Diamagnetic Anisotropy of T7 RNA polymerase
Kim Wadelton1†*, Marianna Worczak1§*, James Ch. Davis1, Anna-Lisa Paul2, and
Mark W. Meisel2
1Department
2Department
of Physics, University of Florida, Gainesville, FL 32611-8440
of Horticultural Sciences, University of Florida, Gainesville, FL 32611-0690
Abstract
The diamagnetic properties of the T7 RNA polymerase have been investigated to test the
hypothesis that strong magnetic fields generate subtle perturbations (alignment or distortion) of
the polymerase due to the structural diamagnetic anisotropy of the molecule. These possible
effects may be the cause of a biochemical stress response previously detected in plants. Utilizing
the known structure of the protein the maximum energy arising from the protein’s orientation in
a strong magnetic field was estimated. At 9 Tesla, this magnetic energy is approximately 10-100
ppm of the ambient thermal energy. A one-dimensional model was proposed for the deformation
of the thumb alpha helix of the polymerase with estimated magnetic and restorative forces acting
upon the thumb. Distortion forces estimated were ~4 orders of magnitude smaller than those
forces required to stop transcription completely.
Introduction
A chemical stress response was observed in the plant Arabidopsis thaliana in a strong
homogenous magnetic field (Paul 2005). This indicated an alteration in gene expression. We
formed the hypothesis that the biomolecules within the plant were either aligned or distorted by
the strong magnetic field, due to the molecule’s structural diamagnetic anisotropy. This
magnetic effect may be the cause of some disruption in normal plant function, and perhaps
produce this stress response.
Single in vitro transcription was chosen to test our hypothesis. Focus was put on this plant
function because the process of transcription is constantly occurring within organisms, and is a
first step in gene expression. The commercially available Promega RiboMax T7 Express In
Vitro transcription kit was used. This kit employs the T7 RNA polymerase enzyme to conduct
the transcription process. The enzyme T7 RNA polymerase has been widely studied and its
structure is known to a resolution of 2.9 Å (Tahirov 2002). The results of these reactions are
discussed in a companion paper (Worczak 2005). To complement the experiments, a theoretical
model of the possible alignment and distortion of the T7 RNA polymerase in a high magnetic
field was developed.
Transcription is the creation of RNA transcripts from a DNA template. The DNA enters the
polymerase through the DNA entry pore (Tahirov 2002). The DNA proceeds through a groove
within the polymerase, where it interacts with the many parts of the polymerase to create an
RNA transcript. The RNA is formed at the active site, where the DNA and RNA temporarily
†Student
in the Department of Physics Sweet Briar College
Contact: wadelton07@sbc.edu
PO Box 906 Sweet Briar, VA 24595
§ Student at Clarkson University
* Summer 2005 NHMFL REU Program Participant
1
form an RNA-DNA hybrid. The RNA separates from the DNA and leaves the polymerase via
the RNA exit pore as more amino acids are added to the RNA. This process is called elongation.
As transcription progresses, the DNA leaves the polymerase through the DNA exit pore. This
process continues until the RNA has been fully formed, and the DNA moves completely outside
the polymerase.
The T7 RNA Polymerase is made up of multiple groups and subgroups. These parts each play
distinct roles in the transcription process. A common model for the T7 RNA polymerase
describes the polymerase as a hand (Cheetham 1999) where the thumb, fingers, and palm are the
major groups of the polymerase (Figure 1a). The thumb and fingers form the outside of the
DNA entry pore, Figure 1b, and they grasp the DNA to guide it into the groove. During
transcription, the thumb is assumed to bend 20 degrees and wrap around the DNA to hold it
securely in place (Gopal 1999).
T7 RNA Polymerase
a
b
Figure 1: (a) The hand model for T7 RNA polymerase provides a simplification of the protein
structure (Tahirov 2002). This structure may be found in the protein data base, PDB# 1QLN
(b) The DNA entry pore is formed by the thumb, palm, and fingers.
Materials and Methods
MODEL
The sections of T7 RNA polymerase consist of primary, secondary, tertiary, and quaternary
structures. The magnetic anisotropy of these structures can be calculated, as well as their
associated energies (Worchester 1978). We sought to model the T7 RNA polymerase as a group
of these structures and predict any alignment or distortion caused by the application of a high
magnetic field. To further simplify the problem, focus was given to a single section of the
polymerase, the thumb alpha helix, which forms the main structure of the thumb, Figure 1a. The
tip of the thumb is located at the DNA entry pore. Along with the fingers, the thumb forms one
wall of the pore (Figure 1b). The diameter of the DNA entry pore must be on the order of 3nm,
to accommodate a DNA helix of approximately 2nm. We suggest, that if the rest of the
polymerase remains rigid and the thumb moves a distance on the order of 10-8 to 10-9 meters
from its natural equilibrium, the DNA entry pore will be too small for the DNA to move through
smoothly and there will be a disrupt in the transcription process (Figure 2). This alteration
would likely result in a slowing of the transcription process. Alternatively, the thumb may move
10-8 to 10-9 meters in the opposite direction, and no longer be able to hold the DNA secure during
2
transcription. A thumb not in its equilibrium position may prevent the polymerase from moving
from the initiation complex into the elongation complex (where the thumb wraps around the
DNA), resulting in short, abortive transcripts.
b
a
Figure 2: A one-dimensional model of the T7 RNA polymerase, (a) before and (b) during the
application of homogenous magnetic field predicts a 1 nm displacement of the thumb.
THEORETICAL ANALYSIS
To predict possible changes to the thumb alpha helix, we estimated the energies and forces
involved in our model. We utilized the following equation for the magnetic energy of an alpha
helix of N peptide bonds in a field B and magnetic susceptibility K (Worcester 1978):
N 2
(1)
B K
4
The thumb alpha helix consists of ~40 peptide bonds. We chose an applied field of 15 Tesla for
the following calculations based upon previous research indicating 14 Tesla as the beginning of
biological effects (Paul 2005). Substituting a corrected value for K to be: K= 5.36x10-5 Joules
per mol Gauss2 (Pauling 1979) we calculate the order of magnitude result:
U  10 26 J
(2)
U 
U  10 26 J
From the energy, a force analysis can be made. Assuming constant force from the magnetic field
(FM) we propose a restoring force (FR), modeled as a spring, to hold the thumb in its equilibrium
position, where s is the displacement from equilibrium, and k is a spring constant:
(3)
FR  ks 2
An equation for the total energy affecting the thumb could then be formed:
1
U  FM s  ks 2
2
(4)
If s is approximately 10-9m then the effect of the restoring force is very small compared to the
magnetic force. Assuming zero restoring force, FM is approximately 10-17 N. Therefore with FR
included, FM should be in a range of 10-16 N to10-18 N.
3
We also made a series of approximations for k, giving a range of 10-3 to 10-9 N/m. This range
stems from three possible ways we found for estimating k. The spring constant should be at least
one or two orders of magnitude larger than the thermal energy, so that it will keep the thumb in
equilibrium under the natural stress conditions. This gives:
2(k BT )
J
(5)
k
 10 4 2
2
s
m
One might also approximate the restoring force itself to be on the order of those molecular forces
which have been measured (Lu 1999):
F
J
(6)
k  R  10 3 2
s
m
Another way to calculate k is to approximate the restoring energy associated with the restoring
force is the same order of magnitude as the magnetic energy. Therefore:
2U
J
k  2  10 9 2
(7)
s
m
This last value for k is the one which we prefer, but further analysis is needed to substantiate this
claim.
Results and Discussion
A simple model of distortion of the thumb alpha helix on the T7 RNA polymerase was
postulated (Figure 2). We found the order of magnitude energy due to magnetic anisotropy
combined with a field of 15 Tesla (U) and estimated the energy (U) and forces (FM and FR)
affecting the thumb alpha helix in our model. We also proposed a possible range of spring
constants for the thumb: 10-3 to 10-9 N/m.
The calculated energy, U= 10-26 Joules, can be compared to the ambient thermal energy for an
interesting result. At 300 Kelvin, the thermal energy is given by: kBT= 4.14x10-21 J, where kB is
the Boltzmann constant and T is the temperature. The magnetic field energy was then only ~10
to 100 ppm the thermal energy where there was an observed effect on Arabidopsis.
FM and FR are comparable to other molecular forces which have been measured. Considering the
forces required to unzip a beta hairpin, to stop the polymerase from proceeding along the DNA,
or to overstretch DNA are all on the order of ~10-11 N, our forces are small. Movement of the
thumb 1 nm is a comparatively diminutive effect relative to the deformations described by these
measurements, and therefore the force required to cause a 1nm movement should be
considerably smaller than those previously measured forces. This assumption must be further
investigated.
Preliminary experimental results have indicated that for T7 RNA polymerase there is some
alteration in transcript production rates in a 9 Tesla field. Tests at 20 and 25 Tesla are yet to be
analyzed. Curiously, tests using the SP6 RNA polymerase have shown a substantial decrease in
overall transcript production at 9 Tesla (Worczak 2005). Further research into modeling the
structure of the SP6 polymerase is recommended.
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Acknowledgments
This work was made possible, in part, by the National High Magnetic Field Laboratory
(NHMFL) Summer 2005 Program, and the University of Florida. We acknowledge R. J. Ferl,
W. B. Gurley, and Norman Anderson for their enlightening conversations. Additional support
was provided by grants from the National Science Foundation (NSFDMR-0305371) and NASA
(NNA045561).
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