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1 results

  • 2 - Input–Output Relationships of Cell Systems

  • Hiroaki Takagi, Nara Medical University, Chikara Furusawa, The University of Tokyo, Satoshi Sawai, The University of Tokyo, Kunihiko Kaneko, Copenhagen University
  • Book:
    Theoretical Biology of the Cell
    Published online:
    05 June 2025
    Print publication:
    19 June 2025, pp 41-71

  • Summary

    Cells regulate their proliferation, differentiation, and motility in response to external stimuli. Often, these responses involve a complex interplay of association, dissociation, and catalytic reactions, characterized by highly specific intermolecular interactions. This chapter examines cellular responses arising from such chemical reactions from a mathematical standpoint. As examples of input–output relationships, we introduce the Hill equation, Adair equation, and the MWC model concerning allosteric regulation, which describe cooperative behaviors. We discuss the Michaelis–Menten equation in enzyme reactions, covering activation, inactivation, push–pull reactions, zero-order ultrasensitivity, and positive feedback switches. Furthermore, we present the formation of a bell-shaped input–output curve by feed-forward loops, and the mechanisms of adaptation and fold-change detection utilizing feed-forward loops, or negative feedback. We explore bacterial chemotaxis mechanisms through models such as the Asakura–Honda model and the Barkai–Leibler model.