Recent computational studies indicate that the molecular noise of a cellular process may be a rich source of information about process dynamics and parameters. However, accessing this source requires stochastic models that are usually difficult to analyze. Therefore, parameter estimation for stochastic systems using distribution measurements, as provided for instance by flow cytometry, currently remains limited to very small and simple systems. Here we propose a new method that makes use of low-order moments of the measured distribution and thereby keeps the essential parts of the provided information, while still staying applicable to systems of realistic size. We demonstrate how cell-to-cell variability can be incorporated into the analysis obviating the need for the ubiquitous assumption that the measurements stem from a homogeneous cell population. We demonstrate the method for a simple example of gene expression using synthetic data generated by stochastic simulation. Subsequently, we use time-lapsed flow cytometry data for the osmo-stress induced transcriptional response in budding yeast to calibrate a stochastic model, which is then used as a basis for predictions. Our results show that measurements of the mean and the variance can be enough to determine the model parameters, even if the measured distributions are not well-characterized by low-order moments only-e.g., if they are bimodal.extrinsic variability | high-osmolarity glycerol pathway | moment dynamics | parameter inference | stochastic kinetic models B uilding predictive computational models of intracellular reaction kinetics is still a dauntingly ill-posed task (1), characterized by low-dimensional experimental readouts of the hypothesized high-dimensional process. Single-cell technologies hold promise to partly alleviate this ill-posedness by exploiting the observed variability for the calibration of stochastic kinetic models (2, 3). The same technologies, however, also reveal that isogenic cells in a single population exhibit large cell-to-cell variability (4, 5). The variation can be shown to be a convolution of two sources, namely the intrinsic molecular noise and extrinsic factors that render single cells different even in the absence of molecular noise; in many cases, the latter was reported to dominate the former (4, 5). Extrinsic factors comprise difference in cell size, cell-cycle stage, expression capacity, local growth conditionsto name but a few (6, 7). Thus, although single-cell technology offers a way out of the predicament of ill-posedness, it requires new methods to deal properly with intrinsic and extrinsic variability. The effect of extrinsic variability on the dynamics of stochastic models is studied in refs. 7 and 8, whereas first attempts have been made to address the inverse problem of quantifying the extrinsic (9) and any additional intrinsic (10) components from measurements. Because the latter is based on path sampling, its applicability remains limited to small systems. Naturally, extrinsic variability is bypassed when...

Inferring molecular networks is a central challenge in computational biology. However, it has remained unclear whether causal, rather than merely correlational, relationships can be effectively inferred in complex biological settings. Here we describe the HPN-DREAM network inference challenge that focused on learning causal influences in signaling networks. We used phosphoprotein data from cancer cell lines as well as in silico data from a nonlinear dynamical model. Using the phosphoprotein data, we scored more than 2,000 networks submitted by challenge participants. The networks spanned 32 biological contexts and were scored in terms of causal validity with respect to unseen interventional data. A number of approaches were effective and incorporating known biology was generally advantageous. Additional sub-challenges considered time-course prediction and visualization. Our results constitute the most comprehensive assessment of causal network inference in a mammalian setting carried out to date and suggest that learning causal relationships may be feasible in complex settings such as disease states. Furthermore, our scoring approach provides a practical way to empirically assess the causal validity of inferred molecular networks.

Mathematical methods combined with measurements of single-cell dynamics provide a means to reconstruct intracellular processes that are only partly or indirectly accessible experimentally. To obtain reliable reconstructions, the pooling of measurements from several cells of a clonal population is mandatory. However, cell-to-cell variability originating from diverse sources poses computational challenges for such process reconstruction. We introduce a scalable Bayesian inference framework that properly accounts for population heterogeneity. The method allows inference of inaccessible molecular states and kinetic parameters; computation of Bayes factors for model selection; and dissection of intrinsic, extrinsic and technical noise. We show how additional single-cell readouts such as morphological features can be included in the analysis. We use the method to reconstruct the expression dynamics of a gene under an inducible promoter in yeast from time-lapse microscopy data.