Download chapter link

Draft 1 Chapter 6.
Magnetic Field Interactions with Biological Materials.
Introduction.
Magnetic fields interact with biological materials both by applying torques to the dipole moments and
by changing the energy levels. The torques can change the orientation of the dipole moments which can
in turn change chemical reaction rates.
The fundamental law describing forces on charged particles is given by




F = q( E + v x B )

(1)


where F is the force, q is the charge on the particle, v is the velocity of the particle, E is the electric



field and B is the magnetic flux density. E and B are coupled by Maxwell’s equations so that a

time-varying magnetic field generates an E field and vice versa . This force may lead to ion
currents and changes in the orientation of dipoles in molecules and changes in molecular
configuration. As indicated in the introduction to this volume time varying magnetic fields lead to
induced electric fields and these induced electric fields lead to time varying current flows. Thus it
is often difficult to separate the direct effects of magnetic fields from those resulting from the
induced electric fields. As indicated in chapter 5 electric fields as small as 10-7V/m (Kalmijn) by
sharks and 10-4V/m (Rosenspire et.al ) in human neutrophils have been shown to result in
significant biological effects. These induced fields are widely used to help heal nonunion broken
bones as described in Chapter --- . These induced fields are also used for transcranial stimulation
of nerves in the brain as describe in Chapter---.
These fields may also lead to transitions between energy levels, shifts in energy level spacing, and



induced dipole moments, P . The magnetic field H is related to the magnetic flux density B by


B = µ H where µ is the magnetic permeability and µo is the permeability of free space.. For magnetic


 
fields the torque   m eff xB where  meff is the effective magnetic dipole moment. The translational
force on a magnetic material is given by

B
Fx  M
x


(2)

Where M is the magnetization of the material. The magnitude of the magnetization vector is equal to

the magnetic moment per unit volume.


B  o ( H  M ) . For materials without permanent dipole


moments the magnetization to first order is given by M =  H where  is the susceptibility tensor per
unit volume. In this case the force

H
F x  V H
x


(3)
where V is the volume occupied by the material. The sign of  is positive for paramagnetic and negative
for diamagnetic materials. [Frankel 1996]. It is some times more convenient to write this expression in
terms of the magnetic flux density and its gradient
   
F
BB
o
Time varying magnetic fields induce electric fields as shown in the introduction and these induced
electric fields and corresponding currents may be used to stimulate nerve cells and other biological
processes which are discussed in other chapters.
Energy Effects of Magnetic Fields
In a magnetic field, the energy is modified as a result of the interaction of the magnetic field with the
magnetic dipole moments of the electrons and neutrons. This leads to shifts in the energy levels with
the magnetic field, called the Zeeman Effect. Generally, for molecules in the 1  states or with no net
electronic angular momentum, these effects are small by comparison to the Stark effect. Exceptions are
molecules which have electronic angular momentum and are paramagnetic. The energy as a function of
the magnetic flux density is given by
W  l  B  s  B
(36)
where  l = B L. L is the angular momentum quantum number in units of Planck’s constant, h, and in
1
 states s  2.00229B S where S is the electron spin angular momentum, and  B is the Bohr
Magneton. B is the magnetic flux density and
B
 1.39967 x 104 MHz /T.
h
(37)
.The shift in energies is often expressed in terms of a constant, g, and the magnetic quantum number,
M, which is the projection of the angular momentum on the direction of the magnetic field so that
W  g J MB H .
(38)
For 1  states  B is reduced by the ratio of electron to proton masses or by
1
which is equal to the
1836
nuclear magneton µn. The allowed transitions are for M  0 for the microwave field parallel to the
static magnetic field and M   1 when it is transverse [Townes and Schawlow 1955 Chapter 11].

If we assume the couplings between the nuclear spins and the free electrons are small the diagram in
Figure 5 can be considered as a first order approximation and the nuclear spin perturbation of the
energy levels leads to broadening of the lines. [Steiner and Ulrich 1989]
Figure 5
Energy
T+
To
S
T-
B
Figure 5. An example of the Zeeman energy level shifts with magnetic flux density for isolated electrons
in a magnetic field. Note the same sort of energy level diagram applies to the nuclear spins, but 10-3 to
10-4 times smaller.
At weak magnetic fields where the hyperfine energy levels are separated by more than the magnetic
field energy g  B B the foregoing diagram is centered on the hyperfine levels. g is a constant that can be
calculated quantum mechanically from the rotational, vibrational energy levels etc. and their projections
on the axis of rotations and the static magnetic field. It often has a value of about 2, For magnetic fields
on the order of the Earth’s magnetic field (≈45µT) the changes in energy with the weak magnetic fields
will remove the zero field degeneracy between the triplet states for the hyperfine levels Because of the
small energy differences between these energy level at thermal equilibrium the population densities
each of these energy levels will be approximately equal. However, biological systems are not at
equilibrium and free radicals are generated as a part of the metabolic process. These free radicals pairs
may be generated preferentially in either singlet or triplet states.
In a typical molecule, the spins of the electrons in the outer orbits are paired in a singlet state. In the
singlet state, S, the spins are aligned in opposite directions  or spin up and spin down parallel to the
external magnetic field. In the triplet state both spins are aligned parallel to the external magnetic field
or
or
and perpendicular to the magnetic field
or
In atoms or ions with unpaired electrons, the S-levels or singlet states correspond to an atom or
molecule with paired spins, one up and one down. The triplet levels T+, T_ and To,, have an unpaired spin,
so that the energy of the external magnetic field may add, subtract, or not interact with the internal
energy. The size of the separation between energy levels corresponds in the classical description to the
Larmor precession frequency, f, for the electron spins, with f 
g B B
, where g is a factor that is a
h
function of the angular momentum and other quantum number, and B is the magnetic flux density.
[Note we have assumed in this section that B=  o H where  o is the permeability of free space.] These
levels are broadened by the nuclear spins. Transitions between levels are coupled by the nuclear spins
and can be driven by AC fields such that hf corresponds to the difference in the energy between
adjacent levels corresponding to M   1 [Timmel 2004].

As an example we consider the case where a molecule is split to form a free radical pair so that each of
molecular fragments contains an outer electron with an unpaired spin. The S and T levels are now
defined by the orientation of the spins in the two different fragments. It is observed in this example
that the energy level gap between the S and T_ level is larger at zero magnetic field than it is at larger
values of the B field that are less than four times the value of the exchange energy J. The lifetime for
transitions between the S and T states typical range from (10-6 to 10-10 seconds). The coupling between
the electrons and the magnetic moment of the nucleus leads to the hyperfine levels. It is difference in
this coupling between the nuclear spins and the electronic spins that leads to the conversion of
electrons in a free radical pair from an S to a T state or from a T to an S state. The conversion from S to
T states is a function of both the coupling between the nuclei and the outer electrons in each of the
fragments and the diffusion lifetime. Both the conservation of angular momentum and the conservation
of energy must be satisfied and this leads to the selection rules for the allowed transitions. Under the
conditions shown in Figure 5 the allowed transitions are for the S to all T states and between T+/- and To.
Radical pairs formed in the T states with the spins aligned parallel to each other are not allowed to
recombine by the Pauli exclusion principle thus they have more time to diffuse away from their initial
partner and combine with other molecules.
Changes in free radical concentrations as a function of magnetic are predicted to take on one of several
shapes as shown in Figure 6. [Figure 6 from Steiner and Ulrich 1989]
The calculations for changes in free radical lifetimes and concentrations in small magnetic fields have
been carried out by Brocklehurst, McLauchlan 1996, Timmel and Henbest 2004, and takes into account a
much more detailed description of the coupling between the nuclear magnetic spin energy levels and
the orbital electrons. The coupling constant A can vary from 0.01mT to 3mT for carbon centered free
radicals. The corresponding separation between hyperfine energy levels for carbon centered free
radicals can vary from about 1.2 x 10-9 eV to about 3x 10-7eV. Detailed calculation for these effects show
a J shaped curve for free radical concentrations similar to that shown in figure 6 C and Figure 7(Figure 4
from Brocklehurst), This inverted J shaped curve leads to an increase in the lifetime for conversion of
singlet born pairs of free radicals as the magnetic fields increases form zero and thus an increase in the
number of free radicals in the triplet state that can diffuse from the site of origin to react with other
molecules. As the magnetic fields increases in this example a maximum concentration of free radicals
occurs at a value below 300µT. Changes in free radical concentrations in the forgoing example saturate
for changes in magnetic fields at higher values (1mT to 100mT).
Figure 7
The chemical reaction rates increase when the energy levels for the initial state and the product
approach each other. The maximum rates occur when the energy levels are equal. Thus both electric
and magnetic fields can shift the energy levels so as to increase or decrease a chemical reaction rate. It
is to be noted that energy shifts, B B, that are small compared to kBT can lead to large changes in
chemical reaction rates if the initial states are in excited energy level [Steiner and Ulrich 1989].
Examples of this are the number of free radicals that survive as a result of the absorption of a UV photon
or a variety of chemical reactions. Excitations by electric fields keep particles that start in a singlet state
in a singlet state. Free radicals may be created by splitting a molecule so that the surviving fragments
each have an odd number of electrons in an orbit. This can be done by hemolytic cleavage of bonds, or
thermolysis in solution leading to a pair of radicals in singlet states, and photolysis in either singlet or
triplet states. In a typical molecule, there is an even number of electrons in the outer orbits and, when
they are split, one fragment has an electron with spin up and the other with spin down. These two
fragments often recombine in about 10-10 seconds. However, if one of the spins flips, then
recombination is forbidden by the Pauli Exclusion Principle and fragments typically survive for about 10-5
seconds. This in turn increases the probability that the fragments may drift apart and diffuse through
the solution as free radicals. The relative energies of the singlet and triplet states of a radical pair in a
magnetic field as a function of distance between the pair particles is shown in Figure 6 [Fossey 1995].
Free radicals can be carbon centered and formed in a number of common compounds including a
variety of methyl and alkyl radicals. They can also be formed in a wide variety of other compounds
including radicals centered on nitroxide, phosphorus, oxygen, and sulfur. * Free radicals that are
important in metabolic processes include O2-, HO  , H3O+ and H2O2 [Rosen 1999]. Free radicals are
chemically very active and important parts of many biological processes. As shown in figure 5, increasing
the DC magnetic flux can either increase or decrease the energy required to move from a singlet to a
triplet state depending on the value of B where the energy for an electron in the T- or T+ equals the
energy in the S state.
* See Fossey for the chemical description of a large number of free radicals and their reaction rates.
An example of when a large magnetic field changes the chemotatic response of neutrophils is given in
the work by Sipka et al [Sipka et. al 2004] and this is likely to be the result of changes in free radical
concentrations as a consequence of the increase separation in energy between the S and T- levels.
Energy level splitting associated with the magnetic dipoles are given to first order by W  g B B and
B = 9.27 x10-24 J/T and g is a number near unity and is approximately 2 for an isolated electron spin.
Thus, earth’s magnetic field of about 50μT leads to transitions with a resonate frequency at about
1.4MHz.
Free Radicals and the Biological Effects of Magnetic Fields
“Free radical molecules are defined to be chemically bonded ions or molecules with uncompensated
spin. They have been found with both one and two uncompensated spins” [Wadas 1991]. These
molecules are paramagnetic and they are typically characterized by measuring the electron spin
resonance spectra. Free radicals are chemically very active and often have short lifetimes as they react
with lipids and many other biological molecules.
Organic molecules that contain Fe+2, Fe+3, Ni+2, Mn+3, Mn+2, Cu+3 and related cations are also
paramagnetic and are important in biological processes. Iron, Fe+2, is present in the largest quantities
and is found in almost every human cell. These paramagnetic ions are often contained in diamagnetic
structures. For example, iron is important in hemoglobin’s ability to transport oxygen and is located in
the interior of the molecule. See Figure 7. Hemoglobin is diamagnetic when it contains oxygen and
paramagnetic without oxygen. In the paramagnetic state the effective dipole moment μeff= 5.35 B per
heme group. . With O2, it is in the low spin state with S =0 and without O2, it is in a high spin state with
S=2. This reduces the energy required to take on oxygen. Additionally, with the uptake of O2, the
complex shrinks the average distance between Fe2+ ions from 3.4l nm to 3.235 nm. The minimum
potential energy for hemoglobin with O2 and paired spins is less than the minimum potential energy
without O2 and uncompensated spins and occupies a smaller volume. It releases 6 x 104 calories/mole on
attaching O2 and requires the same amount of energy to release it [Wadas 1991]. It is to be noted that
both O2 and hemoglobin without O2 are paramagnetic. The chemical reaction involves both an electrical
interaction and magnetic dipole-dipole interaction.
Paramagnetic ions may be contained in both enzymes and coenzymes. The paramagnetic enzymes and
coenzymes act as accelerators for biochemical reactions.
FIG 7. The structure of hemoglobin, www.elp.manchester.ac.uk
Free radicals can be generated by the absorption of external energy, the decomposition of a molecule
as the result of a reaction with another molecule, and the induction of an electron transfer reaction.
Free radicals can be created by the absorption of light and as a part of the metabolic process, as well.
Both singlet and triplet free radicals may be created in biological systems. In a free radical pair, the g
values of weakly coupled electrons are typically different, so that radical pair oscillates from the singlet
to the triplet states.
Weak 50Hz magnetic fields have been shown to reduce the number of free oxygen radicals in rat
lymophocytes in vitro when the applied field reduces the earth’s magnetic field to near zero for at least
part of the cycle. [Zmyslony 2004] One hour exposures to 50Hz fields at levels between 25 and 100µT
have been shown to increase the levels of super oxide radical anions in the human leukemia cell line
K562 along with transiently increased HSP70 levels (>twofold), at several exposure densities, compared
to sham controls [Mannerling 2010] Additionally it has been shown that low levels of magnetic fields can
stimulus for immune relevant cells (e.g., macrophages) to release free radicals.[Simko 2004]
Carlos Martino has shown that growth rate on human umbilical vein cells (HUVECs)[ Martino, 2008] and
two kinds of cancer cells [Martino, 2010] increases as the DC magnetic field is increased from less than a
few microtesla to the earth’s magnetic field of about 45µT. He also showed that he could decrease the
growth rates of the HUVECs cells by adding the antioxidant, superoxide dismutase (SOD) indicating that
increasing the magnetic field may be changing the number of free radicals in the cell culture. Usselman
et.al have shown that they can modulate the O2- and H2O2 concentrations by exciting the hyperfine
transition for mixing the S and T states with 50 μT SMFs combined with 1.4 MHz, 20 μTrms RF magnetic fields at
Zeeman resonance in experimental samples. These changes were dependent on the angle between the static
and RF fields. An extensive review of free radical chemistry and the effects of both low and high
frequency electric and magnetic fields is given by Georgiou (Georgiou 2010). This reference also contains
over 200 references. We have also shown increases in the velocity of from 2 to 6 µm/minute for human
neutrophils in DC magnetic fields from 15 to 100 µT in the presence of a gradient of C-AMP which served
as a chemo attractant. [unpublished]
A related effect is an increase in the release by ferritin molecules of Fe+2 from stored nano particles of
Fe+3 with the aid of 6-hydroxidopamine upon the application of radio frequency fields in the 10 to 100
μT range at 3 to 10 MHz. In this case, the energy absorbed from the RF fields by the nano particle is
likely to contribute to both the conversion for Fe+3 to Fe+2 and a change in the configuration of the
ferritin [Ueno 2008]. It has also recently been shown that the exposure to RF radiation from cell phones
operating from 915MHz to 1822MHz for 20 minutes or more at a maximum electric field intensity of 12
V/m and a corresponding SAR of 0.5 W/kg can lead to the monomerization of acetylcholinesterase
obtained from an electric eel and a reduction in the chemical reaction rate for acetylcholine hydrolysis.
The temperature change was less than 0.2 oC [Barteri 2005].
Water and Proteins
Water performs important functions in determining the shape and function of proteins.
Proteins typically have both hydrophobic and hydrophilic regions. In the hydrophobic
regions the water molecules from structures that form a shield so that this region is not
soluble in water. In the hydrophilic regions the charged regions of the proteins of the
proteins strongly attract water molecules. The regions in water that are affected by
hydrophobic forces can form stable water structures that exclude solutes and micro
spheres out to distances of 200μm [Zheng 2006]. In proteins the hydrophilic regions
repel water and the protein folds so as to exclude water from these regions. Water is also
hydrogen bonded to other regions and forms a diffuse shell around the protein that
increases its size and decreases its mobility in a way that is similar to that previously
described for simple ions. Water may also be folded into the interior of a protein so that
it is not in contact with the bulk water in which it is dissolved. Some of this enclosed
water is bound to fixed positions in the protein structure and some appears to be free to
tumble. The bound water is important in determining the shape of the proteins and
therefore their biological function. Additionally, the bound water H bonds may be
dynamically connected to each other forming water structures that connect water
molecules that are bonded to specific sites on the protein. The dynamic nature of the
water structures provides flexibility to the proteins. Water is also important in
catalyzing the chemical reactions with oxygen that provide the energy for living systems
[Voeiko 2009].
Kalmijn, A.J., Detection of weak electric fields, in Sensory Biology of Aquatic Animals, Atema, E.J. et al.,
Eds., Springer-Verlag, Berlin, Chapter 6, 1987.