Computational Limitations of First-Order Repressor Systems

Almost all current approaches for engineering modular logic components in synthetic biology use first-order regulators, including most CRISPR/CAS, TAL, zinc finger, and RNA interference systems. Many practitioners understand intuitively that second and higher order binding is necessary for scalability, and this is easy to show for single-input single-output systems. However, no study to date has analysed whether a more complex system, utilizing e.g. feedback or error correction, can produce scalable computation from first-order regulators. We prove here that first order repressor systems cannot support bistability. In the process, we introduce a function G to measure signal quality in molecular systems, and we show that G always decreases in dynamic feedback systems as well as static feed-forward logic cascades of first-order repressors. As a result, first order repressors cannot build memory or signal buffering elements. Finally, we suggest G as a potential new property for characterization of standard biological parts.