Page 1 © J.Paul Robinson, Purdue University Cytometry Laboratories BMS 602 LECTURE 9.PPT BMS LECTURE 9 Flow Cytometry: Theory Hansen Hall, B050 Purdue University Office: Fax WEB Data Collection: Linear, log, ratios…. 3 rd Ed.Shapiro J. Paul Robinson Professor of Immunopharmacology Professor of Biomedical Engineering Purdue University

Page 2 © 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 © 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 © 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: mv 10mv 1mv Factor reduction pulse output

Page 5 © 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 ) ( ) corresponding to the range 0-10 V Channels difference is 10/256=40mV per channel V 1V 100mV Channels

Page 6 © J.Paul Robinson, Purdue University Cytometry Laboratories BMS 602 LECTURE 9.PPT Ideal log amp V 1 V 100 mV V1 mV Channels Linear Log 1 V100 mV10 mV Log amp

Page 7 © 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 © 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 © J.Paul Robinson, Purdue University Cytometry Laboratories BMS 602 LECTURE 9.PPT Log/lin display

Page 10 © 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 © J.Paul Robinson, Purdue University Cytometry Laboratories BMS 602 LECTURE 9.PPT 4 colors - simultaneous collection Emission wavelength (nm) FITC PE PE- TR PE-CY5

Page 12 © 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 22.7  sec (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 = 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 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 © 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

Page 14 © 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 © 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 © 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 Definition = St.Dev x 100 MEAN

Page 17 © 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 18 © J.Paul Robinson, Purdue University Cytometry Laboratories BMS 602 LECTURE 9.PPT ,000 10, ,000 1,000,000 Histogram Channel Antibody Binding Capacity Mean 98% Detection Threshold (noise) Slide from Dr. Abe Schwartz

Page 19 © 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 © 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 © 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 © 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 Channel Value Slide from Dr. Abe Schwartz

Page 23 © J.Paul Robinson, Purdue University Cytometry Laboratories BMS 602 LECTURE 9.PPT Determination of UnknownsCellsStandards ,000 10, ,000 Antibody Binding Capacity Detection Level Non-specific Binding Specific Binding Slide from Dr. Abe Schwartz

Page 24 © 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