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ECEN 5341/4341
Lecture 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
Signal to Noise and Signal Detection
• 1. Some sources of noise.
– A. Thermal Noise Pn = kTB
– B. Negative Temperatures and Population inversion
•
•
N2
•
N1
E2
E1
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
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Minimum Detectable Signal
• 1. Common Basic Approach Require
S
1
N
• 2. Assume and external E field on a spherical
cell
Minimum Detectable Signal
J. Weaver, D. Astumian , Science 01/26/1990
• Assume thermal noise
V 
2
kT
 4 RkTf
• 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
Minimum Detectable Signal
J. Weaver, D. Astumian , Science 01/26/1990
•
C= εoεr4πr2/d
• For a sphere in a uniform field
Vmax  1.5E1rcell
The result for minimum E detectable is
Minimum Detectable Signal
J. Weaver, D. Astumian , Science 01/26/1990
• For a long thin Cylinder
Where τ is the exposure time
Emin f
4 RkTf
 kTdf 

 2 2

Lcel
 
1/ 2
1
1/ 2 3 / 2
rcell
L  f 
1/ 2
Typical values for L= 150µm,Δf=10Hz rcell= 25µm
Emin= 8x10-5 V/ m
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.
Ni
Parallel Channels Improve S/N
• 1. For parallel channels the signal is given by
S= m Si
2. For the noise the
N  m Ni
3. Therefore
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
19
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
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Biological Amplifiers
• http://www.unmc.edu/physiology/Mann/man
n13.html
• Neural Transmitter Releases up to 104 calcium ions
• Need to overcome the electrical threshold for firing
A Membrane and Cell Model
29
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.