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An Empirical Method to Accurately Determine PeptideAveraged Protection Factors from Hydrogen Exchange MS Data Benjamin Thomas Walters Anal. Chem., Just Accepted Manuscript • DOI: 10.1021/acs.analchem.6b03908 • Publication Date (Web): 19 Dec 2016 Downloaded from http://pubs.acs.org on December 27, 2016

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Analytical Chemistry

An Empirical Method to Accurately Determine Peptide-Averaged Protection Factors from Hydrogen Exchange MS Data Benjamin T. Walters1,2 1-Department of Early Stage Pharmaceutical Development, Genentech, Inc., South San Francisco, CA 94080 2-Department of Protein Analytical Chemistry-2, Genentech, Inc., South San Francisco, CA 94080 E-mail Address: [email protected]

Abstract Amide hydrogen exchange experiments measured by mass spectrometry have become commonplace to study protein structural dynamics; however, the underdetermined nature of these measurements render extraction of exchange rates unreliable at the level of individual peptides. This prevents orthogonal verification of results and severely limits interpretation of the data. This work describes an easy-toimplement empirical method to determine the change in an observed rate constant or the average change in multiple rate constants as compared to some reference condition. This allows direct empirical computation of the average protection factor (PF) for peptides in isolation requiring no knowledge of actual rate constants themselves. Benchmarking the method by comparison of average peptide PFs with site-resolved NMRderived PFs demonstrates high reliability and accuracy. This empirical method provides the first universally reliable strategy for recovering sub-global structural physics from individual peptides and in doing so, standardizes the HX MS measurement, simplifies interpretation, and facilitates clear communication of the results.

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Introduction Amide hydrogen exchange (HX) experiments are indispensable for characterizing the dynamic structural physics of proteins. The expression of HX rates in terms of a protection factor (PF, kex = kch / PF ) relates the measured rate constant, kex , for any particular backbone amide to its chemical exchange rate defined in absence of structure, kch , isolating the physics of H-bonding in the folded protein, and thereby provide quantitative structural information from the experiment that can be directly compared with orthogonal measurements. PFs are traditionally determined by fitting a first order rate constant1 to observed exchange measurements ( kex ) for each amide site and then comparing this value to kch defined by local amino acid sequence, pH, and temperature2. PFs can also quantitate the change observed between two experimental conditions, such as in epitope mapping experiments. HX experiments measured by bottom-up mass spectrometry (HX MS)3,4 cannot determine PFs from peptide measurements comprising multiple exchange sites because the data is frequently underdetermined. Thus the exchange rate, kex , for each site cannot be fit by traditional optimization routines. Splitting the peptidelevel exchange rate determination problem into chunks with a few exponentials5,6 or stretched exponentials7 to compensate for heterogeneity in rate constants have shown variable, context-dependent success. Global analysis algorithms8,9 achieve site-resolved PFs from HX MS shown to agree with NMR measurements9, but experimental challenges limit their routine application. In absence of PFs, HX MS experiments are limited to two-condition experiments with qualitative interpretations and cannot be compared with orthogonal measurements. Herein a method is presented to empirically quantitate the change in a single rate constant or the average change in multiple rate constants without fitting experimental data, and described in the context of determining the average PF for HX MS peptide-level measurements. The accuracy and reliability are demonstrated by showing that empirical HX MS peptide PFs tightly agree with NMR-derived site-PFs determined by traditional methods, and then averaged over the length of each peptide. Advantages of this method are discussed to highlight how it will standardize HX MS results, enhance interpretation, facilitate orthogonal verification of results, and enable quantitatively-accurate communication of the biophysical phenomena being measured by HX MS experiments. Methods Directional protection factors quantitate the change in an HX rate constant(s), kex , from one experimental /k = k , derived condition to another: PFC1→C2 = kex,C1 ex,C2 . To preserve common conventions, when kex,C1 ch from experimental calibrations2, and kex,C2 represents an experimental rate constant determined from a structured protein, these numerical subscripts C1 and C2 are dropped. Traditionally, the exchange rate f (t ) = 1 − exp ( −kex t ) to constant for a particular condition, kex , is fit from the measurements using d = describe the amount of exchanged deuterium ( d ) with HX labeling time, t, for each exchangeable site in the protein. The empirical method computes PFC1→C2 without determining rate constants directly. The labeling time required to exchange a specific amount of deuterium, d, at condition 2 divided by the amount of time required to observe the same amount of exchange in condition 1 also defines PFC1→C2 for a single exchange

site. This can be shown analytically by inversion, t = f −1 ( d ) = ln (1 − d ) / − kex , where if d is constant,

f C2 −1 ( d )= / f C1−1 ( d ) k= PFC1→C2 . Notice that / f C2 −1 ( d ) f C1−1 ( d ) is constant regardless of d for ex,C1 / kex,C2 a single exchange site. This empirically determines PFC1→C2 directly from the measurement.


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Similarly, the average protection factor PFC1→C2 for a group of N rate constants measured together (i.e. f (t ) = N − ∑ i =1 exp ( − ki t ) ), as is the case with peptide level HX MS measured at two conditions, may also N

be determined empirically. Unlike the single exchange site, now f C2 −1 ( d ) / f C1−1 ( d ) varies with the value

of d and multiple ratios are needed in this scenario. Though an analytical expression for f −1 ( d ) cannot be written for multiple exponentials, it can be shown empirically that the geometric mean (GM) of / f C2 −1 ( d ) f C1−1 ( d ) where = d d1 , d 2 ,…, d n , evenly distributed between 0 and N, is approximately equivalent to the GM of the individual rate ratios for each site (described fully in supporting information). The validity of this approach can be found by examining the role of the GM. In figure 1A, f (t ) = N − ∑ exp ( −kt ) is shown in red with three exchangeable sites and rate constants k = 0.1, 0.2, 3 sec −1

(

)

, N=3. A characteristic mono-exponential for f(t), g = ( t ) N 1 − exp −  GM ( k ) t  , is also shown in blue with a single rate constant defined by GM (k ) = 0.39 sec . Notice how g(t) bisects f(t). Consider that by -1

definition,

GM ( X ) =

(∏ x ) M

i =1 i

1/ M

, where M is the number of entries in X, showing that

= GM ( X= ( X / Y ) GM ( X / GM ( Y ) ) ; thus, GM ( k / GM ( k ) ) = 1 . Dividing exchange ) / GM ( Y ) GM

times corresponding to grey circled points connected by dashed lines in fig 1A and taking the GM of the resulting quotients produces the expected value, GM ( g −1 ( d ) / f −1 ( d ) ) = 1 (fig 1B). Putting everything together, two multi-exponentials representing a peptide with six exchangeable sites are simulated in fig 1C = = with PFC1→C2 GM ( k C1 ) / GM ( k C2 ) 18.49 ; k C1 and k C 2 refer to rate constant vectors for each condition as before; numerical values are listed in the fig.1 legend. This method produces less than a 0.5% error with PFC1→C2 GM f C2 −1 ( d ) / f C1−1 ( d ) ) = 18.39 . An algorithmic description of the method is ( empirical = also included in supporting information. Uniform back-exchange (all sites are equal) has no effect on method accuracy and reasonably homogenous back-exchange, as is expected for a majority of peptides, introduces small error when using this method. The effects of non-uniform back-exchange on method performance are fully characterized in supporting information with specific examples given in Figures S1 and S2. Staphylococcal nuclease (SNase) was chosen to benchmark performance and compare this empirical method with the traditional approach of fitting rate constants to define the PF. NMR-measured exchange rates were available for ~75% of exchange sites10,11 and a compendium of HX MS measurements taken at multiple experimental pHs (described previously9) were used for this purpose. We compute k 1 , k 2 , , … k N , defined by fitting PF NMR = GM(k ch / k ex, NMR ) as a proxy for PF actual where k ex, = NMR NMR site-resolved exchange data, and k ch represents a matched list of chemical exchange rates expected in absence of structure2 for each exchange site on any particular peptide in the HX MS dataset. A total of 85 peptides providing 100% sequence coverage were observed throughout all four HX MS experiments (each at a different pH). The raw uptake data for a representative peptide along with labeling conditions are shown in Figure 2A. Uptake times from each HX MS experiment were scaled to effective labeling time12,13 at an arbitrary reference pH of 6.5 and then datasets were concatenated to produce a composite measurement shown in fig. 2B, effectively spanning 0.1 msec to 694 days of labeling time. Concatenation required correction for peptide-specific, non-uniform back-exchange throughout the four HX MS experiments. Taking the composite trace as 𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 2 and using site-specific kch values for each site to generate an uptake trace for 𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 1 (dashed trace, Fig 2B), PF empirical was determined for each ACS Paragon Plus Environment


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peptide. An algorithmic description of concatenation to produce the composite measurement, backexchange correction, and computation of condition 1 for each peptide are included in supporting information. Results & Discussion In 41 peptides, the range of observed uptake by MS, R=max(d)-min(d), shown on Fig. 2B, was similar to the number of measured rate constants by NMR for each peptide and only these range-matched measurements in blue on Fig. 3 are considered for assessment of method accuracy. Tight agreement (correlation coefficient = 0.96) between the empirical analysis taken for HX MS data and the traditional fitting approach used for HX NMR demonstrates that PF can be determined empirically without any knowledge of the actual rate constants themselves. This empirical method can accurately quantify and extract information of biophysical significance in individual peptides and stands apart as the only direct method that exists for this purpose. For 44 peptides, more information was collected in the MS experiment than by NMR leading to disagreement between NMR and MS (Fig 3, red markers). NMR-derived exchange rates were unavailable for many residues whereas HX MS provided 100% sequence coverage. Further, by modulating pH and concatenating datasets, the exchange of nearly every site was observed by HX MS. For these peptides, the uptake range observed by MS (see fig. 2B for illustration) used to determine PF empirical exceeded the number of NMR-derived site PFs used to compute PF

NMR

by factors of 1.5-6x leading to expected

differences. For more information, see Table S1 which contains the uptake ranges for each peptide from the MS data used in empirical calculations, the number of rate constants available from NMR, and the PF values determined by each for all 85 peptides is listed. The value computed for PFC1→C2

empirical

principally depends on the range of observed uptake measured,

determined by the particular rate constants involved and sampling time points of the experiment. The relative error as a result of partially sampled data cannot be stated generically regardless of the method used to determine PF; however, the magnitude of any resulting error can be assessed through simulation. For example, if the data in fig. 1C had only been sampled from 0.1 to 100 seconds of labeling time, the observed uptake range would be reduced by 36% (from 6 to 3.8) and due to the particular rate constants involved, PF empirical changes by +17 %. Rarely will all of the exchangeable sites be observed to exchange in an HX MS experiment and it is worthwhile to consider the situation of partially sampled data. Universally, for any particular peptide, PFC1→C2 empirical will never be less than the smallest site-PF nor larger than the largest site-PF for sites within that peptide, as can be seen by inspection of the individual comparisons shown in fig 1D. Many HX MS experiments aim to assess the structural consequences of perturbations such as changes in concentration14,15 or pH 13,16, epitope binding 17,18, post-translational modifications19-21, and many others. The PF or PFC1→C2 may be used to estimate structural equilibrium constants22. Recently, this method was used (albeit not described well or tested as is done here) to show that PFfree→ bound measurements by HX MS were comparable with changes in dissociation constants measured by SPR13 quantitatively relating structural dynamics to binding affinity. No post-processing of the HX MS data was needed in this study because the empirical method factors out experimental conditions constant to all measurements, such as back-exchange. This empirical method allows comparisons between HX MS data and orthogonal measurements.


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Reliable determination of PFC1→C2 makes standardization of HX MS results possible independent of the number of observed peptides. The PF is invariant to differences in amino acid sequence or small changes in experimental variables such as pH and temperature. These NMR and HX experiments used to benchmark the method span many years of data collection, multiple data processing packages, completely different measurements, multiple pH’s, different temperatures, and multiple analysts9-11, yet they are in remarkable agreement using PFs. Standardization by such a robust metric facilitates comparison with other HX MS studies between diverse amino acid sequences and peptides of different lengths. Clear communication of HX time dependencies has proven to be challenging for HX MS practitioners. Using deuterium uptake alone is confounded by variable peptide lengths hindering attempts to quantitatively illustrate global results. A stark difference exists between fig 4A and global plots having a similar appearance that show deuterium uptake per peptide, known as a butterfly plot. On butterfly plots, peptides are ordered categorically (usually by sequence, N to C terminus) on the x-axis with deuterium uptake or changes thereof shown on the y-axis. Variable peptide lengths render magnitudes these plots difficult to interpret and raw deuterium uptake has no biophysical significance. PFs do not depend on peptide length and are often directly related to structural thermodynamics22,23. As Fig. 4A shows, PF empirical values can be used to produce a genuine coarse-grained representation of SNase from HX MS that compares well with the site-resolved information from NMR in fig. 4B. In conclusion, an empirical method was introduced and described to determine the change in a single rate constant or average change in multiple rate constants from any two time-dependent measurements of firstorder kinetic processes. Protection factors, or changes in HX rate constants, have particular biophysical significance but these quantities are typically inaccessible from HX MS peptide measurements for a variety of reasons; therefore, this empirical method was described in context of an HX MS application. Close agreement with traditionally determined site-protection factors demonstrates reliability and accuracy of the technique. Incongruities between HX NMR and HX MS highlight the importance of considering what has actually been measured when interpreting results produced by this (or any other) method. This technique provides the first universally reliable strategy for recovering sub-global structural physics from individual peptides and in doing so, standardizes the HX MS measurement, simplifies interpretation, and facilitates clear communication of the results. Acknowledgements The author thanks Zhong-Yuan Kan, Leland Mayne, and Walter Englander for sharing NMR and MS data used for this analysis along with helpful discussions, and Lindsey Walters and Kathleen Abadie for assistance in reviewing this manuscript. Supporting Information Available: Three PDF files are provided: SI_main.pdf (text, Figures S1 and S2), Figure_S3.pdf, and Table_S1.pdf. This material is available free of charge via the Internet at http://pubs.acs.org. References (1) Wand, A. J.; Englander, S. W. Curr. Opin. Biotechnol. 1996, 7, 403-408. (2) Bai, Y.; Milne, J. S.; Mayne, L.; Englander, S. W. Proteins 1993, 17, 75-86. (3) Walters, B. T.; Ricciuti, A.; Mayne, L.; Englander, S. W. J Am Soc Mass Spectrom 2012, 23, 2132-2139. (4) Mayne, L.; Kan, Z.-Y.; Sevugan Chetty, P.; Ricciuti, A.; Walters, B.; Englander, S. J. Am. Soc. Mass Spectrom. 2011, 22, 1898-1905. (5) Zhang, Z.; Smith, D. L. Protein Sci 1993, 2, 522-531. (6) Chik, J. K.; Vande Graaf, J. L.; Schriemer, D. C. Anal. Chem. 2005, 78, 207-214. (7) Chetty, P. S.; Mayne, L.; Lund-Katz, S.; Stranz, D.; Englander, S. W.; Phillips, M. C. Proc Natl Acad Sci U S A 2009, 106, 19005-19010.



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(8) Zhang, Z.; Zhang, A.; Xiao, G. Anal. Chem. 2012, 84, 4942-4949. (9) Kan, Z. Y.; Walters, B. T.; Mayne, L.; Englander, S. W. Proc Natl Acad Sci U S A 2013, 110, 16438-16443. (10) Bedard, S.; Mayne, L. C.; Peterson, R. W.; Wand, A. J.; Englander, S. W. J Mol Biol 2008, 376, 1142-1154. (11) Skinner, J. J.; Lim, W. K.; Bédard, S.; Black, B. E.; Englander, S. W. Protein Sci. 2012, 21, 987-995. (12) Coales, S. J.; E, S. Y.; Lee, J. E.; Ma, A.; Morrow, J. A.; Hamuro, Y. Rapid Commun Mass Spectrom 2010, 24, 3585-3592. (13) Walters, B. T.; Jensen, P. F.; Larraillet, V.; Lin, K.; Patapoff, T.; Schlothauer, T.; Rand, K. D.; Zhang, J. J. Biol. Chem. 2016, 291, 1817-1825. (14) Houde, D.; Nazari, Z. E.; Bou-Assaf, G. M.; Weiskopf, A. S.; Rand, K. D. J Am Soc Mass Spectrom 2016. (15) Arora, J.; Hickey, J. M.; Majumdar, R.; Esfandiary, R.; Bishop, S. M.; Samra, H. S.; Middaugh, C. R.; Weis, D. D.; Volkin, D. B. MAbs 2015, 7, 525-539. (16) Li, J.; Rodnin, M. V.; Ladokhin, A. S.; Gross, M. L. Biochemistry 2014, 53, 6849-6856. (17) Casina, V. C.; Hu, W.; Mao, J. H.; Lu, R. N.; Hanby, H. A.; Pickens, B.; Kan, Z. Y.; Lim, W. K.; Mayne, L.; Ostertag, E. M.; Kacir, S.; Siegel, D. L.; Englander, S. W.; Zheng, X. L. Proc Natl Acad Sci U S A 2015, 112, 96209625. (18) Sevy, A. M.; Healey, J. F.; Deng, W.; Spiegel, P. C.; Meeks, S. L.; Li, R. J Thromb Haemost 2013, 11, 21282136. (19) Majumdar, R.; Esfandiary, R.; Bishop, S. M.; Samra, H. S.; Middaugh, C. R.; Volkin, D. B.; Weis, D. D. MAbs 2015, 7, 84-95. (20) Zheng, K.; Yarmarkovich, M.; Bantog, C.; Bayer, R.; Patapoff, T. W. MAbs 2014, 6, 649-658. (21) Houde, D.; Peng, Y.; Berkowitz, S. A.; Engen, J. R. Mol Cell Proteomics 2010, 9, 1716-1728. (22) Bai, Y.; Englander, J. J.; Mayne, L.; Milne, J. S.; Englander, S. W. Methods Enzymol 1995, 259, 344-356. (23) Englander, S. W.; Mayne, L.; Kan, Z. Y.; Hu, W. Annu Rev Biophys 2016, 45, 135-152.


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Figure 1 – Single Column

A) Rate constants for f(t) are 0.1, 0.2, 3 sec-1. The GM of rate constants in f(t) defines a single rate constant, 0.39 sec-1, for g(t) – see text. B) The value of each ratio is plotted as a function of d, the GM of these values is highlighted by the black arrow. C) Two exchange conditions are shown for a hypothetical six site peptide having rate constants of 1, 5, 10, 0.01, 0.5, 0.2 sec-1 in condition 1 and 0.1, 0.05, 0.005, 0.01, 0.125, 0.04 sec-1 in condition 2 with site protection factors of 10, 100, 2000, 1, 4, and 5. These rates are used in Figure S2 where the effect of back-exchange is further explored. D) As in panel B, individual comparisons are shown for the curves in panel C and their geometric mean is 18.39. For comparison, 〈PF〉actual = 18.49.



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Figure 2 – Double Column

(A) Deuterium uptake vs. experimental labeling time for SNase peptide 61-76 at four different experimental pHs of 4.5 (cyan), 5.6 (green), 8.0 (black), and 8.6 (blue). (B) The same data with color scheme preserved after correcting for back-exchange and D:H ratios at t=0, and scaling actual labeling times to effective time at pH 6.5. The composite exchange trace (grey) obtained by concatenation (see text) serves as condition 2 and the dashed trace as condition 1, defined by site-specific kch (see text) at the reference of pH 6.5. All peptides used in this work are shown in Figure S3.


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In 41 of 85 peptides (blue markers, correlation coefficient of 0.96), the number of NMR defined site PFs was similar to the range used to compute empirical values. In 44 of 85 peptides (red markers) exchange information was more extensively sampled by HX MS by factors of 1.5-6x regarding sequence coverage and therefore is not used for accuracy assessment (see text). This information may be further inspected in Table S1.



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(A) Each residue was assigned the empirical protection factor determined for the shortest peptide containing that particular residue (blue bars). (B) All NMR-derived protection factors for each exchange site are shown in red bars. In both panels, grey bars highlight regions without site-PFs from NMR, including proline residues.


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See manuscript Figure 2 Legend 163x74mm (300 x 300 DPI)


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