Flow cytometry

© 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


Linear and Log circuits

• Linear circuits• Logarithmic circuits• Dynamic range• Fluorescence compensation


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

•


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


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


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


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


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.


Log/lin display


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)


4 colors - simultaneous collection

Emission wavelength (nm)530 580 630 680 730 780

FITC PE PE-TR

PE-CY5


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)


Fluorescence compensation

• Discussed later in series

Precision, sensitivity and accuracy

3rd Ed. Shapiro p 171-177


Precision - C.V.

• Precision: CV• Sensitivity• MESF Units• Accuracy and Linearity• Noise• Background• Laser noise


Conclusion

Shapiro’s 7th Law of Flow Cytometry:

No Data Analysis Technique Can Make Good Data Out of Bad Data!!!


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


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.


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


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.


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)



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



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



Determination of Unknowns

CellsCells

StandardsStandards

200 400 600 80001

10

100

1,000

10,000

100,000

AntibodyBindingCapacity

DetectionLevel

Non-specificBinding

SpecificBinding



Important Components• MESF Units

– Molecules of Equivalent Soluble Fluorochrome

• Accuracy and Linearity• Noise• Background

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Flow cytometry

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