ECEN 5341/4341 Lecture 7 February 1, 2019 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.

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 2x107 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

brid orbitals of oxygen (14) brid orbitals of oxygen (14) Water Dipoles brid orbitals of oxygen (14) brid orbitals of oxygen (14) Figure 2 Two descriptions of bonding in H2O. The observed angle between the two O—H bonds is 105o (a) H2O based on s, px, py and pz orbitals oxygen (b) H2O based on sp3 hy

Water Molecule

Figure 4 Some of the many water molecule clusters (15).    

Figure 5 Theoretical predictions of the stabilities of the five lowest-energy water hexamer structures. Values of De (lower line – lowest equilibrium dissociation energy) and Do (upper line – quantum vibrational zero-point energy) are shown. The zero-point energy is equal to Do-De (18)

Water Clusters Figure 3 An expanded icosahedral water cluster consisting of 280 water molecules with a central dodecahedron (left) and the same structure collapsed into a puckered central dodecahedron (right). (16; 17) .

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.

Figure 7. Water molecules next to a nonpolar solute

Figure 6. Structures for the putative global minimum: (a) Na+(H2O)20, (b) Cl-(H2O)17, and (c) Na+(H2O)100. (25)

Water Molecules 1. Water molecules bind to proteins in different places and are important in the shape of the structure and determining the ability of other molecules and ions to bind or activate things like DNA replication. 2. Water in a cell is more structured than in a pure state and has a higher viscosity.

A Beta-Sheet 1

Table 1 Ionic mobilities in water at 298 K, u/(108 m2 s-1V-1) (12).

Table 2 Limiting ionic conductivities in water at 298 K, /(S cm2 mol-1) where  is molar conductivity (12)

Water Viscosity Additional it has been shown that modulated weak RF fields can modify the diffusion rate for NaCl. Exposures to 450MHz with an SAR of 0.4W/kg and an estimated electric field of 25.6 V/m is shown to reduce the viscosity of NaCl in water increase the rate it diffuses. Hinrikus, H., Lass, J., Karai, D., et al. (2014). Microwave effect on diffusion: A possible mechanism for non-thermal effect. Electromagn. Biol. Med. 34:327–333.

Changes in Resistance of Water by NaCl 1

Forces on Dielectric Sphere with ε2 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 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.

Lecture 8 February 4, 2019

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 (>

Changes in Energy and Energy Levels Only Discreet Transitions Allowed Variable B or E

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

Shift in Energy Levels with Electric Fields [Stark Shift] is the electronic dipole moment for a molecule Typical values for P are = 3.3 x 10-30 to 6.6 x 10-30 Cm To excite transitions between adjacent energy levels fields of E ≅ 2x107V/m for frequencies of a few kilohertz required

Stark Effect Energy levels 𝐸 3 𝐸 2 𝐸 1 𝐹

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.

Magnetic Field Effects Zeeman Shifts in Energy Levels W B

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 Where 𝒏 𝟏 is population of one state, 𝜸=𝟐 𝝅 𝝁 𝑭 𝒉 𝑭 is the gyromagnetic ratio, B1 is the AC 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

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. Many kinds of amplifiers and many steps 2. Start with solar energy and photosynthesis a two step quantum process to convert CO2 N2, H2O, O2 and other atoms in to hydrocarbons. 3. Many steps to carry this through glucose to ATP to moving your arms and legs or activating your brain.

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 Membrane Potentials used to transmit Electro Chemical Signals. 2. More than 3000 signaling proteins and 15 second messengers. 3.Most biological amplifiers contain negative feedback to stabilize the system.

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

Examples 1. Nerve Cells may some the input from may dendrites to fire a synaptic junction to raise the input voltage by 10 to 20mV and this fires an action potential of 50 to 100mV. 2. Sub-threshold inputs can lead to the release of neural transmitters that, in turn, can release from 2 to 10,000 Ca2+ ions from internal stores. 3. There are more than 40 different neural transmitters such as acetylcholine (Ach).

Electronic Amplifiers 1 Basic Amplifier use energy from one source and use it to increase the strength of the desired signal. 2. Electronics we take energy of a DC power supply and use it to increase the amplitude of the desired signal. 3. This is not essential we can get our energy from an AC signal in a parametric amplifier or from noise in stochastic resonate amplifier

Operational Amplifier with Time Delay in the Feedback

Steady State Solution for Vs= Vin cos(ωt) and Vo cos (ωt –θ) where θ=ωτ, = Note change in sign with θ=ωτ so we can get either amplification or attenuation by changing frequency or the time delay τ

Oscillation The system breaks into oscillation when the gain As the gain Af oscillates from zero to

NADPH, ROS, NOS Oscillations NAD(P)H concentration in motile neutrophils is oscillatory, and the amplitude of the oscillation can resonate in the sense that the amplitude increases with externally applied pulsed magnetic fields. NAD(P)H autofluorescence was monitored with a photomultiplier, and photomultiplier counts plotted . Note the amplitude of the signal returns to its normal value when the stimulus is removed. Rosenpire et.al (2005) Figure 2.

Redox Oscillation Reduction Figure 3. Flavoprotein redox oscillations are inhibited by pulsed magnetic fields timed to coincide with minimal flavoprotein autofluorescence and they amplify the oscillations when timed at the minimums. Rosenpire et.al (2005) Figure 11.

Self Limiting Protein Synthesis Suppose that the rate of protein synthesis at present (at time t) depends on the concentration of protein at some time in the past (at time t-τ), where τ is the time delay required for transcription and translation. Then, the governing kinetic equation becomes (2) Béla Novak* and John J. Tyson ” Design Principles of Biochemical Oscillators Nat Rev Mol Cell Biol. 2008 December ; 9(12): 981–991. doi:10.1038/nrm2530.

Current Flows.

Concentration of Electric Fields in Space

Basic Characteristic of Nonlinear Devices. 1. Nonlinear resistance,

Semiconductor Diode The simple one is a diode. I= Vo+αV1+βV2+---- I I

An Ideal Harmonic Generator 1 Two tunnel diodes in series

Test Circuit

Results

Nonlinear Reactance 1. Use to convert power from one frequency to another. 2 Typical diode C~(V)-1/2 for step diode 3 How do you design a diode with a larger nonlinear capacitance? P-_ N_ P+ N+ Ni N+

Capacitors C = Q/V C= εA/d V= QC=Qd/εA

Parametric Amplifiers 1. Conservation of Energy on a photon basis 2. Conservation of momentum where k is the propagation constants

Parametric Amplifiers

Stochastic Resonance