Ligand Depletion in vivo Modulates the Dynamic Range of Cooperative Signal Transduction

Abstract

A common procedure in systems biology is to build models of physiological networks based on simple experimental measurements made under controlled conditions. One of the frequently performed quantitative measurements is the dose-response relationship. Its results are assumed to be characteristic of the target molecule and independent of contingent controlled variables. However, ligand concentrations in vivo are often in the same range as the dissociation constant of their receptors, leading to the phenomenon of ligand depletion. Moreover, biological signaling often involves cooperative interactions for the binding of ligands to their receptors. We show that ligand depletion diminishes cooperativity and broadens the dynamic range of sensitivity to the signaling ligand. The effects are illustrated with the highly cooperative flagella motor of bacteria and with the ubiquitous intracellular calcium-binding molecule, calmodulin. As a result of ligand depletion, the same signal transducer responds to different ranges of signal with various degrees of cooperativity according to its effective cellular concentration. Therefore, results from in vitro dose-response properties cannot be directly applied to understand signaling in vivo. Moreover, receptor concentration is a key element in controlling signal transduction and its modulation constitutes a way of controlling sensitivity to signals. For quantitative measures of cooperative effects of signaling, the commonly used Hill coefficient assigns misleading values under many conditions. To correct this situation, we define a new index, the Greek letter “nu”, based on the dose-response cooperativity of any oligomeric receptor with respect to the hypothetical dose-response properties of an “equivalent monomer”. The index nu provides a robust measure of cooperativity under diverse conditions and reveals that within the context of the Monod-Wyman-Changeux two-state model of cooperative transitions, the true intrinsic cooperativity is equal to the number of ligand-binding subunits in the oligomeric receptor.