BatchKi Reference Manual

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[Progress]

This section of the initialization file controls the analysis of reaction progress curves. The default values are listed below.

[Progress]
  AutomaticDegree = no
  AutomaticDegreeTuning = 1.25
  ExcludeFirstPoint = no
  Extrapolate = no
  MaxDegree = 1
  MaxSeconds = 1000000000
  MinSeconds = 0
  Model = polynomial
  RobustRegression = yes

Parameter Model

This parameter can have one of two values:

• Model = polynomial
• Model = exponential

If Model is set to polynomial, the fitting model for the reaction progress curves are Chebyshev orthogonal polynomials defined in the Appendix.

If Model is set to exponential, the fitting model for the reaction progress curves are exponentials defined by equation 4.2, where $A$ is the observed experimental signal (e.g., absorbance), $A_0$ is the offset on the signal axis, $A_1$ and $A_2$ are exponential amplitudes, $k_1$ and $k_2$ are the corresponding rate constants, and $t$ is reaction time.

$$A = A_0 + A_1 \exp \left ( -k_1 t \right ) + A_2 \exp \left ( -k_2 t \right ) + ...$$ (4.2)

Parameter MaxDegree

This parameter can have one of two values:

• MaxDegree = 1
• MaxDegree = 2

The exact interpretation of this parameter depends on whether Model is set to polynomial or exponential.

Parameter MaxDegree : Polynomial fit

When MaxDegree is set to 1, the program will fit each progress curve to a polynomial with a degree at most one, that is, to the straight line. If the AutomaticDegree parameter is set to `yes' (see below), and in the special cases that the signal does not change at all within the experimental noise, the program will simply compute an average value (``polynomial degree zero''). However, if AutomaticDegree is set to `no', the program will always fit each progress curve to the straight line.

When MaxDegree is set to 2, the program will fit each progress curve to a polynomial with a degree at most two, that is, to the quadratic parabola. Further details in this regard depend on the value of the parameter AutomaticDegree (see Table 4.1 below).

Parameter MaxDegree : Exponential fit

When MaxDegree is set to 1, the program will fit each progress curve to a first-degree exponential, that is, assuming that $A_2$ is zero in equation 4.2. If the AutomaticDegree parameter is set to `yes', and in the special cases that the signal does not change at all within the experimental noise, the program will simply compute an average value (``exponential degree zero''). However, if AutomaticDegree is set to `no', the program will always fit each progress curve to the first-degree exponential.

When MaxDegree is set to 2, the program will fit each progress curve to an exponential with a degree at most two, that is, assuming that $A_2$ is nonzero in equation 4.2.

Parameter AutomaticDegree

This parameter can have two possible values:

• AutomaticDegree = yes
• AutomaticDegree = no

When AutomaticDegree is set to `no', the program always fits all progress curves to the polynomial or exponential of the degree specified by parameter MaxDegree.

When the parameter AutomaticDegree is set to `yes', the program will decide on the most suitable polynomial or exponential degree, up to the degree specified by the parameter MaxDegree. For the polynomial fit, the various possibilities are summarized in Table 4.1.

Table 4.1: Fitting of progress curves: linear or quadratic model

Combination of parameters	Action
MaxDegree = 1 AutomaticDegree = no	Fit all progress curves to straight line.
MaxDegree = 2 AutomaticDegree = no	Fit all progress curves to quadratic parabola.
MaxDegree = 1 AutomaticDegree = yes	Decide on the most suitable polynomial degree for each progress curve, up to first degree (straight line). In some cases compute a simple average (offset on the signal axis) and set the reaction velocity exactly to zero.
MaxDegree = 2 AutomaticDegree = yes	Decide on the most suitable polynomial degree for each progress curve, up to second degree (quadratic parabola). In some cases compute a simple average (offset) and set the reaction velocity exactly to zero. Straight-line fit is also possible.

Parameter AutomaticDegreeTuning

This parameter controls the algorithm for the automatic determination of the polynomial degree. It is applicable only if the control parameter AutomaticDegreeTuning is set to yes. The problem is that sometimes the automatic polynomial degree algorithm results in best-fit model curves that are overparametrized.

In other words, a data set that looks to us that it should be described by a straight line is fitted as a quadratic parabola. If this happens too often for a particular type of experiment, we might adjust the value of AutomaticDegreeTuning to values that are progressively higher than 1.0. The parameter should not have a value smaller than 1.10. A value of 1.25 is probably suitable for most types of enzyme assays. If the best-fit curves still look too ``floppy'', then a value of 1.50 or even 2.0 might be used.

AutomaticDegreeTuning = 1.10	make the polynomial model more flexible
AutomaticDegreeTuning = 1.25	default value
AutomaticDegreeTuning = 1.50	make the polynomial model ``stiffer'' (bias toward the straight line)

Parameter RobustRegression

This parameter controls whether the progress curves will be analyzed by using the standard least-squares analysis, or whether the robust regression analysis [7,8] will be applied instead. It has two possible values:

• RobustRegression = yes
• RobustRegression = no

If RobustRegression is set to `no', the progress curves are subjected to the standard least-squares regression. If the parameter is set to `yes', the statistical analysis of progress curves is performed by minimizing the sum of absolute deviations between the data and the fitting model (typically a polynomial of the given degree).

Robust regression analysis is particularly useful for automatic treatment of outlying data points, which could arise in the course of the enzyme assay. Data points that deviate very significantly from the rest of the reaction progress curve will be de-emphasized under robust regression.

Parameter ExcludeFirstPoint

This parameter can have two possible values:

• ExcludeFirstPoint = yes
• ExcludeFirstPoint = no

In many cases the progress curves have a very regular shape (no outlying points) except the very first point, which can strongly deviate from the rest of the progress curve. Because this special type of defect occurs quite frequently, the user has a provision to automatically exclude the very first data point from all progress curves on the given plate, by setting ExcludeFirstPoint to `yes'. If ExcludeFirstPoint is set to `no' (the default value of this parameter), no action is taken.

Parameter Extrapolate

This parameter can have two possible values:

• Extrapolate = yes
• Extrapolate = no

This parameter can be used in those rare circumstances when the initial reading of time is nonzero for some or all reaction progress curves. If Extrapolate is set to `yes', the initial reaction rate is computed with extrapolation to zero reaction time. If Extrapolate is set to `no' (the default value of this parameter), no action is taken.

Parameter MaxSeconds

This parameter defines the upper bound on the reaction time, in seconds, to be considered for analysis. This is useful for the exclusion of ``late'' portions of all progress curves on the given plate, if and when those segments of the raw experimental data are generally not informative.

For example, the following code with exclude from analysis all data points beyond reaction time $t = 1$ hour:

[Progress]
   ...
   MaxSeconds = 3600

Parameter MinSeconds

This parameter defines the lower bound on the reaction time, in seconds, to be considered for analysis. This is useful for the exclusion of ``early'' portions of all progress curves on the given plate, if and when those segments of the raw experimental data are generally considered anomalous or otherwise not informative. For example, if all progress curves in the given assay exhibit a sigmoid delay phase (for reasons that might not be fully understood), it is possible to exclude the mixing delay phase from analysis.

For example, the following code will exclude the first three minutes of every progress curve from statistical analysis:

[Progress]
   ...
   MinSeconds = 180

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Petr Kuzmic | Jul 12 2008