Jgp_201611751 547..560

Cellular signaling relies on macromolecules to transduce stimuli information into conformational changes (Changeux and Edelstein, 2005). The mechanisms by which macromolecules accomplish this feat are often allosteric: a small stimulus applied at one area of the macromolecule regulates behavior at locations structurally distant from the active site of stimulation. A detailed and mechanistic understanding of allosteric regulation is a major goal of biophysics (Changeux, 2012, 2013). The Monod-Wyman-Changeux (MWC) model, which provides a physical-chemical interpretation of indirect regulation in terms of the geometry of the regulatory molecule (Monod et al., 1963, 1965; Marzen et al., 2013), has emerged as an essential tool in this effort. Operationally, any given MWC model represents a candidate hypothesis for how allosteric conformational change occurs. If a model is not able to quantitatively fit available data, it is rejected. For models that agree with the data, the model parameter values provide estimates of biophysically meaningful properties that cannot be measured directly. Tremendous effort has gone toward determining which mechanistically relevant parameters best fit available macromolecular data (Colquhoun and Hawkes, 1982, 1995; Horn and Lange, 1983; Blatz and Magleby, 1986; Ball and Sansom, 1989; Kienker, 1989; Ball and Rice, 1992; Colquhoun and Sigworth, 1995; Qin et al., 1996, 2000; Colquhoun et al., 2003; Celentano and Hawkes, 2004; Milescu et al., 2005; Moffatt, 2007). However, it has recently been observed that even simple MWC models suffer from parameter non-identifiability: the data in commonly used activity (or binding) curves do not provide sufficient constraining power to find unique values of the parameters, even if essentially noiseless (Hines et al., 2014; Middendorf and Aldrich, 2017a,b). Essentially all work on parameter estimation in MWC models has treated non-identifiability as a hurdle to be overcome toward the estimation of individual MWC parameter values, which clearly confer mechanistically meaningful information about the macromolecule under study. Here, we argue that valuable mechanistic information may be lost by focusing on individual parameter values. We demonstrate that non-identifiable datasets admit identifiable “emergent” parameters and argue that these emergent parameters confer mechanistic information about macromolecular function not available from individual parameter values themselves, no matter how accurate. We begin by studying the causes of parameter non-identifiability in a canonical MWC model of the mSlo large-conductance Ca-activated K (BK) ion channel (Horrigan and Aldrich, 2002; Yan and Aldrich, 2010), with respect to two common assays of functional activity. The non-identifiability is shown The ability of macromolecules to transduce stimulus information at one site into conformational changes at a distant site, termed “allostery,” is vital for cellular signaling. Here, we propose a link between the sensitivity of allosteric macromolecules to their underlying biophysical parameters, the interrelationships between these parameters, and macromolecular adaptability. We demonstrate that the parameters of a canonical model of the mSlo large-conductance Ca-activated K (BK) ion channel are non-identifiable with respect to the equilibrium open probability-voltage relationship, a common functional assay. We construct a reduced model with emergent parameters that are identifiable and expressed as combinations of the original mechanistic parameters. These emergent parameters indicate which coordinated changes in mechanistic parameters can leave assay output unchanged. We predict that these coordinated changes are used by allosteric macromolecules to adapt, and we demonstrate how this prediction can be tested experimentally. We show that these predicted parameter compensations are used in the first reported allosteric phenomena: the Bohr effect, by which hemoglobin adapts to varying pH. Identifiability, reducibility, and adaptability in allosteric macromolecules