Transcript Slide 1
Physical techniques to study molecular structure Radiation X-ray n eRF Sample Detection 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? Brownian motion 1 mm particles 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. Random walk y R qe1 qe2 qe3 ... qeN whereei are unit vectors For random walk we require that R 0 q e2 qe1 x Example(assume only twosteps) 2 R 2 qe1 qe2 q 2 e22 e12 2e2 e1 q 2 1 1 2e2 e1 q 2 2 2e2 e1 Averageover M experiments 2 2 q2 1 m 2 1 M 2 R R q e e e ... e (MN e k 1 2 3 N i e j ) M k 1 M k 1 i j M If we assume thateach step is randomand takesa timeτ and the totaltimeis t, then N 2 t 2 q 2 2q2x q 2x 2 We may write R Nq q 4Dt, where D τ 4τ 4τ 2τ Each step in the x and y directions are random, but otherwise equal, such that qx2=qy2 t whereq 2 q 2x q 2y 2q 2x Random walk MSD y x t 2 q 2x Mean Square Deviation MSD R 4Dt, where D 2τ 1D: MSD=2Dt 2D: MSD=4Dt 3D: MSD=6Dt try to show this yourself! Fick’s law of diffusion Adolf Fick (1855): dC J D dx 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 ) Random walk is due to thermal fluctuations! v ma 0 fv R(t) fv f 6r for a sphericalparticle wherer radius of particles R(t)is a randomforcedue to collision with watermolecules R(t) k BT D (Einstein relationsh ip, 1905) f Diffusion coefficients in different materials D k BT (Einstein relationsh ip, 1905) f State of matter D [m2/s] Solid 10-13 Liquid 10-9 Gas 10-5 Radiation X-ray n eRF Photons and Electromagnetic Waves • Light has a dual nature. It exhibits both wave and particle characteristics – Applies to all electromagnetic radiation 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) 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 de Broglie Wavelength and Frequency • The de Broglie wavelength of a particle is h h l p mv • The frequency of matter waves is E ƒ h Dual Nature of Matter • The de Broglie equations show the dual nature of matter • Matter concepts – Energy and momentum • Wave concepts – Wavelength and frequency 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 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 Spring-8, Japan Scattering Analogical synthesis Object Lens Image Direct imaging method (optical or electronic) Scattering Synthesis by computation (FT) Object Data collection Image Indirect imaging method (diffraction X-ray, neutrons, e-) Scattering of a plane monochrome wave Incident wave Scattered wave Janin & Delepierre A molecule represented by electron density Scattering by an object of finite volume Scattered beam Incident beam Janin & Delepierre 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 Diffraction Grating • The condition for maxima is d sin θbright = m λ • m = 0, 1, 2, … 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 surface • Bragg’s Law gives the conditions for constructive interference 2 d sinθ = mλ; m = 1, 2, 3… A protein crystal X-ray diffraction pattern of a protein crystal http://en.wikipedia.org/wiki/X-ray_crystallography 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 millielectronvolts 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 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 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 Larmor frequency A Spinning Gyroscope in a Gravity Field A Spinning Charge in a Magnetic Field w = g B0 http://www.cem.msu.edu/~reusch/VirtualText/Spectrpy/nmr/nmr2.htm#pulse 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 d = (f - fref)/fref Pulsed Fourier Transform (FT) NMR RF http://www.cem.msu.edu/~reusch/VirtualText/Spectrpy/nmr/nmr1.htm Fourier transform (FT) NMR http://www.cem.msu.edu/~reusch/VirtualText/Spectrpy/nmr/nmr1.htm Fourier transform (FT) NMR http://www.cem.msu.edu/~reusch/VirtualText/Spectrpy/nmr/nmr1.htm Proton 1D NMR spectrum of a protein http://www.cryst.bbk.ac.uk/PPS2/projects/schirra/html/2dnmr.htm#noesy 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 http://www.cryst.bbk.ac.uk/PPS2/projects/schirra/images/2dnosy_1.gif Information obtained by NMR • Distances between nuclei • Angles between bonds • Motions in solution Today’s lesson: 1) Molecules in solution; Brownian motion 2) X-ray 3) Scattering and diffraction 4) Neutron scattering 5) Electron Microscopy (EM) 6) Nuclear Magnetic Resonance (NMR) spectroscopy