retroactivity

Understanding how opposing regulatory factors shape gene expression is essential for understanding complex biological systems. A motivating observation, drawn from cancer epigenetics, is that removing an activating factor can sometimes lead to higher, not lower, expression of a gene that is also subject to a repressing factor. Prior theoretical work explained this counterintuitive behavior by competition of repressors and activators for genomic binding sites. However, it has been difficult to test this directly in natural systems, where layers of regulation obscure causal relationships. This paper introduces a fully synthetic, tunable genetic platform in a prokaryotic model system that reconstitutes this competition mechanism in a controlled and isolated setting. The genetic platform contains a target gene with binding sites for both an activator and a repressor, together with separate overlapping decoy binding sites for the same regulators. Activator and repressor functions are implemented using CRISPRa and CRISPRi, which permit independent control of regulator expression levels, design of the binding sites, and modulation of the binding affinities. Using this minimal system, we demonstrate that increasing activator expression level can reduce expression of the target gene when both regulators are present, consistent with the hypothesis that additional activator molecules displace the repressor from decoy sites, which becomes available to repress the target. By demonstrating how competition for genomic binding sites can invert expected regulatory responses, this synthetic framework provides a system for understanding similar paradoxical behaviors in natural regulatory networks and establishes a foundation for future studies in more complex mammalian contexts.

Implementing logic functions in living cells is a fundamental area of interest among synthetic biologists. The goal of designing biochemical circuits in synthetic biology is to make modular and tractable systems that perform well with predictable behaviors. Developing formalisms towards the design of such systems has proven to be difficult with the diverse retroactive effects that appear with respect to the context of the cell. Repressor-based circuits have various applications in biosynthesis, therapeutics, and bioremediation. Particularly using CRISPRi, competition for components of the system (unbound dCas9) can affect the achievable dynamic range of repression. Moreover, the toxicity of dCas9 via non-specific binding inhibits high levels of expression and limits the performance of genetic circuits. In this work, we study the computation of Boolean functions through CRISPRi based circuits built out of NOT and NOR gates. We provide algebraic expressions that allow us to evaluate the steady-state behaviors of any realized circuit. Our mathematical analysis reveals that the effective non-cooperativity of any given gate is a major bottleneck for increasing the dynamic range of the outputs. Further, we find that under the condition of competition between promoters for dCas9, certain circuit architectures perform better than others depending on factors such as circuit depth, fan-in, and fan-out. We pose optimization problems to evaluate the effects engineerable parameter values to find regimes in which a given circuit performs best. This framework provides a mathematical template and computational library for evaluating the performance of repressor-based circuits with a focus on effective cooperativity.

In the context of epigenetic transformations in cancer metastasis, a puzzling effect was recently discovered, in which the elimination (knock-out) of an activating regulatory element leads to increased (rather than decreased) activity of the element being regulated. It has been postulated that this paradoxical behavior can be explained by activating and repressing transcription factors competing for binding to other possible targets. It is very difficult to prove this hypothesis in mammalian cells, due to the large number of potential players and the complexity of endogenous intracellular regulatory networks. Instead, this paper analyzes this issue through an analogous synthetic biology construct which aims to reproduce the paradoxical behavior using standard bacterial gene expression networks. The paper first reviews the motivating cancer biology work, and then describes a proposed synthetic construct. A mathematical model is formulated, and basic properties of uniqueness of steady states and convergence to equilibria are established, as well as an identification of parameter regimes which should lead to observing such paradoxical phenomena (more activator leads to less activity at steady state). A proof is also given to show that this is a steady-state property, and for initial transients the phenomenon will not be observed. This work adds to the general line of work of resource competition in synthetic circuits.

The identification of constraints on system parameters that will ensure that a system achieves desired requirements remains a challenge in synthetic biology, where components unintendedly affect one another by perturbing the cellular environment in which they operate. This paper shows how to solve this problem optimally for a class of input/output system-level specifications, and for unintended interactions due to resource sharing. Specifically, we show how to solve the problem based on the input/output properties of the subsystems and on the unintended interaction map. Our approach is based on the elimination of quantifiers in monotone properties of the system. We illustrate applications of this methodology to guaranteeing system-level performance of multiplexed and sequential biosensing and of bistable genetic circuits.

Synthetic gene circuits require cellular resources, which are often limited. This leads to competition for resources by different genes, which alter a synthetic genetic circuit's behavior. However, the manner in which competition impacts behavior depends on the identity of the "bottleneck" resource which might be difficult to discern from input-output data. In this paper, we aim at classifying the mathematical structures of resource competition in biochemical circuits. We find that some competition structures can be distinguished by their response to different competitors or resource levels. Specifically, we show that some response curves are always linear, convex, or concave. Furthermore, high levels of certain resources protect the behavior from low competition, while others do not. We also show that competition phenotypes respond differently to various interventions. Such differences can be used to eliminate candidate competition mechanisms when constructing models based on given data. On the other hand, we show that different networks can display mathematically equivalent competition phenotypes.

Synthetic biology constructs often rely upon the introduction of "circuit" genes into host cells, in order to express novel proteins and thus endow the host with a desired behavior. The expression of these new genes "consumes" existing resources in the cell, such as ATP, RNA polymerase, amino acids, and ribosomes. Ribosomal competition among strands of mRNA may be described by a system of nonlinear ODEs called the Ribosomal Flow Model (RFM). The competition for resources between host and circuit genes can be ameliorated by splitting the ribosome pool by use of orthogonal ribosomes, where the circuit genes are exclusively translated by mutated ribosomes. In this work, the RFM system is extended to include orthogonal ribosome competition. This Orthogonal Ribosomal Flow Model (ORFM) is proven to be stable through the use of Robust Lyapunov Functions. The optimization problem of maximizing the weighted protein translation rate by adjusting allocation of ribosomal species is formulated and implemented. Note: publsihed Nov 2020, even though journal reprint says "Nov 2021".

Cells respond to biochemical and physical internal as well as external signals. These signals can be broadly classified into two categories: (a) ``actionable'' or ``reference'' inputs that should elicit appropriate biological or physical responses such as gene expression or motility, and (b) ``disturbances'' or ``perturbations'' that should be ignored or actively filtered-out. These disturbances might be exogenous, such as binding of nonspecific ligands, or endogenous, such as variations in enzyme concentrations or gene copy numbers. In this context, the term robustness describes the capability to produce appropriate responses to reference inputs while at the same time being insensitive to disturbances. These two objectives often conflict with each other and require delicate design trade-offs. Indeed, natural biological systems use complicated and still poorly understood control strategies in order to finely balance the goals of responsiveness and robustness. A better understanding of such natural strategies remains an important scientific goal in itself and will play a role in the construction of synthetic circuits for therapeutic and biosensing applications. A prototype problem in robustly responding to inputs is that of ``robust tracking'', defined by the requirement that some designated internal quantity (for example, the level of expression of a reporter protein) should faithfully follow an input signal while being insensitive to an appropriate class of perturbations. Control theory predicts that a certain type of motif, called integral feedback, will help achieve this goal, and this motif is, in fact, a necessary feature of any system that exhibits robust tracking. Indeed, integral feedback has always been a key component of electrical and mechanical control systems, at least since the 18th century when James Watt employed the centrifugal governor to regulate steam engines. Motivated by this knowledge, biological engineers have proposed various designs for biomolecular integral feedback control mechanisms. However, practical and quantitatively predictable implementations have proved challenging, in part due to the difficulty in obtaining accurate models of transcription, translation, and resource competition in living cells, and the stochasticity inherent in cellular reactions. These challenges prevent first-principles rational design and parameter optimization. In this work, we exploit the versatility of an Escherichia coli cell-free transcription-translation (TXTL) to accurately design, model and then build, a synthetic biomolecular integral controller that precisely controls the expression of a target gene. To our knowledge, this is the first design of a functioning gene network that achieves the goal of making gene expression track an externally imposed reference level, achieves this goal even in the presence of disturbances, and whose performance quantitatively agrees with mathematical predictions.

Utilizing the synthetic transcription-translation (TX-TL) system, this paper studies the impact of nucleotide triphosphates (NTPs) and magnesium (Mg2+), on gene expression, in the context of the counterintuitive phenomenon of suppression of gene expression at high NTP concentration. Measuring translation rates for different Mg2+ and NTP concentrations, we observe a complex resource dependence. We demonstrate that translation is the rate-limiting process that is directly inhibited by high NTP concentrations. Additional Mg2+ can partially reverse this inhibition. In several experiments, we observe two maxima of the translation rate viewed as a function of both Mg2+ and NTP concentration, which can be explained in terms of an NTP-independent effect on the ribosome complex and an NTP- Mg2+ titration effect. The non-trivial compensatory effects of abundance of different vital resources signals the presence of complex regulatory mechanisms to achieve optimal gene expression.

Applying Modular Response Analysis to a synthetic gene circuit, which was introduced in a recent paper by the authors, leads to the inference of a nontrivial "ghost" regulation edge which was not explicitly engineered into the network and which is, in fact, not immediately apparent from experimental measurements. One may thus hypothesize that this ghost regulatory effect is due to competition for resources. A mathematical model is proposed, and analyzed in closed form, that lends validation to this hypothesis.

The connection between optimal biological function and energy use, measured for example by the rate of metabolite consumption, is a current topic of interest in the systems biology literature which has been explored in several different contexts. In [J. P. Barton and E. D. Sontag, Biophys. J. 104, 6 (2013)], we related the metabolic cost of enzymatic futile cycles with their capacity to act as insulators which facilitate modular interconnections in biochemical networks. There we analyzed a simple model system in which a signal molecule regulates the transcription of one or more target proteins by interacting with their promoters. In this note, we consider the case of a protein with an active and an inactive form, and whose activation is controlled by the signal molecule. As in the original case, higher rates of energy consumption are required for better insulator performance.

This paper describes a potential pitfall of perturbation-based approaches to network inference It is shows experimentally, and then explained mathematically, how even in the simplest signaling systems, perturbation methods may lead to paradoxical conclusions: for any given pair of two components X and Y, and depending upon the specific intervention on Y, either an activation or a repression of X could be inferred. The experiments are performed in an in vitro minimal system, thus isolating the effect and showing that it cannot be explained by feedbacks due to unknown intermediates; this system utilizes proteins from a pathway in mammalian (and other eukaryotic) cells that play a central role in proliferation, gene expression, differentiation, mitosis, cell survival, and apoptosis and is a perturbation target of contemporary therapies for various types of cancers. The results show that the simplistic view of intracellular signaling networks being made up of activation and repression links is seriously misleading, and call for a fundamental rethinking of signaling network analysis and inference methods.

A transcriptional system is built based on a 'resource allocator' that sets a core RNAP concentration, which is then shared by multiple sigma fragments, which provide specificity. Adjusting the concentration of the core sets the maximum transcriptional capacity available to a synthetic system.

Complex networks of biochemical reactions, such as intracellular protein signaling pathways and genetic networks, are often conceptualized in terms of ``modules,'' semi-independent collections of components that perform a well-defined function and which may be incorporated in multiple pathways. However, due to sequestration of molecular messengers during interactions and other effects, collectively referred to as retroactivity, real biochemical systems do not exhibit perfect modularity. Biochemical signaling pathways can be insulated from impedance and competition effects, which inhibit modularity, through enzymatic ``futile cycles'' which consume energy, typically in the form of ATP. We hypothesize that better insulation necessarily requires higher energy consumption. We test this hypothesis through a combined theoretical and computational analysis of a simplified physical model of covalent cycles, using two innovative measures of insulation, as well as a new way to characterize optimal insulation through the balancing of these two measures in a Pareto sense. Our results indicate that indeed better insulation requires more energy. While insulation may facilitate evolution by enabling a modular ``plug and play'' interconnection architecture, allowing for the creation of new behaviors by adding targets to existing pathways, our work suggests that this potential benefit must be balanced against the metabolic costs of insulation necessarily incurred in not affecting the behavior of existing processes.

Many reverse-engineering techniques in systems biology rely upon data on steady-state (or dynamic) perturbations –obtained from siRNA, gene knock-down or overexpression, kinase and phosphatase inhibitors, or other interventions– in order to understand the interactions between different ``modules'' in a network. This paper first reviews one such popular such technique, introduced by the author and collaborators, and focuses on why conclusions drawn from its use may be misleading due to ``retroactivity'' (impedance or load) effects. A theoretical result characterizing stoichiometric-induced steady-state retroactivity effects is given for a class of biochemical networks.

Summarized conference version of ``Modularity, retroactivity, and structural identification''.

Modularity plays a fundamental role in the prediction of the behavior of a system from the behavior of its components, guaranteeing that the properties of individual components do not change upon interconnection. Just as electrical, hydraulic, and other physical systems often do not display modularity, nor do many biochemical systems, and specifically, genetic networks. Here, we study the effect of interconnections on the input/output dynamic characteristics of transcriptional components, focusing on a property, which we call "retroactivity," that plays a role analogous to non-zero output impedance in electrical systems. In transcriptional networks, retroactivity is large when the amount of transcription factor is comparable to, or smaller than, the amount of promoter binding sites, or when the affinity of such binding sites is high. In order to attenuate the effect of retroactivity, we propose a feedback mechanism inspired by the design of amplifiers in electronics. We introduce, in particular, a mechanism based on a phosphorylation/dephosphorylation cycle. This mechanism enjoys a remarkable insulation property, due to the fast time scales of the phosphorylation and dephosphorylation reactions. Such a mechanism, when viewed as a signal transduction system, has thus an inherent capacity to provide insulation and hence to increase the modularity of the system in which it is placed.