Homeostasis is a recurring theme in biology. Homeostatic mechanisms commonly ensure that regulated variables robustly and completely adapt to environmental perturbations. This robust perfect adaptation (RPA) feature is achieved by incorporating mathematical integration in a negative feedback strategy. 1, 2 Despite its benefits in natural circuits, the synthetic realization of integral feedback has remained elusive due to the complexity of the required biological computations. Here we first mathematically prove that there is fundamentally a single biomolecular controller topology 3 that realizes integral feedback for arbitrary intracellular networks with noisy dynamics. Such a topology guarantees RPA for both the cell populationaverage and for the time-average of single cells. We then develop the first synthetic gene network implementation of such an integral controller in a living cell, 4 and demonstrate its tunability and adaptation properties. A growth control application shows the inherent capacity of our integral feedback controller to deliver robustness, and highlights its potential use as a versatile controller for regulation of biological variables in uncertain networks. Our results provide new conceptual and practical tools in the area of Cybergenetics 3,5 where control theory and synthetic biology come together to enable the engineering of novel synthetic controllers that steer the dynamics of living systems. [3][4][5][6][7][8][9] Integral feedback control is arguably one the most fundamental regulation strategies in engineering practice. From modern jetliners to industrial plants, integral feedback loops reliably drive physical variables to their desired values with great robustness and precision. 10 It is becoming increasingly appreciated that

A central challenge in computational modeling of biological systems is the determination of the model parameters. Typically, only a fraction of the parameters (such as kinetic rate constants) are experimentally measured, while the rest are often fitted. The fitting process is usually based on experimental time course measurements of observables, which are used to assign parameter values that minimize some measure of the error between these measurements and the corresponding model prediction. The measurements, which can come from immunoblotting assays, fluorescent markers, etc., tend to be very noisy and taken at a limited number of time points. In this work we present a new approach to the problem of parameter selection of biological models. We show how one can use a dynamic recursive estimator, known as extended Kalman filter, to arrive at estimates of the model parameters. The proposed method follows. First, we use a variation of the Kalman filter that is particularly well suited to biological applications to obtain a first guess for the unknown parameters. Secondly, we employ an a posteriori identifiability test to check the reliability of the estimates. Finally, we solve an optimization problem to refine the first guess in case it should not be accurate enough. The final estimates are guaranteed to be statistically consistent with the measurements. Furthermore, we show how the same tools can be used to discriminate among alternate models of the same biological process. We demonstrate these ideas by applying our methods to two examples, namely a model of the heat shock response in E. coli, and a model of a synthetic gene regulation system. The methods presented are quite general and may be applied to a wide class of biological systems where noisy measurements are used for parameter estimation or model selection.

Tunable induction of gene expression is an essential tool in biology and biotechnology. In spite of that, current induction systems often exhibit unpredictable behavior and performance shortcomings, including high sensitivity to transactivator dosage and plasmid take-up variation, and excessive consumption of cellular resources. To mitigate these limitations, we introduce here a novel family of gene expression control systems of varying complexity with significantly enhanced performance. These include: (i) an incoherent feedforward circuit that exhibits output tunability and robustness to plasmid take-up variation; (ii) a negative feedback circuit that reduces burden and provides robustness to transactivator dosage variability; and (iii) a new hybrid circuit integrating negative feedback and incoherent feedforward that combines the benefits of both. As with endogenous circuits, the complexity of our genetic controllers is not gratuitous, but is the necessary outcome of more stringent performance requirements. We demonstrate the benefits of these controllers in two applications. In a culture of CHO cells for protein manufacturing, the circuits result in up to a 2.6-fold yield improvement over a standard system. In human-induced pluripotent stem cells they enable precisely regulated expression of an otherwise poorly tolerated gene of interest, resulting in a significant increase in the viability of the transfected cells.

Motivation: In the noisy cellular environment, stochastic fluctuations at the molecular level manifest as cell-cell variability at the population level that is quantifiable using high-throughput single-cell measurements. Such variability is rich with information about the cell's underlying gene regulatory networks, their architecture and the parameters of the biochemical reactions at their core. Results: We report a novel method, called Inference for Networks of Stochastic Interactions among Genes using High-Throughput data (INSIGHT), for systematically combining high-throughput time-course flow cytometry measurements with computer-generated stochastic simulations of candidate gene network models to infer the network's stochastic model and all its parameters. By exploiting the mathematical relationships between experimental and simulated population histograms, INSIGHT achieves scalability, efficiency and accuracy while entirely avoiding approximate stochastic methods. We demonstrate our method on a synthetic gene network in bacteria and show that a detailed mechanistic model of this network can be estimated with high accuracy and high efficiency. Our method is completely general and can be used to infer models of signal-activated gene networks in any organism based solely on flow cytometry data and stochastic simulations.

The determination of the model parameters is a central challenge in computational modeling of biological systems. Typically, only a fraction of the parameters (such as kinetic rate constants) is experimentally measured, whereas the rest is fitted. The fitting process is usually based on experimental time course measurements of observables, which are used to assign parameter values that minimize some measure of the error between these measurements and the corresponding model prediction. The data, which can come from real-time polymerase chain reaction (PCR), enzymatic reactions, flow cytometry, etc., tend to be very noisy, but the statistics of the noise can often be inferred by performing calibration procedures. In this paper, we show how the knowledge of the properties of the noise, expressed in terms of its cumulative distribution function, can be used to validate or invalidate the estimates provided by an upstream state observer (a particle filter) and to refine them in case they turn out not to be satisfactory. Furthermore, we show how the same tools can be used to discriminate among alternative models of the same biological process. We demonstrate these ideas on a simple gene expression model, and we show how the proposed method is able to handle estimation problems that cannot be effectively solved by classical techniques such as least-squares estimation.For these reasons, the problem of parameter estimation, that is the indirect determination of the unknown parameters from measurements of other quantities, is a key issue in computational and systems biology. Knowledge of the parameter values is crucial whenever one wants to obtain quantitative or even qualitative information from the models [1,2].Not surprisingly, this problem has been given a great deal of attention in the systems biology community. The first systematic approaches mainly involved optimization techniques, such as leastsquares fitting [3], simulated annealing [4], genetic algorithms [5], and evolutionary computation [6,7]. The latter is suggested as the method of choice for large problems [7]. One of the main issues associated with optimization methods is that they tend to be computationally expensive and may not perform well if significant noise is present in the measurements. This is because the data points are usually fitted directly without taking into account the statistics of the noise itself. Also, performance can be highly dependent on the choice of a suitable initial guess.Considerable interest in statistical methods, such as maximum-likelihood estimation [8,9] and Bayesian methods [10], has also been raised. These can extract information from noisy or uncertain data. Uncertainty may include both measurement noise and intrinsic noise, which is well known to play an important role in chemical kinetics when species are present in low copy numbers [11]. The main advantage of these methods is their ability to infer the whole probability distributions of the parameters, rather than just a point estimate. Also, they can handle the estima...