1. Lecture 10 Chapter 5
February 6, 2019

2. 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

3. Biological Amplifiers
Neural Transmitter Releases up to 104 calcium ions
Need to overcome the electrical threshold for firing

4. 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

5. Oscillators Two approach to analysis 1 Negative resistance oscillator
R R C L
2 Feedback oscillators

6. Basic Feedback Oscillator
Vi= Vs+βVo Vo=AVi Vo[1/A-β]=Vs
Vs Vi A Vo β

7. Operational Amplifier with Time Delay in the Feedback

8. 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

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

10. 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.

11. 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.

12. 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 December ; 9(12): 981–991. doi: /nrm2530.

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

14. 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.

15. Basic Characteristic of Nonlinear Devices.
1. Nonlinear resistance,

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

17. An Ideal Harmonic Generator
1 Two tunnel diodes in series

18. Test Circuit

19. Results

20. 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+

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

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

23. Parametric Amplifiers

24. Lecture 10 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

25. Stochastic Resonance

26. Stochastic Resonance

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

28. Current Flows.

29. Concentration of Electric Fields in Space The voltage across the membrane becomes approximately equal to V/2 and the Em ≈ L/2t

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

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

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

33. 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.

34. 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.

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

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

37. Coherence 1.Coherence in Space and Time.
2. Neural Networks and Learning
3. Source of Noise and Minimum Detectable Signals ?

38. 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
τcell= 8 sec

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

40. 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.

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

42. A Neural Network Model for Adaptive Responses1

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

44. Lecture 11

45. 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 10-4 V/m
4. These numbers are all variable

46. Internal Fields 1. Across a membrane of 2 x 107V/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 x10-2V/m
4. These numbers are variable with position, type of cell etc.

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

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

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

50. 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

51. Membrane Example. 1

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

53. Minimum Detectable Electric Field Is a Function of Frequency
Bovine Fibroblast
Cells
I= 10-3—10A/m2