WAXS going beyond SAXS Lee Makowski Northeastern University - - PowerPoint PPT Presentation

WAXS – going beyond SAXS

Lee Makowski Northeastern University Boston

• 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

Advanced Photon Source

Sector 18 – Advanced Photon Source

WAXS Experiment

X-ray beam typically 140x40 microns 1012-1013 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

WAXS Data Set from Hb – 150 mg/ml

Each data set is composed

• f circularly averaged

scattering from (i) Empty capillary (ii) Buffer-filled capillary (iii) Protein solution-filled capillary Protein (x10)

Protein solution

Buffer-filled capillary

Empty capillary

buffer

Iprot = Iobs - Icap - (1-vol%)Isolvent

100 mg/ml buffer 1 mg/ml 10 mg/ml Wide angle scatter largely due to buffer; capillary

Data ~ 100x weaker than SAXS

1/d = q/(2π) = 2 sinθ/λ

Physicists use q (Å-1) Structural biologists use 1/d (Å-1)

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

Nature of the information in WAXS

• 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)
• Debye Formula – WAXS is a reflection of

interatomic vector lengths (rij ): I(q) = Σ Ii(q) + 2 ΣΣ Fi(q) Fj(q) (sin(qrij)/(qrij))

• 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

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

• rder

5 10 15 20 25 30 35 40 45 50

log(eigenvalue)

2 4 6 8 10

q < 3.0 A-1 q < 1.2 A-1

WAXS pattern is a band-limited function 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

closest furthest

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, 731-744.

• 20
• 15
• 10
• 5

5 10 15 20

• 80
• 60
• 40
• 20

20 40

• 20
• 10

10 20

Z D a t a X Data Y D a t a

properties 2; 3; 4 alphas and betas

a-2 vs a-3 vs a-4 b-2 vs b-3 vs b-4

P a r a m e t e r 2 Parameter 3 Parameter 4

Segregation only is clear at very high resolution ~ q>2.5 q ~ 0.6 Å-1 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

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 )

• 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.

Accurate Calculation of WAXS data from atomic coordinates

XS

1/d

0.00 0.05 0.10 0.15 0.20

relative intensity

200 400 600 800 1000 Mb - calculated 146.7 mg/ml - observed

Discrepancies; where they exist, often involve experimental data with weakened peaks or filled in troughs.

Success of this approach also provides strong evidence that MD approaches are getting water of hydration correct

KEY to WAXS – can predict quantitatively the data expected from a given molecular model…

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, 134114. PMID: 19355724 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, 4449–4463. PMID: 19486669 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, 932-943 Virtanen, J.J., L. Makowski, T.R. Sosnick and K.F. Freed (2010) Modeling the hydration layer around Proteins: HyPred. Biop. J. 99, 1611-1619. PMID: 20816074.

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

1/d

0.0 0.1 0.2 0.3 0.4

relative intensity

200 400 600 800 1000 +Ca++

• Ca++

Ligand binding results in structural changes readily observed by WAXS

1/d

0.0 0.1 0.2 0.3 0.4

difference intensity

100 200 300 400

Calmodulin +/- Ca++ When Ca++ added, difference intensity is very distinct

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

• 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, χυ = 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 (χυ = 0.03 between the two ligand-bound forms).

black – apo blue – ATP red - riboflavin

Everybody’s been talking about ensembles…

1/d

0.00 0.05 0.10 0.15 0.20 0.25

relative intensity

5e+5 1e+6 2e+6 2e+6 14 A radius 15 A radius 16 A radius

What is the impact of structural polymorphism (ensemble)

• n solution scattering?

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 so…the broader the ensemble; the greater the effect WAXS is highly sensitive to this effect…

1/d

0.00 0.05 0.10 0.15 0.20 0.25

relative intensity

15 A radius average of 14-16 A radii average of 13-17 A radii

Hemoglobin - ensemble changes as function of protein concentration

1/d

0.0 0.1 0.2 0.3 0.4

relative intensity

500 1000 1500 2000 2500 3000

20 hemoglobin patterns from 4 mg/ml to 270 mg/ml

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

concentration (mg/ml)

20 40 60 80 100 120 140 160 180

relative intensity

0.90 0.95 1.00 1.05 1.10 1.15 1.20 0.0660 A-1

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?)

Can decrease motion of subunits - di-α Hb is a variant in which the two α-chains are covalent linked at their termini

arg1 41 val1

α α α α1 α α α α2

1/d

0.0 0.1 0.2 0.3 0.4

relative intensity

200 400 600 di-alpha (10 mg/ml) HbCO (10 mg/ml)

Molten globules of β β β 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

WAXS of β-lactoglobulin at varying ethanol concentrations

4.7 A peak does not disappear in ‘molten globule’ or ‘denatured’ state

HIV Protease

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 Consider two mutants: T80N - invariant in both treated and untreated populations G48V L63P - MDR

63 48

1/d

0.0 0.1 0.2 0.3 0.4

relative intensity

200 400 600 800 1000 q7k q7k t80n q7k g48v l63p

q7k – 6.6 mg/ml

• thers ~ 10 mg/ml

80 red 48 blue 63 green

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)

1/d

0.00 0.05 0.10 0.15 0.20

difference intensity

• 200
• 100

100 200 1/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 Why?

MD simulations suggest T80N inhibits motion

• f the flap regions

1/d

0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18

relative intensity

200 400 600 800 1000 1200 black - apo red - t80n apo

Form of T80N scattering suggests WT looks similar but exhibits structural fluctuations 1/d

0.00 0.05 0.10 0.15 0.20

relative intensity

200 400 600 800 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

80 red 48 blue 63 green

A single site mutation (t80n) causes a functionally significant suppression of structural fluctuations

wt t80n

… 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

Hck-YEEI – high-affinity mutant

Representatives of families

• f conformations abundant

under different conditions

Catalytic domain – blue SH2 domain green SH3 domain yellow

q

0.0 0.2 0.4 0.6 0.8 1.0

relative intensity

200 400 600 800 black - apo blue - with inhibitor

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 Adenylate kinase +/- inhibitor (with George Phillips)

Adenylate kinase +/- inhibitor … and during catalysis During catalysis closely resembles inhibited form but cannot be constructed as linear combination of the two endpoints

q

0.0 0.2 0.4 0.6 0.8 1.0

relative intensity

200 400 600 800 black - apo blue - with inhibitor red - with ADP (cycling)

Reduced chi-squares apo – inhib 42.75 apo-adp 6.58 Inhib-adp 5.23

Cycling Adenylate Kinase

Aden and Wolf-Watz, 2007

Can we see what some of these states look like?

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 M AP5A, binds both sites - tight binding (nM) ADP, enzyme is catalytic - apparent Kd of 267 M

From thermodynamic measurements can predict relative abundances of different species at any given ligand concentrations

Singular Value Decomposition

D = USV’ A = number of angles N = number of experiments Data Matrix, D (A*N) Orthonormal Basis, U (A*N) Singular Values, S (N*N) Coordinates, V (N*N)

4 significant vectors

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

Bob Fischetti Dave Gore Diane Rodi Suneeta Mandava Amina Aziz Lynda Dieckman 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)

Thanks

DOE ANL NIH

Chien Ho (CMU) George Phillips (UW) Steve Kent (U Ch) Vladimir Torbeev (U Ch) Celia Schiffer (UMass) … I’m looking for a post- doc or two…