Deterministic and probabilistic fate decisions co-exist in a single retinal lineage.

Correct nervous system development depends on the timely differentiation of progenitor cells into neurons. While the output of progenitor differentiation is well investigated at the population and clonal level, how stereotypic or variable fate decisions are during development is still more elusive. To fill this gap, we here follow the fate outcome of single neurogenic progenitors in the zebrafish retina over time using live imaging. We find that neurogenic progenitor divisions produce two daughter cells, one of deterministic and one of probabilistic fate. Interference with the deterministic branch of the lineage affects lineage progression. In contrast, interference with fate probabilities of the probabilistic branch results in a broader range of fate possibilities than in wild-type and involves the production of any neuronal cell type even at non-canonical developmental stages. Combining the interference data with stochastic modelling of fate probabilities revealed that a simple gene regulatory network is able to predict the observed fate decision probabilities during wild-type development. These findings unveil unexpected lineage flexibility that could ensure robust development of the retina and other tissues.

Uniform gene expression in embryos is achieved by temporal averaging of transcription noise.

Transcription is often stochastic. This is seemingly incompatible with the importance of gene expression during development. Here we show that during zebrafish embryogenesis, transcription activation is stochastic due to (1) genes acquiring transcriptional competence at different times in different cells, (2) differences in cell cycle stage between cells, and (3) the stochastic nature of transcription. Initially, stochastic transcription causes large cell-to-cell differences in transcript levels. However, variability is reduced by lengthening cell cycles and the accumulation of transcription events in each cell. Temporal averaging might provide a general context in which to understand how embryos deal with stochastic transcription.

Phosphate sensing in health and disease.

PURPOSE OF REVIEW: Disruptions of phosphate homeostasis are associated with a multitude of diseases with insufficient treatments. Our knowledge regarding the mechanisms underlying metazoan phosphate homeostasis and sensing is limited. Here, we highlight four major advancements in this field during the last 12-18 months. RECENT FINDINGS: First, kidney glycolysis senses filtered phosphate, which results in the release of glycerol 3-phosphate (G-3-P). Circulating G-3-P then stimulates synthesis of the phosphaturic hormone fibroblast growth factor 23 in bone. Second, the liver serves as a postprandial phosphate reservoir to limit serum phosphate excursions. It senses phosphate ingestion and triggers renal excretion of excess phosphate through a nerve-dependent mechanism. Third, phosphate-starvation in cells massively induces the phosphate transporters SLC20A1/PiT1 and SLC20A2/PiT2, implying direct involvement of cellular phosphate sensing. Under basal phosphate-replete conditions, PiT1 is produced but immediately destroyed, which suggests a novel mechanism for the regulation of PiT1 abundance. Fourth, Drosophila melanogaster intestinal cells contain novel organelles called PXo bodies that limit intracellular phosphate excursions. Phosphate starvation leads to PXo body dissolution, which triggers midgut proliferation. SUMMARY: These studies have opened novel avenues to dissect the mechanisms that govern metazoan phosphate sensing and homeostasis with the potential to identify urgently needed therapeutic targets.

Digital Quantification of Proteins and mRNA in Single Mammalian Cells.

Absolute quantification of macromolecules in single cells is critical for understanding and modeling biological systems that feature cellular heterogeneity. Here we show extremely sensitive and absolute quantification of both proteins and mRNA in single mammalian cells by a very practical workflow that combines proximity ligation assay (PLA) and digital PCR. This digital PLA method has femtomolar sensitivity, which enables the quantification of very small protein concentration changes over its entire 3-log dynamic range, a quality necessary for accounting for single-cell heterogeneity. We counted both endogenous (CD147) and exogenously expressed (GFP-p65) proteins from hundreds of single cells and determined the correlation between CD147 mRNA and the protein it encodes. Using our data, a stochastic two-state model of the central dogma was constructed and verified using joint mRNA/protein distributions, allowing us to estimate transcription burst sizes and extrinsic noise strength and calculate the transcription and translation rate constants in single mammalian cells.

Quantifying single-cell diacylglycerol signaling kinetics after uncaging.

Studying the role of molecularly distinct lipid species in cell signaling remains challenging due to a scarcity of methods for performing quantitative lipid biochemistry in living cells. We have recently used lipid uncaging to quantify lipid-protein affinities and rates of lipid trans-bilayer movement and turnover in the diacylglycerol signaling pathway. This approach is based on acquiring live-cell dose-response curves requiring light dose titrations and experimental determination of uncaging photoreaction efficiency. We here aimed to develop a methodological approach that allows us to retrieve quantitative kinetic data from uncaging experiments that 1) require only typically available datasets without the need for specialized additional constraints and 2) should in principle be applicable to other types of photoactivation experiments. Our new analysis framework allows us to identify model parameters such as diacylglycerol-protein affinities and trans-bilayer movement rates, together with initial uncaged diacylglycerol levels, using noisy single-cell data for a broad variety of structurally different diacylglycerol species. We find that lipid unsaturation degree and side-chain length generally correlate with faster lipid trans-bilayer movement and turnover and also affect lipid-protein affinities. In summary, our work demonstrates how rate parameters and lipid-protein affinities can be quantified from single-cell signaling trajectories with sufficient sensitivity to resolve the subtle kinetic differences caused by the chemical diversity of cellular signaling lipid pools.

Cellular abundance of sodium phosphate cotransporter SLC20A1/PiT1 and phosphate uptake are controlled post-transcriptionally by ESCRT.

Inorganic phosphate is essential for human life. The widely expressed mammalian sodium/phosphate cotransporter SLC20A1/PiT1 mediates phosphate uptake into most cell types; however, while SLC20A1 is required for development, and elevated SLC20A1 expression is associated with vascular calcification and aggressive tumor growth, the mechanisms regulating SLC20A1 protein abundance are unknown. Here, we found that SLC20A1 protein expression is low in phosphate-replete cultured cells but is strikingly induced following phosphate starvation, whereas mRNA expression is high in phosphate-replete cells and only mildly increased by phosphate starvation. To identify regulators of SLC20A1 protein levels, we performed a genome-wide CRISPR-based loss-of-function genetic screen in phosphate-replete cells using SLC20A1 protein induction as readout. Our screen revealed that endosomal sorting complexes required for transport (ESCRT) machinery was essential for proper SLC20A1 protein downregulation in phosphate-replete cells. We show that SLC20A1 colocalizes with ESCRT and that ESCRT deficiency increases SLC20A1 protein and phosphate uptake into cells. We also found numerous additional candidate regulators of mammalian phosphate homeostasis, including genes modifying protein ubiquitination and the Krebs cycle and oxidative phosphorylation pathways. Many of these targets have not been previously implicated in this process. We present here a model in which SLC20A1 protein abundance and phosphate uptake are tonically negatively regulated post-transcriptionally in phosphate-replete cells through direct ESCRT-mediated SLC20A1 degradation. Moreover, our screening results provide a comprehensive resource for future studies to elucidate the mechanisms governing cellular phosphate homeostasis. We conclude that genome-wide CRISPR-based genetic screening is a powerful tool to discover proteins and pathways relevant to physiological processes.

Stochasticity and determinism in cell fate decisions.

During development, cells need to make decisions about their fate in order to ensure that the correct numbers and types of cells are established at the correct time and place in the embryo. Such cell fate decisions are often classified as deterministic or stochastic. However, although these terms are clearly defined in a mathematical sense, they are sometimes used ambiguously in biological contexts. Here, we provide some suggestions on how to clarify the definitions and usage of the terms stochastic and deterministic in biological experiments. We discuss the frameworks within which such clear definitions make sense and highlight when certain ambiguity prevails. As an example, we examine how these terms are used in studies of neuronal cell fate decisions and point out areas in which definitions and interpretations have changed and matured over time. We hope that this Review will provide some clarification and inspire discussion on the use of terminology in relation to fate decisions.

Stochastic reaction networks in dynamic compartment populations.

Compartmentalization of biochemical processes underlies all biological systems, from the organelle to the tissue scale. Theoretical models to study the interplay between noisy reaction dynamics and compartmentalization are sparse, and typically very challenging to analyze computationally. Recent studies have made progress toward addressing this problem in the context of specific biological systems, but a general and sufficiently effective approach remains lacking. In this work, we propose a mathematical framework based on counting processes that allows us to study dynamic compartment populations with arbitrary interactions and internal biochemistry. We derive an efficient description of the dynamics in terms of differential equations which capture the statistics of the population. We demonstrate the relevance of our approach by analyzing models inspired by different biological processes, including subcellular compartmentalization and tissue homeostasis.

Control of Hox transcription factor concentration and cell-to-cell variability by an auto-regulatory switch.

The variability in transcription factor concentration among cells is an important developmental determinant, yet how variability is controlled remains poorly understood. Studies of variability have focused predominantly on monitoring mRNA production noise. Little information exists about transcription factor protein variability, as this requires the use of quantitative methods with single-molecule sensitivity. Using Fluorescence Correlation Spectroscopy (FCS), we have characterized the concentration and variability of 14 endogenously tagged TFs in live Drosophila imaginal discs. For the Hox TF Antennapedia, we investigated whether protein variability results from random stochastic events or is developmentally regulated. We found that Antennapedia transitioned from low concentration/high variability early, to high concentration/low variability later, in development. FCS and temporally resolved genetic studies uncovered that Antennapedia itself is necessary and sufficient to drive a developmental regulatory switch from auto-activation to auto-repression, thereby reducing variability. This switch is controlled by progressive changes in relative concentrations of preferentially activating and repressing Antennapedia isoforms, which bind chromatin with different affinities. Mathematical modeling demonstrated that the experimentally supported auto-regulatory circuit can explain the increase of Antennapedia concentration and suppression of variability over time.

Compartor: a toolbox for the automatic generation of moment equations for dynamic compartment populations.

SUMMARY: Many biochemical processes in living organisms take place inside compartments that can interact with each other and remodel over time. In a recent work, we have shown how the stochastic dynamics of a compartmentalized biochemical system can be effectively studied using moment equations. With this technique, the time evolution of a compartment population is summarized using a finite number of ordinary differential equations, which can be analyzed very efficiently. However, the derivation of moment equations by hand can become time-consuming for systems comprising multiple reactants and interactions. Here we present Compartor, a toolbox that automatically generates the moment equations associated with a user-defined compartmentalized system. Through the moment equation method, Compartor renders the analysis of stochastic population models accessible to a broader scientific community. AVAILABILITY AND IMPLEMENTATION: Compartor is provided as a Python package and is available at https://pypi.org/project/compartor/. Source code and usage tutorials for Compartor are available at https://github.com/zechnerlab/Compartor.

Promoters adopt distinct dynamic manifestations depending on transcription factor context.

Cells respond to external signals and stresses by activating transcription factors (TF), which induce gene expression changes. Prior work suggests that signal-specific gene expression changes are partly achieved because different gene promoters exhibit distinct induction dynamics in response to the same TF input signal. Here, using high-throughput quantitative single-cell measurements and a novel statistical method, we systematically analyzed transcriptional responses to a large number of dynamic TF inputs. In particular, we quantified the scaling behavior among different transcriptional features extracted from the measured trajectories such as the gene activation delay or duration of promoter activity. Surprisingly, we found that even the same gene promoter can exhibit qualitatively distinct induction and scaling behaviors when exposed to different dynamic TF contexts. While it was previously known that promoters fall into distinct classes, here we show that the same promoter can switch between different classes depending on context. Thus, promoters can adopt context-dependent "manifestations". Our analysis suggests that the full complexity of signal processing by genetic circuits may be significantly underestimated when studied in only specific contexts.

Molecular circuits for dynamic noise filtering.

The invention of the Kalman filter is a crowning achievement of filtering theory-one that has revolutionized technology in countless ways. By dealing effectively with noise, the Kalman filter has enabled various applications in positioning, navigation, control, and telecommunications. In the emerging field of synthetic biology, noise and context dependency are among the key challenges facing the successful implementation of reliable, complex, and scalable synthetic circuits. Although substantial further advancement in the field may very well rely on effectively addressing these issues, a principled protocol to deal with noise-as provided by the Kalman filter-remains completely missing. Here we develop an optimal filtering theory that is suitable for noisy biochemical networks. We show how the resulting filters can be implemented at the molecular level and provide various simulations related to estimation, system identification, and noise cancellation problems. We demonstrate our approach in vitro using DNA strand displacement cascades as well as in vivo using flow cytometry measurements of a light-inducible circuit in Escherichia coli.

Selected-node stochastic simulation algorithm.

Stochastic simulations of biochemical networks are of vital importance for understanding complex dynamics in cells and tissues. However, existing methods to perform such simulations are associated with computational difficulties and addressing those remains a daunting challenge to the present. Here we introduce the selected-node stochastic simulation algorithm (snSSA), which allows us to exclusively simulate an arbitrary, selected subset of molecular species of a possibly large and complex reaction network. The algorithm is based on an analytical elimination of chemical species, thereby avoiding explicit simulation of the associated chemical events. These species are instead described continuously in terms of statistical moments derived from a stochastic filtering equation, resulting in a substantial speedup when compared to Gillespie's stochastic simulation algorithm (SSA). Moreover, we show that statistics obtained via snSSA profit from a variance reduction, which can significantly lower the number of Monte Carlo samples needed to achieve a certain performance. We demonstrate the algorithm using several biological case studies for which the simulation time could be reduced by orders of magnitude.

Scalable inference of heterogeneous reaction kinetics from pooled single-cell recordings.

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.

Sensitivity estimation for stochastic models of biochemical reaction networks in the presence of extrinsic variability.

Determining the sensitivity of certain system states or outputs to variations in parameters facilitates our understanding of the inner working of that system and is an essential design tool for the de novo construction of robust systems. In cell biology, the output of interest is often the response of a certain reaction network to some input (e.g., stressors or nutrients) and one aims to quantify the sensitivity of this response in the presence of parameter heterogeneity. We argue that for such applications, parametric sensitivities in their standard form do not paint a complete picture of a system's robustness since one assumes that all cells in the population have the same parameters and are perturbed in the same way. Here, we consider stochasticreaction networks in which the parameters are randomly distributed over the population and propose a new sensitivity index that captures the robustness of system outputs upon changes in the characteristics of the parameter distribution, rather than the parameters themselves. Subsequently, we make use of Girsanov's likelihood ratio method to construct a Monte Carlo estimator of this sensitivity index. However, it turns out that this estimator has an exceedingly large variance. To overcome this problem, we propose a novel estimation algorithm that makes use of a marginalization of the path distribution of stochasticreaction networks and leads to Rao-Blackwellized estimators with reduced variance.

Structural insights into gene repression by the orphan nuclear receptor SHP.

Small heterodimer partner (SHP) is an orphan nuclear receptor that functions as a transcriptional repressor to regulate bile acid and cholesterol homeostasis. Although the precise mechanism whereby SHP represses transcription is not known, E1A-like inhibitor of differentiation (EID1) was isolated as a SHP-interacting protein and implicated in SHP repression. Here we present the crystal structure of SHP in complex with EID1, which reveals an unexpected EID1-binding site on SHP. Unlike the classical cofactor-binding site near the C-terminal helix H12, the EID1-binding site is located at the N terminus of the receptor, where EID1 mimics helix H1 of the nuclear receptor ligand-binding domain. The residues composing the SHP-EID1 interface are highly conserved. Their mutation diminishes SHP-EID1 interactions and affects SHP repressor activity. Together, these results provide important structural insights into SHP cofactor recruitment and repressor function and reveal a conserved protein interface that is likely to have broad implications for transcriptional repression by orphan nuclear receptors.

Uncoupled analysis of stochastic reaction networks in fluctuating environments.

The dynamics of stochastic reaction networks within cells are inevitably modulated by factors considered extrinsic to the network such as, for instance, the fluctuations in ribosome copy numbers for a gene regulatory network. While several recent studies demonstrate the importance of accounting for such extrinsic components, the resulting models are typically hard to analyze. In this work we develop a general mathematical framework that allows to uncouple the network from its dynamic environment by incorporating only the environment's effect onto the network into a new model. More technically, we show how such fluctuating extrinsic components (e.g., chemical species) can be marginalized in order to obtain this decoupled model. We derive its corresponding process- and master equations and show how stochastic simulations can be performed. Using several case studies, we demonstrate the significance of the approach.

Moment-based inference predicts bimodality in transient gene expression.

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.

Strengths and limitations of microarray-based phenotype prediction: lessons learned from the IMPROVER Diagnostic Signature Challenge.

MOTIVATION: After more than a decade since microarrays were used to predict phenotype of biological samples, real-life applications for disease screening and identification of patients who would best benefit from treatment are still emerging. The interest of the scientific community in identifying best approaches to develop such prediction models was reaffirmed in a competition style international collaboration called IMPROVER Diagnostic Signature Challenge whose results we describe herein. RESULTS: Fifty-four teams used public data to develop prediction models in four disease areas including multiple sclerosis, lung cancer, psoriasis and chronic obstructive pulmonary disease, and made predictions on blinded new data that we generated. Teams were scored using three metrics that captured various aspects of the quality of predictions, and best performers were awarded. This article presents the challenge results and introduces to the community the approaches of the best overall three performers, as well as an R package that implements the approach of the best overall team. The analyses of model performance data submitted in the challenge as well as additional simulations that we have performed revealed that (i) the quality of predictions depends more on the disease endpoint than on the particular approaches used in the challenge; (ii) the most important modeling factor (e.g. data preprocessing, feature selection and classifier type) is problem dependent; and (iii) for optimal results datasets and methods have to be carefully matched. Biomedical factors such as the disease severity and confidence in diagnostic were found to be associated with the misclassification rates across the different teams. AVAILABILITY: The lung cancer dataset is available from Gene Expression Omnibus (accession, GSE43580). The maPredictDSC R package implementing the approach of the best overall team is available at www.bioconductor.org or http://bioinformaticsprb.med.wayne.edu/.