Combined Model of Intrinsic and Extrinsic Variability for Computational Network Design with Application to Synthetic Biology

Biological systems are inherently variable, with their dynamics influenced by intrinsic and extrinsic sources. These systems are often only partially characterized, with large uncertainties about specific sources of extrinsic variability and biochemical properties. Moreover, it is not yet well understood how different sources of variability combine and affect biological systems in concert. To successfully design biomedical therapies or synthetic circuits with robust performance, it is crucial to account for uncertainty and effects of variability. Here we introduce an efficient modeling and simulation framework to study systems that are simultaneously subject to multiple sources of variability, and apply it to make design decisions on small genetic networks that play a role of basic design elements of synthetic circuits. Specifically, the framework was used to explore the effect of transcriptional and post-transcriptional autoregulation on fluctuations in protein expression in simple genetic networks. We found that autoregulation could either suppress or increase the output variability, depending on specific noise sources and network parameters. We showed that transcriptional autoregulation was more successful than post-transcriptional in suppressing variability across a wide range of intrinsic and extrinsic magnitudes and sources. We derived the following design principles to guide the design of circuits that best suppress variability: (i) high protein cooperativity and low miRNA cooperativity, (ii) imperfect complementarity between miRNA and mRNA was preferred to perfect complementarity, and (iii) correlated expression of mRNA and miRNA – for example, on the same transcript – was best for suppression of protein variability. Results further showed that correlations in kinetic parameters between cells affected the ability to suppress variability, and that variability in transient states did not necessarily follow the same principles as variability in the steady state. Our model and findings provide a general framework to guide design principles in synthetic biology. Author Summary: Variability is inherent in biological systems, and in order to understand them, we need to be able to model different sources of variability. Systems have evolved to harness and control the variability, and more recently, synthetic biologists are trying to learn how to control variability in engineered biological systems. Several sources of variability exist; they arise due to stochastic expression of genes, which is most pronounced when numbers of mRNA and protein molecules are low, as well as due to differences between individual cells. Here we propose a modeling framework that combines different sources of biological variability. Furthermore, current research seeks to control biological variability though robust design of synthetic biological circuits, for example for use in therapies and other biomedical or biotechnological applications. Here we apply our framework to guide design of synthetic circuits that use transcriptional and post-transcriptional regulation to suppress variability in the output protein of interest. We find that certain properties and network designs are better than others in their ability to control variability, and here we report on the design guidelines to aid synthetic circuit design to suppress variability, in spite of our uncertain knowledge of parameters.