ABSTRACT
Electrical engineers have vast experience in modeling and analyzing circuits and systems composed of thousands or even millions of interconnected complex components. One of the most important electrical circuits is the microprocessor. Figure 6.1(a) shows the first microprocessor, Intel’s 4004, which was introduced in 1971. This processor is composed of 2,300 transistors, the basic element of an integrated electrical circuit, and it operates at 108 kilohertz. After 30 years of technology improvements, the complexity of electrical circuits that can be designed has grown at a incredible rate. The circuit shown in Figure 6.1(b) is the Intel R©Pentium R©4 Processor which was introduced in 2000. This processor is composed of 42 million transistors, and it operates at 1.5 gigahertz. The increase in performance over the 4004 is simply amazing. If the speed of automobiles had improved at a similar rate during that 30 year period, one could now drive from San Francisco to New York in only 13 seconds! One reason that we can design circuits such as these is that methods of logical abstraction and analysis help us to deal with this complexity. We are fortunate that the complexity of the biochemical circuits that we
wish to analyze are not increasing, but their initial complexity is staggering. An example biochemical circuit, the reactions involved in E. coli metabolism, is shown in Figure 6.2. While this level of complexity may be manageable, if the regulatory reactions are added then the figure would appear black. In order to analyze circuits such as these, model abstraction is going to be absolutely essential. The question that this chapter addresses is whether the logical abstraction applied to electrical circuits can be applied successfully to biochemical circuits. As mentioned earlier, the regulation of genetic circuits is often controlled by
Hill functions. In the limit, these Hill functions become step functions which can be encoded logically as described in Section 6.1. Using this logical encoding, one can construct piecewise models which are presented in Section 6.2. Section 6.3 presents stochastic finite-state machines that can be analyzed using Markov chain analysis as described in Section 6.4. Finally, Section 6.5 presents qualitative logical models.
