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

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

Role of interaction network topology in controlling microbial population in consortia

Engineering microbial consortia is an important new frontier for synthetic biology given its efficiency in performing complex tasks and endurance to environmental uncertainty. Most synthetic circuits regulate populational behaviors via cell-to-cell interactions, which are affected by spatially heterogeneous environments. Therefore, it is important to understand the limits on controlling system dynamics and provide a control strategy for engineering consortia under spatial structures. Here, we build a network model for a fractional population control circuit in two-strain consortia, and characterize the cell-to-cell interaction network by topological properties, such as symmetry, locality and connectivity. Using linear network control theory, we relate the network topology to system output's tracking performance. We analytically and numerically demonstrate that the minimum network control cost for good tracking depends on locality difference between two cell population's spatial distributions and how strongly the controller node contributes to interaction strength. To realize a robust consortia, we can manipulate the environment to form a strongly connected network. Our results ground the expected cell population dynamics in its spatially organized interaction network, and inspire directions in cooperative control in microbial consortia

Competition Triggers Plasmid-Mediated Enhancement of Substrate Utilisation in Pseudomonas putida

Competition between species plays a central role in the activity and structure of communities. Stable co-existence of diverse organisms in communities is thought to be fostered by individual tradeoffs and optimization of competitive strategies along resource gradients. Outside the laboratory, microbes exist as multispecies consortia, continuously interacting with one another and the environment. Survival and proliferation of a particular species is governed by its competitive fitness. Therefore, bacteria must be able to continuously sense their immediate environs for presence of competitors and prevailing conditions. Here we present results of our investigations on a novel competition sensing mechanism in the rhizosphere-inhabiting Pseudomonas putida KT2440, harbouring gfpmut3b-modified KanR TOL plasmid. We monitored benzyl alcohol (BA) degradation rate, along with GFP expression profiling in mono species and dual species cultures. Interestingly, enhanced plasmid expression (monitored using GFP expression) and consequent BA degradation were observed in dual species consortia, irrespective of whether the competitor was a BA degrader (Pseudomonas aeruginosa) or a non-degrader (E. coli). Attempts at elucidation of the mechanistic aspects of induction indicated the role of physical interaction, but not of any diffusible compounds emanating from the competitors. This contention is supported by the observation that greater induction took place in presence of increasing number of competitors. Inert microspheres mimicking competitor cell size and concentration did not elicit any significant induction, further suggesting the role of physical cell-cell interaction. Furthermore, it was also established that cell wall compromised competitor had minimal induction capability. We conclude that P. putida harbouring pWW0 experience a competitive stress when grown as dual-species consortium, irrespective of the counterpart being BA degrader or not. The immediate effect of this stress is a marked increase in expression of TOL, leading to rapid utilization of the available carbon source and massive increase in its population density. The plausible mechanisms behind the phenomenon are hypothesised and practical implications are indicated and discussed

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

Design and analysis of genetic feedback architectures for synthetic biology

Synthetic Biology seeks to design and assemble novel biological systems with favourable properties. It allows us to comprehend and modify the fundamental mechanisms of life and holds significant promise in revolutionizing current technologies ranging from medicine and biomanufacturing to energy and environmental protection. Biological processes constitute remarkably complex dynamical systems operating impeccably well in messy and constantly changing environments. Their ability to do so is rooted in sophisticated molecular control architectures crafted by natural evolutionary innovation over billions of years. Such control architectures, often blended with human-engineering approaches, are the key to realizing efficient and reliable synthetic biological systems. Aiming to accelerate the development of the latter, the present thesis addresses some fundamental challenges in biomolecular systems and control design. We begin by elucidating biological mechanisms of temporal gradient computation, enabling cells to adjust their behaviour in response to anticipated environmental changes. Specifically, we introduce biomolecular motifs capable of functioning as highly tunable and accurate signal differentiators to input molecular signals around their nominal operation. We investigate strategies to deal with high-frequency input signal components which can be detrimental to the performance of most differentiators. We ascertain the occurrence of such motifs in natural regulatory networks and demonstrate the potential of synthetic experimental realizations. Our motifs can serve as reliable speed biosensors and can form the basis for derivative feedback control. Motivated by the pervasiveness of Proportional-Integral-Derivative (PID) controllers in modern technological applications, we present the realization of a PID controller via biomolecular reactions employing, among others, our differentiator motifs. This biomolecular architecture represents a PID control law with set point weighting and filtered derivative action, offering robust regulation of a single-output biological process with enhanced dynamic performance and low levels of stochastic noise. It is characterized by significant ease of tuning and can be of particular experimental interest in molecular programming applications. Finally, we investigate efficient regulation strategies for multi-output biological processes with internal coupling interactions, expanding previously established single-output control approaches. More specifically, we propose control schemes allowing for robust manipulation of the outputs in various ways, namely manipulation of their product/ratio, linear combinations of them as well as manipulation of each of the outputs independently. Our analysis is centered around two-output biological processes, yet the scalability of the proposed regulation strategies to processes with a higher number of outputs is highlighted. In parallel, their experimental implementability is explored in both in vivo and in vitro settings

Strategies for wheat stripe rust pathogenicity identified by transcriptome sequencing

Stripe rust caused by the fungus Puccinia striiformis f.sp. tritici (Pst) is a major constraint to wheat production worldwide. The molecular events that underlie Pst pathogenicity are largely unknown. Like all rusts, Pst creates a specialized cellular structure within host cells called the haustorium to obtain nutrients from wheat, and to secrete pathogenicity factors called effector proteins. We purified Pst haustoria and used next-generation sequencing platforms to assemble the haustorial transcriptome as well as the transcriptome of germinated spores. 12,282 transcripts were assembled from 454-pyrosequencing data and used as reference for digital gene expression analysis to compare the germinated uredinospores and haustoria transcriptomes based on Illumina RNAseq data. More than 400 genes encoding secreted proteins which constitute candidate effectors were identified from the haustorial transcriptome, with two thirds of these up-regulated in this tissue compared to germinated spores. RT-PCR analysis confirmed the expression patterns of 94 effector candidates. The analysis also revealed that spores rely mainly on stored energy reserves for growth and development, while haustoria take up host nutrients for massive energy production for biosynthetic pathways and the ultimate production of spores. Together, these studies substantially increase our knowledge of potential Pst effectors and provide new insights into the pathogenic strategies of this important organism.J.P.R. is an ARC Future Fellow (FT0992129). This project has been supported by Bioplatforms Australia through funding from the Commonwealth Government NCRIS and Education Investment Fund Super Science programs