From: Input-output relations in biological systems: measurement, information and the Hill equation

– | Psychophysics studies human perception of quantity, such as loudness, temperature or pressure. The early work of Weber and Fechner suggested that perception scales logarithmically: for a given stimulus (input), the perception of quantity (output) changes logarithmically. That work led to modern analysis of measurement and scale. |

– | This article analyzes biological input-output relations. My examples focus on biochemistry. I chose that focus for two reasons. First, most biological input-output relations may ultimately be reducible to cascades of biochemical component reactions. The problem then becomes how to relate the biochemical components and their connections to overall system function. That relation between biochemistry and system function is the core of modern systems biology. Second, the sharp distinction between classical Michaelis-Menten chemical kinetics and the observed patterns of logarithmic scaling in both biochemistry and perception provides a good entry into the unsolved puzzles of the subject and the potential value of my perspective. |

– | Although I focus on biochemistry, my approach derives from other topics. I borrow the deep conceptual foundations of measurement from psychophysics, the principles of aggregation from statistical mechanics, and aspects of information theory that originally developed in studies of communication. My view is that biological input-output relations can only be understood in terms of aggregation, measurement and information. In this article, I evoke those principles indirectly by building a series of specific analyses of biochemistry and simple aspects of systems biology. |

– | The literatures and conceptual spans are vast for psychophysics, measurement theory, statistical mechanics and information theory. Here, I mention a few key entries into each subject. To read this article, it is not necessary to understand all of those topics. But it is necessary to see the project for what it is, an attempt to borrow deep principles from other subjects and apply those principles to biochemical aspects of systems biology, to the nature of biological input-output relations, and to the consequences for natural selection and evolutionary design. |

– | Gescheider [8] summarizes aspects of psychophysics related to my discussion of input-output patterns. History and further references can be obtained from that work. Certain aspects of measurement theory followed from psychophysics [5, 6]. The theory developed into a broader analysis of the principles of quantity [9–11]. Other branches of measurement theory focus on aspects of precision and calibration [12]. |

– | Statistical mechanics analyzes the ways in which aggregation leads to highly ordered systems arising from disordered underlying components. My usage follows from the proposed unity between information theory and aggregate pattern, which transcends the specifics of physical models and instead emphasizes the patterns expressed by probability distributions [3, 40]. That Jaynesian perspective describes how aggregation dissipates information to expose underlying regularity. Later work [41, 42] provided a unified framework for all common probability patterns by combining measurement theory with Jaynes’ information theory interpretation of statistical mechanics. |