New algoritms for electron diffraction of 3D protein crystals. JP Abrahams, D Georgieva, L Jiang, I Sikhuralidze, NS Pannu

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1 New algoritms for electron diffraction of 3D protein crystals JP Abrahams, D Georgieva, L Jiang, I Sikhuralidze, NS Pannu

2 Why new algorithms? New research questions New experimental techniques Better insight in current techniques (New computer hardware)

3 New applications of pixel detectors in EM : Making movies rather than pictures collect data until the sample is gone, use only relevant data reduce problems with drift measure samples many times, with different instrument settings scan the entire grid (5 Pbyte per 1 Å 2 /pixel, 1 byte/pixel, 5 time points/pixel)

4 Why electron diffraction? Electrons diffraction provides more information for a given amount of radiation damage

5 Radiation damage by electrons, X-rays & neutrons Atomic cross-section for carbon in biological specimens (barns = cm 2 ) Wavelength (Å)

6 Comparing scattering of electrons & X-rays Inelastic / elastic scattering events Energy deposited per inelastic event Energy deposited relative to electrons per elastic event Electrons (200 kev) ~3 ~20 ev 1 X-rays (1.5 Å) ~10 8 kev ~1000 Henderson (1995) Quart. Rev. Biophys. 28, 171

7 Comparing scattering of electrons & X-rays (2) Electron flux density in EM: e - s -1 mm -2 is equivalent to a photon flux density of p s -1 mm -2 and allows 1000 times longer measurement time

8 Why electron diffraction? Electrons diffraction provides more information for a given amount of radiation damage Smaller samples Higher resolution Phase information Electrons may show aspects of structures that are hidden to X-rays Membrane protein crystals with stacking artifacts Twinned, mixed, impure samples (charges??)

9 Why X-ray diffraction? Sample handling is easier Instrumentation is more robust No vacuum No dynamic scattering (clean mathematics) Rotation during exposure is possible Proven, mature technology

10 Current challenges in electron diffraction of 3D protein crystals Mounting crystals } See Dilyana Collecting diffraction data Georgieva s talk Processing diffraction patterns

11 Integrating electron diffraction patterns of 3D protein crystals Problem 1: Radiation damage frustrates crystal alignment Hence: random oriented diffraction patterns

12 Data collection: Lysozyme

13 3D diffraction data collection (high resolution) Electron source Ewald sphere Electron detector Reciprocal lattice

14 3D diffraction data collection (low resolution) Electron detector Ewald plane

15 Flatness of the Ewald sphere

16 Integrating electron diffraction patterns of 3D protein crystals Problem 1: Radiation damage frustrates crystal alignment Hence: random oriented diffraction patterns Problem 2: No sample rotation during exposure Hence: no fully recorded reflections

17 Advantages of precession in single exposure data collection

18 Advantages of precession in single exposure data collection More spots per image More fully recorded reflections Reduced dynamic effect??

19 Dynamic electron diffraction Dynamic effect: Excitation of atoms by scattered electrons

20 Dynamic electron diffraction (2) Kinematic ( single ) diffraction coincides with dynamic diffraction

21 Multi-slice description of dynamic electron diffraction F d (s) = δ(s) i.p.f k (s) (p 2 /2).F k (s)*f k (s) + i.(p 3 /6).F k (s)*f k (s)*f k (s) + Where: F d (h): dynamical scattering F k (s): kinematical scattering p: chance of scattering within slice

22 Is dynamical scattering a problem Assume: for protein crystals? Average scattering cross section of protein atoms: ~10-5 nm kv) 50 scattering atoms per nm 3 in a protein (about 30 H 2 O molecules per nm 3 in liquid water) Now we can set up some differential equations

23 Is dynamical scattering a problem for protein crystals? multiple scattering in proteins Fraction of scattered electrons unscattered electrons single scattering 1 scattered fraction scattering 3 scattering 4 scattering fraction scattering 2 scattering 3 scattering 4 scattering 5 scattering scattering thickness (nm) nm Up to 100 nm thickness no major problems are anticipated (90% of electrons that are scattered, scatter kinematically). Precession electron diffraction may increase the range to 300 nm.

24 Integrating electron diffraction patterns of 3D protein crystals Problem 1: Radiation damage frustrates crystal alignment Hence: random oriented diffraction patterns Problem 2: No sample rotation during exposure Hence: no fully recorded reflections Problem 3: Unit cell might not be known Hence cannot predict spot positions

25 Determining the unit cell from single exposures (2) Diffraction patterns Autocorrelation patterns Pairs of short vectors Best fitting pair Unit cell Pairs of short vectors

26 Determining the unit cell from single exposures For each image: find shortest vector pair (facet) For every lattice: fit all facets Return lattice with the overall best fit It actually works! (see Dilyana Georgieva s talk)

27 Conclusions We can collect electron diffraction data from 3D protein nano-crystals. We can determine the unit cell from a set of single, random diffraction patterns. We can index most diffraction patterns New algorithms required for: Lorentz polarisation correction (maths described by Gjonnes) Phasing (molecular replacement in first instance)