Biology Reference
In-Depth Information
techniques to detect significant increases followed by significant
decreases in the time series such as done by CLUSTER.
This algorithm suffers from three potential weaknesses. First, although it
can easily be justified under the assumptions of the central limit
theorem, some might find the assumption that the secretion event could
be described by a Gaussian distribution questionable. Second, circa
1987 computer hardware was substantially slower than today's personal
computers. Thus, the original multiparameter deconvolution algorithm
and software did not include the most rigorous statistical tests for the
existence of a secretion event, simply because the required computer
resources were not available in 1987. Third, the user had to provide
estimates, for the exact number of secretion events and their
approximate locations and sizes. The CLUSTER method can be used to
provide those estimates, but, as this method is just one out of many,
the choice of initial values for the parameters will be somewhat
subjective. Thus, multiparameter deconvolution alternatives that are
more flexible with regard to assumptions and input information would
be preferable.
One such algorithm, called PULSE, is a waveform-independent
deconvolution method that is not based on the assumption that the
secretion function is of the form given in Equation (9-18). In PULSE, the
secretory pulses are assumed to have a general form that increases
from a nadir to a peak and then decreases back to a nadir. It also
eliminates the requirement to specify the number and approximate
positions of the secretory events. Several other deconvolution techniques
have been developed as described in Johnson and Veldhuis (1995) and
Johnson et al. (2004) in an attempt to automate the original
multiparameter deconvolution technique (e.g., PULSE2 and PULSE4).
The history of these automatic algorithms closely parallels the
developments of available computer hardware. Faster computers mean
that more computationally intensive statistical tests can be utilized.
10
2
0
−
2
Figures 9-24 and 9-25 present the results of applying of the PULSE,
method to the LH and GH time series from Figures 9-5 and 9-6. The
lower panel of these figures is the calculated secretion rate as a function
of time, S(t) in Eq. (9-17). The upper panel of these figures presents
the calculated concentration as a function of time, C(t), from Eq. (9-13).
The original data points are represented as vertical error bars. The
middle panel describes the corresponding residuals, R
i
, for the values of
the parameters minimizing the weighted least-squares norm in
Eq. (9-19):
1
0.1
200
400
600
800 1000 1200 1400
Minutes
FIGURE 9-24.
Analysis of the luteinizing hormone data in
Figure 9-5 by multiparameter deconvolution
predicted 10 secretion events with HL
2
X
X
Y
i
C
ð
t
i
Þ
R
i
:
Variance of Fit
¼
¼
(9-19)
¼
46.5
SEM
i
i
i
minutes, C(0)
¼
8.02, S
0
¼
0.0478, and Secretion
SD
3.1 minutes. The concentrations and
secretion rates are expressed on a logarithmic
scale to emphasize the small secretion events.
¼
Based on a visual inspection, it appears that the secretion patterns shown
in Figures 9-24 and 9-25 provide a good description of the actual
