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Current address: Department of Systems Biology, Harvard Medical School, Boston, Massachusetts, United States of America

Conceived and designed the experiments: MM MH PEMP RW. Performed the experiments: MM MH ND SS. Analyzed the data: MM MH ES RW. Contributed reagents/materials/analysis tools: MM MH ES DL. Wrote the paper: MM MH ES RW.

The authors have declared that no competing interests exist.

Synthetic biology efforts have largely focused on small engineered gene networks, yet understanding how to integrate multiple synthetic modules and interface them with endogenous pathways remains a challenge. Here we present the design, system integration, and analysis of several large scale synthetic gene circuits for artificial tissue homeostasis. Diabetes therapy represents a possible application for engineered homeostasis, where genetically programmed stem cells maintain a steady population of

Over the last decade several relatively small synthetic gene networks have been successfully implemented and characterized, including oscillators, toggle switches, and intercellular communication systems. However, the ability to engineer large-scale synthetic gene networks for controlling multicellular systems with predictable and robust behavior remains a challenge. Here we present a novel combination of computational methods to aid the iterative design and optimization of such synthetic biological systems. We apply these methods to the design and analysis of an artificial tissue homeostasis system that exhibits coordinated control of cellular proliferation, differentiation, and cell-death. Achieving artificial tissue homeostasis would be therapeutically relevant for diseases such as Type I diabetes, for instance by transplanting genetically engineered stem cells that stably maintain populations of insulin-producing beta-cells despite normal cell death and autoimmune attacks. To manage complexity in the design process, we employ principles of logic abstraction and modularity and investigate their limits in biological networks. In this work, we find factors often associated with robustness (e.g., multicellular synchronization and noise attenuation) to be actually detrimental, and overcome these problems by engineering genetic modules that generate beneficial population heterogeneity. A combination of computational methods elucidates how these modules function to enhance robust control, and provides guidance for experimental implementation.

One of the key challenges facing synthetic biology today is the ability to engineer large-scale, multicellular systems with sophisticated yet predictable and robust behaviors. Previous work in synthetic biology has successfully implemented and characterized a variety of relatively small synthetic gene networks including oscillators

As a case study, we design a system to control tissue homeostasis, broadly defined as the property of balancing growth, death, and differentiation of multiple cell-types within a multicellular community. Tissue homeostasis represents an important class of problems in biology, and the ability to control it is fundamental to the success of a wide range of tissue engineering goals. At the same time the ability to create and analyze such a system may provide insight into mechanisms of endogenous tissue homeostasis and its misregulation in diseases such as cancer and diabetes. For example, misregulation of tissue homeostasis plays a central role in Type I diabetes, in which natural populations of insulin-producing

As potential solutions for this problem, we propose several increasingly robust variants of a synthetic gene network that are designed to maintain a steady level of

(A) The general tissue homeostasis design. Proliferation of stem cells (blue) is regulated by their population size through negative feedback (dashed blue line). Sequential differentiation into endodermic, pancreatic, and finally

The efforts described here are based on encouraging genetic engineering accomplishments that have demonstrated population control of bacteria and yeast

To gain a detailed understanding of our proposed synthetic gene networks, we carried out theoretical analysis and computational simulations using Ordinary Differential Equations (ODE's), Langevin, and Gillespie algorithms. The analysis revealed that while simple modular composition was useful for initial system design, various factors such as stochastic effects, feedback control, and module interdependence significantly impacted system function and hence had to be taken into account when evaluating system designs. Strikingly, we observed that system features typically associated with robustness, including cell-synchronization, noise attenuation, and rapid signal processing destabilized our systems. To overcome these problems, we propose and analyze mechanisms that generate population diversity, and through this symmetry breaking facilitate proportionate and homeostatic system response to population-wide cues. Endogenous mechanisms of cellular heterogeneity have been previously observed in many physiological processes, including differentiation

We found that the design and optimization of modules for synthetic heterogeneity is both non-intuitive and multifactorial, and in general requires a framework for non-linear and multivariate analysis. For example, with the asynchronous oscillator, we could not

We designed and modeled an artificial tissue homeostasis system where a population of self-renewing stem cells grow and differentiate in a regulated manner to sustain a steady population of adult cells which, in this case, are insulin-producing

Simple mathematical analysis suggested that feedback regulation between the two populations of stem cells and adult cells was necessary for robust homeostatic control, and recent work has explored the essential role of feedback control in stem cell biology (

(A) Circuit diagram: two Population Control modules (in gray) sense the density of stem- and

We model stem cell differentiation as a multistage process that can take several weeks to complete

The differentiation process is generally long

System 2 minimizes feedback delay by using a ‘commitment’ module to decouple the BPC module from the slow differentiation process (

(A) Circuit diagram: two Population Control modules sense the density of stem and committed cells. The AND gate integrates the output of the modules to induce commitment through the switch state (red module). (B) Deterministic time trajectories for System 2 with two different initial conditions: both converge to the same equilibrium populations. (C) Phase space diagram: all trajectories converge to a unique equilibrium point. Black lines correspond to trajectories plotted in

Compared to System 1, the population sizes quickly equilibrated in System 2 (Supplementary

For subsequent analyses, we simplified our model to a two-population system. Given that

Our deterministic model of continuous population dynamics suggested that System 2 stabilized homeostasis sufficiently. However, low molecular count, small population size, and localized reaction/diffusion may constitute critical determinants of system dynamics

These simulations revealed that phenotypic homogeneity within the isogenic stem cell population impedes system performance. More specifically, strong population-wide cues to commit may cause massive simultaneous commitment, thereby depleting the stem-cell pool and leading to homeostasis failure (

In System 3, we incorporated an asynchronous oscillator (e.g.

(A) Circuit diagram for System 3: in addition to System 2 modules, the AND gate integrates the output of the oscillator (red module) that allows commitment only when peaking. (B) Time trajectories for a simulation starting with a small stem cell population. The oscillator activator (

System 4 achieves population heterogeneity through rapid lateral inhibition acting as a throttle on the commitment process during toggle switching (

The integration of several network modules presents a challenge on multiple levels, especially in the context of uncertain biological environments and complex module dynamics. In the following sections, we introduce a framework composed of computational modeling and analysis techniques that addresses these issues in optimizing Systems 2, 3 and 4. We first study overall system robustness to external parameters such as cell survival dynamics, and introduce time-scale analysis as a method for guiding module integration. We then optimize the population control module using a novel ‘clustered sensitivity analysis’ to comprehend global patterns of parametric sensitivity in the context of a detailed biochemical model. Finally, we analyze the synthetic heterogeneity modules with an approach that focuses on module phenotype rather than rate constants alone. Comparisons among the different system architectures ultimately provide guidance for experimental optimization.

We first explored the impact of stochasticity on homeostasis by adjusting the simulated cell volume,

(A) S/N for different cell volume

We analyzed the robustness of the systems to another external parameter, the average committed-cell survival time (

In our system, accurate cell decision processing requires the appropriate integration of modules that generally have well defined behaviors in isolation. Even if we assume input-output behavior that meets our design specifications for each module (see

We used the Random-Sampling High Dimensional Model Representation (RS-HDMR) algorithm

We also modeled System 3 using the Gillespie algorithm to explicitly account for binding and transcription events (for example, the binding of the receiver protein Rec1 to its inducer AI1,

(A) GA optimization progress for three representative generations, using an ODE model of the UPC module. The GA objective function is a three-component step-function, with zero UPC activity below a defined threshold, an ignored transition region, and high activity above the transition region. (B) Gillespie simulations of System 3, corresponding to optimization progress in

We performed RS-HDMR analysis of the UPC subnetwork to understand how rate constants affect hysteresis, which would help guide the experimental construction of the system. We examined local parameter “neighborhoods” around each GA-generated vector of optimized parameters from

When building genetic networks experimentally, precise parameter values and their influence on system behavior may be unknown, presenting a challenge for optimization. Logistical constraints limit the number of parameters that can be reasonably manipulated, but clustered sensitivity analysis can act as a guide for iteratively prioritizing which parameters to mutate. In our system, for example, results suggest that we manipulate the most sensitive parameters from each of the two main clusters (

The impact of the oscillator and throttle modules on the performance of Systems 3 and 4 presents a particular challenge to understand and analyze (

(A,G) Circuit diagrams of the genetic components considered in (A) oscillator and (G) throttle optimization. (B,H) The most significant RS-HDMR sensitivity indices,

For the oscillator, RS-HDMR indicated that the threshold at which

For the throttle, results indicated that the thresholds for

Although a good first step, analysis of the module rate constants alone demonstrated two main drawbacks in this application. First, the statistical relationships between S/N and rate constants are highly convoluted and poorly captured by RS-HDMR. Second, focusing on rate constants can limit the analysis to a particularly defined network structure. To address these issues, we instead turned to analysis of high-level properties, or ‘phenotypes’, of the oscillator and throttle modules.

With the oscillator, examples of phenotypes include the average period of

(A,F) Phenotypic behavior of the oscillator (A) and throttle (F), when isolated from the full system. Roughly 2000 different sets of rate constants were tested, with all oscillator or throttle rate constants simultaneously varied. Module phenotypes were recorded for each set of rate constants. (B) Observed S/N values as a function of variance in the “duration high” of the oscillator. (C) Heat map of the S/N values against the phenotypes resulting from the random parameter sets. (G) Average ‘images’ for the phenotype

For the throttle, we defined phenotypes (Supplementary

We applied Bayesian network inference to graphically represent the strong interdependencies of the module phenotypes and their relations with the rate constants that govern them and the S/N value (

(A) Bayesian network inference using oscillator rate constants and phenotypes. (B) Bayesian network inference using throttle rate constants and phenotypes. Black arrows indicate the most direct connections between a node and S/N. The Bayesian inference describes phenotype groupings relevant to state values (blue), timing (yellow), and variability (red), along with the rate constants that control these phenotypes (green).

The integration of module phenotypes with the underlying rate constants ultimately allowed for efficient experimental optimization. Modules are likely to be experimentally implemented and phenotypically characterized in isolation before being integrated with each other. At this stage of optimization, Bayesian analysis can predict behavioral features of the individual module that will most directly influence performance in the fully integrated system, and such analysis may guide fine-tune adjustments of those module behaviors. In System 3, for example, Bayesian inference suggested that the oscillator's low value critically determined S/N, and that the threshold at which

In this work, we engineer mechanisms of robust control using synthetic generators of heterogeneity, and use a multi-faceted computational framework for design and optimization in the context of a relatively large-scale synthetic gene network. As a case study we chose tissue homeostasis control where individual cell decisions need to be coordinated to obtain desired multi-cellular behavior. To tackle this complex problem, we used top-down decomposition, achieving the overall task through the creation of interconnected modules, where each module has its own specific objective. Throughout this hierarchical optimization process we used different modeling approaches (population-based, Langevin and Gillespie simulations, see

We designed System 1 by coupling four modules together, and simulated this system using a simplified ODE model. Computational analysis elucidated properties of global stability and demarcated regimes of steady vs. oscillatory homeostatic behavior in general tissue homeostasis systems. Analogous oscillatory homeostatic behavior from delayed feedback has been observed in natural mammalian systems, for example with hematopoiesis

The design and analysis methods developed in this work attempt to identify relationships between rate constants, module phenotypes, and overall system performance, while maintaining an appreciation for the high degree of uncertainty and incomplete system knowledge in the experimental setting. For example, relating overall system performance directly to phenomenological definitions of module behavior frees the analysis from constraints to a particular module architecture or set of rate constants. Nonetheless, when more detailed information is desired we can apply global optimization strategies to capture patterns of parametric sensitivity that remain consistent across a broad range of rate constant values. For example, our analysis of the cell-cell communication module used a detailed biochemical reaction model with a large number of unknown rate constants. This level of granularity allowed us to analyze hysteretic response, which is not possible in the more abstract models. Ultimately, we addressed uncertainty by employing a novel technique, clustered sensitivity analysis, that revealed distinct patterns of relative parametric sensitivity for hysteresis that persisted across a wide range of rate constants. Previous reports have shown that bistability and hysteretic responses exist for both natural and engineered bacterial QS systems

The synthetic heterogeneity modules in our systems display complex and multivariate behaviors that depend on the cooperative influence of multiple rate constants. Since existing experimental and computational biological circuit optimization methods do not scale well with system complexity, we decomposed the analysis and optimization processes for Systems 3 and 4 by characterizing modules first in isolation and then by relating their phenotypes to the performance of the overall system. We correlated module phenotypic behaviors with overall system performance, and found several significant correlations that were non-intuitive. Similarly, we identified dependencies between particular rate constants and the ability to maintain homeostasis. While Systems 3 and 4 exhibited comparable overall performances, further analyses revealed several distinguishing strengths and weaknesses (Supplementary

At a high level, our work describes strategies to exploit stochastic effects for enhancing stability of tissue homeostasis. This concept has been recently explored in a number of reports emphasizing the role probabilistic strategies play in natural mechanisms of cell-decision processing, including differentiation

Our optimization process, as well as the different biological examples described above, aim at seemingly contradictory objectives: information has to be processed faithfully from the population control modules to a commitment signal while, at the same time, stochasticity has to be amplified to generate heterogeneity. To achieve the first objective, several of our modules exhibit digital-like behavior, allowing us to effectively match components such that downstream modules react appropriately and with relative certainty to changes in upstream module output, attenuating the effects of noise. At the same time, to generate population heterogeneity, we exploit stochasticity by amplifying its effects in nonlinear modules operating in a transient regime. As a consequence, our modules are optimized to exhibit nonlinear responses to their inputs and, depending on the objective of the module, are tuned to work far from the transition regions for robust processing of information, or near the transition region where the response is highly sensitive to stochastic effects and hence efficiently generates heterogeneity.

We present here an integrated framework for forward-engineering large scale synthetic genetic circuits that combines several distinct computational approaches, and demonstrate its application to the design, analysis, and optimization of systems for controlling artificial tissue homeostasis. This framework represents a conceptual advancement for guiding experimental implementation by introducing hierarchical strategies that coordinate detailed biochemical models with modular phenotypes and optimization of module integration, all while considering parametric uncertainty and incomplete knowledge of the underlying biological context. With regard to methods development, future work may consider how to incorporate iterations of computational design with stepwise experimental implementation. Experiments could be designed to determine rate constants or high-level properties such as module phenotypes that most critically impact system performance, according to the computational modeling. Future work may also explore the limits of design automation. Network-level modeling could benefit from an integration with molecular modeling for directed optimization of molecular rate constants. Importantly, the modular design principles described in this work have been developed in part to facilitate redesign for improved performance or alternative applications. Artificial homeostasis systems have a range of potential applications in lower organisms, including co-culture systems for biosynthetic chemical production

Experimental implementations of the toggle switch and the cell-cell communication receiver were performed using immortalized human embryonic kidney cells (HEK293FT; Invitrogen), further discussed in the

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We would like to thank Joel Wagner and other members of the Weiss and Lauffenburger labs, along with Dr. Xiao-Jeng Feng and Prof. Herschel Rabitz (Princeton University) for helpful discussions.