Shara Balakrishnan

Bio: Shara Balakrishnan is an academic researcher from University of California, Santa Barbara. The author has contributed to research in topics: Engineering & Dynamic mode decomposition. The author has an hindex of 2, co-authored 5 publications receiving 5 citations.

Steady state programming of controlled nonlinear systems via deep dynamic mode decomposition.

Abstract: This paper describes the optimal selection of a control policy to program the steady state of controlled nonlinear systems with hyperbolic fixed points. This work is motivated by the field of synthetic biology, in which saddle points are common (along with limit cycles), and the aim is to program cells to perform both digital and analog computation, though developing genetic digital computation has been the main focus. We frame the analog computing challenge of generating a steady state input-output function inside living cells. To program the steady state, a data-driven approach is taken wherein an approximation of the Koopman operator, identified via deep dynamic mode decomposition, is used to describe the dynamics of the system linearly. The new representation of the dynamics are then used to solve an optimization problem for the input which maximizes a direction in state space. Some added structure on the Koopman operator learning process for controlled systems is given for dynamics that are separable in the state and input. Finally, the methods are demonstrated on simulation examples of an incoherent feedforward loop and a combinatorial promoter system, two common network architectures seen in the field of synthetic biology.

Prediction of fitness in bacteria with causal jump dynamic mode decomposition.

Abstract: In this paper, we consider the problem of learning a predictive model for population cell growth dynamics as a function of the media conditions. We first introduce a generic data-driven framework for training operator-theoretic models to predict cell growth rate. We then introduce the experimental design and data generated in this study, namely growth curves of Pseudomonas putida as a function of casein and glucose concentrations. We use a data driven approach for model identification, specifically the nonlinear autoregressive (NAR) model to represent the dynamics. We show theoretically that Hankel DMD can be used to obtain a solution of the NAR model. We show that it identifies a constrained NAR model and to obtain a more general solution, we define a causal state space system using 1-step,2-step,...,{\tau}-step predictors of the NAR model and identify a Koopman operator for this model using extended dynamic mode decomposition. The hybrid scheme we call causal-jump dynamic mode decomposition, which we illustrate on a growth profile or fitness prediction challenge as a function of different input growth conditions. We show that our model is able to recapitulate training growth curve data with 96.6% accuracy and predict test growth curve data with 91% accuracy.

Learning transcriptome dynamics for discovery of optimal genetic reporters of novel compounds

Abstract: Accelerating the design of synthetic biological circuits requires 1 expanding the currently available genetic toolkit. Although 2 whole-cell biosensors have been successfully engineered and de-3 ployed, particularly in applications such as environmental and 4 medical diagnostics, novel sensing applications necessitate the 5 discovery and optimization of novel biosensors. Here, we ad-6 dress this issue of the limited repertoire of biosensors by de-7 veloping a data-driven, transcriptome-wide approach to discover 8 perturbation-inducible genes from time-series RNA sequencing 9 data, guiding the design of synthetic transcriptional reporters. 10 By combining techniques from dynamical systems and control 11 theory, we show that high-dimensional transcriptome dynamics 12 can be efficiently represented and used to rank genes based on 13 their ability to report the perturbation-specific cell state. We 14 extract, construct, and validate 15 functional biosensors for the 15 organophosphate malathion in the underutilized host organism 16 Pseudomonas fluorescens SBW25, provide a computational ap-17 proach to aggregate individual biosensor responses to facilitate 18 enhanced reporting, and exemplify their ability to be useful out-19 side the lab by detecting malathion in the environment. The 20 library of living malathion sensors can be optimized for use in 21 environmental diagnostics while the developed machine learning 22 tool can be applied to discover perturbation-inducible gene ex-23 pression systems in the compendium of host organisms. 24

The Effect of Sensor Fusion on Data-Driven Learning of Koopman Operators.

Abstract: Dictionary methods for system identification typically rely on one set of measurements to learn governing dynamics of a system. In this paper, we investigate how fusion of output measurements with state measurements affects the dictionary selection process in Koopman operator learning problems. While prior methods use dynamical conjugacy to show a direct link between Koopman eigenfunctions in two distinct data spaces (measurement channels), we explore the specific case where output measurements are nonlinear, non-invertible functions of the system state. This setup reflects the measurement constraints of many classes of physical systems, e.g., biological measurement data, where one type of measurement does not directly transform to another. We propose output constrained Koopman operators (OC-KOs) as a new framework to fuse two measurement sets. We show that OC-KOs are effective for sensor fusion by proving that when learning a Koopman operator, output measurement functions serve to constrain the space of potential Koopman observables and their eigenfunctions. Further, low-dimensional output measurements can be embedded to inform selection of Koopman dictionary functions for high-dimensional models. We propose two algorithms to identify OC-KO representations directly from data: a direct optimization method that uses state and output data simultaneously and a sequential optimization method. We prove a theorem to show that the solution spaces of the two optimization problems are equivalent. We illustrate these findings with a theoretical example and two numerical simulations.

Learning perturbation-inducible cell states from observability analysis of transcriptome dynamics

Abstract: A major challenge in biotechnology and biomanufacturing is the identification of a set of biomarkers for perturbations and metabolites of interest. Here, we develop a data-driven, transcriptome-wide approach to rank perturbation-inducible genes from time-series RNA sequencing data for the discovery of analyte-responsive promoters. This provides a set of biomarkers that act as a proxy for the transcriptional state referred to as cell state. We construct low-dimensional models of gene expression dynamics and rank genes by their ability to capture the perturbation-specific cell state using a novel observability analysis. Using this ranking, we extract 15 analyte-responsive promoters for the organophosphate malathion in the underutilized host organism Pseudomonas fluorescens SBW25. We develop synthetic genetic reporters from each analyte-responsive promoter and characterize their response to malathion. Furthermore, we enhance malathion reporting through the aggregation of the response of individual reporters with a synthetic consortium approach, and we exemplify the library's ability to be useful outside the lab by detecting malathion in the environment. The engineered host cell, a living malathion sensor, can be optimized for use in environmental diagnostics while the developed machine learning tool can be applied to discover perturbation-inducible gene expression systems in the compendium of host organisms.

Modern Koopman Theory for Dynamical Systems.

Abstract: The field of dynamical systems is being transformed by the mathematical tools and algorithms emerging from modern computing and data science. First-principles derivations and asymptotic reductions are giving way to data-driven approaches that formulate models in operator theoretic or probabilistic frameworks. Koopman spectral theory has emerged as a dominant perspective over the past decade, in which nonlinear dynamics are represented in terms of an infinite-dimensional linear operator acting on the space of all possible measurement functions of the system. This linear representation of nonlinear dynamics has tremendous potential to enable the prediction, estimation, and control of nonlinear systems with standard textbook methods developed for linear systems. However, obtaining finite-dimensional coordinate systems and embeddings in which the dynamics appear approximately linear remains a central open challenge. The success of Koopman analysis is due primarily to three key factors: 1) there exists rigorous theory connecting it to classical geometric approaches for dynamical systems, 2) the approach is formulated in terms of measurements, making it ideal for leveraging big-data and machine learning techniques, and 3) simple, yet powerful numerical algorithms, such as the dynamic mode decomposition (DMD), have been developed and extended to reduce Koopman theory to practice in real-world applications. In this review, we provide an overview of modern Koopman operator theory, describing recent theoretical and algorithmic developments and highlighting these methods with a diverse range of applications. We also discuss key advances and challenges in the rapidly growing field of machine learning that are likely to drive future developments and significantly transform the theoretical landscape of dynamical systems.

Learning transcriptome dynamics for discovery of optimal genetic reporters of novel compounds

Abstract: Accelerating the design of synthetic biological circuits requires 1 expanding the currently available genetic toolkit. Although 2 whole-cell biosensors have been successfully engineered and de-3 ployed, particularly in applications such as environmental and 4 medical diagnostics, novel sensing applications necessitate the 5 discovery and optimization of novel biosensors. Here, we ad-6 dress this issue of the limited repertoire of biosensors by de-7 veloping a data-driven, transcriptome-wide approach to discover 8 perturbation-inducible genes from time-series RNA sequencing 9 data, guiding the design of synthetic transcriptional reporters. 10 By combining techniques from dynamical systems and control 11 theory, we show that high-dimensional transcriptome dynamics 12 can be efficiently represented and used to rank genes based on 13 their ability to report the perturbation-specific cell state. We 14 extract, construct, and validate 15 functional biosensors for the 15 organophosphate malathion in the underutilized host organism 16 Pseudomonas fluorescens SBW25, provide a computational ap-17 proach to aggregate individual biosensor responses to facilitate 18 enhanced reporting, and exemplify their ability to be useful out-19 side the lab by detecting malathion in the environment. The 20 library of living malathion sensors can be optimized for use in 21 environmental diagnostics while the developed machine learning 22 tool can be applied to discover perturbation-inducible gene ex-23 pression systems in the compendium of host organisms. 24

The Effect of Sensor Fusion on Data-Driven Learning of Koopman Operators.

Abstract: Dictionary methods for system identification typically rely on one set of measurements to learn governing dynamics of a system. In this paper, we investigate how fusion of output measurements with state measurements affects the dictionary selection process in Koopman operator learning problems. While prior methods use dynamical conjugacy to show a direct link between Koopman eigenfunctions in two distinct data spaces (measurement channels), we explore the specific case where output measurements are nonlinear, non-invertible functions of the system state. This setup reflects the measurement constraints of many classes of physical systems, e.g., biological measurement data, where one type of measurement does not directly transform to another. We propose output constrained Koopman operators (OC-KOs) as a new framework to fuse two measurement sets. We show that OC-KOs are effective for sensor fusion by proving that when learning a Koopman operator, output measurement functions serve to constrain the space of potential Koopman observables and their eigenfunctions. Further, low-dimensional output measurements can be embedded to inform selection of Koopman dictionary functions for high-dimensional models. We propose two algorithms to identify OC-KO representations directly from data: a direct optimization method that uses state and output data simultaneously and a sequential optimization method. We prove a theorem to show that the solution spaces of the two optimization problems are equivalent. We illustrate these findings with a theoretical example and two numerical simulations.

Learning perturbation-inducible cell states from observability analysis of transcriptome dynamics

Abstract: A major challenge in biotechnology and biomanufacturing is the identification of a set of biomarkers for perturbations and metabolites of interest. Here, we develop a data-driven, transcriptome-wide approach to rank perturbation-inducible genes from time-series RNA sequencing data for the discovery of analyte-responsive promoters. This provides a set of biomarkers that act as a proxy for the transcriptional state referred to as cell state. We construct low-dimensional models of gene expression dynamics and rank genes by their ability to capture the perturbation-specific cell state using a novel observability analysis. Using this ranking, we extract 15 analyte-responsive promoters for the organophosphate malathion in the underutilized host organism Pseudomonas fluorescens SBW25. We develop synthetic genetic reporters from each analyte-responsive promoter and characterize their response to malathion. Furthermore, we enhance malathion reporting through the aggregation of the response of individual reporters with a synthetic consortium approach, and we exemplify the library's ability to be useful outside the lab by detecting malathion in the environment. The engineered host cell, a living malathion sensor, can be optimized for use in environmental diagnostics while the developed machine learning tool can be applied to discover perturbation-inducible gene expression systems in the compendium of host organisms.

Data-Driven Observability Decomposition with Koopman Operators for Optimization of Output Functions of Nonlinear Systems

Abstract: When complex systems with nonlinear dynamics achieve an output performance objective, only a fraction of the state dynamics significantly impacts that output. Those minimal state dynamics can be identified using the differential geometric approach to the observability of nonlinear systems, but the theory is limited to only analytical systems. In this paper, we extend the notion of nonlinear observable decomposition to the more general class of data-informed systems. We employ Koopman operator theory, which encapsulates nonlinear dynamics in linear models, allowing us to bridge the gap between linear and nonlinear observability notions. We propose a new algorithm to learn Koopman operator representations that capture the system dynamics while ensuring that the output performance measure is in the span of its observables. We show that a transformation of this linear, output-inclusive Koopman model renders a new minimum Koopman representation. This representation embodies only the observable portion of the nonlinear observable decomposition of the original system. A prime application of this theory is to identify genes in biological systems that correspond to specific phenotypes, the performance measure. We simulate two biological gene networks and demonstrate that the observability of Koopman operators can successfully identify genes that drive each phenotype. We anticipate our novel system identification tool will effectively discover reduced gene networks that drive complex behaviors in biological systems.