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Register a new userBayesian and Algebraic Strategies to Design in Synthetic Biology
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Innovation in synthetic biology often still depends on large-scale experimental trial-and-error, domain expertise, and ingenuity. The application of rational design engineering methods promise to make this more efficient, faster, cheaper and safer. But this requires mathematical models of cellular systems. And for these models we then have to determine if they can meet our intended target behaviour. Here we develop two complementary approaches that allow us to determine whether a given molecular circuit, represented by a mathematical model, is capable of fulfilling our design objectives. We discuss algebraic methods that are capable of identifying general principles guaranteeing desired behaviour; and we provide an overview over Bayesian design approaches that allow us to choose from a set of models, that model which has the highest probability of fulfilling our design objectives. We discuss their uses in the context of biochemical adaptation, and then consider how robustness can and should affect our design approach.
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Synthetic biology brings together concepts and techniques from engineering and biology. In this field, computer-aided design (CAD) is necessary in order to bridge the gap between computational modeling and biological data. An application named TinkerCell has been created in order to serve as a CAD tool for synthetic biology. TinkerCell is a visual modeling tool that supports a hierarchy of biological parts. Each part in this hierarchy consists of a set of attributes that define the part, such as sequence or rate constants. Models that are constructed using these parts can be analyzed using various C and Python programs that are hosted by TinkerCell via an extensive C and Python API. TinkerCell supports the notion of a module, which are networks with interfaces. Such modules can be connected to each other, forming larger modular networks. Because TinkerCell associates parameters and equations in a model with their respective part, parts can be loaded from databases along with their parameters and rate equations. The modular network design can be used to exchange modules as well as test the concept of modularity in biological systems. The flexible modeling framework along with the C and Python API allows TinkerCell to serve as a host to numerous third-party algorithms. TinkerCell is a free and open-source project under the Berkeley Software Distribution license. Downloads, documentation, and tutorials are available at www.tinkercell.com.
Here we introduce a new design framework for synthetic biology that exploits the advantages of Bayesian model selection. We will argue that the difference between inference and design is that in the former we try to reconstruct the system that has given rise to the data that we observe, while in the latter, we seek to construct the system that produces the data that we would like to observe, i.e. the desired behavior. Our approach allows us to exploit methods from Bayesian statistics, including efficient exploration of models spaces and high-dimensional parameter spaces, and the ability to rank models with respect to their ability to generate certain types of data. Bayesian model selection furthermore automatically strikes a balance between complexity and (predictive or explanatory) performance of mathematical models. In order to deal with the complexities of molecular systems we employ an approximate Bayesian computation scheme which only requires us to simulate from different competing models in order to arrive at rational criteria for choosing between them. We illustrate the advantages resulting from combining the design and modeling (or in-silico prototyping) stages currently seen as separate in synthetic biology by reference to deterministic and stochastic model systems exhibiting adaptive and switch-like behavior, as well as bacterial two-component signaling systems.
Migrating cells possess intracellular gradients of Rho GTPases, but it is unknown whether these shallow gradients themselves can induce motility. Here we describe a new method to present cells with induced linear gradients of active, endogenous Rac without receptor activation. Gradients as low as 15% were sufficient to not only trigger cell migration up the synthetic gradient, but also to induce both cell polarization and repolarization. Response kinetics were inversely proportional to Rac gradient values, in agreement with a new mathematical model, suggesting a role for natural input gradient amplification upstream of Rac. Increases in Rac levels beyond a well-defined threshold dramatically augmented polarization and decreased sensitivity to the gradient value. The threshold was governed by initial cell polarity and PI3K activity, supporting a role for both in defining responsiveness to natural or synthetic Rac activation. Our methodology suggests a general way to investigate processes regulated by intracellular signaling gradients.
Though it goes without saying that linear algebra is fundamental to mathematical biology, polynomial algebra is less visible. In this article, we will give a brief tour of four diverse biological problems where multivariate polynomials play a central role -- a subfield that is sometimes called algebraic biology. Namely, these topics include biochemical reaction networks, Boolean models of gene regulatory networks, algebraic statistics and genomics, and place fields in neuroscience. After that, we will summarize the history of discrete and algebraic structures in mathematical biology, from their early appearances in the late 1960s to the current day. Finally, we will discuss the role of algebraic biology in the modern classroom and curriculum, including resources in the literature and relevant software. Our goal is to make this article widely accessible, reaching the mathematical biologist who knows no algebra, the algebraist who knows no biology, and especially the interested student who is curious about the synergy between these two seemingly unrelated fields.
Synthetic biology aims at designing modular genetic circuits that can be assembled according to the desired function. When embedded in a cell, a circuit module becomes a small subnetwork within a larger environmental network, and its dynamics is therefore affected by potentially unknown interactions with the environment. It is well-known that the presence of the environment not only causes extrinsic noise but also memory effects, which means that the dynamics of the subnetwork is affected by its past states via a memory function that is characteristic of the environment. We study several generic scenarios for the coupling between a small module and a larger environment, with the environment consisting of a chain of mono-molecular reactions. By mapping the dynamics of this coupled system onto random walks, we are able to give exact analytical expressions for the arising memory functions. Hence, our results give insights into the possible types of memory functions and thereby help to better predict subnetwork dynamics.
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