Autoregulatory feedback loops occur in the regulation of molecules ranging from ATP to MAP kinases to zinc. Negative feedback loops can increase a system's robustness, while positive feedback loops can mediate transitions between cell states. Recent genome-wide experimental and computational studies predict hundreds of novel feedback loops. However, not all physical interactions are regulatory, and many experimental methods cannot detect self-interactions. Our understanding of regulatory feedback loops is therefore hampered by the lack of high-throughput methods to experimentally quantify the presence, strength and temporal dynamics of autoregulatory feedback loops. Here we present a mathematical and experimental framework for high-throughput quantification of feedback regulation and apply it to RNA binding proteins (RBPs) in yeast. Our method is able to determine the existence of both direct and indirect positive and negative feedback loops, and to quantify the strength of these loops. We experimentally validate our model using two RBPs which lack native feedback loops and by the introduction of synthetic feedback loops. We find that RBP Puf3 does not natively participate in any direct or indirect feedback regulation, but that replacing the native 3'UTR with that of COX17 generates an auto-regulatory negative feedback loop which reduces gene expression noise. Likewise, RBP Pub1 does not natively participate in any feedback loops, but a synthetic positive feedback loop involving Pub1 results in increased expression noise. Our results demonstrate a synthetic experimental system for quantifying the existence and strength of feedback loops using a combination of high-throughput experiments and mathematical modeling. This system will be of great use in measuring auto-regulatory feedback by RNA binding proteins, a regulatory motif that is difficult to quantify using existing high-throughput methods.

These authors contributed equally to this work.Auto regulatory feedback loops occur in the regulation of molecules ranging from ATP to MAP kinases to zinc. Negative feedback loops can increase a system's robustness, while positive feedback loops can mediate transitions between cell states. Recent genome-wide experimental and computational studies predict hundreds of novel feedback loops. However, not all physical interactions are regulatory, and many experimental methods cannot detect self-interactions. Our understanding of regulatory feedback loops is therefore hampered by the lack of high-throughput methods to experimentally quantify the presence, strength, and temporal dynamics of auto regulatory feedback loops. Here we present a mathematical and experimental framework for high-throughput quantification of feedback regulation, and apply it to RNA binding proteins (RBPs) in yeast. Our method is able to determine the existence of both direct and indirect positive and negative feedback loops, and to quantify the strength of these loops. We experimentally validate our model using two RBPs which lack native feedback loops, and by the introduction of synthetic feedback loops. We find that the the RBP Puf3 does not natively participate in any direct or indirect feedback regulation, but that replacing the native 3'UTR with that of COX17 generates an auto-regulatory negative feedback loop which reduces gene expression noise. Likewise, the RBP Pub1 does not natively participate in any feedback loops, but a synthetic positive feedback loop involving Pub1 results in increased expression noise. Our results demonstrate a synthetic experimental system for quantifying the existence and strength of feedback loops using a combination of high-throughput experiments and mathematical modeling. This system will be of great use in measuring auto-regulatory feedback by RNA binding proteins, a regulatory motif that is difficult to quantify using existing high-throughput methods.

Summary Processing time-dependent information requires cells to quantify the duration of past regulatory events and program the time span of future signals. At the single-cell level, timer mechanisms can be implemented with genetic circuits. However, such systems are difficult to implement in single cells due to saturation in molecular components and stochasticity in the limited intracellular space. In contrast, multicellular implementations outsource some of the components of information-processing circuits to the extracellular space, potentially escaping these constraints. Here, we develop a theoretical framework, based on trilinear coordinate representation, to study the collective behavior of populations composed of three cell types under stationary conditions. This framework reveals that distributing different processes (in our case the production, detection and degradation of a time-encoding signal) across distinct strains enables the implementation of a multicellular timer. Our analysis also shows that the circuit can be easily tunable by varying the cellular composition of the consortium.

Processing time-dependent information requires cells to quantify the durations of past regulatory events and program the time span of future signals. Such timer mechanisms are difficult to implement at the level of single cells, however, due to saturation in molecular components and stochasticity in the limited intracellular space. Multicellular implementations, on the other hand, outsource some of the components of information-processing circuits to the extracellular space, and thereby might escape those constraints. Here we develop a theoretical framework, based on a trilinear coordinate representation, to study the collective behavior of a three-strain bacterial population under stationary conditions. This framework reveals that distributing different processes (in our case the production, detection and degradation of a time-encoding signal) across distinct bacterial strains enables the robust implementation of a multicellular timer. Our analysis also shows the circuit to be easily tunable by varying the relative frequencies of the bacterial strains composing the consortium.

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