Principles of Atomic-Structure-Based Modeling Maxim Petoukhov - PowerPoint PPT Presentation

Principles of Atomic-Structure-Based Modeling Maxim Petoukhov EMBL, Hamburg Outstation

Outline Outline • Introduction • Computation of SAS patterns from atomic models • Incorporation of structural information from other methods • Rigid body modelling of macromolecular complexes • Hybrid modelling of multidomain proteins • Examples & questions

Structural methods: resolution, accessible Structural methods: resolution, accessible size and speed of experiment/analysis size and speed of experiment/analysis Time to answer NMR (high) Months EM, Cryo-EM (low) RDC NMR (low) Weeks MX (high) Days FRET (low) Hours SAS (low) Minutes 10 0 10 1 10 2 10 3 10 4 10 5 10 6 MM, kDa (kDa) (MDa) (GDa)

Contrast of electron density ρ el. A -3 ρ = 0.43 particle Δ ρ ρ = 0.335 0 solvent

Sample and buffer scattering

Sample and buffer scattering

SAS Curve From Atomic Model – – SAS Curve From Atomic Model Is Your Structure Correct ? Is Your Structure Correct ?

How to Compute SAS from Atomic Model How to Compute SAS from Atomic Model I solution (s) I solvent (s) I particle (s) ♦ To obtain scattering from the particles, solvent scattering must be subtracted to yield effective density distribution Δρ = < ρ ( r ) - ρ s > , where ρ s is the scattering density of the solvent ♦ Further, the bound solvent density may differ from that of the bulk

Scattering from a Macromolecule in Solution Scattering from a Macromolecule in Solution Atomic scattering - Excluded volume + Shell scattering 9

Wednesday, 05 December, 2012 Scattering Intensity via Amplitudes Scattering Intensity via Amplitudes 2 2 − ρ δρ I(s) = A( ) = A ( ) A ( ) + A ( ) s s s s a s s b b Ω Ω ♦ A a ( s ) : atomic scattering in vacuum ♦ A s ( s ) : scattering from the excluded volume ♦ A b ( s ) : scattering from the hydration shell CRYSOL (X-rays): Svergun et al. (1995). J. Appl. Cryst. 28 , 768 CRYSON ( neutrons): Svergun et al. (1998) P.N.A.S. USA , 95 , 2267 10

Use of of Multipole Multipole Expansion Expansion Use spherical harmonics expansion

Partial Amplitudes and Adjustable Parameters Parameters Partial Amplitudes and Adjustable Partial scattering amplitudes

Wednesday, 05 December, 2012 CRYSOL and and CRYSON CRYSON : CRYSOL : X- -ray and Neutron Scattering from Macromolecules ray and Neutron Scattering from Macromolecules X L l ∑∑ 2 = π − ρ + δρ 2 ( ) 2 ( ) ( ) ( ) I s A s E s B s 0 lm lm lm = = − 0 l m l • The programs: � either fit the experimental data by varying the density of the hydration layer δρ (affects the third term) and the total excluded volume (affects the second term) � or predict the scattering from the atomic structure using default parameters (theoretical excluded volume and bound solvent density of 1.1 g/cm 3 ) � provide output files (scattering amplitudes) for rigid body refinement routines � compute particle envelope function F( ω ) 13

Scattering components (lysozyme lysozyme) ) Scattering components ( Atomic Shape Border Difference SAXS case SAXS case 14

Scattering components (lysozyme lysozyme) ) Scattering components ( Atomic Shape Border Difference SANS case: SANS case: 50% perdeuterated perdeuterated lysozyme lysozyme in 90% D2O in 90% D2O 50% 15

Effect of the hydration shell, X- -rays rays Effect of the hydration shell, X lg I, relative Experimental data Fit with shell Fit without shell 3 Lysozyme 2 Hexokinase 1 EPT 0 PPase -1 0 1 2 3 4 s, nm -1

Josephin Domain Domain of of Ataxin Ataxin- -3 3 Josephin lg I, relative 2 SAXS experiment Fit by 1yzb Fit by 2aga 1 0 0.0 0.2 0.4 0.6 0.8 o s, A -1 Validation of the NMR models against SAXS experiment: red curve and chain: 1yzb; blue curve and chain: 2aga Nicastro, G., Habeck, M, Masino, L., Svergun, D.I., Neri, N., Pastore, A. 2006

Identification of Biologically Active Oligomers Oligomers Identification of Biologically Active Biologically active dimer of myomesin-1 What if none of the models fits the data ? Collaboration: N. Pinotsis, S. Lange (2004)

Updating CRYSOL • Challenge: accurate data acquired at P12 Shell as envelope function Atomic structure in vacuum ‐ Excluded volume + Hydration shell 2 2 − ρ δρ I(s) = A( ) = A ( ) A ( ) + A ( ) s s s s a s s b b Ω Ω

CRYSOL 3.0 An essential prerequisite for reliable hybrid modeling: Accurate computation of Outer shell theoretical scattering patterns from atomic Internal cavities structures Extra excluded volume • Test set of about 20 well ‐ characterized proteins measured at X33 and P12 with and without HPLC (M.Graewert & D.Ruskule) • MD simulations by A.Tuukkanen

SAXS is still useful even if the crystal structure is solved… • Identification of biologically active oligomers • Structure validation in solution

3D modelling against SAS data Monodispersity and ideality of solution are required

General principle of SAS modelling modelling General principle of SAS 1D scattering 3D search model X = { X} = { X 1 …X M } data M parameters (or multiple data Trial-and-error sets) 2 ⎡ ⎤ − Non-linear ( ) ( ) I s cI s 1 ∑ χ = exp j j 2 ⎢ ⎥ discrepancy: search − σ ⎢ ⎥ 1 ( ) N s ⎣ ⎦ j j Additional information is ALWAYS required to resolve or reduce ambiguity of interpretation at given resolution

Constraints Constraints Shape determination & Search volume & EM Restraints Restraints Rigid body Crystallography modelling Atomic models NMR Missing fragments Biochemistry Orientations FRET Oligomeric Interface mixtures mapping Bioinformatics Flexible Secondary systems structure prediction

Use of contrast variation for SAS modelling Neutrons: Isotopic H/D substitution X-rays: D-Protein, 130% D 2 O Addition of sucrose or salts D-RNA, 120% D 2 O RNA, 550 e/nm 3 D 2 O, 6.38 × 10 10 cm -2 H-RNA, 70% D 2 O 60% sucrose, 430 e/nm 3 Protein, 410 e/nm 3 H-Protein, 40% D 2 O H 2 O, 344 e/nm 3 H 2 O, -0.59 × 10 10 cm -2

Use of contrast variation for SAS modelling Neutrons: X-rays: Isotopic H/D substitution Addition of sucrose or salts RNA, 550 e/nm 3 60% sucrose, 430 e/nm 3 Protein, 410 e/nm 3 H 2 O, 344 e/nm 3

Use of contrast variation for SAS modelling • Contrast variation possibilities in SANS – Perdeuteration of subunits – Different % of D 2 O in the solvent = 0% perdeuteration = 50% perdeuteration 0% D 2 O 40% D 2 O 80% D 2 O

Target Function Function Target • To reduce the ambiguity of data analysis ∑ = χ + α 2 ({ }) [( ( ), ( )] E X I s I s i P exp i i is minimized • Penalties describe model-based restraints and/or introduce the available additional information from other methods: MX, NMR, EM etc) • A brute force (grid) search is applied if the number of free parameters is small • Otherwise a Monte-Carlo based technique (e.g. simulated annealing) is employed to perform the minimization of E({X})

Simulated Annealing Protocol Simulated Annealing Protocol • Main idea: Minimization of the target function E( X ) by random modifications of the system always moving to configurations that decrease E( X ) but to also occasionally move to configurations that increase the scoring function.

Simulated Annealing Protocol Simulated Annealing Protocol • The probability of accepting “unprofitable” moves decreases in the course of the minimization (the system is cooled). • At the beginning, the temperature is high and the changes almost random, whereas at the end a configuration with nearly minimum energy is reached.

Simulated Annealing Protocol Simulated Annealing Protocol Start from some initial (e.g. random) configuration X at a high temperature T X : {X 1 …X i …X j …X M } X' : {X 1 …X i '…X j '…X M } Δ E = E( X' ) - E( X ) If Δ E<0 move to X’ else p = exp ( - Δ E / T ) The system is cooled until no improvement is observed

Rigid Body Modelling Modelling of Quaternary of Quaternary Rigid Body Structure: Playing with Molecular Structure: Playing with Molecular Building Blocks Building Blocks

Idea of rigid body modelling modelling Idea of rigid body • The atomic structures of the components (subunits or domains) are known. • Assuming the tertiary structure is not changed by complex formation. • Arbitrary complex can be constructed by moving and rotating the subunits. • For each subunit this operation depends on three orientational and three translational parameters.

Scattering from a complex particle Scattering from a complex particle Shift: x, y, z B B’ A Rotation: α , β , γ The partial amplitudes of a rotated and displaced subunit are expressed via the initial amplitudes, three Euler rotation angles and three Cartesian shifts): lm (s), α (i) , β (i) , γ (i) , x (i) , y (i) , z (i) } . A (i) lm (s) = A (i) (i) lm (s) { A 0 For symmetric particles, L l ( ) ( ) ∑∑ ∑ = 2 π 2 2 n | | there are fewer parameters I s A s lm = = − and the calculations are faster l 0 m l n Svergun, D.I. (1991). J. Appl. Cryst. 24 , 485-492