Download - Flow cytometry
Page 1© 1988-2002 J.Paul Robinson, Purdue University Cytometry Laboratories BMS 602 LECTURE 9.PPT
BMS 631 - LECTURE 9Flow Cytometry: Theory
Hansen Hall, B050Purdue UniversityOffice: 494 0757Fax 494 0517Email: [email protected]
WEB http://www.cyto.purdue.edu
Data Collection: Linear, log, ratios….
3rd Ed.Shapiro 163-171
J. Paul RobinsonProfessor of ImmunopharmacologyProfessor of Biomedical EngineeringPurdue University
Page 2© 1988-2002 J.Paul Robinson, Purdue University Cytometry Laboratories BMS 602 LECTURE 9.PPT
Linear and Log circuits
• Linear circuits• Logarithmic circuits• Dynamic range• Fluorescence compensation
Page 3© 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
•
Page 4© 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 0-10V before performing a digital conversion.
• Assuming this, with 4 decades and a maximum signal of 10 V we have:
10 100 1000 10000
1 100mv 10mv 1mv
Factor reduction
pulse output
Page 5© 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) (28-256) corresponding to the range 0-10 V
• Channels difference is 10/256=40mV per channel
0 50 100 150 200 250
10V1V
100mV
Channels
Page 6© 1988-2002 J.Paul Robinson, Purdue University Cytometry Laboratories BMS 602 LECTURE 9.PPT
Ideal log amp
0 50 100 150 200 250
10 V1 V100 mV
0 50 100 150 200 250
10 V1 mV
Channels
Linear
Log
1 V100 mV10 mVLog amp
Page 7© 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
Page 8© 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.
Page 9© 1988-2002 J.Paul Robinson, Purdue University Cytometry Laboratories BMS 602 LECTURE 9.PPT
Log/lin display
Page 10© 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)
Page 11© 1988-2002 J.Paul Robinson, Purdue University Cytometry Laboratories BMS 602 LECTURE 9.PPT
4 colors - simultaneous collection
Emission wavelength (nm)530 580 630 680 730 780
FITC PE PE-TR
PE-CY5
Page 12© 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 22.7sec (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)
Page 13© 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
Page 14© 1988-2002 J.Paul Robinson, Purdue University Cytometry Laboratories BMS 602 LECTURE 9.PPT
Precision - C.V.
• Precision: CV• Sensitivity• MESF Units• Accuracy and Linearity• Noise• Background• Laser noise
Page 15© 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!!!
Page 16© 1988-2002 J.Paul Robinson, Purdue University Cytometry Laboratories BMS 602 LECTURE 9.PPT
Coefficient of Variation
Crucial in establishing:• alignment• Fluidic stability• Staining of cells
MEAN
CV=3.0
CV=3.0
%CV Definition = St.Dev x 100MEAN
Page 17© 1988-2002 J.Paul Robinson, Purdue University Cytometry Laboratories BMS 602 LECTURE 9.PPT
Quantitative Units - ABCAntiboidy 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.
Page 18© 1988-2002 J.Paul Robinson, Purdue University Cytometry Laboratories BMS 602 LECTURE 9.PPT
0 50 100 150 200 250
1
10
100
1,000
10,000
100,000
1,000,000
Histogram Channel
An
tib
od
y B
ind
ing
Cap
acit
y
Mean98%
Detection Threshold (noise)
Slide from Dr. Abe Schwartz
Page 19© 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.
Page 20© 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
Page 21© 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
Page 22© 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
(3 decade log amp)
Coef. of Res = 64.0
(4 decade Log amp)
ABC Sample Space
Zero ChannelValue
255
0
Slide from Dr. Abe Schwartz
Page 23© 1988-2002 J.Paul Robinson, Purdue University Cytometry Laboratories BMS 602 LECTURE 9.PPT
Determination of Unknowns
CellsCells
StandardsStandards
200 400 600 80001
10
100
1,000
10,000
100,000
AntibodyBindingCapacity
DetectionLevel
Non-specificBinding
SpecificBinding
Slide from Dr. Abe Schwartz
Page 24© 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