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, whereas 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. 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 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.biochemical circuits | dynamical systems | robustness A s we are beginning to understand the mechanisms governing biological systems we are starting to identify potential ways of guiding or controlling the behavior of cellular and molecular systems. Rationally reengineering organisms for biomedical or biotechnological purposes has become the central aim of the fledgling discipline of synthetic biology. By redirecting regulatory and physical interactions or by altering molecular binding affinities we may, for example, control metabolic processes (1, 2) or alter intra-and intercellular communication and decision making processes (3, 4). The range of potential applications of such engineered systems is vast: designing microbes for biofuel production (5, 6) and bioremediation (7); developing control strategies which drive stem cells through the various decisions to become terminally differentiated (or back) (8, 9), with the aim of developing novel therapeutics (10, 11); construction of new drugdelivery systems with homing microbes delivering molecular medicines directly to the site where they are needed (12); use of bacteria or bacterial populations (employing swarming and quorum sensing) as biosensors (13); and gaining better understanding of all manner of biological systems by systematically probing their underlying molecular machinery.A range of tools and building blocks for such engineered biological systems are now available which allow us to, at least in principle, build such systems from simple and reusable biological components (14). In electronic systems, such modularity has been crucial and has allowed the cost-effective production of reliable component...

Pathogenic microbes exist in dynamic niches and have evolved robust adaptive responses to promote survival in their hosts. The major fungal pathogens of humans, Candida albicans and Candida glabrata, are exposed to a range of environmental stresses in their hosts including osmotic, oxidative and nitrosative stresses. Significant efforts have been devoted to the characterization of the adaptive responses to each of these stresses. In the wild, cells are frequently exposed simultaneously to combinations of these stresses and yet the effects of such combinatorial stresses have not been explored. We have developed a common experimental platform to facilitate the comparison of combinatorial stress responses in C. glabrata and C. albicans. This platform is based on the growth of cells in buffered rich medium at 30°C, and was used to define relatively low, medium and high doses of osmotic (NaCl), oxidative (H 2O2) and nitrosative stresses (e.g., dipropylenetriamine (DPTA)-NONOate). The effects of combinatorial stresses were compared with the corresponding individual stresses under these growth conditions. We show for the first time that certain combinations of combinatorial stress are especially potent in terms of their ability to kill C. albicans and C. glabrata and/or inhibit their growth. This was the case for combinations of osmotic plus oxidative stress and for oxidative plus nitrosative stress. We predict that combinatorial stresses may be highly signif cant in host defences against these pathogenic yeasts.

Abstract:The likelihood-free sequential Approximate Bayesian Computation (ABC) algorithms are increa singly popular inference tools for complex biological models. Such algorithms proceed by constructing a succession of probability distributions over the parameter space conditional upon the simulated data lying in an e-ball around the observed data, for decreasing values of the threshold e. While in theory, the distribu tions (starting from a suitably defined prior) will converge towards the unknown posterior as e tends to zero, the exact sequence of thresholds can impact upon the computational efficiency and success of a particular application. In particular, we show here that the current preferred method of choosing thresholds as a pre determined quantile of the distances between simulated and observed data from the previous population, can lead to the inferred posterior distribution being very different to the true posterior. Threshold selection thus remains an important challenge. Here we propose that the threshold-acceptance rate curve may be used to determine threshold schedules that avoid local optima, while balancing the need to minimise the threshold with computational efficiency. Furthermore, we provide an algorithm based upon the unscented transform, that enables the threshold-acceptance rate curve to be efficiently predicted in the case of deter ministic and stochastic state space models.

Experimental design attempts to maximise the information available for modelling tasks. An optimal experiment allows the inferred models or parameters to be chosen with the highest expected degree of confidence. If the true system is faithfully reproduced by one of the models, the merit of this approach is clear - we simply wish to identify it and the true parameters with the most certainty. However, in the more realistic situation where all models are incorrect or incomplete, the interpretation of model selection outcomes and the role of experimental design needs to be examined more carefully. Using a novel experimental design and model selection framework for stochastic state-space models, we perform high-throughput in-silico analyses on families of gene regulatory cascade models, to show that the selected model can depend on the experiment performed. We observe that experimental design thus makes confidence a criterion for model choice, but that this does not necessarily correlate with a model's predictive power or correctness. Finally, in the special case of linear ordinary differential equation (ODE) models, we explore how wrong a model has to be before it influences the conclusions of a model selection analysis.

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We discuss how statistical inference techniques can be applied in the context of designing novel biological systems. Bayesian techniques have found widespread application and acceptance in the systems biology community, where they are used for both parameter estimation and model selection. Here we show that the same approaches can also be used in order to engineer synthetic biological systems by inferring the structure and parameters that are most likely to give rise to the dynamics that we require a system to exhibit. Problems that are shared between applications in systems and synthetic biology include the vast potential spaces that need to be searched for suitable models and model parameters; the complex forms of likelihood functions; and the interplay between noise at the molecular level and nonlinearity in the dynamics owing to often complex feedback structures. In order to meet these challenges, we have to develop suitable inferential tools and here, in particular, we illustrate the use of approximate Bayesian computation and unscented Kalman filtering-based approaches. These partly complementary methods allow us to tackle a number of recurring problems in the design of biological systems. After a brief exposition of these two methodologies, we focus on their application to oscillatory systems.

Chaos and oscillations continue to capture the interest of both the scientific and public domains. Yet despite the importance of these qualitative features, most attempts at constructing mathematical models of such phenomena have taken an indirect, quantitative approach, for example, by fitting models to a finite number of data points. Here we develop a qualitative inference framework that allows us to both reverse-engineer and design systems exhibiting these and other dynamical behaviours by directly specifying the desired characteristics of the underlying dynamical attractor. This change in perspective from quantitative to qualitative dynamics, provides fundamental and new insights into the properties of dynamical systems.

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