Practical identifiability in the frame of nonlinear mixed effects models: the example of the in vitro erythropoiesis.

BACKGROUND: Nonlinear mixed effects models provide a way to mathematically describe experimental data involving a lot of inter-individual heterogeneity. In order to assess their practical identifiability and estimate confidence intervals for their parameters, most mixed effects modelling programs use the Fisher Information Matrix. However, in complex nonlinear models, this approach can mask practical unidentifiabilities. RESULTS: Herein we rather propose a multistart approach, and use it to simplify our model by reducing the number of its parameters, in order to make it identifiable. Our model describes several cell populations involved in the in vitro differentiation of chicken erythroid progenitors grown in the same environment. Inter-individual variability observed in cell population counts is explained by variations of the differentiation and proliferation rates between replicates of the experiment. Alternatively, we test a model with varying initial condition. CONCLUSIONS: We conclude by relating experimental variability to precise and identifiable variations between the replicates of the experiment of some model parameters.

Noise and the molecular processes underlying cell fate decision-making.

Cell fate decision-making events involve the interplay of many molecular processes, ranging from signal transduction to genetic regulation, as well as a set of molecular and physiological feedback loops. Each aspect offers a rich field of investigation in its own right, but to understand the whole process, even in simple terms, we need to consider them together. Here we attempt to characterise this process by focussing on the roles of noise during cell fate decisions. We use a range of recent results to develop a view of the sequence of events by which a cell progresses from a pluripotent or multipotent to a differentiated state: chromatin organisation, transcription factor stoichiometry, and cellular signalling all change during this progression, and all shape cellular variability, which becomes maximal at the transition state.

The quiescent fraction of chronic myeloid leukemic stem cells depends on BMPR1B, Stat3 and BMP4-niche signals to persist in patients in remission.

Chronic myelogenous leukemia arises from the transformation of hematopoietic stem cells by the BCR-ABL oncogene. Though transformed cells are predominantly BCR-ABL-dependent and sensitive to tyrosine kinase inhibitor treatment, some BMPR1B+ leukemic stem cells are treatment-insensitive and rely, among others, on the bone morphogenetic protein (BMP) pathway for their survival via a BMP4 autocrine loop. Here, we further studied the involvement of BMP signaling in favoring residual leukemic stem cell persistence in the bone marrow of patients having achieved remission under treatment. We demonstrate by single-cell RNA-Seq analysis that a sub-fraction of surviving BMPR1B+ leukemic stem cells are co-enriched in BMP signaling, quiescence and stem cell signatures, without modulation of the canonical BMP target genes, but enrichment in actors of the Jak2/Stat3 signaling pathway. Indeed, based on a new model of persisting CD34+CD38- leukemic stem cells, we show that BMPR1B+ cells display co-activated Smad1/5/8 and Stat3 pathways. Interestingly, we reveal that only the BMPR1B+ cells adhering to stromal cells display a quiescent status. Surprisingly, this quiescence is induced by treatment, while non-adherent BMPR1B+ cells treated with tyrosine kinase inhibitors continued to proliferate. The subsequent targeting of BMPR1B and Jak2 pathways decreased quiescent leukemic stem cells by promoting their cell cycle re-entry and differentiation. Moreover, while Jak2-inhibitors alone increased BMP4 production by mesenchymal cells, the addition of the newly described BMPR1B inhibitor (E6201) impaired BMP4-mediated production by stromal cells. Altogether, our data demonstrate that targeting both BMPR1B and Jak2/Stat3 efficiently impacts persisting and dormant leukemic stem cells hidden in their bone marrow microenvironment.

WASABI: a dynamic iterative framework for gene regulatory network inference.

BACKGROUND: Inference of gene regulatory networks from gene expression data has been a long-standing and notoriously difficult task in systems biology. Recently, single-cell transcriptomic data have been massively used for gene regulatory network inference, with both successes and limitations. RESULTS: In the present work we propose an iterative algorithm called WASABI, dedicated to inferring a causal dynamical network from time-stamped single-cell data, which tackles some of the limitations associated with current approaches. We first introduce the concept of waves, which posits that the information provided by an external stimulus will affect genes one-by-one through a cascade, like waves spreading through a network. This concept allows us to infer the network one gene at a time, after genes have been ordered regarding their time of regulation. We then demonstrate the ability of WASABI to correctly infer small networks, which have been simulated in silico using a mechanistic model consisting of coupled piecewise-deterministic Markov processes for the proper description of gene expression at the single-cell level. We finally apply WASABI on in vitro generated data on an avian model of erythroid differentiation. The structure of the resulting gene regulatory network sheds a new light on the molecular mechanisms controlling this process. In particular, we find no evidence for hub genes and a much more distributed network structure than expected. Interestingly, we find that a majority of genes are under the direct control of the differentiation-inducing stimulus. CONCLUSIONS: Together, these results demonstrate WASABI versatility and ability to tackle some general gene regulatory networks inference issues. It is our hope that WASABI will prove useful in helping biologists to fully exploit the power of time-stamped single-cell data.

Calibration, Selection and Identifiability Analysis of a Mathematical Model of the in vitro Erythropoiesis in Normal and Perturbed Contexts.

The in vivo erythropoiesis, which is the generation of mature red blood cells in the bone marrow of whole organisms, has been described by a variety of mathematical models in the past decades. However, the in vitro erythropoiesis, which produces red blood cells in cultures, has received much less attention from the modelling community. In this paper, we propose the first mathematical model of in vitro erythropoiesis. We start by formulating different models and select the best one at fitting experimental data of in vitro erythropoietic differentiation obtained from chicken erythroid progenitor cells. It is based on a set of linear ODE, describing 3 hypothetical populations of cells at different stages of differentiation. We then compute confidence intervals for all of its parameters estimates, and conclude that our model is fully identifiable. Finally, we use this model to compute the effect of a chemical drug called Rapamycin, which affects all states of differentiation in the culture, and relate these effects to specific parameter variations. We provide the first model for the kinetics of in vitro cellular differentiation which is proven to be identifiable. It will serve as a basis for a model which will better account for the variability which is inherent to the experimental protocol used for the model calibration.

Single-Cell-Based Analysis Highlights a Surge in Cell-to-Cell Molecular Variability Preceding Irreversible Commitment in a Differentiation Process.

In some recent studies, a view emerged that stochastic dynamics governing the switching of cells from one differentiation state to another could be characterized by a peak in gene expression variability at the point of fate commitment. We have tested this hypothesis at the single-cell level by analyzing primary chicken erythroid progenitors through their differentiation process and measuring the expression of selected genes at six sequential time-points after induction of differentiation. In contrast to population-based expression data, single-cell gene expression data revealed a high cell-to-cell variability, which was masked by averaging. We were able to show that the correlation network was a very dynamical entity and that a subgroup of genes tend to follow the predictions from the dynamical network biomarker (DNB) theory. In addition, we also identified a small group of functionally related genes encoding proteins involved in sterol synthesis that could act as the initial drivers of the differentiation. In order to assess quantitatively the cell-to-cell variability in gene expression and its evolution in time, we used Shannon entropy as a measure of the heterogeneity. Entropy values showed a significant increase in the first 8 h of the differentiation process, reaching a peak between 8 and 24 h, before decreasing to significantly lower values. Moreover, we observed that the previous point of maximum entropy precedes two paramount key points: an irreversible commitment to differentiation between 24 and 48 h followed by a significant increase in cell size variability at 48 h. In conclusion, when analyzed at the single cell level, the differentiation process looks very different from its classical population average view. New observables (like entropy) can be computed, the behavior of which is fully compatible with the idea that differentiation is not a "simple" program that all cells execute identically but results from the dynamical behavior of the underlying molecular network.

Shaping the Innate Immune Response Through Post-Transcriptional Regulation of Gene Expression Mediated by RNA-Binding Proteins.

Innate immunity is the frontline of defense against infections and tissue damage. It is a fast and semi-specific response involving a myriad of processes essential for protecting the organism. These reactions promote the clearance of danger by activating, among others, an inflammatory response, the complement cascade and by recruiting the adaptive immunity. Any disequilibrium in this functional balance can lead to either inflammation-mediated tissue damage or defense inefficiency. A dynamic and coordinated gene expression program lies at the heart of the innate immune response. This expression program varies depending on the cell-type and the specific danger signal encountered by the cell and involves multiple layers of regulation. While these are achieved mainly via transcriptional control of gene expression, numerous post-transcriptional regulatory pathways involving RNA-binding proteins (RBPs) and other effectors play a critical role in its fine-tuning. Alternative splicing, translational control and mRNA stability have been shown to be tightly regulated during the innate immune response and participate in modulating gene expression in a global or gene specific manner. More recently, microRNAs assisting RBPs and post-transcriptional modification of RNA bases are also emerging as essential players of the innate immune process. In this review, we highlight the numerous roles played by specific RNA-binding effectors in mediating post-transcriptional control of gene expression to shape innate immunity.

Non-equilibrium statistical physics, transitory epigenetic landscapes, and cell fate decision dynamics.

Statistical physics provides a useful perspective for the analysis of many complex systems; it allows us to relate microscopic fluctuations to macroscopic observations. Developmental biology, but also cell biology more generally, are examples where apparently robust behaviour emerges from highly complex and stochastic sub-cellular processes. Here we attempt to make connections between different theoretical perspectives to gain qualitative insights into the types of cell-fate decision making processes that are at the heart of stem cell and developmental biology. We discuss both dynamical systems as well as statistical mechanics perspectives on the classical Waddington or epigenetic landscape. We find that non-equilibrium approaches are required to overcome some of the shortcomings of classical equilibrium statistical thermodynamics or statistical mechanics in order to shed light on biological processes, which, almost by definition, are typically far from equilibrium.

Drugs modulating stochastic gene expression affect the erythroid differentiation process.

To better understand the mechanisms behind cells decision-making to differentiate, we assessed the influence of stochastic gene expression (SGE) modulation on the erythroid differentiation process. It has been suggested that stochastic gene expression has a role in cell fate decision-making which is revealed by single-cell analyses but studies dedicated to demonstrate the consistency of this link are still lacking. Recent observations showed that SGE significantly increased during differentiation and a few showed that an increase of the level of SGE is accompanied by an increase in the differentiation process. However, a consistent relation in both increasing and decreasing directions has never been shown in the same cellular system. Such demonstration would require to be able to experimentally manipulate simultaneously the level of SGE and cell differentiation in order to observe if cell behavior matches with the current theory. We identified three drugs that modulate SGE in primary erythroid progenitor cells. Both Artemisinin and Indomethacin decreased SGE and reduced the amount of differentiated cells. On the contrary, a third component called MB-3 simultaneously increased the level of SGE and the amount of differentiated cells. We then used a dynamical modelling approach which confirmed that differentiation rates were indeed affected by the drug treatment. Using single-cell analysis and modeling tools, we provide experimental evidence that, in a physiologically relevant cellular system, SGE is linked to differentiation.

Automated cell cycle and cell size measurements for single-cell gene expression studies.

OBJECTIVES: Recent rise of single-cell studies revealed the importance of understanding the role of cell-to-cell variability, especially at the transcriptomic level. One of the numerous sources of cell-to-cell variation in gene expression is the heterogeneity in cell proliferation state. In order to identify how cell cycle and cell size influences gene expression variability at the single-cell level, we provide an universal and automatic toxic-free label method, compatible with single-cell high-throughput RT-qPCR. The method consists of isolating cells after a double-stained, analyzing their morphological parameters and performing a transcriptomic analysis on the same identified cells. RESULTS: This led to an unbiased gene expression analysis and could be also used for improving single-cell tracking and imaging when combined with cell isolation. As an application for this technique, we showed that cell-to-cell variability in chicken erythroid progenitors was negligibly influenced by cell size nor cell cycle.