https://hdl.handle.net/1721.1/85574 2026-04-06T23:40:40Z https://hdl.handle.net/1721.1/153914 Competition for binding targets results in paradoxical effects for simultaneous activator and repressor action - Extended Version Al-Radhawi, M. Ali; Manoj, Krishna; Jatkar, Dhruv D.; Duvall, Alon; Del Vecchio, Domitilla; Sontag, Eduardo D. 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. 2024-03-21T00:00:00Z https://hdl.handle.net/1721.1/150329 Error Bound for Hill-Function Approximations in a Class of Stochastic Transcriptional Network Models Hirsch, Dylan; Grunberg, Theodore W.; Del Vecchio, Domitilla Hill functions are often used in stochastic models of gene regulation to approximate the dependence of gene activity on the concentration of the transcription factor which regulates the gene. It is incompletely known, however, how much error one may incur from this approximation. We investigate this question in the context of transcriptional networks (TN). In particular, under the assumption of rapid binding and unbinding of transcription factors with their gene targets, we bound the approximation error associated with Hill functions for TNs in which each transcription factor regulates a gene in a one-to-one fashion and each regulated gene produces a single transcription factor. We also assume that transcription factors do not homodimerize or heterodimerize and that each gene only has a single transcription factor binding site. These results are pertinent for the modeling of TNs and may also carry relevance for more general biological processes. Extended version 2023-04-01T00:00:00Z https://hdl.handle.net/1721.1/150328.2 Robust model invalidation for chemical reaction networks using generalized moments (extended version) Grunberg, Theodore W.; Del Vecchio, Domitilla Many biomolecular systems can be described by chemical reaction networks. Determining which chemical reaction network models are inconsistent with observed data can be done via model invalidation. In this work, we formulate and solve a robust version of the model invalidation problem for the case where only measurements from the stationary distribution are available. This problem corresponds to determining if an observed distribution could have been generated by the given chemical reaction network for some value of the parameters, plus a perturbation of bounded size with respect to total variation distance. The main technical tool we introduce to solve the problem is a set of generalized moments that make the problem amenable to an algorithmic solution. Extended version 2023-03-31T00:00:00Z https://hdl.handle.net/1721.1/150328 Robust model invalidation for chemical reaction networks using generalized moments (extended version) Grunberg, Theodore W.; Del Vecchio, Domitilla Many biomolecular systems can be described by chemical reaction networks. Determining which chemical reaction network models are inconsistent with observed data can be done via model invalidation. In this work, we formulate and solve a robust version of the model invalidation problem for the case where only measurements from the stationary distribution are available. This problem corresponds to determining if an observed distribution could have been generated by the given chemical reaction network for some value of the parameters, plus a perturbation of bounded size with respect to total variation distance. The main technical tool we introduce to solve the problem is a set of generalized moments that make the problem amenable to an algorithmic solution. Extended version 2023-03-31T00:00:00Z https://hdl.handle.net/1721.1/120973 Time-scale separation based design of biomolecular feedback controllers (extended version) Grunberg, Theodore W.; Del Vecchio, Domitilla Time-scale separation is a powerful property that can be used to simplify control systems design. In this work, we consider the problem of designing biomolecular feedback controllers that provide tracking of slowly varying references and rejection of slowly varying disturbances for nonlinear systems. We propose a design methodology that uses time-scale separation to accommodate physical constraints on the implementation of integral control in cellular systems. The main result of this paper gives sufficient conditions under which controllers designed using our time-scale separation methodology have desired asymptotic performance when the reference and disturbance are constant or slowly varying. Our analysis is based on construction of Lyapunov functions for a class of singularly perturbed systems that are dependent on an additional parameter that perturbs the system regularly. When the exogenous inputs are slowly varying, this approach allows us to bound the system trajectories by a function of the regularly perturbing parameter. This bound decays to zero as the parameter's value increases, while an inner-estimate of the region of attraction stays unchanged as this parameter is varied. These results cannot be derived using standard singular perturbation results. We apply our results to an application demonstrating a physically realizable parameter tuning that controls performance. 2019-03-14T00:00:00Z https://hdl.handle.net/1721.1/118380 The Number of Equilibrium Points of Perturbed Nonlinear Positive Dynamical Systems (Extended Version) McBride, Cameron; Del Vecchio, Domitilla The number of equilibrium points of a dynamical system dictates important qualitative properties such as the ability of the system to store different memory states, and may be significantly affected by state-dependent perturbations. In this paper, we develop a methodology based on tools from degree theory to determine whether the number of equilibrium points in a positive dynamical system changes due to structured state-dependent perturbations. Positive dynamical systems are particularly well suited to describe biological systems where the states are always positive. We prove two main theorems that utilize the determinant of the system's Jacobian to find algebraic conditions on the parameters determining whether the number of equilibrium points is guaranteed either to change or to remain the same when a nominal system is compared to its perturbed counterpart. We demonstrate the application of the theoretical results to genetic circuits where state-dependent perturbations arise due to fluctuations in cellular resources. These fluctuations constitute a major problem for predicting the behavior of genetic circuits. Our results allow us to determine whether such fluctuations change the genetic circuit's intended number of steady states. 2019-07-26T00:00:00Z https://hdl.handle.net/1721.1/118144 Genetic Circuit-Host Ribosome Transactions: Diffusion-Reaction Model Barajas, Carlos; Del Vecchio, Domitilla Deterministic models of bacterial genetic circuits commonly assume a well-mixed ensemble of species. This assumption results in ordinary differential equations (ODEs) describing the rate of change of the mean species concentration. It is however well known that species are non-homogenously distributed within a bacterial cell, where genes on the chromosome are found mostly at the center of the cell while synthetic genes residing on plasmids are often found at the poles. Most importantly, ribosomes, the key gene expression resource, are also arranged according to a non-homogenous profile. Therefore, when analyzing the effects of sharing gene expression resources, such as ribosomes, among synthetic genetic circuits and chromosomal genes, it may be important to consider the effects of spatial heterogeneity of the relevant species. In this paper, we use a partial differential equation (PDE) model to capture the spatial heterogeneity of species concentration. Solutions to the model are gathered numerically and approximations are derived via perturbation analysis in the limit of fast diffusion. The solutions are compared to those of the conventional ``well-mixed'' ODE model. The fast-diffusion approximation predicts higher protein production rates for all mRNAs in the cell and in some cases, these rates are more sensitive to the activation of synthetic genes relative to the well-mixed model. This trend is confirmed numerically using common biological parameters to simulate the full PDE system. 2018-09-18T00:00:00Z https://hdl.handle.net/1721.1/110896 Deterministic-like model reduction for a class of multi-scale stochastic differential equations with application to biomolecular systems (Extended Version) Herath, Narmada; Del Vecchio, Domitilla 2017-08-01T00:00:00Z https://hdl.handle.net/1721.1/106135 Signaling architectures that transmit unidirectional information Shah, Rushina; Del Vecchio, Domitilla A signaling pathway transmits information from an upstream system to downstream systems, ideally unidirectionally. A key bottleneck to unidirectional transmission is retroactivity, which is the additional reaction flux that affects a system once its species interact with those of downstream systems. This raises the question of whether signaling pathways have developed specialized architectures that overcome retroactivity and transmit unidirectional signals. Here, we propose a general mathematical framework that provides an answer to this question. Using this framework, we analyze the ability of a variety of signaling architectures to transmit signals unidirectionally as key biological parameters are tuned. In particular, we find that single stage phosphorylation and phosphotransfer systems that transmit signals from a kinase show the following trade-off: either they impart a large retroactivity to their upstream system or they are significantly impacted by the retroactivity due to their downstream system. However, cascades of these architectures, which are highly represented in nature, can overcome this trade-off and thus enable unidirectional information transmission. By contrast, single and double phosphorylation cycles that transmit signals from a substrate impart a large retroactivity to their upstream system and are also unable to attenuate retroactivity due to their downstream system. Our findings identify signaling architectures that ensure unidirectional signal transmission and minimize crosstalk among multiple targets. Our results thus establish a way to decompose a signal transduction network into architectures that transmit information unidirectionally, while also providing a library of devices that can be used in synthetic biology to facilitate modular circuit design. Submitted for review. 2016-12-24T00:00:00Z https://hdl.handle.net/1721.1/104905 Controller design under safety specifications for a class of bounded hybrid automata Hoehener, Daniel; Del Vecchio, Domitilla Motivated by driver-assist systems that warn the driver before taking control action, we study the safety problem for a class of bounded hybrid automata. We show that for this class there exists a least restrictive safe feedback controller that has a simple structure and can be computed efficiently online. The theoretical results are then used to design driver-assist systems for rear-end and merging collision scenarios. 2016-12-01T00:00:00Z https://hdl.handle.net/1721.1/104383 Mitigation of ribosome competition through distributed sRNA feedback (extended version) Qian, Yili; Del Vecchio, Domitilla A current challenge in the robust engineering of synthetic gene networks is context dependence, the unintended interactions among genes and host factors. Ribosome competition is a specific form of context dependence, where all genes in the network compete for a limited pool of translational resources available for gene expression. Recently, theoretical and experimental studies have shown that ribosome competition creates a hidden layer of interactions among genes, which largely hinders our ability to predict design outcomes. In this work, we establish a control theoretic framework, where these hidden interactions become disturbance signals. We then propose a distributed feedback mechanism to achieve disturbance decoupling in the network. The feedback loop at each node consists of the protein product transcriptionally activating a small RNA (sRNA), which forms a translationally inactive complex with mRNA rapidly. We illustrate that with this feedback mechanism, protein production at each node is only dependent on its own transcription factor inputs, and almost independent of hidden interactions arising from ribosome competition. This paper is an extended version of a paper of the same title accepted to Proceedings of the 55th IEEE Conference on Decision and Control (2016). 2016-09-23T00:00:00Z https://hdl.handle.net/1721.1/104333 Hitting time behavior for the solution of a stochastic differential equation Herath, Narmada; Del Vecchio, Domitilla 2016-09-13T00:00:00Z https://hdl.handle.net/1721.1/101877 An N-stage Cascade of Phosphorylation Cycles as an Insulation Device for Synthetic Biological Circuits Shah, Rushina; Del Vecchio, Domitilla Single phosphorylation cycles have been found to have insulation device abilities, that is, they attenuate the effect of retroactivity applied by downstream systems and hence facilitate modular design in synthetic biology. It was recently discovered that this retroactivity attenuation property comes at the expense of an increased retroactivity to the input of the insulation device, wherein the device slows down the signal it receives from its upstream system. In this paper, we demonstrate that insulation devices built of cascaded phosphorylation cycles can break this tradeoff allowing to attenuate the retroactivity applied by downstream systems while keeping a small retroactivity to the input. In particular, we show that there is an optimal number of cycles that maximally extends the linear operating region of the insulation device while keeping the desired retroactivity properties, when a common phosphatase is used. These findings provide optimal design strategies of insulation devices for synthetic biology applications. 2016-03-27T00:00:00Z https://hdl.handle.net/1721.1/101758 A Dynamical Model for the Low Efficiency of Induced Pluripotent Stem Cell Reprogramming (Extended Version) Abdallah, Hussein; Qian, Yili; Del Vecchio, Domitilla In the past decade, researchers have been able to obtain pluripotent stem cells directly from an organism’s differentiated cells through a process called cell reprogramming. This opens the way to potentially groundbreaking applications in regenerative and personalized medicine, in which ill patients could use self-derived induced pluripotent stem (iPS) cells where needed. While the process of reprogramming has been shown to be possible, its efficiency remains so low after almost ten years since its conception as to render its applicability limited to laboratory research. In this paper, we study a mathematical model of the core transcriptional circuitry among a set of key transcription factors, which is thought to determine the switch among pluripotent and blue early differentiated cell types. By employing standard tools from dynamical systems theory, we analyze the effects on the system’s dynamics of overexpressing the core factors, which is what is performed during the reprogramming process. We demonstrate that the structure of the system is such that it can render the switch from an initial stable steady state (differentiated cell type) to the desired stable steady state (pluripotent cell type) highly unlikely. This finding provides insights into a possible reason for the low efficiency of current reprogramming approaches. We also suggest a strategy for improving the reprogramming process that employs simultaneous overexpression of one transcription factor along with enhanced degradation of another. This is an extended version of a paper of the same title accepted to the 2016 American Control Conference (ACC) 2016-03-22T00:00:00Z https://hdl.handle.net/1721.1/101755 Model reduction for a class of singularly perturbed stochastic differential equations : Fast variable approximation (Extended Version) Herath, Narmada; Del Vecchio, Domitilla This is an extended version of a paper of the same title accepted to American Control Conference (ACC) 2016. 2016-03-22T00:00:00Z https://hdl.handle.net/1721.1/101692 Deterministic model derivation and model reduction of an activator-repressor genetic oscillator Kumar, Nithin Senthur; Del Vecchio, Domitilla 2016-03-14T00:00:00Z https://hdl.handle.net/1721.1/101596 Design of a lane departure driver-assist system under safety specifications Hoehener, Daniel; Huang, Geng; Del Vecchio, Domitilla We use a controlled invariance approach to design a semi-autonomous lane departure assist system that is guaranteed to keep the vehicle in the lane. The controlled invariant safe set is the set of system states from which an input exists that can keep the vehicle in the lane. First we provide theoretical conditions under which the controlled invariant safe set has a simple characterization that can be quickly computed in real-time. We then use this characterization to derive a feedback strategy that keeps the vehicle in the lane and overrides the driver only if he/she could otherwise force a future lane departure. We also provide a detailed description of the above mentioned conditions, including algorithmic approaches that allow to verify whether these conditions are satisfied. 2016-03-04T00:00:00Z https://hdl.handle.net/1721.1/98269 Automatic Quantifications of Dynamics of Genetic Circuits in a Single Cell in Chemostat Huang, Hsin-Ho; Del Vecchio, Domitilla Modular design of genetic circuits requires iterations of experimental and theoretical efforts to make the design process reliable and the resulting behaviors predictable. This technical report demonstrates a fully automatic experiment procedure by using the MSP FlowCytoPrep 5000 Sample Prep system to deliver samples prepared from multiplex miniature stirred tank reactors (Flexostat) to the flow cytometer BD Accuri C6 to quantify dynamics of an transcription activator cascade in a single cell in chemostat. 2015-08-31T00:00:00Z https://hdl.handle.net/1721.1/90250 Order Preserving Properties of Vehicle Dynamics with Respect to the Driver's Input Forghani, Mojtaba; Del Vecchio, Domitilla 2014-09-20T00:00:00Z https://hdl.handle.net/1721.1/90249 Technical Report on "Limitations and trade-offs in gene expression due to competition for shared cellular resources" Gyorgy, Andras; Del Vecchio, Domitilla This is a technical report accompanying the paper entitled “Limitations and trade-offs in gene expression due to competition for shared cellular resources”. 2014-09-19T00:00:00Z https://hdl.handle.net/1721.1/85691 Stochastic Stability Properties of a Singularly Perturbed Chemical Langevin Equation Herath, Narmada; Del Vecchio, Domitilla 2014-03-18T00:00:00Z