ECEN 5341/4341 Lecture 11
February 5, 2016
Chapter 5
Assignment
• 1. Finish reading chapter 4 and the first half of
chapter 5. I consider chapter 5 to be
important as a basis for explanations of how
you go from the physics to the biology.
• 2. Read two papers for Monday. One of these
should refer to the material in chapters 4 or 5
Maxwell’s Equations
Basic Equations
The polarization p couples the fields to the materials
The dielectric constant ε may be complex and we usually only
need the first term
MB is the magnetic polarization per unit volume
Forces
• Lorentz Equation
• Examples Typical fields across a membrane are
2x105 V/m and drifts in proteins may occur at
2 V/m or less.
• Thermal velocities for Na+ ≈ 4x102 m/sec in
B≈5x10-5 T yield F≈ q (2x10-2 V/m)
Forces on Dipoles
• 1 First order forces for permanent dipole Po
• 2 For induced dipole moments
• 3. The resulting current flow Ji
Drift Current Flows
• Two components to force on a charged
particle
• The current is summed over all the molecules
and ions
Mobilities
•
Blood
Saline
σ=1.4S/m
Bound Water Molecule
• 1.Computer simulations show a rather large
number of configurations for bound water
that surrounds some of the ions that are of
most interest in the study of the effects of
electric fields on biological systems.
• 2. This leads to the fact that some small ions
my have larger effective radius than big ions
and lower mobility.
Forces on Dielectric Sphere
in
• Assume
• Viscous Drag
Mobility
Osmotic Pressure
• Average diffusion pressure on a particle
• Special case of a sphere.
• Maximum when the field is at the surface of a
membrane
(
Diffusion Currents
)
1 The diffusion currents go with the gradient of
the concentration.
The ratio of the diffusion to drift current
J
 kT  ( N i )
Maximum
J
diff
drift
F
Ni
Voltage required Wi≈ 2mV
Forces
1. Like charges repel and opposites attract. So a
screening double charge layer builds up at the
surface of a membrane.
Van der Waals Forces
• For like particles the forces are repulsive at short
distances ).1 to 0.2nm and attractive at longer
ranges. They are caused by fluctuations in the
induced dipole moments.
• For individual atoms F~ 1/r7 however for two
surfaces at a distance dw
they
decrease much more slowly.
For two membranes this is about 20nm
See Intermolecular and Surface Forces by Jacob
Istaelachvili
Hydration Forces
• 1. These forces are repulsive and rise rapidly between
membrane bilayers
• There are other long range attractive forces between
hydrophobic surfaces that appear to be generated by
the induced dipole moments out to about 25 nm.
Electric Field Effects
• 1. Electric fields add a small drift velocity on to
the large random thermal velocity.
• 2. For E =1kV/m we would expect for Na+
drift velocity v= 5x10-5m/sec ,
• Thermal velocity v= 400m/sec
• 3. For larger particles the drift velocity is
slower so the velocities are microns per
second to microns per minute.
Chemical Reaction Rates
• 1. A basic chemical reaction
• If Ao is large and n = m =1 then
Changes in Collision Rates z
• 1. The drift current may add or subtract from the
number of particles colliding at a membrane surface.
• 2. It can block the reaction or grow it exponentially at
voltages of a few volts/m
• The enhancement of the sorption reaction rate for
charged reactants onto a reactive colloidal particle is
shown to be proportional to E2 ω½ for values of
ω< 1010 radian/second and small applied fields. At high
frequencies, ω> 1010 radians/second the sorption
reaction rate goes as E2 ω-2 [Raudino 1993].
•
.
Steric Effect
• . An electric field exerts a force on a molecule with a
dipole moment to align the molecule along the field.
This effect is in a constant direction for an induced
dipole moment and to first order varies with the
square of the electric field. The average orientation is
governed by the Langevin equation
•
•
<cos ()> =coth
(25)
•
• where  is the angle between the electric field and the
dipole moment. The size of the induced dipole
moment, and thus WDEP, the energy acquired from the
field, will also be dependent on . For weak fields
<cos (> WDEP
3k B T
Changes in Energy
• 1 At study state or constant temperature the
Boltzmann population distribution of energies
Boltzmann distribution function which in turn
leads the ratio of the number of particles N2 with
energy, W2, to the number of particles N1 with
energy W1 so that
•
N2= N1e –ΔW/kB T
• where kB is Boltzmann’s constant. ΔW is the
difference in energy between the two particles.
Fermi Distribution in Solids
• 1 Energy levels reference to thermal
WT =0.026 eV. Need about 0.1 eV to activate
most chemical effects. Catalyst can reduce
this.
Energy Level Diagrams
• Alowed
• Energy
• Levels
• Variable B or E
Energy Levels for NO in B Field
Transitions in NO
Spectra for D2 vs B
Chemical Reactions
Population Saturation
Population difference of states in AC field is
n1
n12 
1   2 B1T2T1
Where 𝒏𝟏 is population of one state, 𝜸 =
𝝁𝑭
𝟐 𝝅 is the gyromagnetic ratio, B1 is the AC
𝒉𝑭
magnetic flux density, T1 is the relaxation time
between states and T2 is the nuclear spin
relaxation time (Bovey et al., 1988).
RF Absorption Spectra
From Woodward et al., 2001
Stark Effect
• 1. These are changes In the energy levels of
atoms and molecules with electric fields.
• 2. They can occur as result in the change in
orientation of dipole moments, induced
dipoles , and changes in vibrational and
rotational energies.
• 3. Rotational energy level transitions often
occur in the microwave region.
• . Townes and Schawlow 1955
Magnetic Field Effects
Zeeman Shifts in Energy Levels
• W
•B
Additional change
• 1. Changes in the conformation of molecules
that change the dipole moment.
• 2. Changes in the rotational velocity.
• 3. Stark Shift in energy levels.
RF Thermal Effects
• 1 Power absorbed.
• 2. Temperature change
• 3. Changes in chemical reaction rates
•
Protein Protein Reactions
• 1. These are important biological reactions
and can take place in at least two ways.
A. Force fit
B. Configuration recognition
2. There are a very large number of possible
configurations . For 100 base pairs 1089
Protein Protein Interactions
• 1
Myoglobin + CO
Biological Amplifiers
• 1. Extract or control energy from another
source with a small signal.
• 2. Convert energy from glocoss to ATP
• 3. Use ATP to drive Na+ and K+ against the E
field to maintain the -50mV to -70mV
membrane bias
• 4. Release as an action potential that can
trigger nerves and then muscles
Biological Amplifiers
• 1 A few molecules can trigger the release of
10,000 Ca++ ions.
• 2. A small voltage can open channels at a gap
junction so that voltage gain can occur for current
flowing from a large cell to a small one with a
larger resistance.
• 3. Most biological systems have negative
feedback to help stabilize the system.
• 4. For temperature control G≈-33 For blood
pressure -2
Current Flows.
Concentration of Electric Fields in
Space
Parametric Amplifiers
• 1. Conservation of Energy on a photon basis
• 2. Conservation of momentum where k is the
propagation constants
Parametric Amplifiers
Stochastic Resonance