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Data Analysis
Flow cytometry is concerned with the measurement of the light intensity of a cell or particle, whether it be scattered laser light or fluorescence emitted by a fluorochrome. Light is detected by a photomultiplier tube (PMT) which converts it via an amplifier to a voltage ie electrical output that is proportional to the original fluorescence intensity and the voltage on the PMT. These voltages, which are a continuous distribution, are converted to a discrete distribution by an Analog to Digital converter (ADC) which places each signal into a specific channel depending on the level of fluorescence. The greater the resolution of the ADC, the closer this reflects the continuous distribution.
Flow cytometric data can be displayed using either a linear or a logarithmic scale. The use of a logarithmic scale is indicated in most biological situations where distributions are skewed to the right. In this case the effect is to normalise the distribution - it is said to be Log Normal and the data has been log-transformed. The use of a logarithmic scale is also required when there is a broad range of fluorescence as this can then be compressed; again this is true of most biological distributions. Linear scaling is used when there is not such a broad range of signals, e.g. in DNA analysis and calcium flux measurement.
Linear signals come through a linear amplifier but the logarithmic transformation may be achieved either by a logarithmic amplifier or by the use of Look Up Tables (LUT). Most ADCs in analytical cytometers are 10-bit, i.e., they divide data into 2e10 or 1024 channels, although there is a growing trend to use 12- or 14-bit ADCs to give greater resolution of data.
Data from a single data channel (scatter or fluorescence) is displayed as a histogram in which the x axis is divided into 1024 channels (for a 10-bit ADC). If the data is in a linear scale, the channel number and the linear value for that channel will be easily obtained. On a logarithmic scale, the x axis is still divided into 1024 channels but is displayed as a 4-log decade scale (in general 4 log decades are used).
For log transformed data, we can choose either channel numbers or linear values. We can relate the two as each log decade takes up a quarter of the available channels. Therefore, the first log decade takes up channels 0 to 255 and linear values 1 to 10; the second log decade channels 256-511 and linear values 10-100; the third log decade channels 512-767 and linear values 100-1000; and the fourth log decade channels 768-1023 and linear values 1000-10000. The linear value for a particular channel number may be calculated by taking the anti-log of channel number/256. Or vice versa, a linear value can be converted to a channel number: log(linear value)*256.The simplest type of experiment involves using an immunofluorescent marker to look for a positive sub-population of cells. In this example, on the left are lymphocytes stained with an inappropriate antibody and on the right lymphocytes stained with CD3-FITC, , the percentage of cells expressing the marker can easily be determined by using a marker and if the percentage of positive cells is all that is required the x-axis scale is immaterial.
However, things become more complicated when we want to get some idea of the level of fluorescence. In the example below the two distributions show different levels of fluorescence.
How can these differences be quantified?
To quantify flow cytometric data we need to look at the measures of the distribution of a population. The measures of central tendency are the mode, the mean and the median. How can each of these be used?
The mode is the channel with the most events in it. However, it is rarely used as it is subject to data blips especially if there is a build-up of data in the first or last channel.
The mean is the 'average' and can be either arithmetic or geometric. The arithmetic mean is calculated as Sigma(x)/n, and the geometric mean as n root(a1 x a2 x a3....an). In general, with log-amplified data the geometric mean should be used as it takes into account the weighting of the data distribution, and the arithmetic mean should be used for linear data or data displayed on a linear scale.
The median is the central value, i.e., the 50th percentile, where half the values are above and half below.
The mean and median can both be used as measures to quantitate cellular fluorescence. In a linear distribution the mean and median are easily calculated, but this is not the case with log amplified data and problems can arise here. We have seen we can use either linear values or channel numbers; how can we use the mean and median to relate levels of fluorescence intensity?
To compare absolute fluorescence values, it is best to use linear values as these can be directly compared, i.e., a cell with a linear value of 100 is 10 times brighter than a cell with a linear value of 10. This cannot be done with channel number - a cell in channel 512 is still 10 times as bright as one in channel 256- we have to talk about 'channel shifts', i.e., a shift in fluorescence intensity of 256 channels.
Logic and consistency are the keys to successful data analysis in flow cytometry, and realising that at best flow cytometry is only semi-quantitative. It is excellent for relative comparisons but more problematic when asking for absolute quantitative data. If you have any queries or questions, we are always available for advice!
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