| Publications of Eduardo D. Sontag jointly with D. Del Vecchio |
| Articles in journal or book chapters |
| 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. |
| In biological processes such as embryonic development, hematopoietic cell differentiation, and the arising of tumor heterogeneity and consequent resistance to therapy, mechanisms of gene activation and deactivation may play a role in the emergence of phenotypically heterogeneous yet genetically identical (clonal) cellular populations. Mathematically, the variability in phenotypes in the absence of genetic variation can be modeled through the existence of multiple metastable attractors in nonlinear systems subject with stochastic switching, each one of them associated to an alternative epigenetic state. An important theoretical and practical question is that of estimating the number and location of these states, as well as their relative probabilities of occurrence. This paper focuses on a rigorous analytic characterization of multiple modes under slow promoter kinetics, which is a feature of epigenetic regulation. It characterizes the stationary distributions of Chemical Master Equations for gene regulatory networks as a mixture of Poisson distributions. As illustrations, the theory is used to tease out the role of cooperative binding in stochastic models in comparison to deterministic models, and applications are given to various model systems, such as toggle switches in isolation or in communicating populations and a trans-differentiation network. |
| This paper is a review of systems and control problems in synthetic biology, focusing on past accomplishments and open problems. It is partially a report on the workshop "The Compositionality Problem in Synthetic Biology: New Directions for Control Theory" held on June 26-27, 2017 at MIT, and organized by D. Del Vecchio, R. M. Murray, and E. D. Sontag |
| Biological signal transduction networks are commonly viewed as circuits that pass along in the process amplifying signals, enhancing sensitivity, or performing other signal-processing to transcriptional and other components. Here, we report on a "reverse-causality" phenomenon, which we call load-induced modulation. Through a combination of analytical and experimental tools, we discovered that signaling was modulated, in a surprising way, by downstream targets that receive the signal and, in doing so, apply what in physics is called a load. Specifically, we found that non-intuitive changes in response dynamics occurred for a covalent modification cycle when load was present. Loading altered the response time of a system, depending on whether the activity of one of the enzymes was maximal and the other was operating at its minimal rate or whether both enzymes were operating at submaximal rates. These two conditions, which we call "limit regime" and "intermediate regime," were associated with increased or decreased response times, respectively. The bandwidth, the range of frequency in which the system can process information, decreased in the presence of load, suggesting that downstream targets participate in establishing a balance between noise-filtering capabilities and a its ability to process high-frequency stimulation. Nodes in a signaling network are not independent relay devices, but rather are modulated by their downstream targets |
| This is an expository paper about certain aspects of Synthetic Biology, including a discussion of the issue of modularity (load effects from downstream components). |
| 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. |
| Conference articles |
| 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. |
| Cellular reprogramming is traditionally accomplished through an open loop control approach, wherein key transcription factors are injected in cells to steer a gene regulatory network toward a pluripotent state. Recently, a closed loop feedback control strategy was proposed in order to achieve more accurate control. Previous analyses of the controller were based on deterministic models, ignoring the substantial stochasticity in these networks, Here we analyze the Chemical Master Equation for reaction models with and without the feedback controller. We computationally and analytically investigate the performance of the controller in biologically relevant parameter regimes where stochastic effects dictate system dynamics. Our results indicate that the feedback control approach still ensures reprogramming even when analyzed using a stochastic model. |
| In the mathematical modeling of cell differentiation, it is common to think of internal states of cells (quanfitied by activation levels of certain genes) as determining different cell types. We study here the "PU.1/GATA-1 circuit" that controls the development of mature blood cells from hematopoietic stem cells (HSCs). We introduce a rigorous chemical reaction network model of the PU.1/GATA-1 circuit, which incorporates current biological knowledge and find that the resulting ODE model of these biomolecular reactions is incapable of exhibiting multistability, contradicting the fact that differentiation networks have, by definition, alternative stable steady states. When considering instead the stochastic version of this chemical network, we analytically construct the stationary distribution, and are able to show that this distribution is indeed capable of admitting a multiplicity of modes. Finally, we study how a judicious choice of system parameters serves to bias the probabilities towards different stationary states. We remark that certain changes in system parameters can be physically implemented by a biological feedback mechanism; tuning this feedback gives extra degrees of freedom that allow one to assign higher likelihood to some cell types over others. |
| This paper adopts a contraction approach to the analysis of the tracking properties of dynamical systems under high gain feedback when subject to inputs with bounded derivatives. It is shown that if the tracking error dynamics are contracting, then the system is input to output stable with respect to the input signal derivatives and the output tracking error. As an application, it iss hown that the negative feedback connection of plants composed of two strictly positive real LTI subsystems in cascade can follow external inputs with tracking errors that can be made arbitrarily small by applying a sufficiently large feedback gain. We utilize this result to design a biomolecular feedback for a synthetic genetic sensor to make it robust to variations in the availability of a cellular resource required for protein production. |
| This tutorial paper presents an introduction to systems and synthetic molecular biology. It provides an introduction to basic biological concepts, and describes some of the techniques as well as challenges in the analysis and design of biomolecular networks. |
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