Applications of scattering theory! From the structure of the proton! to protein structure!

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1 Applications of scattering theory From the structure of the proton to protein structure Nicuşor Tîmneanu 2016 Contents and goals What is scattering and why study it? How is the structure of matter determined? How is the structure of proteins determined?

2 What is scattering? Français: dispersion Auf Deutsch: Streuen In Italiano: dispersione På svenska: spridning Em português: dispersar Românã: împrãştiere English: cause to separate and go in different directions, deflection, collision, dispersion, diffusion, sprinkling Why study scattering? Many processes in nature are scattering processes, where two or several particles interact with each other Collision processes are the main tool for investigating the structure of matter, from the proton to the protein Main variable is the energy, it provides the resolution in the investigation.

3 Scattering and structure Projectile Target Energy Result Field α-particles atoms MeV Atomic structure electrons and nuclei protons nuclei 20 MeV Nuclear structure mass distribution electrons nuclei 200 MeV Nuclear structure charge distribution electrons protons 10 GeV Proton structure quarks and gluons Atomic physics Nuclear physics Nuclear physics Particle physics Time ev - energy required to move an electron over a potential difference of 1 V

4 Particle accelerators - modern microscopes Charged particles (electrons, protons) are accelerated to high energies and collide Discovery of new particles and fields quarks 1968 at Stanford Linear Accelerator Center (SLAC) in electron-proton collisions gluons 1979 at Deutsches Elektronen-Synchrotron (DESY) in Hamburg in electron-electron collissions High energy - high resolution (DeBroglie wavelength m) and possibility for production of heavy particles (M top =170 GeV) Establishing of Standard Model - fundamental building blocks of nature and their interactions + Higgs boson (2012)

5 Large Hadron Geneve 27 km circumference proton-proton collider Energy of proton: 7 TeV % of the speed of light Discovery of Higgs boson (2012) From within the proton towards protein structure? Greek πρωτειος (proteios) - first, primary proton - (Rutherford, 1918) - thought to be the fundamental bulding block in the atom protein - (Berzelius, 1838) - complex macromolecules with various function, fundamental for living organisms Structural biology - studies the structure, dynamics and function of proteins

6 Protein Data Bank (PDB): 123,622 STRUCTURES ,489 X-ray crystallography 2 11,618 NMR Nuclear magnetic resonance 3 1,216 EM - Electron microscopy Other (spectroscopy) Synchrotron radiation discovered 1947 at particle accelerators - nuisance for particle physicists first biological application in 1970 run parasitic with physics experiments end of 1980s, first dedicated synchrotrons today - 30 synchrotrons in the world, with more than 100 experimental stations

7 Scattering by a protein crystal at synchrotron Many copies enhance the signal (interference) and distribute damage DISTRIBUTED DAMAGE Diffraction pattern Atomistic structure Scattering by single proteins with X-ray lasers Image proteins with extremely short and intense pulses before the sample is damaged Detector Protein beam Laser Scattering pattern Atomistic structure

8 SLAC Stanford Linear Acceleration Center 3 km long accelerator Discovery of quarks 1969 Linac Coherent Light Source LCLS (2009) The first photonics center which can reach the goal of determining protein structure with X-ray lasers Cost ~ 300 million $ Wavelength Å Pulse length fs First experiments autumn 2009 DESY Deutsches Elektronen-Synchrotron Hamburg FLASH (2004) & European X-Ray Laser Project (2017) Fre-electron LASer in Hamburg m long - pulse length fs - intensity 1012 photons/pulse - wavelength: nm European XFEL km long - cost ~ 1 billion - pulse length 100 fs - wavelength Å - 5 experimental stations

9 How to get structure from scattering? 1. Investigate the samples through elastic scattering - conservation of energy and transfer of momentum (or deep inelastic scattering, without energy conservation) 2. Momentum space (Fourier space) encodes information from the real space - high momentum transfer gives high resolution 3. Scattering cross section - effective area (classically) or probability for scattering event (quantum mechanically) Rutherford scattering - classical example 1911 discovery of the nucleus Experiment: Au foil bombarded with α particles Observed angles of 140 o deflection Inconsistent with Thompson model Ernest Rutherford ( ) father of nuclear physics

10 Classical scattering Particles have well defined trajectories, completely and uniquely determined by Newtons equations of motion dr dt = 2 m [ E V ( r )] 2Eb2 mr 2 Rutherford differential cross section Probability for scattering in a certain direction (solid angle) dσ Z e Z e = d Ω E 1 θ sin πε 0 4 Thompson Dalton Rutherford Amazing discovery potential (for a classical equation) -- protons/neutrons inside nucleus, quarks inside protons