The art of modeling gene regulatory circuits.

The amazing complexity of gene regulatory circuits, and biological systems in general, makes mathematical modeling an essential tool to frame and develop our understanding of their properties. Here, we present some fundamental considerations to develop and analyze a model of a gene regulatory circuit of interest, either representing a natural, synthetic, or theoretical system. A mathematical model allows us to effectively evaluate the logical implications of our hypotheses. Using our models to systematically perform in silico experiments, we can then propose specific follow-up assessments of the biological system as well as to reformulate the original assumptions, enriching both our knowledge and our understanding of the system. We want to invite the community working on different aspects of gene regulatory circuits to explore the power and benefits of mathematical modeling in their system.

CoRa-A general approach for quantifying biological feedback control.

Feedback control is a fundamental underpinning of life, underlying homeostasis of biological processes at every scale of organization, from cells to ecosystems. The ability to evaluate the contribution and limitations of feedback control mechanisms operating in cells is a critical step for understanding and ultimately designing feedback control systems with biological molecules. Here, we introduce CoRa-or Control Ratio-a general framework that quantifies the contribution of a biological feedback control mechanism to adaptation using a mathematically controlled comparison to an identical system that does not contain the feedback. CoRa provides a simple and intuitive metric with broad applicability to biological feedback systems.

Multidimensional Characterization of Parts Enhances Modeling Accuracy in Genetic Circuits.

Mathematical models can aid the design of genetic circuits, but may yield inaccurate results if individual parts are not modeled at the appropriate resolution. To illustrate the importance of this concept, we study transcriptional cascades consisting of two inducible synthetic transcription factors connected in series. Despite the simplicity of this design, we find that accurate prediction of circuit behavior requires mapping the dose responses of each circuit component along the dimensions of both its expression level and its inducer concentration. Using this multidimensional characterization, we were able to computationally explore the behavior of 16 different circuit designs. We experimentally verified a subset of these predictions and found substantial agreement. This method of biological part characterization enables the use of models to identify (un)desired circuit behaviors prior to experimental implementation, thus shortening the design-build-test cycle for more complex circuits.

Publisher Correction: Modular and tunable biological feedback control using a de novo protein switch.

An amendment to this paper has been published and can be accessed via a link at the top of the paper.

Epigenetic switching as a strategy for quick adaptation while attenuating biochemical noise.

Epigenetic switches are bistable, molecular systems built from self-reinforcing feedback loops that can spontaneously switch between heritable phenotypes in the absence of DNA mutation. It has been hypothesized that epigenetic switches first evolved as a mechanism of bet-hedging and adaptation, but the evolutionary trajectories and conditions by which an epigenetic switch can outcompete adaptation through genetic mutation remain unknown. Here, we used computer simulations to evolve a mechanistic, biophysical model of a self-activating genetic circuit, which can both adapt genetically through mutation and exhibit epigenetic switching. We evolved these genetic circuits under a fluctuating environment that alternatively selected for low and high protein expression levels. In all tested conditions, the population first evolved by genetic mutation towards a region of genotypes where genetic adaptation can occur faster after each environmental transition. Once in this region, the self-activating genetic circuit can exhibit epigenetic switching, which starts competing with genetic adaptation. We show a trade-off between either minimizing the adaptation time or increasing the robustness of the phenotype to biochemical noise. Epigenetic switching was superior in a fast fluctuating environment because it adapted faster than genetic mutation after an environmental transition, while still attenuating the effect of biochemical noise on the phenotype. Conversely, genetic adaptation was favored in a slowly fluctuating environment because it maximized the phenotypic robustness to biochemical noise during the constant environment between transitions, even if this resulted in slower adaptation. This simple trade-off predicts the conditions and trajectories under which an epigenetic switch evolved to outcompete genetic adaptation, shedding light on possible mechanisms by which bet-hedging strategies might emerge and persist in natural populations.

Design and Analysis of a Proportional-Integral-Derivative Controller with Biological Molecules.

The capability to engineer de novo feedback control with biological molecules is ushering in an era of robust functionality for many applications in biotechnology and medicine. To fulfill their potential, these control strategies need to be generalizable, modular, and operationally predictable. Proportional-integral-derivative (PID) control fulfills this role for technological systems. Integral feedback control allows a system to return to an invariant steady-state value after step disturbances. Proportional and derivative feedback control used with integral control modulate the dynamics of the return to steady state following perturbation. Recently, a biomolecular implementation of integral control was proposed based on an antithetic motif in which two molecules interact stoichiometrically to annihilate each other's function. In this work, we report how proportional and derivative implementations can be layered on top of this integral architecture to achieve a biochemical PID control design. We investigate computationally and analytically their properties and ability to improve performance.

Modular and tunable biological feedback control using a de novo protein switch.

De novo-designed proteins1-3 hold great promise as building blocks for synthetic circuits, and can complement the use of engineered variants of natural proteins4-7. One such designer protein-degronLOCKR, which is based on 'latching orthogonal cage-key proteins' (LOCKR) technology8-is a switch that degrades a protein of interest in vivo upon induction by a genetically encoded small peptide. Here we leverage the plug-and-play nature of degronLOCKR to implement feedback control of endogenous signalling pathways and synthetic gene circuits. We first generate synthetic negative and positive feedback in the yeast mating pathway by fusing degronLOCKR to endogenous signalling molecules, illustrating the ease with which this strategy can be used to rewire complex endogenous pathways. We next evaluate feedback control mediated by degronLOCKR on a synthetic gene circuit9, to quantify the feedback capabilities and operational range of the feedback control circuit. The designed nature of degronLOCKR proteins enables simple and rational modifications to tune feedback behaviour in both the synthetic circuit and the mating pathway. The ability to engineer feedback control into living cells represents an important milestone in achieving the full potential of synthetic biology10,11,12. More broadly, this work demonstrates the large and untapped potential of de novo design of proteins for generating tools that implement complex synthetic functionalities in cells for biotechnological and therapeutic applications.

Enhancer Histone Acetylation Modulates Transcriptional Bursting Dynamics of Neuronal Activity-Inducible Genes.

Neuronal activity-inducible gene transcription correlates with rapid and transient increases in histone acetylation at promoters and enhancers of activity-regulated genes. Exactly how histone acetylation modulates transcription of these genes has remained unknown. We used single-cell in situ transcriptional analysis to show that Fos and Npas4 are transcribed in stochastic bursts in mouse neurons and that membrane depolarization increases mRNA expression by increasing burst frequency. We then expressed dCas9-p300 or dCas9-HDAC8 fusion proteins to mimic or block activity-induced histone acetylation locally at enhancers. Adding histone acetylation increased Fos transcription by prolonging burst duration and resulted in higher Fos protein levels and an elevation of resting membrane potential. Inhibiting histone acetylation reduced Fos transcription by reducing burst frequency and impaired experience-dependent Fos protein induction in the hippocampus in vivo. Thus, activity-inducible histone acetylation tunes the transcriptional dynamics of experience-regulated genes to affect selective changes in neuronal gene expression and cellular function.

Complexity-aware simple modeling.

Mathematical models continue to be essential for deepening our understanding of biology. On one extreme, simple or small-scale models help delineate general biological principles. However, the parsimony of detail in these models as well as their assumption of modularity and insulation make them inaccurate for describing quantitative features. On the other extreme, large-scale and detailed models can quantitatively recapitulate a phenotype of interest, but have to rely on many unknown parameters, making them often difficult to parse mechanistically and to use for extracting general principles. We discuss some examples of a new approach-complexity-aware simple modeling-that can bridge the gap between the small-scale and large-scale approaches.

BayFish: Bayesian inference of transcription dynamics from population snapshots of single-molecule RNA FISH in single cells.

Single-molecule RNA fluorescence in situ hybridization (smFISH) provides unparalleled resolution in the measurement of the abundance and localization of nascent and mature RNA transcripts in fixed, single cells. We developed a computational pipeline (BayFish) to infer the kinetic parameters of gene expression from smFISH data at multiple time points after gene induction. Given an underlying model of gene expression, BayFish uses a Monte Carlo method to estimate the Bayesian posterior probability of the model parameters and quantify the parameter uncertainty given the observed smFISH data. We tested BayFish on synthetic data and smFISH measurements of the neuronal activity-inducible gene Npas4 in primary neurons.