Decoupling between activation time and steady-state level in input-output responses
Many biological processes, like gene regulation or cell signalling, rely on molecules (inputs) that bind to targets leading to downstream responses. In the gene regulation field, recent data have shown that higher transcription factor (TF) concentrations may increase transcription levels of a gene without affecting the gene activation time. We call this behaviour output decoupling. Motivated by these observations, here we investigate mechanisms for output decoupling in Markov process models where a readout molecule is produced downstream of ligand binding. Our focus is on identifying regimes where the steady-state level of the readout changes with input concentration, while the activation time, quantified by mean first-passage times, remains unaffected. Through a combination of analytical and numerical investigations, we find two mechanisms through which output decoupling can arise: i) rate scale separation, where the system is comprised of slow and fast transitions that are differentially regulated by the input; and ii) incoherent regulation, where the input acts on two transitions with opposing effects on readout production, with all transitions operating on similar timescales in the absence of input. Such incoherent regulation has emerged as a plausible regulatory mode of TFs, and we suggest decoupling as a new characteristic feature of this regulatory mode. More broadly, our findings offer a mechanistic and conceptual framework for reasoning about output decoupling in input-output systems. Author summaryHow biomolecular systems respond to signals often depends not only on the final level of activity they reach, but also on how quickly they reach it. These two outputs -- steady-state level and activation time-- are usually coupled: higher input concentration tends to produce both higher activity and faster responses. Yet recent experiments suggest that, in some cases, the strength of the response can change while the speed remains constant. In this work, we explore the conditions under which such "output decoupling" can occur. Using mathematical models of molecular systems, we identify two ways this can happen. In one case, the activation time is determined by slow steps in the system that the input does not control. In the other, the input exerts opposing effects on the system, simultaneously promoting and hindering the response, which balances the timing. By revealing how decoupling arises, our study provides a framework for interpreting puzzling experimental results. More broadly, it shows the value of considering both dynamics and steady-state behavior jointly when studying how molecular systems process information.