ECEN 5341/4341 Lecture 9 Chapter 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

Forces Lorentz Equation Examples Typical fields across a membrane are 2x10 5 V/m and drifts in proteins may occur at 2 V/m or less. Thermal velocities for Na + ≈ 4x10 2 m/sec in B≈5x10 -5 T yield F≈ q (2x10 -2 V/m)

Forces on Dipoles 1 First order forces for permanent dipole P o 2 For induced dipole moments 3. The resulting current flow J i

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 Maximum Voltage required W i ≈ 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/r 7 however for two surfaces at a distance d w 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 + v= 5x10 -5 m/sec 3. For larger particles the velocity is slower so the velocities are microns per second to microns per minute.

Chemical Reaction Rates 1. A basic chemical reaction If A o 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 E 2 ω ½ for values of ω radians/second the sorption reaction rate goes as E 2 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 =coth (25) where  is the angle between the electric field and the dipole moment. The size of the induced dipole moment, and thus W DEP, the energy acquired from the field, will also be dependent on . For weak fields. 

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 N 2 with energy, W 2, to the number of particles N 1 with energy W 1 so that N 2 = N 1 e –ΔW/k B T where k B is Boltzmann’s constant. ΔW is the difference in energy between the two particles.

Fermi Distribution in Solids 1 Energy levels reference to thermal ΔW =0.026 eV. Need about 0.1 eV to activate most chemical effects. Catalyst can reduce this.

Energy Level Diagrams Alloswed Energy Levels Variable B or E

Energy Levels for NO in B Field

Transitions in NO

Spectra for D 2 vs B

Chemical Reactions

Population Saturation

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 10 89

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