Schedule for: 23w2007 - Emerging Mathematical Challenges in Synthetic Biological Network Design

Note: the Lecture rooms are available after 16:00.

Beverages and a small assortment of snacks are available in the lounge on a cash honour system.

A buffet breakfast is served daily between 7:00am and 9:00am in the Vistas Dining Room, the top floor of the Sally Borden Building. Note that BIRS does not pay for meals for 2-day workshops.

A brief introduction to BIRS with important logistical information, technology instruction, and opportunity for participants to ask questions.

Horizontal gene transfer (HGT) of mobile genetic elements (MGEs) plays a critical role in modulating the dynamics and functions of microbial communities. For instance, the presence of MGEs can augment the function of a community and affect the diversity and stability of the latter. Conversely, the composition of community members can affect the fate of MGEs. The ability to predict and control the fate of MGEs has implications for curbing the spread of antibiotic resistance and for precision microbiome engineering. In this talk, I will discuss our recent efforts in understanding the quantitative dynamics of HGT in microbial communities, as well as development of intervention strategies.

Synthetic biology harnesses the code of life to reprogram biological systems using engineering principles. As the synthetic biology toolbox expands, we can develop increasingly advanced living systems to harness nature's power, but practical implementation relies on their robustness and reliability. Control theory, which studies the control of dynamical systems, has been instrumental in advancing various engineering disciplines. However, applying it to biomolecular networks is challenging due to its complex nature. My work combines control theory, systems modeling, and experimental synthetic biology to analyze the dynamics and control strategies of biomolecular networks. The goal of my research is to understand nature's robust dynamic control and establish guiding principles for designing and engineering robust synthetic biological systems. This talk will highlight key aspects of my previous work on implementing layered feedback control within living cells to address performance trade-offs in synthetic biosystems. Additionally, I will briefly discuss our ongoing work on modeling gene expression dynamics as a function of growth and implementing electronics-facilitated feedback control to regulate gene expression dynamics.

Biology’s inherent nonlinearities have historically necessitated the use of simplifying assumptions such as Michaelis-Menten-style approximations to enable the tractable analysis of even the simplest models of biomolecular reaction systems. However, the next generation of synthetic genetic circuits will likely derive key functional attributes from operating regimes that are not captured by such approximations. It is therefore critical to develop mathematical frameworks that tractably describe system behavior in such “non-Michaelis-Menten” regimes. Here we present one such framework, based on two key ideas: first, biomolecular reaction systems can be partitioned into binding networks and catalysis networks such that the binding network constrains the system’s possible behaviors and the catalysis network defines the system’s movement within behavior space. Second, encoding the system’s behavior via the log derivative (“Reaction Order”) represents these constraints as polyhedra in behavior space, enabling the use of geometric tools to tractably analyze these systems. We apply our framework to case studies of classic biomolecular systems to illustrate its ability to reveal previously-overlooked insights that emerge from their behavior outside of conventional operating regimes.

The functions performed by microbiomes hold tremendous promise to address grand challenges facing society ranging from improving human health to promoting plant growth. To design their properties, flexible computational models that can predict the temporally changing behaviors of microbiomes in response to key environmental parameters are needed. When considering bottom-up design of microbiomes, the number of possible communities grows exponentially with the number of organisms and environmental factors, which makes it challenging to navigate the microbiome function landscape. To overcome these challenges, we present a physically constrained machine learning model for microbiomes and a Bayesian experimental design framework to efficiently navigate the space of possible communities and environmental factors.

Population heterogeneity can promote bacterial fitness in response to unpredictable environmental conditions. A major mechanism of phenotypic variability in the human gut symbiont Bacteroides fragilis involves the inversion of seven promoters that drive the expression of capsular polysaccharides, which determine the architecture of the cell surface. Using a novel ultra-high-throughput single-cell sequencing technique, we found substantial population heterogeneity generated through combinatorial promoter inversion regulated by a common invertase. We developed a stochastic mathematical model to describe and analyze the population diverging dynamics, where we found that populations with different initial compositions converge to a unique stationary distribution over time. By fitting the model to experimental data, we showed that the differential rates of promoter inversion are a major mechanism shaping population distribution dynamics.

A buffet lunch is served daily between 11:30am and 1:30pm in the Vistas Dining Room, the top floor of the Sally Borden Building. Note that BIRS does not pay for meals for 2-day workshops.

Meet in foyer of TCPL to participate in the BIRS group photo. The photograph will be taken outdoors, so dress appropriately for the weather. Please don't be late, or you might not be in the official group photo!

We address and solve the fundamental problem of maximal robust perfect adaptation (maxRPA), whereby for a designated output variable, adaptation is achieved with respect to perturbations in virtually all network parameters. In particular, we show that the maxRPA property imposes certain structural constraints on the network. We then demonstrate that these constraints are fully characterized by simple linear algebraic stoichiometric conditions which differ between deterministic and stochastic descriptions of the dynamics. Using these results, we derive a new internal model principle (IMP) for biomolecular maxRPA networks, akin to the celebrated IMP in control theory. These results are exemplified through several known biological examples.

In this talk, I'll review a few different areas of theoretical research in synthetic biology that I have been involved in, centered around questions of resource-limited computation. I'll describe the idea of "competition phenotype" (to distinguish mRNA from ribosome competition, for example), the use of PINNs ("physics-inspired neural networks") to find hidden competition terms, the use of polyhedral Lyapunov functions for "safety" checking, and the implementation of Boolean circuits through distributed colonies.

Biological systems are known to exhibit an extraordinary robustness, which guarantees survival in the most diverse and changeable environmental conditions. We overview approaches to assess the stability of biological models regardless of parameter values, including a constructive method to compute a structural polyhedral Lyapunov function based on a decomposition that decouples the known system structure (interconnection topology) from the unknown, or uncertain, system parameters. Then, we consider the special case of biological networks where the nodes are associated with first-order linear dynamics and their interactions, which can be either activating or inhibitory, are modelled by nonlinear Michaelis–Menten functions. These networks are shown to always admit a single positive equilibrium, which is locally asymptotically stable, regardless of parameter values, regardless of the network topology and of the size of the network, and also in the presence of arbitrary delays in the interaction functions. In this special case of biological robustness, stability is not only structural (i.e., preserved in spite of arbitrary changes in the system parameters), but also topology-independent (i.e., preserved in spite of arbitrary changes in the web of interactions) and delay-independent (i.e., preserved even when the interactions among key players include arbitrary time delays).

Feedback control is a fundamental underpinning of life, underlying the homeostasis of biological processes at every scale of organization, from cells to ecosystems. The ability to evaluate the contribution and limitations of feedback control mechanisms operating in cells is a critical step for understanding and ultimately designing feedback control systems with biological molecules. We have developed a novel general framework that quantifies perturbation suppression by a biological feedback control mechanism using a mathematically controlled comparison to an identical system that lacks such feedback. This controlled comparison effectively isolates the contribution of the feedback control, while considering the impact of all the intrinsic biomolecular constraints of the system. This conceptual framework is named CoRa –or Control Ratio–, and can be applied to any given feedback control system, regardless of the underlying complexity of the biomolecular network. CoRa produces a readily interpretable value, evaluating either the system’s steady state, and in its newest version also the dynamic response after a perturbation. We show how the easy implementation and interpretability of CoRa allows an effective characterization of control systems, revealing unexpected effects over the control performance of alternative mechanistic hypotheses. Additionally, CoRa provides a unifying framework that allows for the comparison of different control strategies. We show how this comparison highlights fundamental operational principles shared by these strategies. Finally, we are systematically evaluating the control performance of diverse feedback control mechanisms over a wide range of conditions. We focus on the diverse systems proposed in the synthetic biology field as potential mechanisms for feedback control with biological molecules. By analyzing the resulting dataset, we aim to identify signature behaviors associated with specific structural components. In summary, CoRa is a simple, generalizable and informative approach that can guide efforts for dissecting and designing biomolecular feedback control.

Previously a variety of engineered biological circuits to control cell population have been developed. One possible implementation uses paradoxical feedback, where population control is achieved by using the same quorum sensing signal, produced and sensed by the cell population, to provide both positive (cell proliferation) and negative (cell death) feedback. Here, we extend the paradoxical feedback population control circuit with the addition of a detector to manipulate the activation of the circuit via modulation of an external signal. The detector design utilizes the inherent bi-stability within paradoxical feedback control to switch the cell population dynamics between two equilibrium states via an external signal. Through simulation, we first demonstrate that the bi-stability of the paradoxical feedback controller remains unaffected after the introduction of the detector. Also, the modified detector-population controller can automatically detect and respond to the external signal. We then show how the modified circuit can trigger the total elimination of the cell population using an additional external signal. Finally, we propose a solution for disturbance rejection by adjusting the concentration of a certain gene. Although the detector-population controller is used in the context of gut infection detection, it follows generalizable principles that can be used in various contexts.

Cell-free transcription-translation (TXTL) enables the rapid execution of gene circuits outside cells. TXTL has proven useful to accelerate the DBTL cycle of synthetic gene networks. In this talk, I will give an overview of the current TXTL capabilities for prototyping gene circuits, and I will discuss the future of this discipline.

The ability to control gene expression has been paradigm shifting for all areas of biological research, especially for synthetic biology. This talk will focus on two recent advancements in gene expression control. First, TULIP (TUnable Ligand Inducible Plasmid) is presented: a self-contained plasmid with inducible copy number control, designed for portability across various Escherichia coli strains commonly used for cloning, protein expression, and metabolic engineering. As demonstrated through multiple application examples, flexible plasmid copy number control via TULIP accelerates the design and optimization of gene circuits, enables efficient probing of metabolic burden, and facilitates the prototyping and recycling of modules in different genetic contexts. Second, the blueprint of a genetic feedback module is presented to optimize a broadly defined performance metric by adjusting the production and decay rate of a set of regulator species. The optimizer can be implemented by combining available synthetic biology parts and components, and it can be readily integrated with existing pathways and genetically encoded biosensors to ensure its successful deployment in a variety of settings when relying on mass action kinetics-based dynamics and parameter values typical in Escherichia coli.

A buffet dinner is served daily between 5:30pm and 7:30pm in the Vistas Dining Room, the top floor of the Sally Borden Building. Note that BIRS does not pay for meals for 2-day workshops.

Synthetic biology aims to develop engineering-driven approaches to the programming of cellular functions that could yield transformative technologies. Synthetic gene circuits that combine DNA, protein, and RNA components have demonstrated a range of functions such as bistability, oscillation, feedback, and logic capabilities. Despite many advances, technical challenges remain for scaling up the complexity of these networks due to the limited number of designable, orthogonal, high-performance parts, the empirical and often tedious composition rules, and substantial resource requirements for encoding and operation. Here, we report a strategy for constructing RNA-only nanodevices to evaluate complex logic in living cells. Such ‘ribocomputing’ systems are composed of de novo designed parts and operate via predictable and designable base-pairing rules, allowing for effective in silico design of computing devices with prescribed configurations and functions in complex cellular environments. We demonstrate that these ribocomputing devices in Escherichia coli can evaluate two-input logic expressions with dynamic range up to 900-fold and scale them to four-input AND, six-input OR, and a complex 12-input logic expression [1]. We further demonstrate that ribocomputing design strategy can be used to develop a large library of high-performance translational repressors and 4-input NAND logic gates [2]. Successful operation of ribocomputing devices based on programmable RNA interactions suggests that systems employing the same design principles could be implemented in other host organisms or in extracellular settings. References: 1. Alexander A. Green, Jongmin Kim, et al., Complex cellular logic computation using ribocomputing devices (2017), Nature, 548(7665), 117-121 2. Jongmin Kim, et al., De novo-designed translation-repressing riboregulators for multi-input cellular logic (2019), Nature Chemical Biology, 15(12), 1173-1182

A proper dynamical description of gene expression is foundational to predict the dynamics of genetic circuits. Canonical model of gene expression involves a synthesis term governed by (regulated) promoter activity, and a dilution term arise from the exponential volume growth. We have shown recently that the dilution effect is largely "canceled out” by a global growth-rate dependent transcriptional regulation. I will discuss an alternative dynamical framework for gene expression.

Rational design of synthetic gene regulatory systems requires well-characterized parts, whose heterogeneous responses can be accurately and quantitatively predicted. When inferred from appropriate single-cell experiments, such as single-molecule Fluorescence in situ Hybridization (smFISH) or immunocytochemistry (ICC), discrete stochastic models can unravel the subtleties of gene regulation mechanisms to enable such predictions. Unfortunately, in principle, an infinite number of different smFISH/ICC experiment designs could be proposed (e.g., at different induction levels, for different measurement times, or considering different observed biological species). Moreover, each experiment can be time consuming or expensive to perform and will result in labeling, imaging, or data processing errors. Toward determining which experiments are best suited to identify a model, we adopt the chemical master equation framework to define likelihood functions, and we calculate the Finite State Projection based Fisher Information Matrix (FSP-FIM) to estimate and compare the information content inherent to different experiment designs. We extend the FSP-FIM with an empirically determined probabilistic distortion operator to estimate how measurement errors affect model identification. By analyzing different combinations of models, experiment designs, and image distortions, we discover practical working principles to optimize smFISH experiments despite inexact imaging. We validate our FSP-FIM approach using smFISH data for an HIV1 reporter construct as well as for DUSP1 gene regulation upon Dexamethasone stimulation.

The ability of cells to rapidly sense and respond to changes in their external environment via networks of phosphorylation-based signaling proteins is essential for their survival and function. Despite the importance of these networks, and the clear potential for harnessing them to create cell-based technology, the ability to engineer artificial phospho-signaling networks remains underexplored. To address this deficit, we recently developed a framework for the bottom-up engineering of artificial phospho-signaling networks in human cells. Our approach is based on the construction of reversible enzymatic amplifiers—or “push-pull” motifs—from protein domain building blocks. We demonstrate the ability to interlink and and tune push-pulls; by coupling circuits to synthetic receptors, push-pull networks can be engineered to sense and respond on a fast timescale to the presence of extracellular ligands, while downstream connections can enable regulation of gene expression, secretion, molecular condensate formation, and reconstitution of diverse reporter proteins. Our work defines a broadly applicable framework for engineering post-translational signaling networks that can be used to create cell-based theranostic devices capable of sensing disease markers and responding with a therapeutic output.

2-day workshop participants are welcome to use BIRS facilities (TCPL) until 15:00 on Sunday, although participants are still required to checkout of the guest rooms by 11 M. There is no coffee break service on Sunday afternoon, but self-serve coffee and tea are always available in the 2nd floor lounge, Corbett Hall.

Large gene circuits with the complexity required for tasks like strategic board gameplay have posed challenges for the rational design. For gene circuits to achieve advanced functions, they must rapidly adapt to various cues without requiring prior understanding of the necessary adaptations. This advancement suggests moving beyond conventional genes, indicating a potential layer for analog information storage. Here we demonstrate the application of artificial intelligence principles to engineer gene circuits iteratively, paralleling algorithmic feedback adaptation. We introduced "AdaptoCells", a minimal gene circuit designed for inducer-dependent antibiotic adaptation. These circuits encode an analog memory that allows them to evolve strategies through human-led reinforcement without needing predefined memory levels. Analogous to a memristor in neuromorphic electronic circuits, an AdaptoCell enhances adaptation during active gene expression. The approach with AdaptoCells shifts the design's complexity from standard biological parts to an analog encoding, which is inscribed during the live manipulation of cells, drawing parallels with reinforcement learning algorithms. Recognizing that AdaptoCells adapt to changing chemical input patterns, they are promising for applications like therapeutic pattern discrimination, where a redesigned microbiome could adaptively discern evolving chemical patterns, triggering a precise therapeutic action. Our methodology sets the stage for evolving behaviors beyond conventional genetic encoding, harnessing self-adaption akin to Darwinian selection and scalable to metabolic, regulatory, and signalling gene circuits.

Advancements in the field of bioelectronics presents opportunities for real-time feedback control of biological systems from cell systems to animal models. I present current advancements and challenges in the design of feedback control algorithms that guide system response towards desired system level outcomes. This work is presented in the context of work aimed at accelerating wound healing through a programmed intelligent band aid with real-time sensors and actuators.

Microbial communities are involved in a wide range of processes in health, agriculture, biomanufacturing, water treatment, and environmental remediation. Rational manipulation of those communities can result in improvements in activity, but the complexity of microbial community interactions makes it difficult to predict the effects of intervention. Here we take a bottom-up approach by investigating the behaviour of simple two-species communities in idealized laboratory environments. This talk will describe ongoing work in validating dynamic models (differential equation- and agent-based) of community activity against time-series observations. In addition, we discuss the complementary development of tools for model-based optimal experimental design in this context.

The ability to program ad hoc cells via genetic circuits offers exciting opportunities in basic research, in the biotechnology industry and in the clinic. Despite the enormous progress in the area, challenges in the design and engineering of scalable and robust genetic circuits remain. For example, there are limitations on the complexity of these circuits, also due to the high metabolic load imposed on host cells. Another crucial issue is the robustness of engineered gene circuits to variations in physical parameters; mathematical modelling is mostly used to study such robustness, but model uncertainties can inevitably result in misleading conclusions. In this talk, I will first present different control- and model-based approaches to design and prototype gene networks. The first approach leverages a novel multicellular control strategy to enable higher modularity and reduced burden as compared to gene circuit implementation is a single cellular population; the strategy is effective in regulating a phenotype of interest in a bacterial target population even in the presence of variations of the consortium composition. I will also propose an approach based on whole-cell modelling to predict burden effects upon engineering exogenous circuits in bacterial cells. I will finally show how external feedback controllers should allow the prototyping of gene circuits by tracking their nonlinear dynamics upon parameter variations also when mathematical models of the systems are not available; in silico control-based continuation results will be shown for the bacterial toggle switch. Our tools and results should make the design of gene networks and laboratory engineering a step closer.