BMS 631 LECTURE 9 Flow Cytometry Theory J

BMS 631 - LECTURE 9 Flow Cytometry: Theory J. Paul Robinson Professor of Immunopharmacology Professor of Biomedical Engineering Purdue University Data Collection: Linear, log, ratios…. 3 rd Ed. Shapiro 163 -171 Hansen Hall, B 050 Purdue University Office: 494 0757 Fax 494 0517 Email: robinson@flowcyt. cyto. purdue. edu WEB http: //www. cyto. purdue. edu Page 1 © 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 2 © 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 m. V 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 3 © 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 010 V 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 mv 1000 10 mv 10000 1 mv Page 4 © 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 (2 n) (28256) corresponding to the range 0 -10 V • Channels difference is 10/256=40 m. V per channel 1 V 100 m. V 0 50 100 150 Channels 200 250 Page 5 © 1988 -2002 J. Paul Robinson, Purdue University Cytometry Laboratories BMS 602 LECTURE 9. PPT

Ideal log amp 1 V 100 m. V 10 V Linear 0 Log amp 1 m. V 50 10 m. V 100 150 100 m. V 200 1 V 250 10 V Log 0 50 100 150 Channels 200 250 Page 6 © 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 -10 volt scale will be 610 u. V per channel • Thus a 1 channel change produces a value of 1220 u. V or 100% possible error at the low end – since the bottom 10 m. V of this scale is represented by channels 1 -16, the voltage at channel 16 is 9765 m. V or at ch# 15 is 9765 u. V 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 1 m. V signal will appear in ch# 7 and a 10 m. V signal in Ch# 65 giving an error of 6% at the bottom end and only 2% at the top end Page 7 © 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 linear scale are expanded in the log scale. Page 8 © 1988 -2002 J. Paul Robinson, Purdue University Cytometry Laboratories BMS 602 LECTURE 9. PPT

Log/lin display Page 9 © 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. • p. H can also be measured using ratio circuits • Calcium ratio (using Indo-1) is also used (discussed in later lecture) Page 10 © 1988 -2002 J. Paul Robinson, Purdue University Cytometry Laboratories BMS 602 LECTURE 9. PPT

4 colors - simultaneous collection FITC PE PETR PE-CY 5 530 580 630 680 730 Emission wavelength (nm) 780 Page 11 © 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. 1 k. Hz • Two conversions are performed (one for each stereo channel) of at least 16 bit resolution are performed every 22. 7 msec (44. 1 k/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 12 © 1988 -2002 J. Paul Robinson, Purdue University Cytometry Laboratories BMS 602 LECTURE 9. PPT

Fluorescence compensation • Discussed later in series Precision, sensitivity and accuracy 3 rd Ed. Shapiro p 171 -177 Page 13 © 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 14 © 1988 -2002 J. Paul Robinson, Purdue University Cytometry Laboratories BMS 602 LECTURE 9. PPT

Conclusion Shapiro’s 7 th Law of Flow Cytometry: No Data Analysis Technique Can Make Good Data Out of Bad Data!!! Page 15 © 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 MEAN Crucial in establishing: • alignment • Fluidic stability • Staining of cells Page 16 © 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. Page 17 © 1988 -2002 J. Paul Robinson, Purdue University Cytometry Laboratories BMS 602 LECTURE 9. PPT

Detection Threshold (noise) 1, 000 Antibody Binding Capacity 100, 000 1, 000 10 1 0 50 Mean 100 98% 150 200 250 Histogram Channel Slide from Dr. Abe Schwartz Page 18 © 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 19 © 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 20 © 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 21 © 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 Page 22 © 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 Page 23 © 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 Page 24 © 1988 -2002 J. Paul Robinson, Purdue University Cytometry Laboratories BMS 602 LECTURE 9. PPT