Compression algorithms reveal memory effects and static disorder in single-molecule trajectories

High-order Michaelis-Menten equations allow inference of hidden kinetic parameters in enzyme catalysis

“…A key insight coming from the renewal approach is that the Michaelis-Menten equation is universal. 35 Namely, regardless of the details of the underlying distributions of binding, unbinding, and catalysis times, the mean turnover time always shows a linear dependence on the reciprocal of the substrate concentration. Yet, extensions of this fundamental result to higher moments of the turnover time have so far remained elusive.…”

“…Thus, by allowing for arbitrary transition time distributions, one can effectively account for hidden degrees of freedom, e.g., different conformational states and branching pathways, that are lost in the coarse-graining procedure.A key insight coming from the renewal approach is that the Michaelis-Menten equation is universal. 35 Namely, regardless of the details of the underlying distributions of binding, unbinding, and catalysis times, the mean turnover time always shows a linear dependence on the reciprocal of the substrate concentration. Yet, extensions of this fundamental result to higher moments of the turnover time have so far remained elusive.Generalizing the Michaelis-Menten equation to moments of any order will open the door to systematic analysis of turnover time data, thus allowing for characterization of enzyme catalysis beyond the classical, yet incomplete, description of the maximal turnover rate and the Michaelis-Menten constant.…”

“…Markovian 14,[33][34][35] , or has parallel branching pathways or non-sequential motifs, this modeling approach fails. 27 One is then left to wonder how to systematically extract useful information from higher moments of enzymatic turnover times in a general way and without making restricting assumptions on the underlying kinetics.…”

“…[28][29][30] Using these, information on the number of interim states involved in substrate binding, the total number of states present in the catalytic network, and the number of non-substrate binding states, can be extracted by measuring the mean and second moment of the catalysis time distribution as a function of substrate concentration. 27,29,31,32 Yet, if the conformational dynamics is non-Markovian 14,[33][34][35] , or has parallel branching pathways or non-sequential motifs, this modeling approach fails. 27 One is then left to wonder how to systematically extract useful information from higher moments of enzymatic turnover times in a general way and without making restricting assumptions on the underlying kinetics.Addressing this research problem, several studies have made distinctive progress within the renewal approach to Michaelis-Menten enzyme kinetics [36][37][38][39][40] .…”