IMAGING OF SINGLE PARTICLES AND BIOMOLECULES

Janos HajduUppsala University

CONTRIBUTORS:GERMANY: Jochen Schneider, Edgar Weckert, Josef Feldhaus, Elke Plönjes, Thomas Möller, Christoph Bostedt, Ivan Vartaniants, Christian Schroer, FRANCE: Hamed Merdji, Philippe Zeitoun, SWEDEN: Janos Hajdu, David van der Spoel, Nicusor Timneanu, Martin Svenda,Gösta Huldt, Carl Caleman, Magnus Bergh, Sara Lejon, Alexandra Patriksson, Richard Neutze, Arjan Snijder, Susanna Tornroth, Jan Isberg, PORTUGAL: Martha Fajardo, Nelson Lopes, Joao M Dias, Goncalo Figueira, Luis Silva, Ricardo Fonseca, Fabio Peano, POLAND: Beata Ziaja, HUNGARY: Gyula Faigel, UK: Carol Robinson, AUSTRALIA: Keith Nugent, USA: Keith Hodgson, Abraham Szöke, David Sayre, John Miao, Ian Robinson, James Fienup, Veit Elser, Janos Kirz, Ian McNulty, Lukas Novotny, Pascal Anger, Chris Jacobsen, David Shapiro, Enju Lima, Huije Miao, Helmut Strey, RogerFalcone, Musahid Ahmed, John C.H. Spence, Eugene Ingerman,, Henry Chapman, Stefan Hau-Riege, Hope Ishii, Stefano Marchesini, Rodney Balhorn, Henry Benner, Matthias Frank, Aleksandr Noy, Anton Barty, Brent Segelke, Richard London, DanielBarsky, Peter Young, Richard Lee

Institutions:ACCELERATOR-BASED LIGHT SOURCES AND SYNCHROTRON SOURCES- Deutsche Elektronen-Synchrotron, Germany- VUV-FEL at DESY, Germany- Stanford Synchrotron Radiation Laboratory, USA- Advanced Light Source, Lawrence Berkeley National Laboratory, USA- Advanced Photon Source, Argonne National Laboratory, USALASER FACILITIES- Service des Photons Atomes et Molecules, Commissariat à l’Energie Atomique, France- Laboratoire d’Optique Appliquée, Palaiseau, FranceUNIVERSITIES AND RESEARCH INSTITUTES- ICM Molecular Biophysics, Uppsala University, Sweden- Department of Chemistry & Bioscience, Chalmers University, Sweden- Division for Electricity and Lightning Research, Uppsala University, Sweden- Grupo de Lasers e Plasmas, Centro de Fisica dos Plasmas, Lisbon, Portugal- The Henryk Niewodniczanski Institute of Nuclear Physics, Krakow, Poland- Research Institute for Solid State Physics and Optics, Budapest, Hungary- The School of Physics, The University of Melbourne, Australia- Department of Chemistry, Cambridge University, UK- Institute for Atomic Physics, Technical University Berlin, Germany- Department of Physics, Cornell University, USA- The Institute of Optics, University of Rochester, USA- Department of Physics and Astronomy, Stony Brook University, USA- Department of Biomedical Engineering, Stony Brook University, USA- Department of Physics, University of Illinois at Urbana-Champaign, USA- Department of Physics, University of California Berkeley, USA- The Lawrence Berkeley National Laboratory, Berkeley, USA- Department of Physics and Astronomy, Arizona State University, USA - Center for Biophotonics Science and Technology, UC Davis, USA- The Lawrence Livermore National Laboratory, USA

CONVENTIONAL METHODS CANNOT ACHIEVE ATOMIC RESOLUTION on NON-REPETITIVE (or non-reproducible) STRUCTURES - DAMAGE DEVELOPS DURING THE EXPERIMENT

DAMAGE TOLERANCE MAY BE EXTENDED TO NEW LIMITS AT EXTREME DOSE RATES WITH ULTRA-SHORT EXPOSURES Neutze, R., Wouts, R., van der Spoel, D., Weckert, E. Hajdu, J. (2000) Nature 406, 752-757

QuickTime™ and aGIF decompressorded to see this picture.

300 nm

1 nm

RUBISCO

MYCOPLASMAS

DISTRIBUTED DAMAGE

THEORY predicts XFELs may allow high resolution imaging of single particles / moleculesNeutze, Wouts, van der Spoel, Weckert, Hajdu Nature 406, 752-757 (2000)

Just before XFEL pulse

During the pulse

After pulse

Diffraction pattern

3D reconstruction possible from many views

Concept: Capture an image with a short and intense X-ray pulse, before the sample has time to respond (explode)

Interaction chamber and detector arrangementParticle injection

XFEL beam

(focussed,Compressed)

Pixel detector 2

Intelligent beam-stop

Pixel detector 1

Electrostatic trap

Optical and x-ray

diagnosticsReadout and

reconstruction

Particle orientation

beam

To mass spectrometer

NEED TO UNDERSTAND WHAT HAPPENS TO THE SAMPLE IN THE BEAM

X-ray scattering and energy deposition during exposure12 keV photons (~1Å), biological samples: C,N,O,H,S, P.

X-RAYS INTERACT WITH MATTER THROUGH ABSORPTION AND SCATTERING:

(1) PHOTOELECTRIC EFFECT (~90%) followed by Auger emission, shake-up excitations, and secondary electron cascades (large samples)

(2) ELASTIC SCATTERING (~7-10%)

(3) INELASTIC SCATTERING (~3%)

K

L

Primary photoelectron

K

L

Augerelectron

τK ≅ 10 fs for carbon

K

LUnstablehollow ion

hν'

K

L

hν

In light elements

In heavy elements

PHOTOELECTRIC EFFECT, AUGER EMISSIONand X-RAY FLUORESCENCE

Fluorescence

e-

e-

τK = h/ΓAuger-

+ shake-processes

Low-energy electron cascades in diamond

1fs

10fs

100fs

y (Å)

x (Å)Ziaja, Szöke, van der Spoel, Hajdu (2001) Phys. Rev. B. 64, 214104

Energy of primary impact electron: 250 eV

Results from 2,000 Monte Carlo simulations plotted

Within 100 fs after impact:

10,000-35,000 elastic interactions

10-50 inelastic interactions

Electron propagation is dominated by elastic interaction

5-13 ionisations

250 eV

The mean free path scales inversely with the density of scattering centres in the sample

Expected dimensions of low-energy electron cascades in biological samples

1fs10fs

100fs

The mean free path of an electron scales inversely with the density of scattering centres in the sample

y (Å)

x (Å)

Results from 2,000 Monte Carlo simulations plotted

250 eV

The density of a biomolecule is about three times smaller than that of diamond

Soluble proteins

Picorna viruses

-600

-300

-150

-450

150

450

600

300

-600 -450 -300 -150 150 450 600300

PRED

ICTE

D S

IZE

REG

IME

FOR

PR

OTE

INS

y

(Å)

PREDICTED SIZE REGIME FOR PROTEINS x (Å)Ziaja, Szoke, van der Spoel, Hajdu (2002) Phys. Rev. B, 66, 024116

CASCADES PRODUCED BY a 12 keV PHOTOELECTRON

1000

2000

6000

1000 2000 3000 4000 5000 6000 7000 8000

5000

4000

3000

1 fs

10 fs

100 fs

~1000 ionisations in 100 fs

12 keV impactenergy

7000

y (Å)

x(Å)

0.25 keV impactEnergy

(AUGER CASCADE)5-13 ionisations

in 100 fs

SAMPLE SIZE and IONISATION with X-RAYS

AUGER-CRITICAL SIZE REGIME900 Å < Ø < 9,000 ÅAuger electrons trapped Photoelectrons leave

MACROSCOPIC SAMPLES Ø > 100,000 ÅAuger electrons trapped Photoelectrons trapped

SMALL SAMPLESØ < 300 ÅPhotoelectrons leaveAuger electrons leave ~0.25 keV

1 elastic scattering event

10 photoelectrons 10 Auger electrons

12 keV X-ray photons

~12 keV

~20 e-

10 x 10 cascade electrons

1 elastic scattering event

10 Auger electrons10 photoelectrons

~120 e-

INC

REA

SING

SAM

PLE SIZE 1 elastic scattering event

10 Auger electrons10 photoelectrons

1000 cascade electrons

-10,000 e

10 x 10 cascade electrons

~10 fs

~10 fs ~100 fs

~10 fs ~100 fs~1000 fs

~0.25 keV

f(t)

Model 1: An MD model for damage formation and X-ray scatteringXMD interfaced with GROMACS (van der Spoel et al.)

HEATING conserving momentum

BOND BREAKAGE through Morse potential

IONISATION primary and secondary effects

IONISATION DYNAMICS calculate changes in the elastic, inelastic and photoelectric cross-sections for each atom during exposure

INVENTORY kept on all electrons in the sample

(Neutze, R., Wouts, R., van der Spoel, D., Weckert, E. Hajdu, J. (2000) Nature 406, 752-757)

Coulomb explosion of lysozyme (50 fs)Coulomb explosion of a small protein (lysozyme)

Radiation damage interferes with atomic scattering factors and

atomic positions

50 fs3x1012 photons/100 nm spot12 keV

Radiation damage interferes with atomic positions and atomic scattering factors

Coulomb Explosion of Lysozyme

Neutze, R., Wouts, R., van der Spoel, D., Weckert, E. Hajdu, J. (2000) Nature 406, 752-757

20 fs3x1012 photons/100 nm spot12 keV

We compute the effect of the explosion on the diffraction pattern

I(q) = Ωre2 I(t) f j (q, t)exp iq ⋅ x j (t)

j∑

2

−∞

∞

∫ dt

Compute time-integrated diffraction intensity:

Calculate “degradation (R) factor” to see how the explosion degrades the image

R =K−1 Ireal (u) − Iideal (u)

Iideal (u' )u'∑u

∑ K =Ireal (u)

u∑

Iideal (u)u∑

R = 0 is ideal; larger R means larger errorFor two totally random arrays: R 0.67Typical R -values in Protein Database: 0.20

Landscape of damage tolerance

40%

30%

20%15%

Relec

1010

1011

1012

1013

1014

1 10 100 1000

Tolerable damage(single exposures)

Initial LCLSparameters

Initial TESLAparameters

Ionisation and subsequent sample explosion cause diffraction intensities to change

Time (fs)

Damage-induced error:

I(t) - Io Io

R =

Crystallographic R-factors in the PDB (~20%)

10 8

10 9

RMS error

Time (fs)

Pho

tons

/pul

se/1

00 n

m s

pot

CLASSICAL DOSE LIMIT at LOW DOSE RATES in LARGE SAMPLES (~200 photon / Å2, 10-12 keV X-rays, CRITERION: 50% loss of intensity in the image)

Henderson, Proc. R. Soc. 241, 6-8, 1990

CLASSICAL LIMIT with SMALL SAMPLES(~8000 photon / Å2, 10-12 keV X-RAYS)

Predicted scattering from a single RUBISCO molecule (12 keV photons, Relectronic = 15%)

100 fs3 x 1011

50 fs8 x 1011

10 fs5 x 1012

5 fs1 x 1013

1 fs5 x 1013

562kDa

2 Å resolution

Sample Size and Scattering

RUBISCO 562,000 Da

HRV ~3,000,000 DaLYSOZYME 19,806 Da

Structure of content unknown

Single virus particles look very promising even with initial LCLS parameters

Scattering to 2.4 Å with 5×1010 ph/(100nm)2 in 230 fs (initial LCLS params)

Scattering to 3 Å with 1013 ph/(100nm)2 in <10 fs

Scattering to 3 Å with 1012 ph/(100nm)2 in 20 fs

Model 2: Hydrodynamic model of sample explosionHau-Riege S.P., London R.A., Szoke A. (2004) Dynamics of biological molecules irradiated by short X-ray pulses. Phys. Rev. E 69 (5): Art. No. 051906

(1) Sample is initially homogeneous (do not consider individual atoms, rather a continuum of matter with average atomic composition of H, C, N, O, S,…)

(2) Sample has spherical symmetry

“Real” molecule Spherical, continuum model

R

r

Model includes:Coulomb force due to escaped electronsPressure force due to trapped electronsDebye shielding due to trapped electrons

The model is based on the hydrodynamic partial differential equations:

Equations

continuity: DρDt

+ ρ∇⋅ u = 0

momentum: ρDuDt

= Fc − ∇P

energy: DεDt

+ P DVDt

= H

Definitions

DDt

≡ time derivative in fluid fram

ρ ≡ mass densityu ≡ velocityP ≡ pressureFc ≡ Coulomb force/volumee ≡ internal energyV ≡ volume (=1/ρ)H ≡ heating rate/mass

2-layer configuration through Debye shielding by low energy electrons

Neutralizedcore

Positively charged outer layer

Escapingelectrons

VQ =V

1 + βVolume of charged layer:

Sample dynamics in the hydrodynamic onion model

Coulomb Force

Coulomb ForceDebye Shielding

Coulomb ForcePressure ForceDebye Shielding

Pressure Force

r / R

Fluence = 3x1012 photons/100 nm spot, 12 keV, 20 fs pulse

POTENTIAL BENEFITS

FROM USING

A TAMPER

Centre of 20 fs pulse

R

rSound velocity

Time (fs)

A sacrificial layer of an H-rich material can be used to carry away positive charges from the surface without significant scattering by moving protons.

TAMPER: e.g. structural water on the surface of the protein

Protons boil off

EFFEECT OF A TAMPER

Results from hydro model are in good agreement with results from molecular dynamics

2211 33

6644 55

Neutze, et al (2000)# photons in100 nm spot

15 %

15 %

Damage-Induced Error

R-factors (%)Point MD hydro

1 7 42 15 153 30 37

4 13 175 17 196 28 36

(No tamper)

Neutze, et al (2000)

pulse length (fs)

Model 3: Molecular dynamics with electrons

Electrons released in the sample shield repulsive interactions between ions.

Two models have been described:

1. Explicit electrons (Jurek et al. Eur. Phys. J., D29, 217-229, 2004).Advantage: Very detailed information Disadvantage: Difficult to model interactions between ions andelectrons, expensive due to short integration time steps (1 as)

2. Implicit electrons modeled through an electron density on a grid(Bergh et al. Phys. Rev. E70, 051904, 2004). Plasma approximation.

Advantage: Average electron density correctDisadvantage: Expensive due to grid calculations

Preparatory work until the first XFEL comes to life

Many open questions remain for single-molecule imaging, including

•What are the dynamics of the molecule explosion? • How short a pulse is required? • Can image reconstruction be performed on noisy data at random orientations?• How can we inject single molecules into the x-ray beam?• What are the requirements of the focusing optics?

We need improved predictions of focusing requirements, pulse length, etc.

We plan to conduct preparatory work at synchrotron facilities, at SPPS(SLAC), at the VUV-FEL (DESY), and on high-harmonic laser sources (UCB, LLNL, Paris).

CRITICAL EXPERIMENTAL TESTS

(1) SYNCHROTRONSRight wavelength, but 'wrong' intensity and pulse lengthTASK: Coherent imaging of non-repetitive objects, reconstruction tests

(2) SPPS (SALC) Right wavelength, right pulse length, but 'wrong' intensityTASK: electron cascades, laser plasmas, ablation

(3) VUV-FEL (DESY) Right pulse length, right intensity, but 'wrong' wavelengthTASK: atomic physics, explosion dynamics, flash imaging

NEED EARLY ACCESS to LCLS to finalise tests

Sample handlingPurification: High-mass mass spectrometryInjection: ElectrosprayManipulation: Optical tweezers

Electrostatic trappingAcoustic levitationMagnetic trapping

Detection/veto: Fluorescence

- SPRAYING TECHNIQUES- SAMPLE EMBEDDED IN VITREOUS ICE (EM)

- random sample orientation - high vacuum- cryogenic temperatures

QUESTION OF REPRODUCIBILITY (contribution to overall “B-factor”)- crystal structures (diffraction)- solution structures (NMR, EM)- gas phase structures (ribosome, single viral particles, proteins + structural water)

Determination of 3D structure will require multiple samples and multiple orientations

Protein molecule gun

detectorXFEL pulsesSerial method

Protein molecules arranged in a regular nanocluster

XFEL pulseParallel method

detector

"OVERSAMPLED" DIFFRACTION PATTERN HELPS PHASING

A section of the 3D diffraction pattern assembled from

many images (2.5 Å resolution)

The reconstructed electron density

(with noise)

Electron density of RUBISCO

from the PDB

IT SEEMS POSSIBLE TO DETERMINE DIRECTLY 3D STRUCTURES FOR SINGLEMOLECULES FROM OVERSAMPLED DIFFRACTION IMAGES XFEL

Miao, J., Hodgson, K.O., Sayre, D. (2001) An approach to three-dimensional structures of biomolecules by using single-molecule diffraction images. Proc. Natl. Acad. Sci. USA 98, 6641–6645.

3D RECONSTRUCTION - image properties EM tomograms Diffraction images

Diffraction images: - centred (redundant at low angles)- spherical sections- background is mixed with object- almost ‘perfect’ images

Tomograms: - planar sections- not centred (need to find molecules)- background is partly separated - ‘imperfect’ images due to the CTF

Van Heel et al. ICL

The resolution limit can be extended by averaging images from the same orientation

3D RECONSTRUCTION - IMAGE CLASSIFICATION

The BASIC REQUIREMENT for CLASSIFICATION and AVERAGING is the ability to tell if two noisy images show the same view of the sample or two different views

CORRELATION METHODS, ANALYTICAL SOLUTION EXISTS

3D reconstruction in electron tomography/microscopy:

COMMON LINEPROJECTION THEOREM

The COMMON LINE is a hinge

axis in EM

A 3D DATA SET CAN BE ASSEMBLED FROM INDIVIDUAL IMAGES BASED ON COMMON LINES OF INTERSECTIONS

A 3D DATA SET CAN BE ASSEMBLED FROM INDIVIDUAL IMAGES BASED ON THEIR COMMON ARCS OF INTERSECTION

COMMON ARCS OF INTERSECTION:

3 images

INTERSECTION OF DIFFRACTION IMAGES IN 3D:

A SINGLE ARCGIVES A ~3D FIX

Huldt, Szöke, Hajdu: Diffraction imaging of single particles and biomolecules. J. Struct. Biol. 144, 219 –227 (2003).

Diffraction imaging

1952: Sayre: Bragg diffraction - critical sampling of the autocorrelation function1972: Gerchberg & Saxton: iterative phase reconstruction1988: Fienup: demonstrated reconstruction at visible light1999: Miao: demonstrated reconstruction with x-rays (but requires a low-

resolution image)

2003: Miao: Stained E. coli bacteria imaged with λ = 2Å, at resolution = 30 nm

J. Miao et al. Proc. Nat. Acad. Sci. (2003)

3D imaging in a pulse

Chris Jacobsen, SUNY

Diffractive optics to provide many viewing angles simultaneously

X-Ray Fourier Transform Spectro-Holography at λ = 1.6 nm

Experiment performed at BESSY

Eisebitt et al. (2004) Scalable approach for lensless imaging at x-ray wavelengths. Applied Physics Letters 84 (17): 3373-3375.

Issues related to the BIO case for the XFEL

Optimum machine time structure and time resolution?Bunch length and bunch pattern? As short as possibleIs a duty cycle higher than 10 Hz necessary? About 100 Hz would be ideal

Optimum wavelength and/or wavelength tunability?Hard X-rays (around 10-20 keV), tunability not necessary

Role of coherence and coherence parameters? Needed for imaging of single particles and molecules (>sample size)

Specific experiment on the beamline lay-out? Sample handling, selection, and injection integrated into the beam line

Use of spontaneous emission? Important for synchrotron-like experiments (see SPPS). Useful for classical structural biology with very high time resolution.