An N-stage Cascade of Phosphorylation Cycles as an Insulation Device for Synthetic Biological Circuits

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.NIH P50 GMO98792 gran

A control theoretic framework for modular analysis and design of biomolecular networks

Control theory has been instrumental for the analysis and design of a number of engineering systems, including aerospace and transportation systems, robotics and intelligent machines, manufacturing chains, electrical, power, and information networks. In the past several years, the ability of de novo creating biomolecular networks and of measuring key physical quantities has come to a point in which quantitative analysis and design of biological systems is possible. While a modular approach to analyze and design complex systems has proven critical in most control theory applications, it is still subject of debate whether a modular approach is viable in biomolecular networks. In fact, biomolecular networks display context-dependent behavior, that is, the input/output dynamical properties of a module change once this is part of a network. One cause of context dependence, similar to what found in many engineering systems, is retroactivity, that is, the effect of loads applied on a module by downstream systems. In this paper, we focus on retroactivity and review techniques, based on nonlinear control and dynamical systems theory, that we have developed to quantify the extent of modularity of biomolecular systems and to establish modular analysis and design techniques

Modular cell biology: retroactivity and insulation

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. 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 timescales of the phosphorylation and dephosphorylation reactions

Retroactivity attenuation in signaling cascades

It has been shown in an earlier work that impedance-like effects, called retroactivity, are found at the interconnection of biomolecular systems just as they occur in several engineering systems. These effects are particularly relevant in signaling cascades that have several downstream targets. These cascades have been extensively studied to determine how a stimulus at the top of the cascade is transmitted and amplified as it propagates toward the bottom of the cascade. In principle, because of retroactivity, a perturbation at the bottom of the cascade can propagate upstream. In this paper, we study the extent to which this propagation occurs by analytically finding retroactivity gains at each stage of the cascade. These gains determine whether a perturbation at the bottom of the cascade is amplified or attenuated as it propagates upstream.United States. Air Force Office of Scientific Research (Grant FA9550-09-1-0211

Phosphorylation based insulation devices design and implementation

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2013.Cataloged from PDF version of thesis.Includes bibliographical references (p. 85-87).This thesis presents the analysis of a phosphorylation based insulation device implemented in Saccharomyces cerevisae and the minimization of the retroactivity to the input and retroactivity to the output of a single cycle phosphorylation device by means of optimal substrate and phosphatase concentration selection. Characterizing and improving the performance of insulation devices brings us a step closer to their successful implementation in biological circuits, and thus to modularity. To this end, an insulation device was designed and implemented in Saccharomyces cerevisae employing the principle of timescale separation. It was shown experimentally (data pending publication), that the dynamics of the insulation device output remained unchanged in the presence of promoter sites (load) providing retroactivity. In this thesis, the underlying mechanism by which the insulation device retains its dynamic performance in the presence of load is explained through singular perturbation and parameter sensitivity analysis. It was determined that the fast phosphotransfer reactions of the insulation device indeed allowed for retroactivity attenuation provided the substrate and phosphatase concentration are in sufficient amounts. Furthermore, the retroactivity to the input and retroactivity to the output of phosphorylation based insulation devices were parameterized with the substrate and phosphatase concentrations using a single cycle model. While previous works have focused on showing output retroactivity attenuation through high substrate and phosphatase concentration, it is shown that this has detrimental effects on the insulation device performance even in isolation. Employing singular perturbation and contraction theory tools, this work provides a framework to determine an optimal substrate and phosphatase concentration to reach a tradeoff between the retroactivity to the input and the retroactivity to the output.by Phillip M. Rivera Ortiz.S.M

Signaling architectures that transmit unidirectional information

Submitted for review.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.NSF Expedition award number 1521925, NIGMS grant P50 GMO9879

Characterizing biological systems: quantitative methods for synthetic genetic circuits in plants and intracellular mechanics

2018 Summer.Includes bibliographical references.To view the abstract, please see the full text of the document

Physics of epigenetic landscapes and statistical inference by cells

Biology is currently in the midst of a revolution. Great technological advances have led to unprecedented quantitative data at the whole genome level. However, new techniques are needed to deal with this deluge of high-dimensional data. Therefore, statistical physics has the potential to help develop systems biology level models that can incorporate complex data. Additionally, physicists have made great strides in understanding non-equilibrium thermodynamics. However, the consequences of these advances have yet to be fully incorporated into biology. There are three specific problems that I address in my dissertation. First, a common metaphor for describing development is a rugged "epigenetic landscape" where cell fates are represented as attracting valleys resulting from a complex regulatory network. I introduce a framework for explicitly constructing epigenetic landscapes that combines genomic data with techniques from spin-glass physics. The model reproduces known reprogramming protocols and identifies candidate transcription factors for reprogramming to novel cell fates, suggesting epigenetic landscapes are a powerful paradigm for understanding cellular identity. Second, I examine the dynamics of cellular reprogramming. By reanalyzing all available time-series data, I show that gene expression dynamics during reprogramming follow a simple one-dimensional reaction coordinate that is independent of both the time and details of experimental protocol used. I show that such a reaction coordinate emerges naturally from epigenetic landscape models of cell identity where cellular reprogramming is viewed as a "barrier-crossing" between the starting and ending cell fates. Overall, the analysis and model suggest that gene expression dynamics during reprogramming follow a canonical trajectory consistent with the idea of an "optimal path"' in gene expression space for reprogramming. Third, an important task of cells is to perform complex computations in response to external signals. Intricate networks are required to sense and process signals, and since cells are inherently non-equilibrium systems, these networks naturally consume energy. Since there is a deep connection between thermodynamics, computation, and information, a natural question is what constraints does thermodynamics place on statistical estimation and learning. I modeled a single chemical receptor and established the first fundamental relationship between the energy consumption and statistical accuracy of a receptor in a cell