Chapter 5 Lecture 13 February 10, 2016

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

Lecture Assignment. Finish reading chapter 5. Two papers for Monday. Note the paper that Marisa found on tilapia is one I think is worth reading and Kim should have it posted shortly.

Nonlinear Elements 1. A nonlinear resistance 2. A nonlinear reactance 3. A time varying element in you circuit or system. 4. These elements show up in many form and the biological ones are more complicated than the electronic ones.

Basic Characteristic of Nonlinear Devices. 1. Nonlinear resistance,

Semiconductor Diode The simple one is a diode. I= V o +αV 1 +βV I V

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 + N i N +

Capacitors C = Q/VC= εA/dV= 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

Biological Amplifiers n13.html n13.html Neural Transmitter Releases up to 10 4 calcium ions Need to overcome the electrical threshold for firing

Lecture 14 Reference on Stochastic Resonance “Tuning in to Noise” Adi Bulsara and Luca Gammaitoni Physics Today March 1996 Stochastic Resonance addition to BEMS paper Kendra Krueger October 2011

Stochastic Resonance

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S/N Ratio vs N 1 SNR External Noise Intensity Optimal noise level

Nonlinear Effects at Cell Membranes 1.Current flow for 2.R m is the membrane resistance. The result is that the membrane is a poor rectifier. However AC voltages make the interior more negative.

AC Induced Current Flows At Low Frequencies Induced DC Currents for V AC from -60 to + 40mV For a spherical cell.

Shift in Membrane Firing Time Shift in firing time for Where u(t) is unit step function

Basic Feedback Oscillator V i = V s +βV o V o =AV i V o [1/A-β]=Vs V s + V i AV o β

Mode Locking of Oscillators Theory for injection locking of electronic oscillators is give by The theory is good for case where This worked for Aplysia pacemaker cells.

Threshold Injection Locking for an Aplysia Pacemaker Cell Frequency range from 2 to 10 Hz

Signal Noise Requirements for Phase Locking The phase of the inject signal must be stable enough so that the phase φ Where K is the linear control characteristic in units (2π Hz/V) and is closely related to the loop gain.

Locking of a Pacemaker Cell Response to various frequencies of injected currents.

Signal Coherence Litovitz showed that for 10µT coherence for 10 seconds or longer was required for signals at 55 or 65 Hz was required to change the activity of τ cell = 8 sec

Litovitz shows both space and time coherence help separate signals from Noise

Results Show 1. Both Space and time Coherence are important. 2 Small electric fields can lead to biological changes. 3. Magnetic fields can affect biological changes by a separate mechanism.

Effects of Time Delay Between E and J This can give Z in all four quadrants.

Membrane Capacity as a Function of Frequency Membrane Capacity is only a slowly varying function of frequency.

A Neural Network Model for Adaptive Responses 1

Training to Recognize 60Hz as a Function of S/N with 97% Accuracy

Lecture 15 We have test 1 coming up after chapter 6 You also have a midterm paper due the week after the test.

Thermal Calculations Power in and rate of change of temperature Maximum Temperature change for a small sphere with total energy in H

Thermal Chemistry S = fraction that under gone chemical change K’ is the chemical reaction rate. R’ is the gas constant H’ is free energy, S’ is the entropy. This leads to an exponential of an exponential

Thermal Chemistry 1. Rule of thumb we are likely to see biological changes when 2. The body typically holds your temperature to +/- 0.5 o C 3. Very rapid changes in chemical reaction rates above a threshold. !!

The Rate of Change of Temperature is also Important. 1 We have shown the changes of 1/10 o C can change the firing rate of a pacemaker cell at 1 o C/sec. From the Nernst Equation for K + Slow increases in T increased firing rates of a pacemaker cell. A rapid one decreased it. Changes seen with as little as 0.1 o C at rates of 1 o C/sec

Effects of Rapid Heating Picture from Aplysia

Discussion 1. It takes high powers and short pulses to get significant temperature differences on small objects. 2. Thin films have larger surface to volume ratios and cool faster than spheres. 3. Blood flow cools hot spots. 4. The thermal time constant is an important parameter and the sensitive to temperature change is one of the first measurements to make on any experiments involving RF or Microwaves.

Repetitive Stimulation 1. Repetitive microwave pulse resulted in decreasing the amount of slowing for a pacemaker cell in Aplysia. 2. Repetitive electrical stimulation lead to decreases in the resistance of gap junctions and to a 62% increase in coupling between cells. 3. These are likely to be the result of feedback leading to adaptive responses.

Discussion 1. Temperature pulses lead to thermal expansion and can cause acoustic waves that can be sensed at a distance. 2. Example radar hearing.

Natural and Man-Made Fields 1. The atmosphere charged about 100/sec world wide with about an 18 sec time constant to about 130V/m 2. Peak values at about 3000V/m 3. Rapid decrease with frequency to typical value > 1 Hz of V/m 4. These numbers are all variable

Internal Fields 1. Across a membrane of 2 x 10 7 V/m 2. Nerve pulses about 0.4ms, rise time 0.1ms fall time 0.5ms. Dead space 1 to 3ms 3. Fields along the outside of a nerve cell 5x10 -2 V/m 4. These numbers are variable with position, type of cell etc.

Types of Noise 1. Thermal 2. Shot Noise 3. C/f n Noise 4. Noise generated by other electrical activity in the Body.

Thermal Noise. 1. Black body radiation For h f <<kT P n = kTB = kTΔf 2. Other forms for matched loads 3 For thermal equilibrium. Non-equilibrium get negative temperatures.

Spontaneous Emission and Shot Noise 1 Spontaneous Emission P= hfΔf 2. Shot Noise 3. 1/f Noise or Where S(f) is the power spectral density

Example 1/f noise for a hole in a mylar film 1. For mylar film b is a geometrical factor a is a constant r is the radius of the hole Φ is the applied voltage

Membrane Example. 1

Lecture 16

Other Electrical Activity 1. EEG 2. ECG or EKG 3 Muscle movement. 4. Nerve Cells Firing

Minimum Detectable Electric Field Is a Function of Frequency Bovine Fibroblast Cells I= —10A/m 2