BMS 631 - LECTURE 9
Flow Cytometry: Theory
J. Paul Robinson
Professor of Immunopharmacology
Professor of Biomedical Engineering
Purdue University
Data Collection:
Linear, log, ratios….
3rd Ed.Shapiro 163-171
Hansen Hall, B050
Purdue University
Office: 494 0757
Fax 494 0517
Email: robinson@flowcyt.cyto.purdue.edu
WEB http://www.cyto.purdue.edu
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© 1988-2002 J.Paul Robinson, Purdue University Cytometry Laboratories BMS 602 LECTURE 9.PPT
Linear and Log circuits
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Linear circuits
Logarithmic circuits
Dynamic range
Fluorescence compensation
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© 1988-2002 J.Paul Robinson, Purdue University Cytometry Laboratories BMS 602 LECTURE 9.PPT
Linear circuits
• Output signal is proportion to the sum and/or difference
of their input signal
• To collect any signal based on stoichiometric
relationships e.g. DNA staining you must have 10 bit
resolution
• The higher the accuracy desired the hire the number of
bits must be collected
• Current instruments have 4 decade logarithmic scales
thus an ADC must provide at least accuracy to 1/10,000
of the full scale which equals 1 mV in a 0-10 V scale
• Thus to achieve this accuracy level you must have at
least 14 bits of data (16,384 bits) since 13 bits would
only be 8,192 bits
•
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© 1988-2002 J.Paul Robinson, Purdue University Cytometry Laboratories BMS 602 LECTURE 9.PPT
Why use linear amps?
• The problem with compensation is that it needs to be
performed on linear data, not logarithmic data. Thus, either
the entire electronics must be built in linear electronics,
which requires at least 16 bit A-D converters, or a
supplementary system must be inserted between the preamp
and the display.
• We need the dynamic range for immunologic type markers,
but we can’t calculate the compensation easily using log amps
- certainly not without complex math.
• Flow cytometers amplify signals to values ranging between 010V before performing a digital conversion.
• Assuming this, with 4 decades and a maximum signal of 10 V
we have:
Factor reduction 10
pulse output
1
100
100mv
1000
10mv
10000
1mv
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© 1988-2002 J.Paul Robinson, Purdue University Cytometry Laboratories BMS 602 LECTURE 9.PPT
How many bits?
• Assume we convert linear analog signals using an 8
bit ADC - we have 256 channels of range (2n) (28256) corresponding to the range 0-10 V
• Channels difference is 10/256=40mV per channel
1V
10V
100mV
0
50
100
150
Channels
200
250
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© 1988-2002 J.Paul Robinson, Purdue University Cytometry Laboratories BMS 602 LECTURE 9.PPT
Ideal log amp
1V
100 mV
10 V
Linear
0
Log amp
1 mV
50
10 mV
100
150
100 mV
200
1V
250
10 V
Log
0
50
100
150
200
250
Channels
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© 1988-2002 J.Paul Robinson, Purdue University Cytometry Laboratories BMS 602 LECTURE 9.PPT
Where is the inaccuracy?
• Consider the 14 bit data (16,384 channels)
• The smallest signal on a 0-10volt scale will be 610 uV per
channel
• Thus a 1 channel change produces a value of 1220 uV or 100%
possible error at the low end – since the bottom 10mV of this
scale is represented by channels 1-16, the voltage at channel 16
is 9765 mV or at ch# 15 is 9765 uV or an error of about 6%
• This is an unacceptable high error at the low end so we must
try to digitize at a higher bit rate say for example 16 bits (65,
536)
• Now the same range as above a 1mV signal will appear in ch# 7
and a 10 mV signal in Ch# 65 giving an error of 6% at the
bottom end and only 2% at the top end
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© 1988-2002 J.Paul Robinson, Purdue University Cytometry Laboratories BMS 602 LECTURE 9.PPT
Log amps & dynamic range
Compare the data plotted on a linear scale (above) and a 4 decade log scale (below).
The date are identical, except for the scale of the x axis. Note the data compacted
at the lower end of the the linear scale are expanded in the log scale.
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© 1988-2002 J.Paul Robinson, Purdue University Cytometry Laboratories BMS 602 LECTURE 9.PPT
Log/lin display
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© 1988-2002 J.Paul Robinson, Purdue University Cytometry Laboratories BMS 602 LECTURE 9.PPT
Ratio circuits
• Ratio circuits are analog circuits which produce an output
proportional to the ratio of the 2 input signals.
• They are usually made from modules called analog multipliers.
• Examples are calculation of surface density or antigenic receptor
sites by dividing the number of bound molecules by the cell surface
area.
• E.g. Could use 2/3 power of volume to obtain surface area - but few
cytometers make this parameter so can use the square of the cell
diameter of scatter instead to approximate.
• pH can also be measured using ratio circuits
• Calcium ratio (using Indo-1) is also used (discussed in later lecture)
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© 1988-2002 J.Paul Robinson, Purdue University Cytometry Laboratories BMS 602 LECTURE 9.PPT
4 colors - simultaneous
collection
FITC
PE
PETR
PE-CY5
530
580 630
680 730
Emission wavelength (nm)
780
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© 1988-2002 J.Paul Robinson, Purdue University Cytometry Laboratories BMS 602 LECTURE 9.PPT
Digital Signal Processing (DSP)
• DSP processors signal continuously at very high rates
• e.g. Take a compact disc which samples at 44.1kHz
• Two conversions are performed (one for each stereo
channel) of at least 16 bit resolution are performed every
22.7msec (44.1k/1 second)
• Thus for 16 bit data (2 bytes) at 2 samples per measurement
we would have 2 x 44.1 x 2 bytes = 176400 bytes/sec =
10,584,000 bytes/min = 635,040,000 bytes/hour (=620
Mbytes/hour)
• So for really high speed samples we need very high sampling
indeed around 20-40 MHz
• This is very costly and is now being achieved at different
levels by the manufacturers and essentially removes a huge
amount of electronics (pulse width, integration circuits,
thresh-holding circuits, comparator circuits, etc)
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© 1988-2002 J.Paul Robinson, Purdue University Cytometry Laboratories BMS 602 LECTURE 9.PPT
Fluorescence compensation
• Discussed later in series
Precision, sensitivity and accuracy
3rd Ed. Shapiro p 171-177
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© 1988-2002 J.Paul Robinson, Purdue University Cytometry Laboratories BMS 602 LECTURE 9.PPT
Precision - C.V.
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•
•
•
•
•
•
Precision: CV
Sensitivity
MESF Units
Accuracy and Linearity
Noise
Background
Laser noise
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© 1988-2002 J.Paul Robinson, Purdue University Cytometry Laboratories BMS 602 LECTURE 9.PPT
Conclusion
Shapiro’s 7th Law of Flow Cytometry:
No Data Analysis Technique Can Make
Good Data Out of Bad Data!!!
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© 1988-2002 J.Paul Robinson, Purdue University Cytometry Laboratories BMS 602 LECTURE 9.PPT
Coefficient of Variation
%CV Definition =
St.Dev x 100
MEAN
CV=3.0
CV=3.0
MEAN
Crucial in establishing:
• alignment
• Fluidic stability
• Staining of cells
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© 1988-2002 J.Paul Robinson, Purdue University Cytometry Laboratories BMS 602 LECTURE 9.PPT
Quantitative Units - ABC
Antiboidy Binding Capacity
• The number of antibodies that bind to a
specific cell or microbead population
• Note: ABCs are not necessarily the number
of antigens or epitopes on the cell.
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© 1988-2002 J.Paul Robinson, Purdue University Cytometry Laboratories BMS 602 LECTURE 9.PPT
Detection Threshold (noise)
1,000,000
Antibody Binding Capacity
100,000
10,000
1,000
100
10
1
0
50
Mean
100
98%
150
200
250
Histogram Channel
Slide from Dr. Abe Schwartz
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© 1988-2002 J.Paul Robinson, Purdue University Cytometry Laboratories BMS 602 LECTURE 9.PPT
What is the Importance of
the Detection Threshold?
Indicates the lowest level that
a specific antibody may be
detected by the instrument.
Indicates if the noise level
will interfere with the assay.
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© 1988-2002 J.Paul Robinson, Purdue University Cytometry Laboratories BMS 602 LECTURE 9.PPT
Coefficient of Response
• The slope of the calibration line determined from
a 256 Histogram Scale
• Also indicates the number of Histogram Channels
per Decade of amplification.
Examples:
• Coef of Res = 256/4 = 64.0 HC/Decade
• (4 decade amplifier) 85.3 HC/Decade
• Coef of Res = 256/3 = (3 decade amplifier)
Slide from Dr. Abe Schwartz
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© 1988-2002 J.Paul Robinson, Purdue University Cytometry Laboratories BMS 602 LECTURE 9.PPT
Zero Channel Value?
• It is the intercept of the calibration line on
the ABC axis.
• represents the lowest ABC value
theoretically observable in the Window of
Analysis.
• It anchors the left hand corner of the
Window of Analysis in Sample Space
Slide from Dr. Abe Schwartz
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© 1988-2002 J.Paul Robinson, Purdue University Cytometry Laboratories BMS 602 LECTURE 9.PPT
Comparison of Windows of Analysis
in Sample Space
Coef. of Res = 85.3
Coef. of Res = 64.0
(3 decade log amp)
(4 decade Log amp)
255
Zero
Channel
Value
0
ABC Sample Space
Slide from Dr. Abe Schwartz
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© 1988-2002 J.Paul Robinson, Purdue University Cytometry Laboratories BMS 602 LECTURE 9.PPT
Determination of Unknowns
Antibody
Binding
Capacity
Specific
Binding
100,000
10,000
Non-specific
Binding
Detection
Level
1,000
Cells
100
Standards
10
1
0
200
400
600
800
Slide from Dr. Abe Schwartz
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© 1988-2002 J.Paul Robinson, Purdue University Cytometry Laboratories BMS 602 LECTURE 9.PPT
Important Components
• MESF Units
– Molecules of Equivalent Soluble
Fluorochrome
• Accuracy and Linearity
• Noise
• Background
http://www.cyto.purdue.edu
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© 1988-2002 J.Paul Robinson, Purdue University Cytometry Laboratories BMS 602 LECTURE 9.PPT