Estimating the Stochastic Bifurcation Structure of Cellular Networks

High throughput measurement of gene expression at single-cell resolution, combined with systematic perturbation of environmental or cellular variables, provides information that can be used to generate novel insight into the properties of gene regulatory networks by linking cellular responses to external parameters. In dynamical systems theory, this information is the subject of bifurcation analysis, which establishes how system-level behaviour changes as a function of parameter values within a given deterministic mathematical model. Since cellular networks are inherently noisy, we generalize the traditional bifurcation diagram of deterministic systems theory to stochastic dynamical systems. We demonstrate how statistical methods for density estimation, in particular, mixture density and conditional mixture density estimators, can be employed to establish empirical bifurcation diagrams describing the bistable genetic switch network controlling galactose utilization in yeast Saccharomyces cerevisiae. These approaches allow us to make novel qualitative and quantitative observations about the switching behavior of the galactose network, and provide a framework that might be useful to extract information needed for the development of quantitative network models

Quantitative Epistasis Analysis and Pathway Inference from Genetic Interaction Data

Inferring regulatory and metabolic network models from quantitative genetic interaction data remains a major challenge in systems biology. Here, we present a novel quantitative model for interpreting epistasis within pathways responding to an external signal. The model provides the basis of an experimental method to determine the architecture of such pathways, and establishes a new set of rules to infer the order of genes within them. The method also allows the extraction of quantitative parameters enabling a new level of information to be added to genetic network models. It is applicable to any system where the impact of combinatorial loss-of-function mutations can be quantified with sufficient accuracy. We test the method by conducting a systematic analysis of a thoroughly characterized eukaryotic gene network, the galactose utilization pathway in Saccharomyces cerevisiae. For this purpose, we quantify the effects of single and double gene deletions on two phenotypic traits, fitness and reporter gene expression. We show that applying our method to fitness traits reveals the order of metabolic enzymes and the effects of accumulating metabolic intermediates. Conversely, the analysis of expression traits reveals the order of transcriptional regulatory genes, secondary regulatory signals and their relative strength. Strikingly, when the analyses of the two traits are combined, the method correctly infers ∼80% of the known relationships without any false positives

YeastNet: Deep-Learning-Enabled Accurate Segmentation of Budding Yeast Cells in Bright-Field Microscopy

Accurate and efficient segmentation of live-cell images is critical in maximizing data extraction and knowledge generation from high-throughput biology experiments. Despite recent development of deep-learning tools for biomedical imaging applications, great demand for automated segmentation tools for high-resolution live-cell microscopy images remains in order to accelerate the analysis. YeastNet dramatically improves the performance of the non-trainable classic algorithm, and performs considerably better than the current state-of-the-art yeast-cell segmentation tools. We have designed and trained a U-Net convolutional network (named YeastNet) to conduct semantic segmentation on bright-field microscopy images and generate segmentation masks for cell labeling and tracking. YeastNet enables accurate automatic segmentation and tracking of yeast cells in biomedical applications. YeastNet is freely provided with model weights as a Python package on GitHub

Disappearance of the low subpopulation at higher galactose concentrations, in the galactose pre-growth condition.

<p>Empirical count distributions for the four replicates are shown, smoothed using a width-11 moving average to improve visibility. (A) At the galactose concentration (0.0132%). (B) At the galactose concentration (0.0152%). (C) At the galactose concentration (0.0174%).</p

Comparison of subpopulation means and sizes across replicates.

<p>(A) Subpopulation means as extracted by the three fitting methods, in all four replicates of the gal-pregrowth condition. (B) Subpopulation means in the four raf-pregrowth replicates. (C,D) Estimated sizes of the low subpopulations in the gal-pregrowth and raf-pregrowth conditions respectively.</p

Comparison of goodness-of-fit between methods and biological replicates.

<p>(A) For each method, the mean negative log likelihood of the data. “Training” means each model is evaluated on the same data to which it is fit, whereas “testing” means each model is evaluated on the data from the other three replicates having the same pregrowth condition. Black bars indicate 95% confidence intervals. (B,C) Variability in the estimated locations of four subpopulations: the low (and only) subpopulation at the zero galactose concentration (P1), the low subpopulation at the galactose concentration (P2), the high subpopulation at the galactose concentration (P3), the high (and only) subpopulation at the largest tested galactose concentration (P4). Cyan bars show the variability attributed to different estimation methods, whereas green bars show the variability attributed to different biological repliciates.</p

Fluorescence data for the reporter protein indicating activity level of the galactose utilization network in <i>S. cerevisiae</i>.

<p>Fluorescence is reported as a function of galactose level in culture (expressed as percent weight per volume; 1% = 10g/L), under the galactose pregrowth condition (A), and the raffinose pregrowth condition (B). All four biological replicates are shown stacked on each other. The blue area represents the number of cells counted in each fluorescence channel in replicate 1, the next lighter blue area is the sum of the counts in the first two replicates, and so on.</p

Examples of bifurcation behavior.

<p>(A) Bifurcation diagram of the system in Equation 1, an idealized model of a gene activated by signal as well as by its own protein product , with parameters , , . The three colored curves identify low, high, and unstable steady states for (i.e., values for which ), as a function of the activating input . Black arrows show the direction of change of , assuming constant. (B) With noise in the dynamics, individual cells would fluctuate in the vicinity of the steady states, leading to some overall distribution for over time or across cells.</p

Results of mixture modeling on replicate one.

<p>(A) Means of subpopulations, as extracted by: mixture models estimated by the expectation-maximization algorithm (EM), mixture models estimated by a combination of mode estimation and expectation-maximization (ME+EM), and a conditional mixture model estimated by expectation-maximization (CEM). The x-axis represents the 17 levels of galactose tested, in order of increasing concentration. The y-axis represents fluorescence channels of the flow cytometer, which are proportional to the logarithm of fluorescent intensity. Darker background shading represents more cells counted in the channel at the given galactose level. (B) Estimated mixture coefficients (prior probabilities) of the low subpopulation as a function of galactose concentration. (C) Estimated standard deviations of the Gaussian distributions representing low (darker) and high (lighter) subpopulations as a function of galactose concentration.</p