ECEN 5341/4341 Lecture 15 Feb 17,2014

1. . ECEN 5341/4341Lecture 15 Feb 17,2014 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.ZhaoPhysiol Rev. 85 943-978 (2005)

2. Signal to Noise and Signal Detection • 1. Some sources of noise. • A. Thermal Noise Pn = kTB • B. Negative Temperatures and Population inversion • E2 N2 • E1 N1

3. Sources of Noise • 3. Shot Noise • 4. 1/f Noise is seen in Membranes etc.

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

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

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

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

8. Minimum Detectable SignalJ. 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

9. 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.

10. 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. 2. m is the number of measurements 3.

11. Standard Approach to Determining an Effect • 1. P value represents the probability that the difference in the value of the means is random. • 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.

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

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

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

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

16. Noise for Multiple Relaxation Processes • 1 Power spectral Density

17. 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.

18. Membrane Noise at Low Frequencies.

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

20. 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 50- 60Hz ranges the factor is about 100. • 3. Note get noise from opening and closing of channels as well as shot noise of the ions

21. 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

22. Resistor Noise • 1. a has 4 times as much noise as b for the same R

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

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

25. 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

26. Cell Membrane Cartoon

27. 1

28. Biological Amplifiers • http://www.unmc.edu/physiology/Mann/mann13.html • Neural Transmitter Releases up to 104 calcium ions • Need to overcome the electrical threshold for firing

29. A Membrane and Cell Model

30. 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

31. 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.

32. 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.