The measurement of chemical shifts and scalar couplings as spectral

peak positions and splittings yields primary and secondary molecular

structure information, while changes in peak intensities due to the

relaxation-based NOE provide 3D tertiary structure and quaternary

structural details (ie. binding site structure). Recently, many researchers

have shown that higher resolution molecular structures can be obtained in

liquid phase by measurement of residual dipolar couplings which can be

spectrally reintroduced using magnetically aligned phospholipid bicelles,

bacteriorhodopsin purple membranes, or bacteriophages to destroy

isotropic molecular tumbling.

Our lab has been investigating an alternate method of molecular

alignment to recover residual dipolar and quadrupolar couplings, namely

the application of strong DC and AC electric fields. This approach has the

advantages of field strength variability and alignment switching on the time

scale of multi-dimensional NMR experiments. While the techniques work

well for electrically insulating liquids using the hardware and pulse

programming highlighted in this introduction, the highly conducting aqueous

solutions of interesting biological molecules present obvious experimental

challenges. Below we present recent work involving the electrical

orientation of Pf1 bacteriophage including preliminary NMR results and

optical birefringence studies. The designs of the HV DC power supply and

HV power switch used for these studies are included.

Application of an electric field E

will partially align molecules in a

liquid due to electric dipole or

polarizability.

C6D5NO2 2H NMR B=7.04T

The E = 0 kV/cm deuterium NMR

spectrum for nitrobenzene is three

peaks (above-top). Applying a 64

kV/cm DC field partially aligns the

molecules, recovering quadrupolar

splittings and giving the six peak

spectrum shown above-bottom.

D2O2H NMR splittings in magnetically aligned Pf1Electron micrograph of Tobacco Mosaic Virus

It is well known that macromolecules like viruses, DNA fragments, and filamentous

bacteriophages align when subjected to strong magnetic or electric fields. The alignment

of these species can partially align solute molecules allowing measurement of residual

couplings as shown by A. Pardi and co-workers. This is demonstrated in the 2H NMR

spectra above-right in which magnetically aligned Pf1 phage partially align D2O giving rise

to quadrupolar splittings. The measurement of residual couplings in solute molecules in

this fashion provides a practical means by which E field alignment techniques may be

developed and experimentally fine tuned.

As shown below, while orientation in combined E and B fields is calculable using

Kirkwood's rotational diffusion formalism, many experimental conditions need to be

investigated before the NMR studies may procede.

Pulse sequences (see below) were

developed to counteract the spectral

effects of molecular motion using

continuous or, in aqueous samples,

pulsed fields to minimize heating,

electrolysis, and electrophoresis.

The sequences also make use of

multiple dimensions for simplification

of anticipated congested spectra.

Shown here are results of

nitrobenzene at 55 kV/cm.

),(QP),(P)tD(d

),(dP 2

2

ϕθ+ϕθ∇=ϕθ

+θ

ϕ∂∂ϕθ

ϕ∂∂+

θ∂∂θϕθ

θ∂∂

θ=ϕθ

2

12

D

Dcot

W),(P

Wsin),(P

sin

1

kT

1),(QP

on a table top where the condition of the

solution may be monitored, the method of

optical birefringence was employed.

0 0.5 1 1.5time sec

1 mg/mL Pf1

I/Io

arb

. uni

ts

The wave number κ of the electromagnetic wave is given by κ=2πn/λ. With

the polarizer at 45° off vertical, we can write ( )t1E as

( ) ( ) ( ) jtxktxt �cos2

E�cos2

E oo1 ω−κ+ω−κ=E

Transforming into a frame given by k ′� and j′� with k ′� at 45° from k� gives

( ) ( )( ) ( )( )jktxjktxt ′+′ω−κ+′−′ω−κ= ��cos2

E��cos

2

E oo1E

( )( ) ( )[ ]( ) ( )[ ]

′ω−κ+ω−κ

+′ω−κ+ω−κ=

⊥

⊥

jtxtx

ktxtxt

�coscos

�coscos

2

E

||

||o2E

( ) ( ) ( )

( ) ( )j

xtx

kxtx

t

′

κ−κ

ω−κ+κ+

′

κ−κ

ω−κ+κ=

⊥⊥

⊥⊥

�2

sin2

2sinE

�2

cos2

2cosE

||||o

||||o2E

Subtracting and adding the term( ) ( )

kxtx ′

κ−κ

ω−κ+κ ⊥⊥ �

2sin

2

2cos ||||

( ) ( ) ( ) ( )

( ) ( ) ( )′

ω−κ+κ+

′

ω−κ+κ

κ−κ+

′

κ−κ−′

κ−κ

ω−κ+κ=

⊥⊥⊥

⊥⊥⊥

jtx

ktxx

kx

kxtx

t

�2

2sin�

2

2cos

2sinE

�2

sin�2

cos2

2cosE

||||||o

||||||o2E

( ) ( ) ( ) ( )[ ]( ) ( )[ ( ) ]jtxktxx

kxxtxt

′ω−σκ+′ω−σκκ∆+

′κ∆−κ∆ω−σκ=

�2

2sin�2

2cos2sinE

�2sin2cos2

2cosE

o

o2E

( ) ( ) ( ) ( )[ ]( ) ( ) jtxx

kxxtxt

′ω−σκκ∆+

′κ∆−κ∆ω−σκ=

�2

cos2sinE

�2sin2cos2

2cosE

o

o3E

( ) ( ) ( ) jtxxt ′ω−σκκ∆= �2

cos2sinEo4E

( ) ( ) ( )δ−=κ∆−=κ∆∝ cos12

Ecos1

2

E2sinEI

2

o

2

o22

o xx

( )δ−= cos1I

I

o

−=δ

oI

I1arccos

( ) λ−π=κ−κ=κ∆=δ ⊥⊥ xxx )nn(2 ||||

0 400 800 1200 16000

0.5

1

1.5

microseconds

radians

350 us pulse, 1.0 mg/mL Pf1

600 1000 1400 1800 22000

0.4

0.8

1.22.0 mg/mL 1.0 mg/mL

0.5 mg/mL

volts

radians

birefringence at end of 350 µs pulse

0 500 1000 1500

0

0.5

0.97 mg/mL

0.47 mg/mL

microseconds

norm

alizedI/I o

Cooperativity observed

0 400 800 1200 1600

radians

microseconds

0

0.2

0.4

0.6

V=1069+/-14 Volts, 0.5 mg/mL Pf1

Future Work

Acknowledgements

HV Power Supply and Switch

The HV power supply and

switch diagrammed here

were designed to 1) provide

enough power so as not to

current-limit the applied

voltage and 2) switch on

timescales faster than that

cabable of a mechanical

vacuum relay.

The power supply as

shown delivers 2.1 kV DC at

500 mA continuous, 2.5 A

pulsed. The solid-state

switch is constructed of

APT1001 type MOSFETs

each capable of sustaining

1000 V DC at 11 A. As

drawn, the switch will pulse

up to 3000 V DC at 44 A and

is TTL controlled for pulse

lengths of 150 µs to 2 ms.

The TTL source may be a

pulse generator, oscilloscope

or NMR console.

D2O2H NMR splitting vs. buffer concentration

0 1 2 3 4 5

0

1

2

3

seconds

I/I oarb.units

12V DC birefringence of Pf1 in Tris/EDTA buffer

Buffer Concentration

1 mM5 mM10 mM15 mM20 mM

1 kHz birefringence of TMV in phosphate buffer

Buffer Concentration

0.01 mM0.05 mM0.10 mM0.50 mM1.00 mM

time ms

δarb.units

When linearly polarized light passes through an

anisotropic distribution of assymetric molecules like

Pf1 which has a different refractive index along its

different axes, the light becomes elliptically polarized.

This is true when an electric field is used to partially

align the molecules. Using a series of optics a zero

background measurement of this change in the light

polarization may be made. According to the

mathematics describing the electric field vector of the

light (see bottom of poster), the light observed is a

measure of the degree of anisotropy (alignment) of the

sample.

Using this optics setup, the Pf1 alignment due to

pulsed electric fields under a variety of conditions may

be measured. Results suggest DC fields to be more

effective than AC fields of various frequencies (audio

to rf) and low ionic strengths of 1- 5 mM buffer

concentrations to be favorable. (see left)

45o

E1(t)

E2(t)

E3(t)

E4(t)

Polarizer

Kerr Cell

Rhomb

Analyzer45 o

0.0

2.0

4.0

6.0

8.0

0 40 80 120

DC

2 MHz

4 MHz

7.8 MHz

15.3 MHz

19 MHz

lightintensity

Vrms or Vdc

1 mg/mL Pf1

AC versus DC Electric Fields

0 20 40 60 80

degrees from vertical

changeinechomaximum

0

50

100

150

200

250E Field Orientation

100 V applied

20 mg/mL Pf1

0 200 400 600-2000

0

2000

4000

milliseconds

20 mg/mL Pf1

Echo Train Modulation

Hz0 3 6 9 12 150

0.2

0.4

0.6

0.8

1

Echo Train Modulation20 mg/mL Pf1

0 V

100 V

Like the Tobacco Mosaic Virus (left)

Pf1 bacteriophage is rod-like but much

longer: 2000 nm long x 6 nm in diameter.

Its preparation is relatively simple with the

phage and pseudomonas host available

from ATCC. High yields of 400 mg were

obtained...not bad for physical chemists!

One such condition shown to the

right is the ionic strength of the

solution. Others include AC vs.

DC fields and pulse lengths. To

investigate these properties

Using DC power supplies on hand

capable of 1000 V at 20 mA, low buffer

concentrations, and 20 mg/mL Pf1

solutions containing 50% D2O, a series of

preliminary NMR experiments of Pf1

subjected to an E field were conducted.

The results of an attempt to measure a

change in the quadrupolar modulation of

an echo train following a 15 ms DC pulse

are shown to the left. With the E field

oriented parallel to Bo, the observed

decrease in modulation frequency is

suggestive of a lowering of order, possibly

due to turbulent flow due to conduction.

The simple echo sequence to the

lower right was used to check for a

dependence on angle between the E and

Bo fields of the echo intensity. Using the

same concentration of Pf1 and 15 ms 100

V DC pulses, the difference between the

echo maximum with field on and off was

measured for various angles. Little

change in the zero E field echo was

observed for the angles, suggesting the

behavior to be E field induced and not an

artifact of field inhomogeneity due to

sample geometry.

While an E field effect is suggested,

these rather lack-luster results prompted

us to further optimize the experiment

again making use of optical birefringence.

One attempt to further optimize

the experiment was to measure the

birefringence of Pf1 in the bore of

the 7T magnet. Using the setup

shown to the left employing a Kerr

Cell mounted to the top of an NMR

probe chassis fitted with two 90o

prisms, birefringence traces like the

one to the left were observed. Here,

no change in the light intensity is

seen during the E field pulse shown

in the lower trace. Instead, a

change is observed after the pulse

on a long time scale, suggesting the

dominant force to be not the E field

directly, but instead flow alignment

caused by turbulence in the cell

following the pulse. Such turbulence

was observed using Dante encoded

MRI (below) of the PPS sample cell

performed at 7 T using a micro-

gradient coil set.

In order to overcome the strong

orientation due to Bo in Pf1 and

achieve larger E field alignment, a

HV power supply and HV switch

were designed.

1H MRI slice of Pf1 in sample cell with Dante grid.

E=0 E=200 V/cm

Using the HV power supply and switch diagramed

to the left and using the mathematics of birefringence

to calculated the optical retardation δ, the figures to

the left were obtained. The maximum δ achievable is

π/2=1.571 which is almost obtained using this setup.

Because the retardation is also a function of path

length through the sample, it is possible that at 2.1

kV DC and 1-2 mg/mL Pf1 solutions, the alignment is

not yet saturated even though δ≈π/2. In order to

search for saturation, higher voltages should be

tested to see if δ continues to oscillate (see math).

At a Pf1 concentration of 2.0 mg/mL, such an

oscillation may be occurring above applied voltages

of 1400 V as seen on the third graph down.

Having maximized the phage alignment, we will

again turn back to NMR experiments.

We are greatly indebted to the following individuals

and grant agencies

Skipp May

Paul Feldstein

Jeff Walton

Shashi Vyas

April Weekley

NSF #CHE-9984654

The Packard Foundation

Optical Birefringence E Field NMR of Pf1 Optimizing Alignment

Pf1: A Model SystemE Field NMR: Introduction

NMR and Optical Birefringence Studies of Aligned Pf1 Bacteriophage

in AC and DC Electric Fields

Department of Chemistry University of California Davis, CA 95616

Scott A. Riley and Matthew P. Augustine

Optical Birefringence: Math