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Open Discussion of Modeling and Computational Approaches to Cellular Signaling

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Mathematical Models of Cellular Signaling

11 June 2004

Richard G. Lanzara

In the interest of stimulating further discussion of this important topic, I would like to leap into the fray. However, part of the problem is that there is no fray. We need to have a more substantive discussion based upon recognized biophysical principles. Therefore, allow me to attempt an opening.

Cellular signaling is one of the most basic of interactions that requires an understanding of many physical, chemical, and biological concepts. Unfortunately, few people either know or take the time to understand many of these basic principles because they cross many scientific boundaries. Such older concepts as LeChatlier's principle and the Weber-Fechner law are often ignored when considering the pharmacological modeling of ligand-receptor response. We often don't question some of the underlying concepts assumed by the more recent attempts to fit mathematical models to receptor responses. Some of the questions that could be raised are fundamental. Such questions as what is really meant by an equilibrium or reaction quotient? Do we really understand the descriptive nature of these expressions and how they relate to what we're trying to describe? I think not (see http://www.bio- balance.com/Lanzara_APPENDIX.htm and http://www.bio- balance.com/Graphics.htm).

With regard to Weber's law, most modelers don't address why it is that all of our senses appear to obey this basic law (see http://www.bio- balance.com/Ref.htm). After all, our senses work as signaling networks too and should be incorporated into a complete model for the receptor response.

Perhaps the key to understand cellular signaling lies with an understanding of rapid receptor desensitization also called tachyphylaxis or fade. This phenomenon occurs for a large number of receptors and normal physiological signaling networks. Some have tried to model desensitization with mathematical models or intracellular events, such as downstream effectors, that seem to become more complex than useful. Many of these intracellular explanations either fail to prove rapid or unequivocal enough to make a believer out of me. In addition, the use of antagonists with agonists suggest that much of the rapid desensitization can be prevented (see http://www.bio-balance.com/Ref.htm). This doesn't fit with most of the recent pharmacologic models or theories.

I don't wish to appear as a "bull in a china shop", but sometimes the emperor has no clothes.

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Science Signaling. ISSN 1937-9145 (online), 1945-0877 (print). Pre-2008: Science's STKE. ISSN 1525-8882