Nov 20, 1998 - The brackets on the left side of eq (2.1) denote .... The potential energy of a permanent dipole moment at an angle 6 to the electric field \s.
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PUBLICATIONS! '"ifl'W!*'^
Nisr
United States Department of
Commerce
Technology Administration National Institute of Standards and
Technology
NIST Technical Note 1509
Electrical Properties
and
Dielectric Relaxation of
DNA
James
in
Solution
Baker-Jarvis Chriss A. Jones Bill Riddle
QC 100 .U5753 NO. 1509
1998 k.
4
N/ST Technical Note 1509 Electrical Properties
and
Dielectric Relaxation of
DNA
in
Solution
James
Baker-Jarvis Chriss A. Jones Bill Riddle
Radio-Frequency Technology Division Electronics and Electrical Engineering Laboratory National Institute of Standards and Technology
325 Broadway Boulder, Colorado
80303-3328
November 1998
'^ITES O^
U.S.
DEPARTMENT OF COMMERCE,
William M. Daley, Secretary
TECHNOLOGY ADMINISTRATION, Gary R. Bachula, Acting Under Secretary for Technology NATIONAL INSTITUTE OF STANDARDS AND TECHNOLOGY, Raymond G. Kammer, Director
National Institute of Standards and Technology Technical Note Natl. Inst. Stand. Technol.,
Tech. Note 1509, 72 pages (Novennber 1998)
CODEN:NTNOEF
U.S.
GOVERNMENT PRINTING
OFFICE
WASHINGTON: 1998
For sale by the Superintendent of
Documents, U.S. Government
Printing Office,
Washington,
DC 20402-9325
Contents 1
Introduction
2
Amino
3
Structure and Electrical Properties of
4
5
6
2
and Proteins: An Overview
Acids, Peptides,
DNA
3.1
Charges and Electrical Properties of the
3.2
Dielectric Properties of
3.3
Response of
3.4
Dynamics
3.5
The
DNA
7 10
DNA
Bound Water and
Molecule
Polyelectrolytes
10
Around
DNA
in Electric Driving Fields
14
of Polarization Relaxation
Electric Field near the
DNA
17
Molecule
19
Counterions and the Helix 4.1
Cations
4.2
Hehx-Coil Transition
13
19 19
in
DNA
23
DNA
Modeling the Potential around the
DNA
Molecule
Dynamics
5.1
Phenomenological Models of
5.2
Poisson-Boltzmann Equation
5.3
Poisson-Boltzmann Apphed to Modeling the
5.4
Numerical Models
for
DNA
26 26 27
DNA
29
Helix
Dynamics
30
Phenomenological Models of Dipole Moment, Relaxation Time, and 31
Polarizability 6.1
Persistence Length and Radius of Gyration
31
6.2
Polarization
31
6.3
Simple Model of Dipole
6.4
Dipole Moment, Permittivity, and Relaxation Time
6.5
Statistical-Mechanical
7
Charge Transfer
8
Measurements of
in
Moment
Model
33
of Polarization for Rod-Like
DNA
35
DNA
36
39
DNA
42
8.1
Overview of Past Measurements
42
8.2
Permittivity Measurements and Electrode Polarization
43
111
5.3
8.4
9
Measurement Methods
47
8.3.1
Capacitive Measurement Techniques
47
8.3.2
Four-Probe Technique
47
8.3.3
The Open- Circuited Holder
Dielectric
Measurements on
DNA
for
Liquid Measurement
in Solution
Discussion and Conclusions
48 49
58 59
10 References
IV
and
Electrical Properties
of
DNA
James Baker-Jarvis
*
in Solution
Chriss A. Jones
November
In this report
Dielectric Relaxation
DNA. We
Bill
Riddle
20, 1998
we overview and summarize the
relaxation of solvenated
*
electrical properties
and
dielectric
review models for counterion dynamics, dipole
and relaxation in both double- and single-stranded DNA. measurements on double- and single-stranded DNA from herring sperm in protamine solutions. The analysis is based on polymer dynamics and statistical mechanics. The observed dipole moment of DNA is induced through the distortion of the counterion atmosphere by the applied electric field. Doublestranded DNA does not possess a permanent dipole moment except in the case where ligands are attached. We find evidence that denaturation proceeds in stages. The first stage is when counterions are expelled from the molecule which causes dissociation through strong phosphate-phosphate repulsion between strands. This
moment,
We
polarizability,
also present dielectric
We also analyze dispersion of DNA We found evidence of low-frequency counterion-sheath relaxation models. We also
increases the conductivity of the solution.
solutions from low to microwave frequencies.
dispersion which
is
consistent with
found a dispersion at megahertz frequencies which
is
consistent with site-bound
counterion models.
Key
words:
factor;
counterions: dielectric constant; dipole
single-stranded
CO
liquids; loss
DNA.
"HadioFreqiu'iicy Technology Division. Boulder,
moment; DNA:
microwave measurements: permittivity measurement: protamine: relaxation:
MS
S13.01. National In-tiiute of Standards
80303-3328 einailijjarvislibouider. nist.gov
and Technology,
.
1.
Introduction
This report examines the dielectric relaxation and electrical properties of deoxyribonu-
(DNA)
cleic acid
The a
in alternating electric fields [1,2].
hterature on dielectric relaxation of
number
DNA
is
copious
DNA
of reviews of the polyelectrolyte properties of
electrical properties
and
dielectric relaxation of
DNA.
[1-16].
There have been
[10-14],
but none on
[3-5]
Nucleic acids are high-molecular mass polymers formed of pyrimidine and purine bases, a sugar, and phosphoric- acid
up
built
backbone
of nucleotide units which are
as
composed
shown
in figure 1.1. Nucleic acids are
of sugar, base,
and phosphate groups
in helical conformation.
Nucleotides are linked by three phosphates groups which are
designated a, P, and 7.
The phosphate groups
The
bond.
are linked through the pyrophosphate
individual nucleotides are joined together by groups of phosphates that
form the phosphodiester bond between the
3'
These phosphate groups are
(see figure 1.2).
and
carbon atoms of successive sugars
5'
acidic.
Polynucleotides have a hydroxyl
group at one end and a phosphate group on the other end. Nucleosides are subunits of nucleotides is
and contain a base and a sugar. The bond between the sugar and base
called the glycosidic bond as indicated in figure 1.3.
The base can
rotate only in
stericaUy permissible orientations about the glycosidic bond.
The
helix
formed from two strands. The bases in adjacent strands combine by
is
hydrogen bonding, an electrostatic interaction, with a pyrimidine on one side and purine
on the other. In
DNA
the purine adenine (A) pairs with the pyrimidine thymine (T)
The purine guanine (G) figures 1.2
and
1.3.
hydrogen atom that
A-T
A is
hydrogen bond
is
positively charged
genetic code
amino
acid.
is
The
base-pair sequence
The
pairs associate
by
the carrier of genetic information.
TTT AAA AAG GCT lyso
lys
determines an amino
ala
phenylalanine-lysine-lysine-alanine.
DNA molecule has a net negative charge due to the phosphate backbone. When
dissolved in a cation solution, cations.
is
C-G base
formed of a sequence of three base pairs which determines a type of
phe of:
in
and a negatively charged acceptor atom. The
For example, the sequence of
acid sequence
These are shown
formed between a covalently bonded donor
base pair associates by two hydrogen bonds, whereas
three hydrogen bonds.
The
pairs with the pyrimidine cytosine (C).
It is
some
of the charge of the molecule
generally thought that the double-stranded
DNA
is
neutralized by
molecule has
little in-
Figure
1.1.
The right-handed hehcal conformation
of
DNA.
>Vci^nlr\^
^y-t^*lrt^
O bond
rv'oc>«lci Ic
M
3"
Figure
1.2.
Single strand of
DNA
Inycirojcyl •rtci
and the phosphodiester and glycosidic bonds.
-kT
NH,
OH
OH
Figure
trinsic
permanent
compose the
dipole
Glycosidic
1.3.
moment
bond denoted by X.
(see figure 1.4).
helix are oriented so the dipole
However, when
DNA
moment forms due
is
This
moment
is
because the two strands that
of one strand cancels the other.
dissolved in a solvent, such as sahne solution, an induced dipole
to reorganization of charge into a layer around the molecule called
the counterion sheath.
Watson and Crick concluded through X-ray of
DNA
is
in the
periments on
form of a double-stranded
DNA,
helix.
In addition to x-ray structure ex-
information has been gleaned through nuclear magnetic resonance
(NMR)
experiments.
Type Z
DNA
is
diffraction studies that the structure
Types
A
and
B DNA
are in the form of right-handed helices.
in a left-handed conformation.
tween conformations.
A
dissolved in a solvent
[6]
an approximation. In
transition from .
Type
A
There to
is
DNA of DNA
Type B
The Watson-Crick conception
reality
a Type
DNA exists in many conformations
B
Z transition be-
DNA
is
as a uniform helix
is
occurs
when
and may contain inho-
mogeneities such as attached proteins. In general, double-stranded rod, but rather a
to
DNA
is
not a rigid
meandering worm-like chain. Once formed, even though the individual
bonds composing
DNA
are weak, the molecule as a whole
is
very stable.
The hehcal
o
o
O
c
-
o
(b)
(a)
OH
H^O
-^
^
«r^^
'=n«t
.
(6.14)
z=l
This model correctly predicts the dependence of the dipole
moment on
polymer, but not the temperature dependence. In the next section this
the length of the
we
will
generahze
model to get correct temperature dependence.
6.4.
Dipole Moment, Permittivity, and Relaxation Time
Minakata developed a comprehensive, phenomenological model binding on rod- like polymers
This model
sites.
is
[73]. It
for discrete
counterion
includes three different types of counterion binding
important since
it
correctly predicts a
number
of the important
measurable quantities in the relaxation process. The mean-squared dipole moment
is
defined as
=
n^
q^J^^i^J
){nj- < n
>)
>=
q^ Yl^^^^^i+'^^^Jl^^iJ^^'^J^i+j')^
ij
ij
i
(6.15)
where n AimTi
is
=
—
Ae = Here
B
N
number
it
is
is
site,
A|n =
—
^, and
This model yields
^^^|2^|An^ + 2EA.nl.
the ratio of the internal to external of polyions per unit volume.
fields,
L
is
The important
correctly predicts the dielectric increment to
dependence to be of the form 1/T.
35
(6.16)
length of the molecule, and result of this
model
is
that
be proportional to L? and temperature
10®
10«
10 l:^
-10-
10^
10'
-
lOf 10^
Figure
6.2.
10^
10^ l\/lolecular
Relaxation time and dipole
Another model developed by Sakamoto
mass
moment
[32],
versus molecular mass.
relates dipole
moment
of the counterion
sheath to dielectric increment from counterion fluctuation theory and agrees well with
experiment
[32]
< /P > 3kBT
47tN
Ac Sakamoto defined the
fm
in the loss
spectrum by tq
was proportional
moment was Td
~
6.5.
proportional to
Here
77^
= is
Mw
namics
[68].
terms of the
mass of water
(see figure 6.2).
RT
solvent viscosity
the
is
and
He
Zimm
iq^ed is
also
maximum
Mw
frequency
thymus DNA, td
and the mean dipole
found that
for coiled
DNA,
viscoelastic relaxation time (see
the reduced viscosity.
Model of Polarization
we consider a more
We
in
l/27rfm- For double-stranded calf
^A2Myjr]sr}red/
Statistical-Mechanical
In this section
=
time
to the square of the molecular
2r2, where tz
figure 6.3).
dielectric relaxation
(6.17)
for
rigorous model of coupled
Rod-Like
DNA
DNA
and counterion dy-
solve a generalized diffusion equation or Fokker-Planck equation for
the counterion sheath dynamics in an applied electric
ment equations from the model. The model equations.
36
field
and we develop new mo-
yields relaxation times
and time-evolution
10-1
io-«
io-»
10-*
10-^
TO-o
(S)
Figure
6.3. Dielectric relaxation
The instantaneous
dipole
time [td) versus
moment
is
yL/
=
Zimm
nq5^ where S
relaxation time tz-
is
the displacement along
the major axis of the molecule from the center of charge distribution and q charge.
In addition there
can be expressed
The
in
may be
a permanent dipole
terms of the fluctuations a
=
/ksT =
The n^q^
electronic
is
polarizability
/ksT.
potential energy of the counterion sheath in the absence of an electric field
V{5) This potential-energy function oscillator potential.
Using
is
= n^q^Sy2a.
is
(6.18)
quadratic in displacement analogous to the harmonic
this potential, the
Fokker-Planck equation, which gives the
probability that a certain counterion distribution will be realized, can be written as dp{S,t)
dt
Here
/3
= l/ksT
and
D
is
oliM^^Pi'-m,isM. "' 05 dS' dS
a diffusion constant.
The
steady-state solution
(6.19)
is
Gaussian
exp(-/3V0 (6.20)
If
we perform the
integrations,
we obtain the Gaussian 2^2 'PiT^q
PeqiS)
distribution
exp{-Pn^q'5y2a)
ZTTa
37
(6.21)
Since the solution dipole
moment,
= ksTa,
however,
is
nonzero.
be
will
The mean-squared
0.
The time-dependent
solution of
is
/-
1
/
N
"(*•'>
= V^
where r
Gaussian the average dipole moment
is
2.rD(l -exp(-2t/r)
= a/DPrrq^.
If
( +G(2sin^cos"+i
+m{m -
1)D < 5^
+2pDnmqE{t)
cos^+^ 9
^
-
ssin^ ^cos^-^ ^)
r
>
(6.32)
.
Equation (6.29) indicates that the time rate of change of the dipole moment to a relaxation term plus a driving term that
is
hnear in electric
field.
This
is
is
due
similar to
the Debye equation. Comparison to eq. (6.24) indicates that the effect of the electric field is to
add a driving term to
The model developed rion sheath (eq.
(6.29))
eq. (6.29).
in this section yields
and polarization. In
an equation of motion
this
for the counte-
model the polarization has a
single
relaxation time.
7.
Charge Transfer
in
DNA
Szent-Gyorgyi concluded from experiments on proteins that biological materials have
semiconducting properties.
In the ensuing years a great deal of research has been
39
.
performed on conduction
whereas the phosphate backbone addition,
DNA
The base-pair sequences
in biopolymers.
periodic. Periodicity
is
bound
contains counterions and
a self-consistent
field
comphcated structure has
from being uncovered. Recently,
theory has been used for modeling biopolymers
The semiconducting
due to protonic and electronic
transfer in single-stranded
DNA
and
are on the order of
activity. In
both by electrons and protons. Risser
rigidly attached donors
[74]
properties originate in internal charge-transfer mechanisms
The semiconducting activation energies
In
DNA
DNA are aperiodic,
promotes semiconductivity. In
water. This
prevented the details of electronic conduction in
in
to 1.5 eV.
1
[2]
The conduction
is
the dry state, biopolymers exhibit conduction
and Stemp
et al. [75]
and found
it
to
have studied electron
[76]
be a good sensor of strand length with
receptors.
DNA the periodic component of the base pairs produces band gaps.
component
.
The
aperiodic
band gap formed by the phosphate
of the base pairs acts as impurities in the
bax:kbone. Typical valence and conduction-band gaps are in the order of 0.3 to 0.8
eV
around 10 to 12 eV. Bloch wavefunctions can be used
for
and energy band gaps
of
modeling since the system
is
approximately periodic.
In proteins, there are two in the
main areas
of charge transport.
The charge
transport
is
main polypeptide chains and through the hydrogen-bonded crosshnks. Recent
research has concluded that conduction through the
over the hydrogen-bond mechanism
[74].
Beratan
main polypeptide chains dominates
et al. [77]
proposed a model of electron
tunneling in proteins with donor- acceptor interaction which
bonds between amino
is
mediated by the covalent
acids.
Electron transfer in
DNA
takes place primarily along the axis of the molecule in
which there are four basic types. These include extra electrons, type molecular excited states, and holes.
and do not participate a molecule. localized
On
and
triplet
tt-
electrons in 7r-orbitals are delocahzed
are free to
move about the carbon
nuclei in
the other hand, a"-orbitals are symmetrical about the bond axis with
C-C and C-H bonds. The
line joining the
They
in bonding.
The
singlet
electrons participating in these bonds are around the
two nuclei and are localized. The bases
in
DNA
possess an electronic
tt
system, exhibit electron delocalization, and have low-lying 7r-type orbitals where excited electrons
may
reside
.
[75,78-81] Since the bases are stacked close together, charge
transfer can occur from base to base.
found a higher density of protons
in
Hanlon
[82]
studied protonation of
DNA
and
the minor groove than in the counterion solution
40
surrounding the molecule.
The
electron-transfer rate between donor
and acceptor has been measured with
photo-induced, excited state, and flash-quenching ground state techniques and with
The
transient- absorption methods.
where
T
between
The
is
electron transfer rate
is
- /\Em? /AksXT),
A;
=
iyexp(-(A
temperature, A
is
reorganization energy, and
(7.1)
AZsm
is
potential difference
sites.
predicted decay length of charge transfer
transfer rate transfer in
example,
is
10^ s~^.
DNA
many
13
is
nm
and typical electron charge-
This large decay with distance makes sense since long-range
would not be advantageous from a molecular damage standpoint. For
proteins attached to the
DNA
would not function normally with large
charge transfer taking place. Additionally, molecular damage becomes more probable
during times of high charge transport
The
eSiciency of
DNA
[79]
in allowing long-range electron transfer gives
notion that stacked aromatic heterocycles can serve as 7r-ways.
DNA
in this area raise the possibility that
Electromagnetic
DNA.
fields
may be
The
results of research
uses electron transfer in gene replication.
able to stimulate biosynthesis in
Electric fields surely interact with cell
cells,
this could
applied magnetic
happen
fields.
is
through strong charge transport
in
The
[83].
DNA
process
interacting with
Recent experiments on charge transport have demonstrated
that current densities of at least 1x10"^
A/m^
can be achieved
in
DNA. The
localization
segment through charge transport could be achieved either from bending or
of the gene
rolfing of the base pairs or fields
particularly in
membranes, but recent evidence points to
the possibifity that magnetic fields can play a role in gene activation
by which
support to the
by enzyme interaction with base pairs
in a
could also play a role in gene activation through bending of
segment. Electric
DNA
or formation of
double layers affecting charge fiow in the molecule.
There
is
ity [27,84].
DNA promotes conductivity and semiconductivrelaxation of double-stranded DNA in an applied
evidence that hydration of
These studies found that
d.c. electric field of
1500 to 3000
semi-conductivity in
DNA
V/cm had
a 10 percent increased conductivity. Intrinsic
increases exponentially with water content
tions of 25 percent. Thereafter the effects are
studies of Bonincontro
[27],
dominated by protonic
mixtures of NaCl and
41
DNA
up
to concentra-
activit}'.
from herring sperm of
In
tlie
sizes of
300 to 1000 nucleotide pairs were dissolved in water at a concentration of 2 mg/ml. The samples were then dialyzed with solutions of 0.4 mol counterion solution (Na and
then lyophilized (freeze drying) and ground to a powder. For
many
Li)
biomolecules the
conductivity follows a temperature dependence similar to inorganic semiconductors
(T^(jQe^^{-E/kBT).
8.
DNA
Measurements of
8.1.
Overview of Past Measurements
Measurements on conducting
liquids are complicated
by low- frequency dispersion (LFD)
up
(7.2)
of conducting ions
[86].
by electrode polarization
Electrode polarization
on the capacitor plates producing an
and
[85]
caused by the build-
is
electrical
double
layer.
Electrode polarization influences primarily the real part of the permittivity. Since the electrode capacitance
is
not a property of the material under test
it
must be removed
from the measurement. In the literature three relaxations have been reported, 7, figure 3.2.
The 7
5 relaxation
is
This relaxation
relaxation occurs near 18
weak, occurs around 100 is
Oi
MHz, and
and a as indicated
The a
relaxation occurs for
in
has been ascribed to water. The
is
independent of molecular mass.
DNA
due to the motion of condensed ions within a subunit of the
molecule [37,87,88]. frequency
GHz and
5^
DNA in the range 1 to
relaxation depends on molecular mass and length and
is
100 Hz.
The
low-
due to fluctuations
in the counterion sheath.
DNA
in solution have
the years [32,36,40].
Good
overviews of measurements of dielectric relaxation of
are given in Sorriso
[5],
Measurements on
Takashima
[1],
and Grant
divided between those studies that measured
measured
at low frequencies
been performed by many researchers over
DNA
The measurements can be
[88].
above
DNA
1
MHz
and those studies that
(< 1000 Hz). Higher- frequency measurements were made
by a number of authors [40,89-92]. Low- frequency measurements have been made by Takashima, Sakamoto, Hanss, and Tung [16,20,32,93]. In studies of the relaxation of
DNA in saline solutions, Takashima observed an a relaxation at around 100 Hz 16], for DNA molecular masses of 5 x 10^ D. Hanss and Sakamoto [10, 20, 32, 35, 36, 94] [1,
performed experiments on the same length molecules and found relaxations in the 5 to 1000
Hz
range.
Takashima used a capacitor with platinum-blacked electrodes to 42
measure permittivity from
and a conductivity standard conductivity
kHz and found a
DNA
of molecular
relaxation near 5 Hz.
2000 ^S to 13,000
iJ,S.
[16]
Sakamoto used a four-terminal device
to 1000 Hz.
mass 4 x 10^
The conductivity
Hanss and Bernengo
D
from
Hz
0.2
of their solution
and above. Sakamoto attributes
to 30
was from
obtained a decrease in dielectric increment for calf-thymus
found that concentration dependence of the
d.c.
found a peak at 1-10 Hz. Tung
[20]
concentration increased, whereas Sakamoto found the reverse trend
[40]
DNA
Sakamoto
[10].
as
[10]
DNA became important around 0.02 percent
this to intermolecular interaction. In figure 8.1, a Cole-
Cole plot of dielectric increment
is
plotted from
Sakamoto [10,32,35,36].
8.2.
Permittivity Measurements and Electrode Polarization
The
permittivity
is
and
to eliminate the effects of electrode polarization
He measured
[32].
and Takashima
Hz
1
can be written e*
in the
=
form
eo[e',-j{e';
+
-)].
(8.1)
UJ
At low frequencies, a number of conductivity where
phenomena the
a
