Gabriele Lillacci

Parameter Estimation and Model Selection in Computational Biology

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.

The Signal within the Noise: Efficient Inference of Stochastic Gene Regulation Models using Fluorescence Histograms and Stochastic Simulations

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 cells 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 networks 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. AVAILABILITY A free C source code implementing the INSIGHT algorithm, together with test data is available from the authors. CONTACT mustafa.khammash@bsse.ethz.ch SUPPLEMENTARY INFORMATION Supplementary data are available at Bioinformatics online.

MUC1* Ligand, NM23-H1, Is a Novel Growth Factor That Maintains Human Stem Cells in a More Naïve State

We report that a single growth factor, NM23-H1, enables serial passaging of both human ES and iPS cells in the absence of feeder cells, their conditioned media or bFGF in a fully defined xeno-free media on a novel defined, xeno-free surface. Stem cells cultured in this system show a gene expression pattern indicative of a more “naïve” state than stem cells grown in bFGF-based media. NM23-H1 and MUC1* growth factor receptor cooperate to control stem cell self-replication. By manipulating the multimerization state of NM23-H1, we override the stem cells inherent programming that turns off pluripotency and trick the cells into continuously replicating as pluripotent stem cells. Dimeric NM23-H1 binds to and dimerizes the extra cellular domain of the MUC1* transmembrane receptor which stimulates growth and promotes pluripotency. Inhibition of the NM23-H1/MUC1* interaction accelerates differentiation and causes a spike in miR-145 expression which signals a cells exit from pluripotency.

A synthetic integral feedback controller for robust tunable regulation in bacteria

We report on the first engineered integral feedback control system in a living cell. The controller is based on the recently published antithetic integral feedback motif [1] which has been analytically shown to have favorable regulation properties. It is implemented along with test circuitry in Escherichia coli using seven genes and three small-molecule inducers. The closed-loop system is highly tunable, allowing a regulated protein of interest to be driven to a desired level and maintained there with precision. Realized using a sigma/anti-sigma protein pair, the integral controller ensures that regulation is maintained in the face of perturbations that lead to the regulated protein’s degradation, thus serving as a proof-of-concept prototype of integral feedback implementation in living cells. When suitably optimized, this integral controller may be utilized as a general-purpose robust regulator for genetic circuits with unknown or partially-known topologies and parameters.

Model selection in stochastic chemical reaction networks using flow cytometry data

The model selection problem, that is picking the model that best explains an experimental data set from a list of candidates, arises frequently when studying unknown biological processes. Here, we propose a new method for model selection in stochastic chemical reaction networks using measurements from flow cytometry. A distinctive feature of our approach is its ability to perform statistically significant selection using a very small number of Monte Carlo simulations of the candidate stochastic models. After a comprehensive review of the theory associated with our procedure, we describe the model selection algorithm and we demonstrate it on an example drawn from molecular biology.

Parameter identification of biological networks using extended Kalman filtering and χ 2 criteria

Parameter estimation is a central issue in systems biology, as it represents the key step in obtaining information from computational models of biological systems. The extended Kalman filter (EKF) in its various implementations has been proposed as a parameter estimator by several authors. However, in many cases, and in particular when the estimation problem involves a large number of unknown parameters, the EKF can perform poorly. In this paper we show how the knowledge of the statistics of the measurement noise can be used to validate or invalidate the estimates provided by the filter, and to refine them in case they turn out not to be satisfactory. We demonstrate these ideas on a simple gene expression model, and we show how the proposed method offer advantages over classical techniques such as least-squares estimation.

Synthetic control systems for high performance gene expression in mammalian cells

Abstract 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.

Measurement noise distribution as a metric for parameter estimation in dynamical systems

Approximate Bayesian computation (ABC) has been demonstrated by several authors as an effective approach to infer unknown parameters in dynamical models of biological systems. ABC methods require the choice of a metric, which measures the distance between the model simulations and the experimental data. This choice is arbitrary, and the Euclidean metric (least-squares) tends to be the preferred one. In this paper, we propose the use of a specific metric based on the distribution of the measurement noise that is superimposed to the data points. We demonstrate our approach on a simple model of the p53 gene regulatory network, and we show that it can lead to better performance than ABC with the standard least-squares metric.