WAXS going beyond SAXS. Lee Makowski Northeastern University Boston

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1 WAXS going beyond SAXS Lee Makowski Northeastern University Boston

2 WAXS (wide angle x-ray solution scattering) What can you gain by collecting to the highest possible resolution? Cannot use WAXS to directly calculate structure (ambiguous once away from the SAXS regime) BUT can be an excellent tool for testing molecular models (because we can quantitatively calculate WAXS data from molecular models) Can add to SAXS information in details about: Ligand binding Protein ensembles Structural changes

3 Advanced Photon Source o

4 WAXS Experiment Sector 18 Advanced Photon Source X-ray beam typically 140x40 microns photons per second Flow cell (100 ms x-ray exposure) Temperature controlled 1.5 mm path length (typical) 10 microliter sample volumes possible > 5 mg/ml concentration preferred

5 WAXS Data Set from Hb 150 mg/ml buffer 1 mg/ml 100 mg/ml 10 mg/ml Iprot = Iobs - Icap - (1-vol%)Isolvent Wide angle scatter largely due to buffer; capillary Data ~ 100x weaker than SAXS Protein (x10) Buffer-filled capillary Each data set is composed of circularly averaged scattering from (i) (ii) (iii) Empty capillary Buffer-filled capillary Protein solution-filled capillary Protein solution buffer Empty capillary 1/d = q/(2π) = 2 sinθ/λ Physicists use q (Å -1 ) Structural biologists use 1/d (Å -1 )

6 That s nice What does it mean? What kind of information is really in the pattern?

7 Nature of the information in WAXS Debye Formula WAXS is a reflection of interatomic vector lengths (r ij ): I(q) = Σ I i (q) + 2 ΣΣ F i (q) F j (q) (sin(qr ij )/(qr ij )) Can be used to calculate p(r) Can in principle be calculated from atomic coordinate set Very sensitive to structural changes at all length scales (literally a histogram of the lengths of all interatomic vectors in the protein Size and shape (radius of gyration) Tertiary/quaternary structure Secondary structure Alpha helices 1.5 Å axial separation of amino acids along helix 5.4 Å pitch 10 Å diameter (center-to-center distance) Beta sheets 4.7 Å strand-to-strand distance 7.0 Å pleat distance (2 residue separation) Molecular envelopes are limited in resolution no matter how much data you collect wider angle data cannot be used to construct unique shapes; correspond to internal structural patterns

8 Z Data 10 WAXS pattern is a band-limited function 8 Shannon Sampling theorem indicates for ~ 25 A diameter protein; q~1.2: ~ 10 independent samples q~3.0 ~ 25 independent samples > Treat each scattering pattern as a vector > Look at distribution of proteins in this high-dimensionality space 500 distinct protein domains > major structural classes segregate in that space log(eigenvalue) q < 3.0 A -1 q < 1.2 A order properties 2; 3; 4 alphas and betas closest furthest Parameter a-2 vs a-3 vs a-4 b-2 vs b-3 vs b-4 Parameter 3 Y Data X Data Parameter 2 Makowski, L., D.J. Rodi, S. Mandava, S. Devrapahli, and R.F. Fischetti (2008) Characterization of Protein Fold using Wide Angle X-ray Solution Scattering. J. Mol. Biol. 383,

9 q ~ 0.6 Å -1 Segregation only is clear at very high resolution ~ q>2.5 q ~ 1.2 Å -1 q ~ 2.4 Å -1 So there certainly exists information about secondary and tertiary structure but not going to be finding protein fold anytime soon

10 To be a rigorous test of molecular models it will be necessary to calculate scattering from atomic coordinate sets CRYSOL is fabulous at small angles, but at wider angles, a uniform hydration layer is inadequate (which - in and of itself says something about the power of WAXS )

11 Accurate Calculation of WAXS data from atomic coordinates WAXS patterns were computed from proteins using explicit atomic representations for water. Proteins were placed in droplets generated by MD simulations and scattering was calculated using an average over 100 snapshots. Water contribution was accounted for by subtraction of scattering from droplets containing water without proteins. XS

12 KEY to WAXS can predict quantitatively the data expected from a given molecular model relative intensity Mb - calculated mg/ml - observed Discrepancies; where they exist, often involve experimental data with weakened peaks or filled in troughs /d Success of this approach also provides strong evidence that MD approaches are getting water of hydration correct

13 Park, S., J. P. Bardhan, B. Roux, and L. Makowski (2009) Simulated X-Ray Scattering of Protein Solutions Using Explicit- Solvent Molecular Dynamics. J. Chem. Phys. 130, PMID: Yang, S., S. Park, L. Makowski, and B. Roux (2009) A Rapid Coarse Residue-Based Computational Method for X-Ray Solution Scattering Characterization of Protein Folds and Multiple Conformational States of Large Protein Complexes. Biop. J. 96, PMID: Bardhan, J.P., S. Park, and L. Makowski (2009) SoftWAXS: A Computational Tool for Modeling Wide-Angle X-ray Solution Scattering from Biomolecules. J.. Appl. Cryst. 42, Virtanen, J.J., L. Makowski, T.R. Sosnick and K.F. Freed (2010) Modeling the hydration layer around Proteins: HyPred. Biop. J. 99, PMID:

14 great what can we do with it? can we see ligand-induced structural changes?

15 Ligand binding results in structural changes readily observed by WAXS Ca ++ -Ca ++ relative intensity /d 400 Calmodulin +/- Ca ++ difference intensity When Ca ++ added, difference intensity is very distinct /d

16 Riboflavin Kinase (RFK,) is an essential enzyme which has been demonstrated to bind its two small molecule ligands at adjacent sites on the surface of the molecule black apo blue ATP red - riboflavin Each ligand (riboflavin and ATP) modulates the protein in such a manner as to shift a surface flap to a new position. Not only does the addition of each ligand produce a statistically significant change in the scattering profile (reduced chi square, χ υ = 2.94 for ATP and 2.90 for riboflavin respectively vs. apo RFK normalized for error), but the profiles for ATP and riboflavin are virtually indistinguishable (χ υ = 0.03 between the two ligand-bound forms).

17 Everybody s been talking about ensembles

18 What is the impact of structural polymorphism (ensemble) on solution scattering? 2e+6 relative intensity 2e+6 1e+6 14 A radius 15 A radius 16 A radius relative intensity 15 A radius average of A radii average of A radii 5e /d scattering from spheres of 14; 15 and 16 Å radius minima at ~ 1/(radius) scattering from a solution of all three spheres looks like the average sphere but with minima filled in and maxima muted 1/d so the broader the ensemble; the greater the effect WAXS is highly sensitive to this effect

19 Hemoglobin - ensemble changes as function of protein concentration hemoglobin patterns from 4 mg/ml to 270 mg/ml relative intensity /d At concentrations below about 50 mg/ml, the scattering from met-hb indicates a progressive increase in polydispersity - broadening of the structural ensemble. Lack of change in higher angle scatter suggests this is due to rigid body motions

20 Can decrease motion of subunits - di-α Hb is a variant in which the two α-chains are covalent linked at their termini α1 val1 α A -1 arg1 41 relative intensity concentration (mg/ml) di-α-hb appears far more rigid than CO-Hb suggests that rigid bodies are the subunits (why should this linkage should alter helix motion?) relative intensity /d di-alpha (10 mg/ml) HbCO (10 mg/ml)

21 Molten globules of β-lactoglobulin Forms molten globules at ethanol concentrations of 25-40% Samples in the 25-40% EtOH range appear to have an intermediate structure (molten globule form) distinct from native and from denatured 0-12% native dimer 20% native monomer

22 WAXS of β-lactoglobulin at varying ethanol concentrations 4.7 A peak does not disappear in molten globule or denatured state

23 HIV Protease 48 Active site protected by two 'flaps' When inhibitors (or substrate) bind to active site flaps fold down over them Their flexibility is required for access to active site Extensive information available on mutants including MDR All studies use Q7K to prevent self-digestion 63 Consider two mutants: T80N - invariant in both treated and untreated populations G48V L63P - MDR

24 scattering from apo protease is altered in mutant t80n t80n appears to restrict movement of flaps in apo form and prevent binding of inhibitor (or substrate) 1000 relative intensity q7k q7k t80n q7k g48v l63p 80 red 48 blue 63 green /d q7k 6.6 mg/ml others ~ 10 mg/ml

25 difference intensity /d vs q7k inhib-apo 1/d vs t80n inhib-apo 1/d vs g48vl63p-apo Differences between WAXS patterns +/- inhibitor Indicate Wt binds inhibitor t80n does not bind inhibitor /d Why?

26 MD simulations suggest T80N inhibits motion of the flap regions

27 Form of T80N scattering suggests WT looks similar but exhibits structural black - apo fluctuations red - t80n apo relative intensity t80n wt /d 80 red 48 blue 63 green relative intensity /d 1/d vs t80n 1/d vs wt 1/d vs 0.15 Using t80n as a model for a rigid protease - adding fluctuations results in a predicted WAXS pattern indistinguishable from WT A single site mutation (t80n) causes a functionally significant suppression of structural fluctuations

28 change in fluctuations may lead to change in function But what about detection of functional conformational changes in solution? If we can generate all abundant structures, WAXS can be used to calculate their relative abundances

29 Representatives of families of conformations abundant under different conditions Catalytic domain blue SH2 domain green SH3 domain yellow Hck-YEEI high-affinity mutant

30 Adenylate kinase +/- inhibitor (with George Phillips) black - apo blue - with inhibitor relative intensity q Catalyzes the interconversion of AMP; ADP and ATP 2 ADP AMP + ATP Flaps cover the reagents once in the active site Form of scattering suggests flaps very flexible in unliganded form

31 Adenylate kinase +/- inhibitor and during catalysis black - apo blue - with inhibitor red - with ADP (cycling) relative intensity During catalysis closely resembles inhibited form q but cannot be constructed as linear combination of the two endpoints Reduced chi-squares apo inhib apo-adp 6.58 Inhib-adp 5.23

32 Cycling Adenylate Kinase Can we see what some of these states look like? Aden and Wolf-Watz, 2007

33 Collect WAXS data from AdK under many different conditions AMP, binds both sites - apparent Kd of 3.2 mm ATP, binds LID domain - Kd of 43 µm AP5A, binds both sites - tight binding (nm) ADP, enzyme is catalytic - apparent Kd of 267 µm From thermodynamic measurements can predict relative abundances of different species at any given ligand concentrations

34 Singular Value Decomposition D = USV A = number of angles N = number of experiments 4 significant vectors Data Matrix, D (A*N) Orthonormal Basis, U (A*N) Singular Values, S (N*N) Coordinates, V (N*N)

35 WAXS Characterizing ligand-induced structural changes changes in ensemble Screening reagent libraries for functional binding Validating results of MD simulations Validating/refining results of molecular modeling Homology models Coarse grain (CG) MD

36 Thanks Bob Fischetti Dave Gore Chien Ho (CMU) George Phillips (UW) Diane Rodi Suneeta Mandava Amina Aziz Lynda Dieckman Steve Kent (U Ch) Vladimir Torbeev (U Ch) Celia Schiffer (UMass) I m looking for a postdoc or two Sanghyun Park (ANL) Jaydeep Bardhan (Rush) David Minh (ANL) Jyotsana Lal (ANL) Sichun Yang (Case) Benoit Roux (UCh) Tobin Sosnick (UCh) Karl Freed (UCh) Juoko Virtanen (UCh) DOE ANL NIH