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.Zhao Physiol Rev. 85 943-978 (2005)

1

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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

2

Sources of Noise• 3. Shot Noise

• 4. 1/f Noise is seen in Membranes etc.

3

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

4

Minimum Detectable Signal

• 1. Common Basic Approach Require

• 2. Assume and external E field on a spherical cell

1NS

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

fRkTV kT 42

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 cellrEV 1max 5.1

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

2/12/32/1

2/1

min122

4

fLr

fkTdL

fRkTE

cellcelf

rcell= 25µm

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.

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.

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.

Another Approach (S/N)

• Note this approach has the advantage of not depending on the number of measurements but assumes constant σ

Detection Criteria

• 1. No effect 2. An effect • 3. This is a conservative set of numbers with

respect to setting as the break point.

Parallel Channels Improve S/N

• 1. For parallel channels the signal is given byS= m Si

2. For the noise the

Ni

3. Therefore

Ni

mN

Non Equilibrium Noise

• 1.From Relaxation of Excited States that decay as

• 2. The Fourier Transform is

• 3. The power spectral density

Noise for Multiple Relaxation Processes

• 1 Power spectral Density

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.

Membrane Noise at Low Frequencies.

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

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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

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

Resistor Noise

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

Chemical Noise

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

Generalized S/N

• 1 Total competing molecular change

• 2. Alternate form

• 3. Leads to

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

Cell Membrane Cartoon

• 1

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

A Membrane and Cell Model

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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

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.

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.