- Dynamic Modeling 105
By transposition, Eq. (9.2) can be further expressed as
m(t+Δt)=m(t)+f(m, t)Δt
=g(m, t) (9.3)which becomes a discrete dynamic model (or difference equation). The
physical meaning of the discrete dynamic model is that the value of the state
variablemat timet+Δtis a function of the state variablemat timet.In
other words, given the value of state variablemat timetand the discrete
dynamic model (9.3), the value of the state variablemat timet+Δtcan
always be computed. In the following sections, the discrete dynamic model
will be used to describe the interactions/regulations between the components
of the biological system.
- The modeling procedure
In this section, the step-by-step modeling procedure will be introduced
in detail. Here, the analysis of transcriptomics data using dynamic model
to investigate the regulations among genes is taken as an example to
demonstrate the modeling procedure.
3.1. Problem formulation and key factor determination
The first step of the modeling procedure is to define the problem and to
set the goal based on experimental data we have.Suppose that we have a
set of transcriptomics data which measured the time-course gene expression
profiles under a specific experimental condition, e.g., some kind of drug
treatment. The goal of the analysis is to investigate gene regulations between
the genes of interest, i.e., the construction of gene regulatory network for
the specific experimental condition. In this situation, how to determine the
gene regulation relationships based on the transcriptomics data is our main
concern.
There are thousands of genes in an organism, indicating that it is not
practical to investigate gene regulations among all genes. Therefore, we
need to determine the genes of interest for further analysis. Generally,
the selection of genes can be divided into two categories: expression-
based selection and function-based selection. For expression-based selection,
statistical methods such as one-way analysis of variance (ANOVA) or simply