Physical techniques to study molecular structure

Detection Sample Radiation X-ray n e- RF

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

1 mm particles 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. History of Brownian motion

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

1D: MSD=2Dt 2D: MSD=4Dt try to show this yourself! 3D: MSD=6Dt Random walk

Fick’s law of diffusion Adolf Fick (1855): 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 ) J A

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

Diffusion coefficients in different materials

Radiation X-ray n e- RF

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 The frequency of matter waves is

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

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

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

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

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

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

A molecule represented by electron density

Scattering by an object of finite volume 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, …

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

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

Electrically Neutral Microscopically Magnetic Ångstrom wavelengths Energies of millielectronvolts Why use neutrons?

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 http://en.wikipedia.org/wiki/Nuclear_magnetic_resonance Superconducting magnets 21.5 T Earth’s magnetic field 5 x 10-5 T

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: Spin and magnetic moment m = għ I

A Spinning Gyroscope in a Gravity Field A Spinning Charge in a Magnetic Field http://www.cem.msu.edu/~reusch/VirtualText/Spectrpy/nmr/nmr2.htm#pulse Larmor frequency w = g B0

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

http://www.cryst.bbk.ac.uk/PPS2/projects/schirra/html/2dnmr.htm#noesy Proton 1D NMR spectrum of a protein

Proton 1D NMR spectrum of a DNA fragment

http://www.bruker-nmr.de/guide/ A 2D NMR spectrum

Nuclear Overhauser Effect Spectroscopy (NOESY) provides information on proton-proton distances http://www.cryst.bbk.ac.uk/PPS2/projects/schirra/images/2dnosy_1.gif NOE ~ 1/r6

Distances between nuclei Angles between bonds Motions in solution Information obtained by NMR

Today’s lesson: Molecules in solution; Brownian motion X-ray Scattering and diffraction Neutron scattering Electron Microscopy (EM) Nuclear Magnetic Resonance (NMR) spectroscopy