation prone and more solvent exposed at the N-terminus and at the beginning 481 of the NAC region ( Purification was performed on an ÄKTA Pure (GE Healthcare). Protein concentration was determined 519 by measuring the absorbance at 280 nm on a Nanovue spectrometer using the extinction coefficient 520 5960 M -1 cm -1 . 521 Protein purity was analysed using analytical reversed phase chromatography. Each purification batch 522 was analysed using a Discovery BIO Wide Pore C18 column, 15cm x 4.6mm, 5µm, column with a guard 523 cartridge (Supelco by Sigma-Aldrich) with a gradient of 95% to 5% H2O + 0.1% trifluroacetic acid (TFA) 524 and acetonitrile + 0.1% TFA at a flow-rate of 1 mL/min. The elution profile was monitored by UV 525 absorption at 220 nm and 280 nm on an Agilent 1260 Infinity HPLC system (Agilent Technologies LDA 526 UK Limited, UK) equipped with an autosampler and a diode-array detector (a representative 527 chromatograph is shown in Figure S1A). Protein purity fell between 89 -96 %. 528 Purification of aSyn for nuclear magnetic resonance experiments 529 E. coli was grown in isotope-enriched M9 minimal medium containing 15N ammonium chloride, and 530 13C-glucose similar to our previous protocol 73 . Briefly, to isolate expressed aSyn the cell pellets were 531 resuspended in lysis buffer (10mM Tris-HCl pH 8, 1mM EDTA and EDTA-free complete protease 532 inhibitor cocktail tablets (Roche, Basel, Switzerland), 0.2 mM phenylmethylsulfonyl fluoride (PMSF) 533 and Pepstatin A and lysed by sonication. The cell lysate was centrifuged at 22,000 g for 30 min to 534 remove cell debris and the supernatant was then heated for 20 min at 90 °C to precipitate the heat-535 sensitive proteins and subsequently centrifuged at 22,000 g. Streptomycin sulfate (Sigma-Aldrich) 536 10mg/ml was added to the supernatant to precipitate DNA. The mixture was stirred for 15 min 537 followed by centrifugation at 22,000 x g, then repeated. Ammonium sulfate 360 mg/ml was added to 538 the supernatant precipitate the protein aSyn. The solution was stirred for 30 min and centrifuged again 539 at 22,000 x g. The resulting pellet was resuspended in 25mM Tris-HCl, pH 7.7 and dialysed overnight. 540 The protein was purified by IEX on a HiPrep Q FF anion exchange column (GE Healthcare) and then 541 further purified by SEC on a HiLoad 16/60 Superdex 75 prep grade column (GE Healthcare). All the 542 fractions containing the monomeric protein were pooled together and concentrated by using amicon 543 10 k MWCO centrifugal filtration devices (Merck). 544 545 Purification of phosphorylated serine 129 aSyn 546 WT α-syn 13 C/ 15 N-labelled (α-syn 13 C/ 15 N) was expressed and purified as previously described 71,74 . 547 Briefly, E.coli BL21(DE3) cells were transfected with a pT7-7 plasmid containing WT aSyn and was 548 cultured in an isotopically supplemented minimal media according to a previously described protocol 549 71 , then aSyn 13 C/ 15 N was purified using an anion exchange chromatography followed by reversed-550 phase HPLC (RP-HPLC) purification using a Proto 300 C4 column and a gradient from 30 to 60% B over 551 35 min at 15 ml/min, where solvent A was 0.1% TFA in water and solvent B was 0.1% TFA in 552 acetonitrile, the fractions containing the protein were pooled and lyophilized and the protein was 553 stored at -20°C. For the preparation of phosphorylated S129 α-syn 13 C/ 15 N ( aSyn 13 C/ 15 N pS129), we 554 used a previously established protocol using PLK3 kinase to introduce selectively the phosphorylation 555 at S129 75 . The WT aSyn 13 C/ 15 N was resuspended in the phosphorylation buffer (50 mM HEPES, 1 mM 556 MgCl2, 1 mM EGTA, 1 mM DTT) at a concentration of ∼150 µM and then 2 mM of ATP and 0.42 μg of 557 PLK3 kinase ( Invitrogen) per 500 g of protein were added. The enzymatic reaction was left at 30°C 558 overnight without shaking. Upon complete phosphorylation, as monitored by mass spectroscopy 559 (LC/MS), aSyn 13 C/ 15 N pS129 was purified from the reaction mixture by RP-HPLC using an Inertsil 560 WP300-C8 semiprep column. Finally, the fractions containing the protein of interest were pooled and 561 quality control of aSyn 13 C/ 15 N pS129 was performed using mass spectroscopy, UPLC, and SDS-PAGE, 562 the protein was 99.89% phosphorylated ( Figure S1B-D). 563

Solution nuclear magnetic resonance (NMR) 564
In order to probe the structure and thermodynamics of calcium binding with aSyn WT, pS129 and 565 D121A at a residue specific level, we employed a series of 1  When using this fitting model in the case of WT aSyn we obtained a KD of 21 (± 5) μM and an L of 7.8 592 (± 0.51) 39 . Based on the present MS data, we here fixed the value of L to 3. 593 We then used a different model that accounts for the cooperativity of the binding. In particular, we 594 used the Hill equation to fit our data: 595 Where the Hill coefficient, n, describes the cooperativity of the binding. A n value higher than 1 597 indicates a positive cooperativity for the binding.