Reliable ligand discrimination in stochastic multistep kinetic proofreading: First passage time vs. product counting strategies

Cellular signaling, crucial for biological processes like immune response and homeostasis, relies on specificity and fidelity in signal transduction to accurately respond to stimuli amidst biological noise. Kinetic proofreading (KPR) is a key mechanism enhancing signaling specificity through time-delayed steps, although its effectiveness is debated due to intrinsic noise potentially reducing signal fidelity. In this study, we reformulate the theory of kinetic proofreading (KPR) by convolving multiple intermediate states into a single state and then define an overall "processing" time required to traverse these states. This simplification allows us to succinctly describe kinetic proofreading in terms of a single waiting time parameter, facilitating a more direct evaluation and comparison of KPR performance across different biological contexts such as DNA replication and T cell receptor (TCR) signaling. We find that loss of fidelity for longer proofreading steps relies on the specific strategy of information extraction and show that in the first-passage time (FPT) discrimination strategy, longer proofreading steps can exponentially improve the accuracy of KPR at the cost of speed. Thus, KPR can still be an effective discrimination mechanism in the high noise regime. However, in a product concentration-based discrimination strategy, longer proofreading steps do not necessarily lead to an increase in performance. However, by introducing activation thresholds on product concentrations, can we decompose the product-based strategy into a series of FPT-based strategies to better resolve the subtleties of KPR-mediated product discrimination. Our findings underscore the importance of understanding KPR in the context of how information is extracted and processed in the cell. Author summaryKinetic proofreading (KPR) is mechanism often employed by cells to enhance specificity of ligand-receptor. However, the performance of kinetic proofreading may be hampered by noise and a low signal-to-noise ratio. By consolidating multiple kinetic proofreading steps into a single state and assigning an associated waiting, or "processing time," we developed an analytic approach to quantify the performance of KPR in different biological contexts. Despite a trade-off between speed and accuracy inherent to a first-passage time KPR strategy, we show that a signaling molecule-based discrimination strategy can enhance the performance benefits of KPR. We further decompose the product-based discrimination strategy into a set of first-passage times to different thresholds of signaling molecules produced. Through this decomposition, we find that a threshold that adjusts dynamically throughout the recognition process depends on the duration of the process. We propose that this more nuanced product-based KPR-mediated recognition process can be realized biologically. The precise structural basis for a dynamic threshold merits further experimental exploration, as it may hold significant implications for understanding biological mechanisms of information transmission at a molecular level.