A blueprint for a synthetic genetic feedback optimizer.

Biomolecular control enables leveraging cells as biomanufacturing factories. Despite recent advancements, we currently lack genetically encoded modules that can be deployed to dynamically fine-tune and optimize cellular performance. Here, we address this shortcoming by presenting the blueprint of a genetic feedback module to optimize a broadly defined performance metric by adjusting the production and decay rate of a (set of) regulator species. We demonstrate that the optimizer can be implemented by combining available synthetic biology parts and components, and that it can be readily integrated with existing pathways and genetically encoded biosensors to ensure its successful deployment in a variety of settings. We further illustrate that the optimizer successfully locates and tracks the optimum in diverse contexts when relying on mass action kinetics-based dynamics and parameter values typical in Escherichia coli.

Cell-in-the-loop pattern formation with optogenetically emulated cell-to-cell signaling.

Designing and implementing synthetic biological pattern formation remains challenging due to underlying theoretical complexity as well as the difficulty of engineering multicellular networks biochemically. Here, we introduce a cell-in-the-loop approach where living cells interact through in silico signaling, establishing a new testbed to interrogate theoretical principles when internal cell dynamics are incorporated rather than modeled. We present an easy-to-use theoretical test to predict the emergence of contrasting patterns in gene expression among laterally inhibiting cells. Guided by the theory, we experimentally demonstrate spontaneous checkerboard patterning in an optogenetic setup, where cell-to-cell signaling is emulated with light inputs calculated in silico from real-time gene expression measurements. The scheme successfully produces spontaneous, persistent checkerboard patterns for systems of sixteen patches, in quantitative agreement with theoretical predictions. Our research highlights how tools from dynamical systems theory may inform our understanding of patterning, and illustrates the potential of cell-in-the-loop for engineering synthetic multicellular systems.

Designing Spatially Distributed Gene Regulatory Networks To Elicit Contrasting Patterns.

Pattern formation and differential interactions are important for microbial consortia to divide labor and perform complex functions. To obtain further insight into such interactions, we present a computational method for simulating physically separated microbial colonies, each implementing different gene regulatory networks. We validate our theory by experimentally demonstrating control over gene expression patterns in a diffusion-mediated lateral inhibition circuit. We highlight the importance of spatial arrangement as a control knob for modulating system behavior. Our systematic approach provides a foundation for future applications that require understanding and engineering of multistrain microbial communities for sophisticated, synergistic functions.

Investigation of analysis methods for hyperpolarized 13C-pyruvate metabolic MRI in prostate cancer patients.

MRI using hyperpolarized (HP) carbon-13 pyruvate is being investigated in clinical trials to provide non-invasive measurements of metabolism for cancer and cardiac imaging. In this project, we applied HP [1-13 C]pyruvate dynamic MRI in prostate cancer to measure the conversion from pyruvate to lactate, which is expected to increase in aggressive cancers. The goal of this work was to develop and test analysis methods for improved quantification of this metabolic conversion. In this work, we compared specialized kinetic modeling methods to estimate the pyruvate-to-lactate conversion rate, kPL , as well as the lactate-to-pyruvate area-under-curve (AUC) ratio. The kinetic modeling included an "inputless" method requiring no assumptions regarding the input function, as well as a method incorporating bolus characteristics in the fitting. These were first evaluated with simulated data designed to match human prostate data, where we examined the expected sensitivity of metabolism quantification to variations in kPL , signal-to-noise ratio (SNR), bolus characteristics, relaxation rates, and B1 variability. They were then applied to 17 prostate cancer patient datasets. The simulations indicated that the inputless method with fixed relaxation rates provided high expected accuracy with no sensitivity to bolus characteristics. The AUC ratio showed an undesired strong sensitivity to bolus variations. Fitting the input function as well did not improve accuracy over the inputless method. In vivo results showed qualitatively accurate kPL maps with inputless fitting. The AUC ratio was sensitive to bolus delivery variations. Fitting with the input function showed high variability in parameter maps. Overall, we found the inputless kPL fitting method to be a simple, robust approach for quantification of metabolic conversion following HP [1-13 C]pyruvate injection in human prostate cancer studies. This study also provided initial ranges of HP [1-13 C]pyruvate parameters (SNR, kPL , bolus characteristics) in the human prostate.

Spatio-Temporally Constrained Reconstruction for Hyperpolarized Carbon-13 MRI Using Kinetic Models.

We present a method of generating spatial maps of kinetic parameters from dynamic sequences of images collected in hyperpolarized carbon-13 magnetic resonance imaging (MRI) experiments. The technique exploits spatial correlations in the dynamic traces via regularization in the space of parameter maps. Similar techniques have proven successful in other dynamic imaging problems, such as dynamic contrast enhanced MRI. In this paper, we apply these techniques for the first time to hyperpolarized MRI problems, which are particularly challenging due to limited signal-to-noise ratio (SNR). We formulate the reconstruction as an optimization problem and present an efficient iterative algorithm for solving it based on the alternation direction method of multipliers. We demonstrate that this technique improves the qualitative appearance of parameter maps estimated from low SNR dynamic image sequences, first in simulation then on a number of data sets collected in vivo. The improvement this method provides is particularly pronounced at low SNR levels.

Pattern Formation over Multigraphs.

Two of the most common pattern formation mechanisms are Turing-patterning in reaction-diffusion systems and lateral inhibition of neighboring cells. In this paper, we introduce a broad dynamical model of interconnected modules to study the emergence of patterns, with the above mentioned two mechanisms as special cases. Our results do not restrict the number of modules or their complexity, allow multiple layers of communication channels with possibly different interconnection structure, and do not assume symmetric connections between two connected modules. Leveraging only the static input/output properties of the subsystems and the spectral properties of the interconnection matrices, we characterize the stability of the homogeneous fixed points as well as sufficient conditions for the emergence of spatially non-homogeneous patterns. To obtain these results, we rely on properties of the graphs together with tools from monotone systems theory. As application examples, we consider patterning in neural networks, in reaction-diffusion systems, and contagion processes over random graphs.

A Tug-of-War Mechanism for Pattern Formation in a Genetic Network.

Synthesizing spatial patterns with genetic networks is an ongoing challenge in synthetic biology. A successful demonstration of pattern formation would imply a better understanding of systems in the natural world and advance applications in synthetic biology. In developmental systems, transient patterning may suffice in order to imprint instructions for long-term development. In this paper we show that transient but persistent patterns can emerge from a realizable synthetic gene network based on a toggle switch. We show that a bistable system incorporating diffusible molecules can generate patterns that resemble Turing patterns but are distinctly different in the underlying mechanism: diffusion of mutually inhibiting molecules creates a prolonged "tug-of-war" between patches of cells at opposing bistable states. The patterns are transient but longer wavelength patterns persist for extended periods of time. Analysis of a representative small scale model implies the eigenvalues of the persistent modes are just above the threshold of stability. The results are verified through simulation of biologically relevant models.

Optimizing Flip Angles for Metabolic Rate Estimation in Hyperpolarized Carbon-13 MRI.

Hyperpolarized carbon-13 magnetic resonance imaging has enabled the real-time observation of perfusion and metabolism in vivo. These experiments typically aim to distinguish between healthy and diseased tissues based on the rate at which they metabolize an injected substrate. However, existing approaches to optimizing flip angle sequences for these experiments have focused on indirect metrics of the reliability of metabolic rate estimates, such as signal variation and signal-to-noise ratio. In this paper we present an optimization procedure that focuses on maximizing the Fisher information about the metabolic rate. We demonstrate through numerical simulation experiments that flip angles optimized based on the Fisher information lead to lower variance in metabolic rate estimates than previous flip angle sequences. In particular, we demonstrate a 20% decrease in metabolic rate uncertainty when compared with the best competing sequence. We then demonstrate appropriateness of the mathematical model used in the simulation experiments with in vivo experiments in a prostate cancer mouse model. While there is no ground truth against which to compare the parameter estimates generated in the in vivo experiments, we demonstrate that our model used can reproduce consistent parameter estimates for a number of flip angle sequences.

Modular Synthetic Inverters from Zinc Finger Proteins and Small RNAs.

Synthetic zinc finger proteins (ZFPs) can be created to target promoter DNA sequences, repressing transcription. The binding of small RNA (sRNA) to ZFP mRNA creates an ultrasensitive response to generate higher effective Hill coefficients. Here we combined three "off the shelf" ZFPs and three sRNAs to create new modular inverters in E. coli and quantify their behavior using induction fold. We found a general ordering of the effects of the ZFPs and sRNAs on induction fold that mostly held true when combining these parts. We then attempted to construct a ring oscillator using our new inverters. Our chosen parts performed insufficiently to create oscillations, but we include future directions for improvement upon our work presented here.

A Compartmental Lateral Inhibition System to Generate Contrasting Patterns.

We propose a lateral inhibition system and analyze contrasting patterns of gene expression. The system consists of a set of compartments interconnected by channels. Each compartment contains a colony of cells that produce diffusible molecules to be detected by the neighboring colonies. Each cell is equipped with an inhibitory circuit that reduces its production when the detected signal is sufficiently strong. We characterize the parameter range in which steady-state patterns emerge.

Decoupling translational and rotational effects on the phase synchronization of rotating helices.

The locomotion of swimming microorganisms often relies on synchronized motions; examples include the bundling of flagella and metachronal coordination of cilia. It is now generally accepted that such behavior can result from hydrodynamic interactions alone. In this paper we consider the interactions between two side-by-side rigid helices driven by constant torques. We use the method of regularized Stokeslets to simulate an end-pinned model, in which restoring forces and torques are applied at one end of each helix. This allows us to decouple the respective effects of translation and rotation on phase synchronization. We find that while translational freedom leads to synchrony, rotational freedom can result in either synchrony or antisynchrony, depending on the stiffness of the system. In addition, we characterize the nature of the physical mechanisms driving these behaviors, focusing on the individual effects of each applied force and torque. For translational freedom, there is a single underlying mechanism in which the interaction forces indirectly influence the helix rotation rates. Multiple mechanisms are at play for rotational freedom: the interaction torques may exert either direct or indirect influence depending on stiffness. These characterizations are important to the future development of reduced-order models, which should capture not only the expected end behaviors (synchrony or antisynchrony), but also the nature of the driving mechanisms.

A GRAPH PARTITIONING APPROACH TO PREDICTING PATTERNS IN LATERAL INHIBITION SYSTEMS.

We analyze spatial patterns on networks of cells where adjacent cells inhibit each other through contact signaling. We represent the network as a graph where each vertex represents the dynamics of identical individual cells and where graph edges represent cell-to-cell signaling. To predict steady-state patterns we find equitable partitions of the graph vertices and assign them into disjoint classes. We then use results from monotone systems theory to prove the existence of patterns that are structured in such a way that all the cells in the same class have the same final fate. To study the stability properties of these patterns, we rely on the graph partition to perform a block decomposition of the system. Then, to guarantee stability, we provide a small-gain type criterion that depends on the input-output properties of each cell in the reduced system. Finally, we discuss pattern formation in stochastic models. With the help of a modal decomposition we show that noise can enhance the parameter region where patterning occurs.

A feedback quenched oscillator produces turing patterning with one diffuser.

Efforts to engineer synthetic gene networks that spontaneously produce patterning in multicellular ensembles have focused on Turing's original model and the "activator-inhibitor" models of Meinhardt and Gierer. Systems based on this model are notoriously difficult to engineer. We present the first demonstration that Turing pattern formation can arise in a new family of oscillator-driven gene network topologies, specifically when a second feedback loop is introduced which quenches oscillations and incorporates a diffusible molecule. We provide an analysis of the system that predicts the range of kinetic parameters over which patterning should emerge and demonstrate the system's viability using stochastic simulations of a field of cells using realistic parameters. The primary goal of this paper is to provide a circuit architecture which can be implemented with relative ease by practitioners and which could serve as a model system for pattern generation in synthetic multicellular systems. Given the wide range of oscillatory circuits in natural systems, our system supports the tantalizing possibility that Turing pattern formation in natural multicellular systems can arise from oscillator-driven mechanisms.

A passivity-based stability criterion for a class of biochemical reaction networks.

This paper presents a stability test for a class of interconnected nonlinear systems motivated by biochemical reaction networks. The main result determines global asymptotic stability of the network from the diagonal stability of a dissipativity matrix which incorporates information about the passivity properties of the subsystems, the interconnection structure of the network, and the signs of the interconnection terms. This stability test encompasses the secant criterion for cyclic networks presented in [1], and extends it to a general interconnection structure represented by a graph. The new stability test is illustrated on a mitogen-activated protein kinase (MAPK) cascade model, and on a branched interconnection structure motivated by metabolic networks. The next problem addressed is the robustness of stability in the presence of diffusion terms. A compartmental model is used to represent the localization of the reactions, and conditions are presented under which stability is preserved despite the diffusion terms between the compartments.