1. An Important Reference
ECEN 5341/4341 Lecture 19 March 1,2017 .
Read Chapter 7 for some important concepts.
1 Noise Sources
2. Minimal levels of signal detection.
3. Some characteristic s of Neurons.
An Important Reference
“Controlling Cell Behavior Electrically Current views and Future Potential” C. McCaig , A Rajnicek , B Song, M.Zhao Physiol Rev (2005)

2. Some Background
1. The problem is often determining cause and effect with many uncontrolled variables.
2. Separating the effect of an applied field from the on going effects of the environment.
3. The shark can sense electric fields of about
5x10-7V/m to find prey
4. Birds can sense magnetic fields of about 15nT for navigation.
5. These systems contain both a sensor and amplifiers.

3. Some Background
1. With this known sensitivity for biological systems that are designed to detect small signals how do we determine when a signal is too small to be important?
2. This becomes harder when we do not know how the biological systems work.
3. We can define known sources of noise or variability and set criteria for when we have a meaningful result.

4. How do we define a Detectable Signal?
1. As a signal which we can identify reliably?
2. Signal to Noise Ratio S/N?
3. Probability that our interpretation of the measurement is not in error? P value
4. Bayesian Hypothesis Testing?
P(H|X) the probability of H given X

5. Standard Approach to Determining an Effect
1. P value represents the probability that the difference in the value of the means is random and not due to the input signal.
2. Assumes the distributions are Gaussian
3. Typical values are P<0.05 and P<0.01 for saying that you have a statistically significant effect.
4. Note this means that there is difference but may not determine the cause. E,B, ΔT etc.

6. Signal to Noise and Signal Detection
1. Some sources of noise.
A. Thermal Noise Pn = kTB
B. Negative Temperatures and Population inversion
E N2
E N1

7. Sources of Noise 3. Shot Noise 4. 1/f Noise is seen in Membranes etc.
5. Noise generated by other electrical activity in the body.

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

9. Minimum Detectable Signal
1. Common Basic Approach Require
2. Assume and external E field on a spherical cell

10. Minimum Detectable Signal J. Weaver, D. Astumian , Science 01/26/1990
Assume thermal noise
kT= 4.3x10-21 J = 0.025ev at 310K
Let the resistance of the cell membrane be R and the capacitance C then Δf = 1/4RC

11. Minimum Detectable Signal J. Weaver, D. Astumian , Science 01/26/1990
C= εoεr4πr2/d
For a sphere in a uniform field
The result for minimum E detectable is

12. Minimum Detectable Signal J. Weaver, D
Minimum Detectable Signal J. Weaver, D. Astumian , Science 01/26/1990
For a long thin Cylinder
Where τ is the exposure time
Typical values for L= 150µm,Δf=10Hz
Emin= 8x10-5 V/ m

13. Signal/Noise Detection
1 The question is how do we decide when we have an effect of E or B on a biological system.
2. The effects are often small , 5% to a factor of 2.
3. We do not control many variables so you plot distribution functions of the controls and the exposed biological system.

14. S/N and the Detection of an Effect
1. Given a variable x and its variance σ and we wish to determine the separation of the mean values of the controls and the exposed.
m is the number of measurements 3.

15. Another Approach (S/N)
Note this approach has the advantage of not depending on the number of measurements but assumes constant σ

16. Detection Criteria 1. No effect 2. An effect
3. This is a conservative set of numbers with respect to setting as the break point.

17. Parallel Channels Improve S/NNi
1. For parallel channels the signal is given by
S= m Si
2. For the noise the Ni
3. Therefore

18. Non Equilibrium Noise
1.From Relaxation of Excited States that decay as
2. The Fourier Transform is
3. The power spectral density

19. Noise for Multiple Relaxation Processes
1 Power spectral Density

20. 1/f Noise 1. 1/f noise is generated by processes that have memory.
2. It takes about one pole per decade to synthesis 1/f noise from Gaussian noise in transmission network.

21. Example 1/f noise for a hole in a mylar film
1. For mylar film
b is a geometrical factor Φ +
a is a constant
r is the radius of the hole -
Φ is the applied voltage r
Sφ(f) is the power spectral density

22. Membrane Noise at Low Frequencies.

23. Noise at the Node of Ranvier in a Frog as a Function of Voltage

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

25. New Data
1. At 1 Hz the 1/f noise is about 1000 times the thermal noise and is constant to about 10Hz when it decays as approximately 1/f at about 10KHz.
2. In the Hz ranges the factor is about 100.
3. Note get noise from opening and closing of channels as well as shot noise of the ions

26. 1/f In a Resistor 1.The 1/f noise is added to the thermal noise
And increase with the power W
g is a constant the where
V is the volume

27. Resistor Noise
1. (a) has 4 times as much noise as (b) for the same R

28. Chemical Noise
1 Small perturbations on the basic rate. Many contributing processes.

29. Generalized S/N 1 Total competing molecular change 2. Alternate form
3. Leads to

30. Chemical Noise
1. Overall variation in temperature need to be controlled tightly as reaction rates vary exponentially with Temperature
2. Concentration variations.
3. Vibrations or movement.
4. Stray E and B fields

32. A Different Approach to Cell Structure and the Function of Membranes.
1. Reference
Cells, Gels and the Engines of Life by Gerald H. Pollack Published by Ebner and Sons Seattle Washington. 2001
2 On the Web Human Physiology - Cell structure and function for some good pictures and standard model with channels for Na , K

33. Outline of Material 1. Problems with the current model for cells
2. Some properties water , H2O, Solutes , Ions and cell potential
3. Properties of Gels and Cytoplasm ,
4. Phase Transitions a Mechanism for Action
5. Action potentials.

34. Some Problems. 1. Not enough energy for all the pumps.
2. Need 50 or more types of channels and pumps
2. the concentration ratios and voltages are still there when the membrane is removed.
3. You can still get an action potential to propagate along a nerve cell with no Na or K if you have enough Ca.