Hard Limits And Performance Tradeoffs In A Class Of Sequestration Feedback Systems

Feedback regulation is pervasive in biology at both the organismal and cellular level. In this article, we explore the properties of a particular biomolecular feedback mechanism implemented using the sequestration binding of two molecules. Our work develops an analytic framework for understanding the hard limits, performance tradeoffs, and architectural properties of this simple model of biological feedback control. Using tools from control theory, we show that there are simple parametric relationships that determine both the stability and the performance of these systems in terms of speed, robustness, steady-state error, and leakiness. These findings yield a holistic understanding of the behavior of sequestration feedback and contribute to a more general theory of biological control systems

Modularity in signaling systems

Modularity is a property by which the behavior of a system does not change upon interconnection. It is crucial for understanding the behavior of a complex system from the behavior of the composing subsystems. Whether modularity holds in biology is an intriguing and largely debated question. In this paper, we discuss this question taking a control system theory view and focusing on signaling systems. In particular, we argue that, despite signaling systems being constituted of structural modules, such as covalent modification cycles, modularity does not hold in general. As in any engineering system, impedance-like effects, called retroactivity, appear at interconnections and alter the behavior of connected modules. We further argue that while signaling systems have evolved sophisticated ways to counter-act retroactivity and enforce modularity, retroactivity may also be exploited to finely control the information processing of signaling pathways. Testable predictions and experimental evidence are discussed with their implications

Stability and Control of Biomolecular Circuits through Structure

Due to omnipresent uncertainties and environmental disturbances, natural and engineered biological organisms face the challenging control problem of achieving robust performance using unreliable parts. The key to overcoming this challenge rests in identifying structures of biomolecular circuits that are largely invariant despite uncertainties, and building feedback control through such structures. In this work, we develop the tool of log derivatives to capture structures in how the production and degradation rates of molecules depend on concentrations of reactants. We show that log derivatives could establish stability of fixed points based on structure, despite large variations in rates and functional forms of models. Furthermore, we demonstrate how control objectives, such as robust perfect adaptation (i.e. step disturbance rejection), could be implemented through the structures captured. Due to the method's simplicity, structural properties for analysis and design of biomolecular circuits can often be determined by a glance at the equations

Satisfiability, sequence niches, and molecular codes in cellular signaling

Biological information processing as implemented by regulatory and signaling networks in living cells requires sufficient specificity of molecular interaction to distinguish signals from one another, but much of regulation and signaling involves somewhat fuzzy and promiscuous recognition of molecular sequences and structures, which can leave systems vulnerable to crosstalk. This paper examines a simple computational model of protein-protein interactions which reveals both a sharp onset of crosstalk and a fragmentation of the neutral network of viable solutions as more proteins compete for regions of sequence space, revealing intrinsic limits to reliable signaling in the face of promiscuity. These results suggest connections to both phase transitions in constraint satisfaction problems and coding theory bounds on the size of communication codes

Variational cross-validation of slow dynamical modes in molecular kinetics

Markov state models (MSMs) are a widely used method for approximating the eigenspectrum of the molecular dynamics propagator, yielding insight into the long-timescale statistical kinetics and slow dynamical modes of biomolecular systems. However, the lack of a unified theoretical framework for choosing between alternative models has hampered progress, especially for non-experts applying these methods to novel biological systems. Here, we consider cross-validation with a new objective function for estimators of these slow dynamical modes, a generalized matrix Rayleigh quotient (GMRQ), which measures the ability of a rank-$m$ projection operator to capture the slow subspace of the system. It is shown that a variational theorem bounds the GMRQ from above by the sum of the first $m$ eigenvalues of the system's propagator, but that this bound can be violated when the requisite matrix elements are estimated subject to statistical uncertainty. This overfitting can be detected and avoided through cross-validation. These result make it possible to construct Markov state models for protein dynamics in a way that appropriately captures the tradeoff between systematic and statistical errors

Hard Limits And Performance Tradeoffs In A Class Of Sequestration Feedback Systems

Feedback regulation is pervasive in biology at both the organismal and cellular level. In this article, we explore the properties of a particular biomolecular feedback mechanism implemented using the sequestration binding of two molecules. Our work develops an analytic framework for understanding the hard limits, performance tradeoffs, and architectural properties of this simple model of biological feedback control. Using tools from control theory, we show that there are simple parametric relationships that determine both the stability and the performance of these systems in terms of speed, robustness, steady-state error, and leakiness. These findings yield a holistic understanding of the behavior of sequestration feedback and contribute to a more general theory of biological control systems

Architecture, Design, and Tradeoffs in Biomolecular Feedback Systems

A core pursuit in systems and synthetic biology is the analysis of the connection between the low-level structure and parameters of a biomolecular network and its high-level function and performance. Elucidating this mapping has become increasingly feasible as precise measurements of both input parameters and output dynamics become abundant. At the same time, cross-pollination between biology and engineering has led to the realization that many of the mathematical tools from control theory are well-suited to analyze biological processes. The goal of this thesis is to use tools from control theory to analyze a variety of biomolecular systems from both natural and synthetic settings, and subsequently yield insight into the architecture, tradeoffs, and limitations of biological network. In Chapter 2, I demonstrate how allosteric proteins can be used to respond logarithmically to changes in signal. In Chapter 3, I show how control theoretic techniques can be used to inform the design of synthetic integral feedback networks that implement feedback with a sequestration mechanism. Finally, in Chapter 4 I present a novel simplified model of the E. coli heat shock response system and show how the the mapping of circuit parameters to function depends on the network's architecture. The unifying theme of this research is that the conceptual framework used to study engineered systems is remarkably well-suited to biology. That being said, it is important to apply these tools in a way that is informed by the molecular details of biological processes. By combining structural and biochemical data with the functional perspective of engineering, it is possible to understand the architectural principles that underlie living systems.</p

Restoring circadian gene profiles in clock networks using synthetic feedback control

The circadian system—an organism’s built-in biological clock—is responsible for orchestrating biological processes to adapt to diurnal and seasonal variations. Perturbations to the circadian system (e.g., pathogen attack, sudden environmental change) often result in pathophysiological responses (e.g., jetlag in humans, stunted growth in plants, etc.) In view of this, synthetic biologists are progressively adapting the idea of employing synthetic feedback control circuits to alleviate the effects of perturbations on circadian systems. To facilitate the design of such controllers, suitable models are required. Here, we extend our recently developed model for the plant circadian clock—termed the extended S-System model—to model circadian systems across different kingdoms of life. We then use this modeling strategy to develop a design framework, based on an antithetic integral feedback (AIF) controller, to restore a gene’s circadian profile when it is subject to loss-of-function due to external perturbations. The use of the AIF controller is motivated by its recent successful experimental implementation. Our findings provide circadian biologists with a systematic and general modeling and design approach for implementing synthetic feedback control of circadian systems