Abstract
Synthetic constructs in biotechnology, biocomputing, and modern gene therapy interventions are often based on plasmids or transfected circuits which implement some form of “on-off” switch. For example, the expression of a protein used for therapeutic purposes might be triggered by the recognition of a specific combination of inducers (e.g., antigens), and memory of this event should be maintained across a cell population until a specific stimulus commands a coordinated shut-off. The robustness of such a design is hampered by molecular (“intrinsic”) or environmental (“extrinsic”) noise, which may lead to spontaneous changes of state in a subset of the population and is reflected in the bimodality of protein expression, as measured for example using flow cytometry. In this context, a “majority-vote” correction circuit, which brings deviant cells back into the required state, is highly desirable, and quorum-sensing has been suggested as a way for cells to broadcast their states to the population as a whole so as to facilitate consensus. In this paper, we propose what we believe is the first such a design that has mathematically guaranteed properties of stability and auto-correction under certain conditions. Our approach is guided by concepts and theory from the field of “monotone” dynamical systems developed by M. Hirsch, H. Smith, and others. We benchmark our design by comparing it to an existing design which has been the subject of experimental and theoretical studies, illustrating its superiority in stability and self-correction of synchronization errors. Our stability analysis, based on dynamical systems theory, guarantees global convergence to steady states, ruling out unpredictable (“chaotic”) behaviors and even sustained oscillations in the limit of convergence. These results are valid no matter what are the values of parameters, and are based only on the wiring diagram. The theory is complemented by extensive computational bifurcation analysis, performed for a biochemically-detailed and biologically-relevant model that we developed. Another novel feature of our approach is that our theorems on exponential stability of steady states for homogeneous or mixed populations are valid independently of the number N of cells in the population, which is usually very large (N ≫ 1) and unknown. We prove that the exponential stability depends on relative proportions of each type of state only. While monotone systems theory has been used previously for systems biology analysis, the current work illustrates its power for synthetic biology design, and thus has wider significance well beyond the application to the important problem of coordination of toggle switches.
Highlights
In the short period since the pioneering milestones in synthetic biology [1, 2], outstanding progress has been made, and considerable practical experience has accumulated, in the construction of genetic circuits that perform various tasks, such as memory storage and logical operations, as well as support biomedical interventions and biotechnological manipulations in response to both exogenous and endogenous stimuli [3,4,5,6,7,8,9]
We begin this section with results on the application of monotone systems theory to the S design, as these results constitute the main conceptual and practical subject motivating this work (Application of Monotone Systems Theory to the S Design)
We analyze single S and A toggles decoupled from the environment (Bistability in Single S and A Toggles), and observe that the S toggle remains bistable even if “redundant” repressor genes are removed from the corresponding plasmids
Summary
In the short period since the pioneering milestones in synthetic biology [1, 2], outstanding progress has been made, and considerable practical experience has accumulated, in the construction of genetic circuits that perform various tasks, such as memory storage and logical operations, as well as support biomedical interventions and biotechnological manipulations in response to both exogenous and endogenous stimuli [3,4,5,6,7,8,9]. The expression of a protein used for gene therapy could be triggered by the recognition of some combination of inducers such as antigens, and memory of this event should be maintained across a cell population until a specific stimulus commands a coordinated shut-off [1, 3, 4] In this context, as well as in many others, it is desirable for populations of cells to achieve coordinated static and/or dynamic functionalities. Synthetic biology design has adopted QS communication in its toolbox [15], because natural and artificially engineered QS modules can be used to interface synthetic circuits with exogenous and endogenous cues [4], and a systematic modular approach to standardize engineering toggle genetic circuits that would allow programmed cells to be designed for various specific purposes and to communicate their states to other cells was suggested as a bioengineering “plug-and-play” modular approach [4] The design of such QS-toggle combinations is the focus of this paper
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