Biomedical Engineering Reference
In-Depth Information
14.3 SHOWING COORDINATED EXPRESSIONS
What is interesting about this paradigm shift is that we have always known the
proper way of analyzing and displaying our data. In the 1980s, Loken and Wells
[2, 3] described B lymphoid maturation with charts such as the one shown in
Figure 14.2. The changes in antigenic expression of markers such as CD19, CD34,
CD10, CD20, CD22, and CD45 were shown against a common axis. There were
never any units for this axis. It was simply used as a means of showing coordinated
changes in expression. We always knew that these charts provided valuable
information about the coordinated expression of a large number of parameters, but
we never realized that it was possible to compute this axis or one like it directly from
the data.
14.3.1 Time As a Parametric Parameter
What units should we use for this axis? Since it normally shows some kind of
progression, our first guess would be some sort of time unit. This makes sense since
cellular progressions are really just a set of kinetic reactions. There are a host of papers
that attempt to describe systems with time-dependent differential equations [4-6].
The problem, of course, is that when we take our snapshot set of measurements on
cells, we lose time. This means that all the rate constants for these differential
equations must be measured from other experiments and it must be assumed that the
rate constants are applicable to the cells being measured. Valuable information can be
gleaned from this approach [7], but it does put limits on the scope and complexity of
the system being investigated.
14.3.2 Relative Time or Cell Age
In order to explain how to create this common axis and parameter, we will first visit a
figure that I first used in my PhD thesis [8] back in 1979 to clarify the implicit cell
cycle relations in a DNA histogram (see Figure 14.3, top panel). On the x-axis is
relative cell age, ranging from 0 to 1. When a cell has a cell age of 0, it has just been
created after its parent cell
s division and when it has a cell age of 1, it is just about to
divide into two daughter cells. The cell depicted in this figure begins to synthesize
DNA at a cell age of 0.4 and stops at 0.8when theDNA is duplicated. The phases of the
cell cycle are defined by these two cell ages and are normally represented as G1, S, and
G2M.
14.3.3 Number of Cells Versus Cell Age
We can use this same cell age parameter to look at the number of cells that are at each
relative cell age unit (see Figure 14.3, bottom panel). We used to state that for
exponentially growing population with no cell loss, the number of cells is a decreasing
exponential. Since that ideal relation is rarely found in practice, we will make no
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