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Investigating bistability via reachable sets of a stem cell differentiation model. Shaded regions show a conservative estimate of the achievable mean Nanog levels over time. The dark blue region is an over-approximation of the reachable set of the bistable system, when the analysis is started from an initial set of bistability, i.e. a set enclosing states leading to both fixed points. N0=0.6±0.15. Red and green shades show reachable sets computed from ‘monostable’ initial sets, from which all trajectories converge to the differentiation fixed point (low-Nanog level, in red) or to the stem cell fixed point (high-Nanog level, in green). Initial Nanog values are 0.4±0.1 and 2±0.5, respectively.
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Controlling the behaviour of cells by rationally guiding molecular processes is an overarching aim of much of synthetic biology. Molecular processes, however, are notoriously noisy and frequently nonlinear. We present an approach to studying the impact of control measures on motifs of molecular interactions that addresses the problems faced in many...
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The design and implementation of synthetic circuits that operate robustly in the cellular context is fundamental for the advancement of synthetic biology. However, their practical implementation presents challenges due to low predictability of synthetic circuit design and time-intensive troubleshooting. Here, we present the Cyberloop, a testing fra...
Citations
... [15,21], where some controls model external disturbances that need to be taken into account, see e.g. [17,20,23], or where the reachable set models a spatial object to be controlled, see e.g. [11,12]. ...
... Models that learn to make robust predictions for cell fates under such noise carry clear motivation [16]. Further, if we are able to design these models to also provide basic biological insight, we will have a pragmatic tool, based on decision stumps [17,18,19], with which to (i) study high-dimensional developmental dynamics; or (ii) develop engineering strategies e.g. to control cellular behaviour [20,21,22]. ...
Here we introduce repeated decision stumping, to distill simple models from single cell data. We develop decision trees of depth one – hence ‘stumps’ – to identify in an inductive manner, gene products involved in driving cell fate transitions, and in applications to published data we are able to discover the key-players involved in these processes in an unbiased manner without prior knowledge. The approach is computationally efficient, has remarkable predictive power, and yields robust and statistically stable predictors: the same set of candidates is generated by applying the algorithm to different subsamples of the data.
Single-cell data afford unprecedented insights into molecular processes. But the complexity and size of these data sets have proved challenging and given rise to a large armory of statistical and machine learning approaches. The majority of approaches focuses on either describing features of these data, or making predictions and classifying unlabeled samples. In this study, we introduce repeated decision stumping (ReDX) as a method to distill simple models from single-cell data. We develop decision trees of depth one-hence "stumps"-to identify in an inductive manner, gene products involved in driving cell fate transitions, and in applications to published data we are able to discover the key players involved in these processes in an unbiased manner without prior knowledge. Our algorithm is deliberately targeting the simplest possible candidate hypotheses that can be extracted from complex high-dimensional data. There are three reasons for this: (1) the predictions become straightforwardly testable hypotheses; (2) the identified candidates form the basis for further mechanistic model development, for example, for engineering and synthetic biology interventions; and (3) this approach complements existing descriptive modeling approaches and frameworks. The approach is computationally efficient, has remarkable predictive power, including in simulation studies where the ground truth is known, and yields robust and statistically stable predictors; the same set of candidates is generated by applying the algorithm to different subsamples of experimental data.
The predictive power of machine learning models often exceeds that of mechanistic modeling approaches. However, the interpretability of purely data-driven models, without any mechanistic basis is often complicated, and predictive power by itself can be a poor metric by which we might want to judge different methods. In this work, we focus on the relatively new modeling techniques of neural ordinary differential equations. We discuss how they relate to machine learning and mechanistic models, with the potential to narrow the gulf between these two frameworks: they constitute a class of hybrid model that integrates ideas from data-driven and dynamical systems approaches. Training neural ODEs as representations of dynamical systems data has its own specific demands, and we here propose a collocation scheme as a fast and efficient training strategy. This alleviates the need for costly ODE solvers. We illustrate the advantages that collocation approaches offer, as well as their robustness to qualitative features of a dynamical system, and the quantity and quality of observational data. We focus on systems that exemplify some of the hallmarks of complex dynamical systems encountered in systems biology, and we map out how these methods can be used in the analysis of mathematical models of cellular and physiological processes.
A fundamental question in systems biology is what combinations of mean and variance of the species present in a stochastic biochemical reaction network are attainable by perturbing the system with an external signal. To address this question, we show that the moments evolution in any generic network can be either approximated or, under suitable assumptions, computed exactly as the solution of a switched affine system. We then propose a new method to approximate the reachable set of such switched affine system. A remarkable feature of our approach is that it allows one to easily compute projections of the reachable set for pairs of moments of interest, without requiring the computation of the full reachable set, which can be prohibitive for large networks. As a second contribution, we also show how to select the external signal in order to maximize the probability of reaching a target set. To illustrate the method we study a renown model of controlled gene expression and we derive estimates of the reachable set, for the protein mean and variance, that are more accurate than those available in the literature and consistent with experimental data.
Single molecule microarrays have been used in quantitative proteomics, in particular, single cell analysis requiring high sensitivity and ultra-low limits of detection. In this paper, several image analysis methods are evaluated for their ability to accurately enumerate single molecules bound to a microarray spot. Crucially, protein abundance in single cells can vary significantly and may span several orders of magnitude. This poses a challenge to single molecule image analysis. In order to quantitatively assess the performance of each method, synthetic image datasets are generated with known ground truth whereby the number of single molecules varies over 5 orders of magnitude with a range of signal to noise ratios. Experiments were performed on synthetic datasets whereby the number of single molecules per spot corresponds to realistic single cell distributions whose ground truth summary statistics are known. The methods of image analysis are assessed in their ability to accurately estimate the distribution parameters. It is shown that super-resolution image analysis methods can significantly improve counting accuracy and better cope with single molecule congestion. The results highlight the challenge posed by quantitative single cell analysis and the implications to performing such analyses using microarray based approaches are discussed.
