Fundamental limits on the suppression of molecular fluctuations.

Negative feedback is common in biological processes and can increase a system's stability to internal and external perturbations. But at the molecular level, control loops always involve signalling steps with finite rates for random births and deaths of individual molecules. Here we show, by developing mathematical tools that merge control and information theory with physical chemistry, that seemingly mild constraints on these rates place severe limits on the ability to suppress molecular fluctuations. Specifically, the minimum standard deviation in abundances decreases with the quartic root of the number of signalling events, making it extremely expensive to increase accuracy. Our results are formulated in terms of experimental observables, and existing data show that cells use brute force when noise suppression is essential; for example, regulatory genes are transcribed tens of thousands of times per cell cycle. The theory challenges conventional beliefs about biochemical accuracy and presents an approach to the rigorous analysis of poorly characterized biological systems.

Nonautonomous elementary net systems and their application to programmable logic control

In this paper, a novel approach to Petri net modeling of programmable logic controller (PLC) programs is presented. The modeling approach is a simple extension of elementary net systems, and a graphical design tool that supports the use of this modeling approach is provided. A key characteristic of the model is that the binary sensory inputs and binary actuation outputs of the PLC are explicitly represented. This leads to the following two improvements: outputs are unambiguous, and interaction patterns are more clearly represented in the graphical form. The use of this modeling approach produces programs that are simple, lightweight, and portable. The approach is demonstrated by applying it to the development of a control module for a MonTech Positioning Station. © 2008 IEEE.