Physical techniques to study molecular structure

1. Physical techniques to study molecular structure

2. Sample Radiation Detection X-ray n e- RF

3. About samples of biomolecules Example: How many protein molecules are there in the solution sample (volume, 100 ml) at the concentration of 0.1 mM?

4. Brownian motion 1 mm particles

5. History of Brownian motion 1785: Jan Ingenhousz observed irregular motion of coal dust particles in alcohol. 1827: Robert Brown watched pollen particles performing irregular motion in water using a microscope. He repeated his experiments with dust to rule out that the particles were alive. 1905: Einstein provided the first physical theory to explain Brownian motion. 1908: Jean Perrin did experiments to verify Einstein’s predictions. The measurements allowed Perrin to give the first estimate of the dimensions of water molecules. Jean Perrin won the Nobel Prize of Physics in 1926 for this work.

6. y x Random walk Each step in the x and y directions are random, but otherwise equal, such that qx2=qy2

7. y MSD x t Random walk 1D: MSD=2Dt 2D: MSD=4Dt try to show this yourself! 3D: MSD=6Dt

8. Fick’s law of diffusion Adolf Fick (1855): J A J= flux of particles (number of particles per area and time incident on a cross-section) [m-2s-1] D= diffusion coefficient [m2s-1] C=concentration of particles [m-3] (sometimes n is used instead of C to represent concentration )

9. fv Random walk is due to thermal fluctuations! v R(t)

10. Diffusion coefficients in different materials

11. Radiation X-ray n e- RF

12. Photons and Electromagnetic Waves • Light has a dual nature. It exhibits both wave and particle characteristics • Applies to all electromagnetic radiation

13. Particle nature of light • Light consists of tiny packets of energy, called photons • The photon’s energy is: E = h f = h c /l h = 6.626 x 10-34 J s (Planck’s constant)

15. Wave Properties of Particles • In 1924, Louis de Broglie postulated that because photons have wave and particle characteristics, perhaps all forms of matter have both properties

16. de Broglie Wavelength and Frequency • The de Broglie wavelength of a particle is • The frequency of matter waves is

17. Dual Nature of Matter • The de Broglie equations show the dual nature of matter • Matter concepts • Energy and momentum • Wave concepts • Wavelength and frequency

18. X-Rays • Electromagnetic radiation with short wavelengths • Wavelengths less than for ultraviolet • Wavelengths are typically about 0.1 nm • X-rays have the ability to penetrate most materials with relative ease • Discovered and named by Röntgen in 1895

19. Production of X-rays • X-rays are produced when high-speed electrons are suddenly slowed down

20. Wavelengths Produced

21. Production of X-rays in synchrotron European synchrotron Grenoble, France

23. European synchrotron Electron energy: 6 Gev

24. European synchrotron Bending magnets Undulators

25. A typical beamline

26. The three largest and most powerful synchrotrons in the world APS, USA ESRF, Europe-France Spring-8, Japan

27. Scattering Analogical synthesis Image Lens Object Direct imaging method (optical or electronic)

28. Scattering Synthesis by computation (FT) Image Data collection Object Indirect imaging method (diffraction X-ray, neutrons, e-)

29. Scattering of a plane monochrome wave Incident wave Scattered wave Janin & Delepierre

30. A molecule represented by electron density

31. Scattered beam Incident beam Scattering by an object of finite volume Janin & Delepierre

32. Schematic for X-ray Diffraction • The diffracted radiation is very intense in certain directions • These directions correspond to constructive interference from waves reflected from the layers of the crystal

33. Diffraction Grating • The condition for maxima is d sin θbright = m λ • m = 0, 1, 2, …

34. X-ray Diffraction of DNA Photo 51 http://en.wikipedia.org/wiki/Image:Photo_51.jpg

35. Planes in crystal lattice

36. Bragg’s Law • The beam reflected from the lower surface travels farther than the one reflected from the upper surface • Bragg’s Law gives the conditions for constructive interference 2 d sinθ = mλ; m = 1, 2, 3…

37. A protein crystal

38. X-ray diffraction pattern of a protein crystal http://en.wikipedia.org/wiki/X-ray_crystallography

39. Electron density of a protein

40. Scattering and diffraction of neutrons Institut Laue-Langevin, Grenoble, France

41. Why use neutrons? Electrically NeutralMicroscopically Magnetic Ångstrom wavelengths Energies of millielectronvolts

42. The Electron Microscope • The electron microscope depends on the wave characteristics of electrons • Microscopes can only resolve details that are slightly smaller than the wavelength of the radiation used to illuminate the object • The electrons can be accelerated to high energies and have small wavelengths

43. Nuclear Magnetic Resonance (NMR) spectroscopy Superconducting magnets 21.5 T Earth’s magnetic field 5 x 10-5 T http://en.wikipedia.org/wiki/Nuclear_magnetic_resonance

44. Spin and magnetic moment • Nuclei can have integral spins (e.g. I = 1, 2, 3 ....): 2H, 6Li, 14N • fractional spins (e.g. I = 1/2, 3/2, 5/2 ....): 1H, 15N • or no spin (I = 0): 12C, 16O • Isotopes of particular interest for biomolecular research are • 1H, 13C, 15N and 31P, which have I = 1/2. • Spins are associated with magnetic moments by: m = għ I

45. Larmor frequency A Spinning Gyroscopein a Gravity Field A Spinning Chargein a Magnetic Field w = gB0 http://www.cem.msu.edu/~reusch/VirtualText/Spectrpy/nmr/nmr2.htm#pulse

46. Continuous wave (CW) NMR http://www.cem.msu.edu/~reusch/VirtualText/Spectrpy/nmr/nmr1.htm

47. Chemical shift http://www.cem.msu.edu/~reusch/VirtualText/Spectrpy/nmr/nmr1.htm

48. Chemical shift http://www.cem.msu.edu/~reusch/VirtualText/Spectrpy/nmr/nmr1.htm

49. Chemical shift http://www.cem.msu.edu/~reusch/VirtualText/Spectrpy/nmr/nmr1.htm

50. Chemical shift d = (f - fref)/fref