Lecture 5 - Physics - University of Florida

Supported by the National Science Foundation via DMR-1202033 (MWM) and DMR-0654118 (NHMFL), and UF CCMS.

Mesoscale Science:Selected perspectives of (some) past, present, and future

issues at the crossroads of physics, chemistry,

molecular biology, and You!

(The CCMS Summer Lecture Series - 2012)

Mark W. Meisel

Department of Physics and NHMFL, UF(http://www.phys.ufl.edu/~meisel/CCMS-SLS-2012.docx)

Lecture 5: Form follows Function (vice versa?) –

bis [continuation of Lecture 3 and other tidbits]

Where have we been and Where are we going?

Lecture 3: Form follows Function (vice versa?) [Amplitude and Phase in Experiments]

Lecture 4: BEC vs. “eyeless” gene, “Smallest transistor, meandering means, and lysozyme”

Next Week

Lecture 5: Form follows Function (vice versa?) – bis

Lecture 6: Quantum Spins: Chains, Planes, and Wheels (Magnetic Mesoscale)

Skip a Week

Last Week

Lecture 7: TBA

Lecture 8: TBA BREAKING FLASH (Sweet!):

“Tiny Talk” script for “homework” has been received!

Outline for Today Lecture 5 (Form follows Function)

* A. Goal: Structure of Biomolecules

* B. X-ray Crystallography: Overview and Phase Info

C. NMR Spectroscopy: Solution is Closer to Real World

* D. Errors of Phase cause Problems

E. The Challenge to You! (and the “homework”)

F. What’s to come in the near-future lectures

* Covered in Lecture 3

Form follows Function: NMR allows Structural Determinations in Solution

TONS (oodles of sites, references by a Gadzillion number of researchers)

No need to reinvent the wheel… or spin it again…

www.nmr2.buffalo.edu/.../Introduction-1D-2D-NMR-KDBishop.ppt

http://www.nmr2.buffalo.edu/

http://www.nmr2.buffalo.edu/nesg.wiki/Main_Page

1993 or 1981

Structure Determination by NMR

CHY 431 Biological ChemistryKarl D. Bishop, Ph.D.

Lecture 1 - Introduction to NMR

Lecture 2 - 2D NMR, resonance assignments

Lecture 3 - Structural constraints, 3D structure calculation


Structure Determination by NMR

A good online book about basic NMR is athttp://www.cis.rit.edu/htbooks/nmr/

Biological molecules such as proteins and nucleic acids can be large and complex. They can easily exceed 2000 atoms.Knowing their structure is critical in understanding the relationship between structure and function.

X-ray crystallography is an excellent method to determine detailed3D structures of even some of the largest biological molecules. However, it has some significant difficulties. Getting crystals andis the structure biologically relevant.

NMR can be used to determine 3D structure and dynamics in solution!It’s limitation is molecular size. However, this is changing.


NMR Structure Determination

• What is NMR?

• How does NMR work?

• How is a three dimensional structure elucidated?


Nuclear Magnetic Resonance

Nuclear spin

µ = γ I h

µ - magnetic moment

γ - gyromagnetic ratio

I - spin quantum number

h - Planck’s constant

µ

I is a property of the nucleus

Mass # Atomic # I

Odd Even or odd 1/2, 3/2, 5/2,…

Even Even 0

Even Odd 1, 2, 3

As an exercise determine I for each of the following 12C, 13C, 1H, 2H, 15N .


Bo

ω ω = γ Bo = ν/2π

ω - resonance frequencyin radians per second,also called Larmor frequency

ν - resonance frequencyin cycles per second, Hz

γ - gyromagnetic ratioBo - external magnetic

field (the magnet)

Apply an external magnetic field(i.e., put your sample in the magnet)

z

µ

µ

ωSpin 1/2 nuclei will have two orientations in a magnetic field+1/2 and -1/2.


Bo

ωz

µ

µ

ω

+1/2

-1/2

Net magnetic moment


Bo = 0 Bo > 0Randomly oriented Highly oriented

Bo

Ensemble of Nuclear Spins

N

S

Each nucleus behaves likea bar magnet.


The net magnetization vector

z

x

y

ω

ωz

x

y

Mo - net magnetization vector allows us tolook at system as a whole

z

x

ω

one nucleus

many nuclei


Bo = 0 Bo > 0

E ∆E

Allowed Energy States for aSpin 1/2 System

antiparallel

parallel

∆E = γ h Bo = h ν

-1/2

+1/2

Therefore, the nuclei will absorb light with energy ∆E resulting ina change of the spin states.


Energy of Interaction

∆E = γ h Bo = h ν

The frequency, ν, corresponds to light in the radiofrequency range when Bo is in the Teslas.

This means that the nuclei should be able to absorblight with frequencies in the range of 10’s to 100’s ofmegaherz.

Note: FM radio frequency range is from ~88MHz to 108MHz. 77Se, γ = 5.12x107 rad sec-1 T-1

ν = γ Bo/2πwww.nmr2.buffalo.edu/.../Introduction-1D-2D-NMR-KDBishop.ppt

http://shop.cafepress.com/nmr

Brain Dump Intermission:

Have you ever worked with a

NEGATIVE Temperature?

Nuclear Spin Dynamics

z

x

y

Mo

z

x

y

Mo

z

x

y

Mo

RF off

RF on

RF off

Effect of a 90o x pulse


Nuclear Spin Evolution

z

x

y

Mo

z

x

y

Mo

ω

z

x

y

Time

x

y

RF receivers pick up the signals I


Free Induction Decay

The signals decay away due to interactions with the surroundings.

A free induction decay, FID, is the result.

Fourier transformation, FT, of this time domain signal produces a frequency domain signal.

FT

TimeFrequency


Spin Relaxation

There are two primary causes of spin relaxation:

Spin - lattice relaxation, T1, longitudinal relaxation.

Spin - spin relaxation, T2, transverse relaxation.

lattice


Nuclear Overhauser EffectCaused by dipolar coupling between nuclei.

The local field at one nucleus is affected by the presence of another nucleus. The result is a mutual modulation of resonance frequencies.

N

S

N

S


Nuclear Overhauser Effect

The intensity of the interaction is a function of the distance between the nuclei according to the following equation.

I = A (1/r6)I - intensityA - scaling constantr - internuclear distance

1H 1Hr1,2

1 2

1H3

r1,3 r2,3

Arrows denote cross relaxation pathwaysr1,2 - distance between protons 1 and 2r2,3 - distance between protons 2 and 3

The NOE provides a link between anexperimentally measurable quantity, I, andinternuclear distance. NOE is only observed up to ~5Å.


Scalar J Coupling

Electrons have a magnetic moment and are spin 1/2 particles.

J coupling is facilitated by the electrons in the bonds separating the two nuclei. This through-bond interactionresults in splitting of the nuclei into 2I + 1states. Thus, for a spin 1/2 nucleus the NMR lines are split into 2(1/2) + 1 = 2 states.

1H

12C 12C

1HMultiplet = 2nI + 1

n - number of identical adjacent nucleiI - spin quantum number


Scalar J Coupling

The magnitude of the J coupling is dictated by the torsionangle between the two coupling nuclei according to the Karplus equation.

CC

H

HH

H θ

J = A + Bcos(θ) + C cos2(θ)Α = 1.9, Β = −1.4, Χ = 6.4

0

2

4

6

8

10

12

0 100 200 300 400

θ

3 J

Karplus Relation

A, B and C on the substituent electronegativity.www.nmr2.buffalo.edu/.../Introduction-1D-2D-NMR-KDBishop.ppt

Torsion Angles

Coupling constants can be measured from NMR data.

Therefore, from this experimental data we can use the Karplus relation to determine the torsion angles, θ.

Coupling constants can be measured between mostspin 1/2 nuclei of biological importance,

1H, 13C, 15N, 31P

The most significant limitation is usually sensitivity, S/N.


Chemical Shift, δ

The chemical is the most basic of measurements in NMR.

The Larmor frequency of a nucleus is a direct result of thenucleus, applied magnetic field and the local environment.

If a nucleus is shielded from the applied field there is a net reduction if the magnetic field experienced by the nucleuswhich results in a lower Larmor frequency.

δ is defined in parts per million, ppm.

δ = (ω - ωo)/ωo * 106


Biomolecular NMR Experiments

J Correlated Based Experiments• COSY - Correlated Spectroscopy• 2QF-COSY - Double Quantum Filtered Spectroscopy• HETCOR - Heteronuclear Correlated Spectroscopy• E.COSY - Exclusive COSY• HOHAHA - Homonuclear Hartmann Hahn (TOCSY)

Nuclear Overhauser Based Experiments• NOESY - Nuclear Overhauser Effect Spectroscopy• ROESY - Rotating Frame Overhauser Effect Spectroscopy

Three Dimensional Experiments Use a Combination• NOESY - TOCSY• NOESY - NOESY


Summary

There are three primary NMR tools used to obtain structural information

Nuclear Overhauser effect - internuclear distances

J Coupling - torsion angles

Chemical shift - local nuclear environment

(Chemical exchange can also be monitored by NMR.)


Biophysics Textbook

On-Line

Sponsored by the Biophysical Society

(last updated in 2000)

http://private.nmr.ru/manuals/biophys/OLTB/index.html

Biophysical Journal Teaching Article

Teaching High-Resolution Nuclear Magnetic Resonance to

graduate Students in Biophysics

Laura Lerner and David A. Horita

Biophys. J. 65(6): 2692-2697 (1993)

http://private.nmr.ru/manuals/biophys/OLTB/BJ/Lerner.pdf

L. Lerner and D.A. Horita, Biophys. J. 65(6): 2692-2697 (1993), http://private.nmr.ru/manuals/biophys/OLTB/BJ/Lerner.pdf

FIGURE 1 Pulse sequence for exchange (or NOE) spectroscopy. (For clarity, phase cycling is

omitted.) For the exchanging methyl groups on the nitrogen of N,N-dimethylacetamide, protons of

the methyl group at one position during t1, that exchange to the other position during the mixing

time will have a different precession frequency during t2.


FlGURE 2 These figures are included for the convenience of readers without access to an

NMR spectrometer and are meant to illustrate the origin of higher dimensions in NMR

spectroscopy. The data were generated with the pulse sequence shown in Fig. 1, using a

sample of 15 ml N•Ndimethylacetamide in 700 ml d-chloroform at 29o C on a Varian UNlTY

500-MHz spectrometer. For clarity, not all traces are shown. (A) Series of free induction

decays recorded in real time (t2) for incremented values of tl. This helps students think of

two-dimensional experiments as a series of one-dimensional experiments, with different t1

values. (B) Transposed spectra, after first Fourier transform. This helps students visualize

that the signals will have some periodic dependence on t1,which can be revealed by a

second Fourier transform with respect to t1. (C) Stacked plot after second Fourier

transform. The small peak slightly downfield of the nonexchanging methyl protons

arose from an impurity in the sample. (D) Contour plot of C, to display diagonal and cross-

peaks. This will orient students to the usual mode of displaying two-dimensional spectra.










TAKE HOME QUIZ (from PHY 3063 in yesteryear) (“links” here are NOT HOT)

For detailed instructions, see: http://www.phys.ufl.edu/~meisel/09q8.pdf

You may use any computer-based tools (Excel, MatLab, Maple, Mathematica, Origin, et al.) that you have

available, but you must identify the software on the materials that you return to be graded. Please note

that “fast” Fourier transforms (or “FFTs”) are fine. In addition, please note that the specific normalization

may be software dependent, so do not concern yourself with the normalization factor.

1. (1 point) Download the 1X1024 vector in Excel format at:

http://www.phys.ufl.edu/~meisel/PHY3063-vector.xls

Consider the entries to be equally spaced in time by one second. These data consist of one or more

frequency components. Plot the data. Can you resolve the number and values of the frequencies? Now,

perform a one-dimensional Fourier transform, and plot the results. Can you identify the number and

values of these frequencies? (You might even be able to resolve the ratio of the amplitudes of the two

components.)

2. (2 points) Download the 16X16 matrix in Excel format at:

http://www.phys.ufl.edu/~meisel/PHY3063-matrix-Magnitudes.xls

Perform a two-dimensional inverse Fourier transform. On the basis of the absolute values, i.e. A*A, can

you resolve the original image? Provide the matrix or a plot of it to justify your response.

3. (2 points) Download the 16X16 matrix in Excel format at:

http://www.phys.ufl.edu/~meisel/PHY3063-matrix-Complex.xls

Perform a two-dimensional inverse Fourier transform. On the basis of the complex (real and imaginary)

information, i.e. A = R + iI, can you resolve the original image? Provide the matrix or a plot of it to justify

your response.

What are the LIMITS? … at high magnetic fields?

in vivo imaging of gene regulation?

At what magnetic field strength would YOU become

concerned about having MRI performed? Duration?

http://thewritersguidetoepublishing.com/

forward-to-the-future-tomorrow-always-comes/no-limits-283x300

http://nmr.magnet.fsu.edu/facilities/900_105mm_TLH.htm

900 MHz

105 mm bore

Effects of High Magnetic Fields on in vitroTranscription of T7 and SP6 RNA Polymerases*

Marianna Worczak†, Kimberly Wadelton†,

James Ch. Davis, and Mark W. Meisel

Department of Physics and NHMFL, University of Florida

Anna-Lisa Paul and Robert J. Ferl

Department of Horticultural Sciences, University of Florida

* Supported, in part, by the NSF via the NHMFL, DMR-0305371 (MWM),and NASA grant NNA04CC61 (ALP and RJF).

† NHMFL Research for Undergraduates (REU) Summer 2005.

Motivation via work on whole plants

The “Working” Hypothesis

Transcription and T7 Structure

Results with T7 and SP6

Future Directions

Moved to

Lecture 7?









Friday, 08 June = Lecture 6:

Quantum Spins: Chains, Ladders, Planes, and Wheels

(Magnetic Mesoscale) Ferromagnetism, Antiferromagnetism, and

Spin Glass-like behavior at Mesoscales of length/time and spatial/spin

dimensions, PLUS what a “bad” magnetometer signal might look like?

Skip a Week (in Greece)

Back for two more lectures with subjects TBA

“things I wished I knew before I knew them (Mesoscale)”

Exponetial fits, et al., negative temperature

Friday, 22 June, Lecture 8 (last one) and end of Summer A:

Topics can be suggested –costume party, pizza, chicken wings, …?

“Tutorial Wednesdays” and “Brain Speculation Fridays”

http://www.phys.ufl.edu/~meisel/CCMS-SLS-2012.docx

The Plan: Wednesdays and Fridays, 4:05 pm to 5:00 pm

(but not for one week of 13 and 15 June)

“Tutorial Wednesdays” and “Brain Speculation Fridays”

(cold beverages available on Fridays for the after session)

The Detailed Plan and Notes:

(http://www.phys.ufl.edu/~meisel/CCMS-SLS-2012.docx)

Documents

Lecture 5 - Physics - University of Florida