Physical techniques
to study molecular structure
Sample
Radiation            Detection

X-ray
n
e-
RF
About samples of biomolecules



Example:

How many protein molecules are there in the solution
sample (volume, 100 µl) at...
Brownian motion




                  1 µm particles
History of Brownian motion

1785: Jan Ingenhousz observed irregular motion of coal dust particles in
alcohol.



1827: Rob...
y                                Random walk

                                                                  
   ...
Random walk


                          MSD
y




                     x
                                                 ...
Fick’s law of diffusion

   Adolf Fick (1855):

                                     J
         dC
  J = −D
              ...
Random walk is due to thermal fluctuations!
      v
            ma = 0 = −fv + R(t)   f = 6πrη for a spherical particle wh...
Diffusion coefficients in different materials


           k BT
      D=        (Einstein relationship, 1905)
            ...
Radiation




            X-ray
            n
            e-
            RF
Photons and Electromagnetic Waves


• Light has a dual nature. It exhibits both wave and
  particle characteristics
   – A...
Particle nature of light


• Light consists of tiny packets of energy, called photons

• The photon’s energy is:


       ...
Wave Properties of Particles



• In 1924, Louis de Broglie postulated that because
  photons have wave and particle chara...
de Broglie Wavelength and Frequency


  • The de Broglie wavelength of a particle is

                    h  h
           ...
Dual Nature of Matter



• The de Broglie equations show the dual nature of matter

• Matter concepts
  – Energy and momen...
X-Rays


• Electromagnetic radiation with short wavelengths
   – Wavelengths less than for ultraviolet
   – Wavelengths ar...
Production of X-rays

• X-rays are produced when high-speed electrons are
  suddenly slowed down
Wavelengths Produced
Production of X-rays in
synchrotron




 European synchrotron
 Grenoble, France
European synchrotron
                       Electron energy: 6 Gev
European synchrotron




   Bending magnets     Undulators
A typical beamline
The three largest and most powerful synchrotrons in the world




  APS, USA             ESRF, Europe-France            Sp...
Scattering
                        Analogical synthesis



                                     Image
 Object          Len...
Scattering
                           Synthesis by computation (FT)



                                         Image
    ...
Scattering of a plane monochrome wave




         Incident
         wave



                                Scattered
   ...
A molecule represented by electron density
Scattering by an object of finite volume



                                    Scattered
                                ...
Schematic for X-ray Diffraction



• The diffracted radiation is very
  intense in certain directions
   – These direction...
Diffraction Grating




                      • The condition for maxima is
                         d sin θbright = m λ
 ...
X-ray Diffraction of DNA




     Photo 51




                           http://en.wikipedia.org/wiki/Image:Photo_51.jpg
Planes in crystal lattice
Bragg’s Law


•   The beam reflected from the lower
    surface travels farther than the one
    reflected from the upper ...
A protein crystal
X-ray diffraction pattern of a protein crystal




                                           http://en.wikipedia.org/wiki...
Electron density of a protein
Scattering and diffraction of neutrons




Institut Laue-Langevin,
Grenoble, France
Why use neutrons?




   Electrically Neutral
   Microscopically Magnetic
   Ångstrom wavelengths
   Energies of millielec...
The Electron Microscope


•   The electron microscope depends on
    the wave characteristics of electrons

•   Microscope...
Nuclear Magnetic Resonance (NMR) spectroscopy




              Superconducting magnets 21.5 T
              Earth’s magne...
Spin and magnetic moment

• Nuclei can have integral spins (e.g. I = 1, 2, 3 ....): 2H, 6Li, 14N
fractional spins (e.g. I ...
Larmor frequency




    A Spinning Gyroscope                     A Spinning Charge
    in a Gravity Field                ...
Continuous wave (CW) NMR




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




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




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




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




                 δ = (f - fref)/fref
Pulsed Fourier Transform (FT) NMR
              RF




                                    http://www.cem.msu.edu/~reusch/...
Fourier transform (FT) NMR




                             http://www.cem.msu.edu/~reusch/VirtualText/Spectrpy/nmr/nmr1.h...
Fourier transform (FT) NMR




                             http://www.cem.msu.edu/~reusch/VirtualText/Spectrpy/nmr/nmr1.h...
Proton 1D NMR spectrum of a protein




                                 http://www.cryst.bbk.ac.uk/PPS2/projects/schirra/...
Proton 1D NMR spectrum of a DNA fragment
A 2D NMR spectrum




                    http://www.bruker-nmr.de/guide/
Nuclear Overhauser Effect Spectroscopy (NOESY)
provides information on proton-proton distances




   NOE ~ 1/r6




     ...
Information obtained by NMR




      • Distances between nuclei

      • Angles between bonds

      • Motions in solution
Today’s lesson:

•   Molecules in solution; Brownian motion
•   X-ray
•   Scattering and diffraction
•   Neutron scatterin...
NMR Spectroscopy
NMR Spectroscopy
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NMR Spectroscopy

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NMR Spectroscopy

  1. 1. Physical techniques to study molecular structure
  2. 2. Sample Radiation Detection X-ray n e- RF
  3. 3. About samples of biomolecules Example: How many protein molecules are there in the solution sample (volume, 100 µl) at the concentration of 0.1 mM?
  4. 4. Brownian motion 1 µm particles
  5. 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. 6. y Random walk       R = qe1 + qe2 + qe3 + ... + qeN where ei are unit vectors  For random walk we require that R = 0  Example (assume only two steps)  qe2  qe1 x   2 ( 2    ) (   ) (   R 2 = ( qe1 + qe 2 ) = q 2 e 2 + e12 + 2e 2 ⋅ e1 = q 2 1 + 1 + 2e 2 ⋅ e1 = q 2 2 + 2e 2 ⋅ e1 ) Average over M experiments 2 1 m 2 1  M 2     2  q2   R = ∑ R k = M ∑ q ( e1 + e2 + e3 + ... + e N )  = M (MN + ∑ ei ⋅e j ) M k =1  k =1  i≠ j t If we assume that each step is random and takes a time τ and the total time is t, then N = τ 2 t 2 q 2 2q 2 q 2 We may write R = Nq = q = 4Dt, where D = 2 = x = x where q 2 = q 2 + q 2 = 2q 2 x y x τ 4τ 4τ 2τ Each step in the x and y directions are random, but otherwise equal, such that qx2=qy2
  7. 7. Random walk MSD y x t 2 q2 Mean Square Deviation = MSD = R = 4Dt, where D = x 2τ 1D: MSD=2Dt 2D: MSD=4Dt try to show this yourself! 3D: MSD=6Dt
  8. 8. Fick’s law of diffusion Adolf Fick (1855): J dC J = −D A dx 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. 9. Random walk is due to thermal fluctuations! v ma = 0 = −fv + R(t) f = 6πrη for a spherical particle where r = radius of particles R(t) is a random force due to collision with water molecules fv R(t) k BT D= (Einstein relationship, 1905) f
  10. 10. Diffusion coefficients in different materials k BT D= (Einstein relationship, 1905) f State of matter D [m2/s] Solid 10-13 Liquid 10-9 Gas 10-5
  11. 11. Radiation X-ray n e- RF
  12. 12. Photons and Electromagnetic Waves • Light has a dual nature. It exhibits both wave and particle characteristics – Applies to all electromagnetic radiation
  13. 13. Particle nature of light • Light consists of tiny packets of energy, called photons • The photon’s energy is: E = h f = h c /λ h = 6.626 x 10-34 J s (Planck’s constant)
  14. 14. 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
  15. 15. de Broglie Wavelength and Frequency • The de Broglie wavelength of a particle is h h λ = = p mv • The frequency of matter waves is E ƒ= h
  16. 16. Dual Nature of Matter • The de Broglie equations show the dual nature of matter • Matter concepts – Energy and momentum • Wave concepts – Wavelength and frequency
  17. 17. 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
  18. 18. Production of X-rays • X-rays are produced when high-speed electrons are suddenly slowed down
  19. 19. Wavelengths Produced
  20. 20. Production of X-rays in synchrotron European synchrotron Grenoble, France
  21. 21. European synchrotron Electron energy: 6 Gev
  22. 22. European synchrotron Bending magnets Undulators
  23. 23. A typical beamline
  24. 24. The three largest and most powerful synchrotrons in the world APS, USA ESRF, Europe-France Spring-8, Japan
  25. 25. Scattering Analogical synthesis Image Object Lens Direct imaging method (optical or electronic)
  26. 26. Scattering Synthesis by computation (FT) Image Object Data collection Indirect imaging method (diffraction X-ray, neutrons, e-)
  27. 27. Scattering of a plane monochrome wave Incident wave Scattered wave Janin & Delepierre
  28. 28. A molecule represented by electron density
  29. 29. Scattering by an object of finite volume Scattered beam Incident beam Janin & Delepierre
  30. 30. 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
  31. 31. Diffraction Grating • The condition for maxima is d sin θbright = m λ • m = 0, 1, 2, …
  32. 32. X-ray Diffraction of DNA Photo 51 http://en.wikipedia.org/wiki/Image:Photo_51.jpg
  33. 33. Planes in crystal lattice
  34. 34. 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…
  35. 35. A protein crystal
  36. 36. X-ray diffraction pattern of a protein crystal http://en.wikipedia.org/wiki/X-ray_crystallography
  37. 37. Electron density of a protein
  38. 38. Scattering and diffraction of neutrons Institut Laue-Langevin, Grenoble, France
  39. 39. Why use neutrons? Electrically Neutral Microscopically Magnetic Ångstrom wavelengths Energies of millielectronvolts
  40. 40. 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
  41. 41. 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
  42. 42. 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 1 H, 13C, 15N and 31P, which have I = 1/2. • Spins are associated with magnetic moments by: m = γħ I
  43. 43. Larmor frequency A Spinning Gyroscope A Spinning Charge in a Gravity Field in a Magnetic Field ω = γ B0 http://www.cem.msu.edu/~reusch/VirtualText/Spectrpy/nmr/nmr2.htm#pulse
  44. 44. Continuous wave (CW) NMR http://www.cem.msu.edu/~reusch/VirtualText/Spectrpy/nmr/nmr1.htm
  45. 45. Chemical shift http://www.cem.msu.edu/~reusch/VirtualText/Spectrpy/nmr/nmr1.htm
  46. 46. Chemical shift http://www.cem.msu.edu/~reusch/VirtualText/Spectrpy/nmr/nmr1.htm
  47. 47. Chemical shift http://www.cem.msu.edu/~reusch/VirtualText/Spectrpy/nmr/nmr1.htm
  48. 48. Chemical shift δ = (f - fref)/fref
  49. 49. Pulsed Fourier Transform (FT) NMR RF http://www.cem.msu.edu/~reusch/VirtualText/Spectrpy/nmr/nmr1.htm
  50. 50. Fourier transform (FT) NMR http://www.cem.msu.edu/~reusch/VirtualText/Spectrpy/nmr/nmr1.htm
  51. 51. Fourier transform (FT) NMR http://www.cem.msu.edu/~reusch/VirtualText/Spectrpy/nmr/nmr1.htm
  52. 52. Proton 1D NMR spectrum of a protein http://www.cryst.bbk.ac.uk/PPS2/projects/schirra/html/2dnmr.htm#noesy
  53. 53. Proton 1D NMR spectrum of a DNA fragment
  54. 54. A 2D NMR spectrum http://www.bruker-nmr.de/guide/
  55. 55. Nuclear Overhauser Effect Spectroscopy (NOESY) provides information on proton-proton distances NOE ~ 1/r6 http://www.cryst.bbk.ac.uk/PPS2/projects/schirra/images/2dnosy_1.gif
  56. 56. Information obtained by NMR • Distances between nuclei • Angles between bonds • Motions in solution
  57. 57. Today’s lesson: • Molecules in solution; Brownian motion • X-ray • Scattering and diffraction • Neutron scattering • Electron Microscopy (EM) • Nuclear Magnetic Resonance (NMR) spectroscopy
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