
Chapter 1
The Rationale for Kinetic Modeling
There are several good reasons for adding kinetic modeling to
your skills for biological investigation. First, experience has
shown, over and over again, that there is much more information
contained in dynamic biological data than can be extracted by
simple inspection. So it's a matter of efficient use of
resources; if the data you've already collected contain answers
that no one knows, then an investment in computing can give you a
competitive advantage both in new knowledge and in productive
experimental design. Second, building successful dynamic or
kinetic models is heavily dependent on knowing or discovering the
underlying biological mechanisms. We are not interested in
correlational models where cause and effect are often obscure,
but instead are interested in physical and chemical processes
that are known or hypothesized to take place in the biological
system of interest.
Mechanism and dynamics are intimately related, and much of the
value of kinetic modeling lies in the unique ability of dynamic
experiments to reveal new and useful information about inherently
complex biological control systems. One simple illustration of
this point is provided by the diagram below:
The graph shows an experimental observation recorded as a
function of time. During the time indicated by the solid bar, a
physiological or pharmacological perturbation is applied to the
biological system and its effect on the observation is recorded.
Before the perturbation, the system is in steady state. In
response to the perturbation, the system passes through a
transient before arriving at a new steady state. If you, as an
investigator, restrict yourself to measurements made in the two
steady states, you are discarding valuable information on
mechanism. This is because each of the different transients in
figure 1 corresponds to a different underlying mechanism, and
none of the information on these mechanisms is available if only
the two steady state values are recorded. Our overall rationale
for bringing modeling tools to bear on biological problems is
best illustrated in the following diagram, which shows the role
of mathematical modeling in scientific method.
Nearly everyone is familiar with the experimental aspect of scientific
investigation that is depicted in the lower half of this diagram.
You have a theory or hypothesis you wish to test, you create an
experimental design that tests a critical part of the hypothesis,
you apply methods you already know or you develop new methods
to make the required measurements or observations, and you compare
the collected observations with the predictions of the hypothesis.
If there is a match, you have the backbone of a new contribution
to the scientific literature. If you don't have a match, you are
usually welladvised to reconsider your hypothesis. Restructuring
an inadequate hypothesis is an act of pure scientific imagination,
despite Francis Bacon's insistence that hypotheses can be constructed
from an assemblage of facts by a process he called "induction."
Indeed, a famous 19th century recitation of Bacon's method written
by John F.W. Herschel comes very close to the 21st century viewpoint.
Other scientists and philosophers of science, notably Karl
Popper, have argued that it is the mismatch between hypothesis
and observation that increases our understanding. I'm certain
Popper would argue that publication is warranted when the
hypothesis fails and that publication is redundant when the
hypothesis succeeds. His book, The Logic of Scientific Discovery
(especially Chapter 10: Corroboration...) (Harper 1968), will
reward your careful reading. Nevertheless, I suspect most
published hypotheses are formulated after the data are collected.
In this way the authors can privately abandon the hypothesis that
actually prompted the experiments and publicly endorse a modified
hypothesis that appears consistent with the reported data. In
this way the editors and readers are treated to a
"positive" result and the rejection of hypotheses
occurs between publications rather than in publications. This
quirk of modern science means that most published papers
represent not just the experimental test of a hypothesis, but
also the reformulation of the hypothesis based on the
experimental results obtained. What, then, is the role of
mathematical modeling in scientific method? As depicted in Figure
2, predictions are essential to the comparison, and we view
modeling as the method of choice for obtaining precise
predictions.
Figure 2 The Role of Modeling in Scientific Method
If you don't have recourse to a quantitative model, you must
rely on your best guess as to what should happen if your
experimental design is applied to your theory or hypothesis. This
is an ordinary act of science, and a great deal of effort is
directed at the design of experiments whose outcomes are binary,
yesno measurements so that the prediction process is manageable
by a thoughtful man or woman. But as science confronts the
necessity for integrating information so as to comprehend the
function of complex systems such as intact cells, tissues, and
organisms, guesswork becomes less and less trustworthy as a
source of precise predictions. In fact, cognitive psychologists
have found that when an observable system consists of more than 3
interacting parts, the human mind is incapable of making accurate
predictions concerning the result of a perturbation imposed on
the system. If, on the other hand, you have formulated your
hypothesis as a system of equations, it is a relatively simple
task to obtain precise predictions for a given experimental
design through the use of computer simulation. This book will
have a great deal to say about some of the processes in Figure 2.
Those that will get particular attention are repeated in Figure
3.
Figure 3: Parts of scientific method discussed in this
cybertextbook.
Our first concern is the process of model building. We will
explore
 how to assemble your experimental data
 how to construct a rigorous symbol and arrow diagram for
your system
 how to translate your diagram to mathematics
Second, you will want to use simulation tools. We will examine
 how to use software tools to automate much of the modeling
process
 how to estimate initial values of your model's parameters
 how to impose experimental protocols on your model
 how to solve your model's equations
 how to link your model's variables to your experimental
observations
 how to explore your model's behavior
Next, you will want to test your model against experimental
data as a means of testing the hypothesis or theory that you
model represents. You will learn
 how to use modeling software in hypothesis testing
 how to do least squares fitting
 how to do parameter estimation
When you discover a mismatch between model prediction and
experimental data, you have to decide which to believe.
Traditionally, we accept the experimental data as true, and we
opt to modify our theory, hoping to make our next prediction
match the data. In the diagram, the pathway leading from a
mismatch to a new hypothesis is labelled,
"imagination." Computers cannot yet help here; this is
still a purely human activity. We find, however, that modeling
still helps because it enables you to know with precision what
your imagination must accomplish. As you explore the behavior of
more and more models, your imagination is assisted by your
subconscious knowledge of more and more possibilities. Finally,
you may wish to take advantage of your model for the design of
informative experiments. We will discuss how to design
experiments that yield useful information the elements of
including a kinetic model in a manuscript for publication.
Definitions:
 Model
 A simultaneous system of differential equations and
associated algebraic equations that defines the state
variables and rate laws for a particular physical,
chemical or biological system. The model is a
quantitative statement of our theory as to how the
reallife system operates. In this hypertext, models
embody the principle of cause and effect, and are based
on descriptions of the physicochemical processes that
comprise the biological system under study. Consequently,
purely mathematical descriptions such as curve fitting,
and statistical regression are not "models" in
the sense used here.
 Dynamics
 Kinetics
 Dynamics and Kinetics are roughly synonymous terms
referring to the study of physicochemical (including
biological) systems that change with time. The
mathematical tools for this discipline are the
differential equations invented by Newton and Leibniz in
about 1640. The tools of classical and modern control
theory, numerical analysis, and systems theory are also
frequently applied to dynamic or kinetic problems.
 