Genetic control circuits: Mathematical comparison of elementary circuits with different patterns of regulator and effector gene expression.
Hlavacek, William Scott
1996
Abstract
The design principles of elementary gene circuits are the subject of this work. An elementary gene circuit, such as the well-known lactose (lac) system in Eschericia coli, involves a regulator gene and an associated set of effector genes. The regulator gene encodes a regulator protein that, in response to the level of a small signal molecule, controls expression of the effector genes, which encode functionally related enzymes. The regulator protein also can control expression of its own gene. This possibility of autoregulation, and the possibility of a regulator protein to have different influences on transcription depending on the target gene, allows an elementary gene circuit to produce any one of three qualitatively distinct steady-state patterns of regulator and effector gene expression: (1) direct coupling, in which regulator and effector gene expression change in the same direction; (2) uncoupling, in which only effector gene expression changes; and (3) inverse coupling, in which regulator and effector gene expression change in opposite directions. Special forms of direct coupling and uncoupling are also found in Nature, and these are of interest here, because they represent two extremes and because their mathematical analysis is somewhat less complicated than that of the circuits with direct coupling, uncoupling, or inverse coupling. The influence of the different forms of coupling on the functional effectiveness of a system has been determined by using a mathematical approach. Models for inducible systems, in which effector genes are negatively or positively regulated, and for repressible systems, in which effector genes are negatively or positively regulated, have been developed. These models have then been used to make controlled comparisons of circuits with the different forms of coupling. In these comparisons, which are based on a priori criteria for functional effectiveness, circuits are chosen to eliminate irrelevant differences during comparison. The only differences that remain are related to the form of coupling. The results for inducible or repressible systems indicate that given the choice of perfect coupling or complete uncoupling, perfect coupling is preferred in negatively regulated systems, whereas complete uncoupling is preferred in positively regulated systems. Given an expanded range of choices--direct coupling, uncoupling, or inverse coupling--the results for inducible systems indicate that direct coupling is preferred in a negatively regulated system, whereas inverse coupling is preferred in a positively regulated system. These preferred forms of coupling allow a faster response to a change in the level of the signal molecule than other forms of coupling. The results further indicate that if the gain of system is high, then the preferred form of coupling cannot be realized, due to a physical constraint related to the subunit structure of regulatory proteins. The results lead to predictions that can be tested, and these predictions are consistent with data currently available in the literature.Subjects
Autoregulation Circuits Comparison Control Coupling Different Effector Elementary Expression Gene Genetic Mathematical Patterns Regulator
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