Stem cell fate analysis revisited: interpretation of individual clone dynamics in the light of a new paradigm of stem cell organization

A mixed-effects stochastic model reveals clonal dominance in gene therapy safety studies

BACKGROUND

Mathematical models of haematopoiesis can provide insights on abnormal cell expansions (clonal dominance), and in turn can guide safety monitoring in gene therapy clinical applications. Clonal tracking is a recent high-throughput technology that can be used to quantify cells arising from a single haematopoietic stem cell ancestor after a gene therapy treatment. Thus, clonal tracking data can be used to calibrate the stochastic differential equations describing clonal population dynamics and hierarchical relationships in vivo.

RESULTS

In this work we propose a random-effects stochastic framework that allows to investigate the presence of events of clonal dominance from high-dimensional clonal tracking data. Our framework is based on the combination between stochastic reaction networks and mixed-effects generalized linear models. Starting from the Kramers-Moyal approximated Master equation, the dynamics of cells duplication, death and differentiation at clonal level, can be described by a local linear approximation. The parameters of this formulation, which are inferred using a maximum likelihood approach, are assumed to be shared across the clones and are not sufficient to describe situation in which clones exhibit heterogeneity in their fitness that can lead to clonal dominance. In order to overcome this limitation, we extend the base model by introducing random-effects for the clonal parameters. This extended formulation is calibrated to the clonal data using a tailor-made expectation-maximization algorithm. We also provide the companion  package RestoreNet, publicly available for download at https://cran.r-project.org/package=RestoreNet .

CONCLUSIONS

Simulation studies show that our proposed method outperforms the state-of-the-art. The application of our method in two in-vivo studies unveils the dynamics of clonal dominance. Our tool can provide statistical support to biologists in gene therapy safety analyses.

Merging concepts - coupling an agent-based model of hematopoietic stem cells with an ODE model of granulopoiesis

Background

Hematopoiesis is a complex process involving different cell types and feedback mechanisms mediated by cytokines. This complexity stimulated various models with different scopes and applications. A combination of complementary models promises to provide their mutual confirmation and to explain a broader range of scenarios. Here we propose a combination of an ordinary differential equation (ODE) model of human granulopoiesis and an agent-based model (ABM) of hematopoietic stem cell (HSC) organization. The first describes the dynamics of bone marrow cell stages and circulating cells under various perturbations such as G-CSF treatment or chemotherapy. In contrast to the ODE model describing cell numbers, our ABM focuses on the organization of individual cells in the stem population.

Results

We combined the two models by replacing the HSC compartment of the ODE model by a difference equation formulation of the ABM. In this hybrid model, regulatory mechanisms and parameters of the original models were kept unchanged except for a few specific improvements: (i) Effect of chemotherapy was restricted to proliferating HSC and (ii) HSC regulation in the ODE model was replaced by the intrinsic regulation of the ABM. Model simulations of bleeding, chronic irradiation and stem cell transplantation revealed that the dynamics of hybrid and ODE model differ markedly in scenarios with stem cell damage. Despite these differences in response to stem cell damage, both models explain clinical data of leukocyte dynamics under four chemotherapy regimens.

Conclusions

ABM and ODE model proved to be compatible and were combined without altering the structure of both models. The new hybrid model introduces model improvements by considering the proliferative state of stem cells and enabling a cell cycle-dependent effect of chemotherapy. We demonstrated that it is able to explain and predict granulopoietic dynamics for a large variety of scenarios such as irradiation, bone marrow transplantation, chemotherapy and growth factor applications. Therefore, it promises to serve as a valuable tool for studies in a broader range of clinical applications, in particular where stem cell activation and proliferation are involved.

A review of spatial computational models for multi-cellular systems, with regard to intestinal crypts and colorectal cancer development

Colon rectal cancers (CRC) are the result of sequences of mutations which lead the intestinal tissue to develop in a carcinoma following a "progression" of observable phenotypes. The actual modeling and simulation of the key biological structures involved in this process is of interest to biologists and physicians and, at the same time, it poses significant challenges from the mathematics and computer science viewpoints. In this report we give an overview of some mathematical models for cell sorting (a basic phenomenon that underlies several dynamical processes in an organism), intestinal crypt dynamics and related problems and open questions. In particular, major attention is devoted to the survey of so-called in-lattice (or grid) models and off-lattice (off-grid) models. The current work is the groundwork for future research on semi-automated hypotheses formation and testing about the behavior of the various actors taking part in the adenoma-carcinoma progression, from regulatory processes to cell-cell signaling pathways.

A review of spatial computational models for multi-cellular systems, with regard to intestinal crypts and colorectal cancer development

Colon rectal cancers (CRC) are the result of sequences of mutations which lead the intestinal tissue to develop in a carcinoma following a "progression" of observable phenotypes. The actual modeling and simulation of the key biological structures involved in this process is of interest to biologists and physicians and, at the same time, it poses significant challenges from the mathematics and computer science viewpoints. In this report we give an overview of some mathematical models for cell sorting (a basic phenomenon that underlies several dynamical processes in an organism), intestinal crypt dynamics and related problems and open questions. In particular, major attention is devoted to the survey of so-called in-lattice (or grid) models and off-lattice (off-grid) models. The current work is the groundwork for future research on semi-automated hypotheses formation and testing about the behavior of the various actors taking part in the adenoma-carcinoma progression, from regulatory processes to cell-cell signaling pathways.

A novel validation algorithm allows for automated cell tracking and the extraction of biologically meaningful parameters

Automated microscopy is currently the only method to non-invasively and label-free observe complex multi-cellular processes, such as cell migration, cell cycle, and cell differentiation. Extracting biological information from a time-series of micrographs requires each cell to be recognized and followed through sequential microscopic snapshots. Although recent attempts to automatize this process resulted in ever improving cell detection rates, manual identification of identical cells is still the most reliable technique. However, its tedious and subjective nature prevented tracking from becoming a standardized tool for the investigation of cell cultures. Here, we present a novel method to accomplish automated cell tracking with a reliability comparable to manual tracking. Previously, automated cell tracking could not rival the reliability of manual tracking because, in contrast to the human way of solving this task, none of the algorithms had an independent quality control mechanism; they missed validation. Thus, instead of trying to improve the cell detection or tracking rates, we proceeded from the idea to automatically inspect the tracking results and accept only those of high trustworthiness, while rejecting all other results. This validation algorithm works independently of the quality of cell detection and tracking through a systematic search for tracking errors. It is based only on very general assumptions about the spatiotemporal contiguity of cell paths. While traditional tracking often aims to yield genealogic information about single cells, the natural outcome of a validated cell tracking algorithm turns out to be a set of complete, but often unconnected cell paths, i.e. records of cells from mitosis to mitosis. This is a consequence of the fact that the validation algorithm takes complete paths as the unit of rejection/acceptance. The resulting set of complete paths can be used to automatically extract important biological parameters with high reliability and statistical significance. These include the distribution of life/cycle times and cell areas, as well as of the symmetry of cell divisions and motion analyses. The new algorithm thus allows for the quantification and parameterization of cell culture with unprecedented accuracy. To evaluate our validation algorithm, two large reference data sets were manually created. These data sets comprise more than 320,000 unstained adult pancreatic stem cells from rat, including 2592 mitotic events. The reference data sets specify every cell position and shape, and assign each cell to the correct branch of its genealogic tree. We provide these reference data sets for free use by others as a benchmark for the future improvement of automated tracking methods.

Bone marrow mesenchymal stem cells differentiate into urothelial cells and the implications for reconstructing urinary bladder mucosa

To determine the ability of cultured bone marrow-derived mesenchymal stem cells (BMSCs) to differentiate into functional urothelium. BMSCs were isolated from the long bones of aborted fetal limbs by Percoll density gradient centrifugation and characterized by flow cytometry. Human fetal urinary bladders were cut into small pieces and cultured for 3-5 days until the growth of urothelial cells was established. BMSCs were then cocultured with neonatal urothelial cells and subsequently evaluated for antigen expression and ultramicrostructure, by immunocytochemistry and electron microscopy, respectively. A subset of BMSCs expressed the differentiation marker CD71. The BMSC markers CD34, CD45, and HLA-DR were barely detectable, confirming that these cells were not derived from hematopoietic stem cells or differentiated cells. In contrast, the stem cell markers CD29, CD44, CD105, and CD90 were highly expressed. BMSCs possessed the ability to differentiate into a variety of cellular subtypes, including osteocytes, adipocytes, and chondrocytes. The shapes of BMSCs changed, and the size of the cells increased, following in vitro coculture with urothelial cells. After 2 weeks of coculture, immunostaining of the newly differentiated BMSCs positively displayed the urothelial-specific keratin marker. Electron microscopy revealed that the cocultured BMSCs had microstructural features characteristic of epithelial cells. Pluripotent BMSCs can transdifferentiate into urothelial cells in response to an environment conditioned by neonatal urothelial cells, providing a means for the time-, labor- and cost-effective reconstruction of urinary bladder mucosa.

Enabling stem cell therapies through synthetic stem cell-niche engineering

Enabling stem cell-targeted therapies requires an understanding of how to create local microenvironments (niches) that stimulate endogenous stem cells or serve as a platform to receive and guide the integration of transplanted stem cells and their derivatives. In vivo, the stem cell niche is a complex and dynamic unit. Although components of the in vivo niche continue to be described for many stem cell systems, how these components interact to modulate stem cell fate is only beginning to be understood. Using the HSC niche as a model, we discuss here microscale engineering strategies capable of systematically examining and reconstructing individual niche components. Synthetic stem cell-niche engineering may form a new foundation for regenerative therapies.

From genes to cells to tissues--modelling the haematopoietic system

Haematopoiesis (or blood formation) in general and haematopoietic stem cells more specifically represent some of the best studied mammalian developmental systems. Sophisticated purification protocols coupled with powerful biological assays permit functional analysis of highly purified cell populations both in vitro and in vivo. However, despite several decades of intensive research, the sheer complexity of the haematopoietic system means that many important questions remain unanswered or even unanswerable with current experimental tools. Scientists have therefore increasingly turned to modelling to tackle complexity at multiple levels ranging from networks of genes to the behaviour of cells and tissues. Early modelling attempts of gene regulatory networks have focused on core regulatory circuits but have more recently been extended to genome-wide datasets such as expression profiling and ChIP-sequencing data. Modelling of haematopoietic cells and tissues has provided insight into the importance of phenotypic heterogeneity for the differentiation of normal progenitor cells as well as a greater understanding of treatment response for particular pathologies such as chronic myeloid leukaemia. Here we will review recent progress in attempts to reconstruct segments of the haematopoietic system. A variety of modelling strategies will be covered from small-scale, protein-DNA or protein-protein interactions to large scale reconstructions. Also discussed will be examples of how stochastic modelling may be applied to multi cell systems such as those seen in normal and malignant haematopoiesis.

Cell lineages and the logic of proliferative control

It is widely accepted that the growth and regeneration of tissues and organs is tightly controlled. Although experimental studies are beginning to reveal molecular mechanisms underlying such control, there is still very little known about the control strategies themselves. Here, we consider how secreted negative feedback factors ("chalones") may be used to control the output of multistage cell lineages, as exemplified by the actions of GDF11 and activin in a self-renewing neural tissue, the mammalian olfactory epithelium (OE). We begin by specifying performance objectives-what, precisely, is being controlled, and to what degree-and go on to calculate how well different types of feedback configurations, feedback sensitivities, and tissue architectures achieve control. Ultimately, we show that many features of the OE-the number of feedback loops, the cellular processes targeted by feedback, even the location of progenitor cells within the tissue-fit with expectations for the best possible control. In so doing, we also show that certain distinctions that are commonly drawn among cells and molecules-such as whether a cell is a stem cell or transit-amplifying cell, or whether a molecule is a growth inhibitor or stimulator-may be the consequences of control, and not a reflection of intrinsic differences in cellular or molecular character.

Characterization and quantification of clonal heterogeneity among hematopoietic stem cells: a model-based approach

Hematopoietic stem cells (HSCs) show pronounced heterogeneity in self-renewal and differentiation behavior, which is reflected in their repopulation kinetics. Here, a single-cell-based mathematical model of HSC organization is used to examine the basis of HSC heterogeneity. Our modeling results, which are based on the analysis of limiting dilution competitive repopulation experiments in mice, demonstrate that small quantitative but clonally fixed differences of cellular properties are necessary and sufficient to account for the observed functional heterogeneity. The model predicts, and experimental data validate, that competitive pressures will amplify small clonal differences into large changes in the number of differentiated progeny. We further predict that the repertoire of HSC clones will evolve over time. Last, our results suggest that larger differences in cellular properties have to be assumed to account for genetically determined differences in HSC behavior as observed in different inbred mice strains. The model provides comprehensive systemic and quantitative insights into the clonal heterogeneity among HSCs with potential applications in predicting the behavior of malignant and/or genetically modified cells.

Noise-driven stem cell and progenitor population dynamics

BACKGROUND

The balance between maintenance of the stem cell state and terminal differentiation is influenced by the cellular environment. The switching between these states has long been understood as a transition between attractor states of a molecular network. Herein, stochastic fluctuations are either suppressed or can trigger the transition, but they do not actually determine the attractor states.

METHODOLOGY/PRINCIPAL FINDINGS

We present a novel mathematical concept in which stem cell and progenitor population dynamics are described as a probabilistic process that arises from cell proliferation and small fluctuations in the state of differentiation. These state fluctuations reflect random transitions between different activation patterns of the underlying regulatory network. Importantly, the associated noise amplitudes are state-dependent and set by the environment. Their variability determines the attractor states, and thus actually governs population dynamics. This model quantitatively reproduces the observed dynamics of differentiation and dedifferentiation in promyelocytic precursor cells.

CONCLUSIONS/SIGNIFICANCE

Consequently, state-specific noise modulation by external signals can be instrumental in controlling stem cell and progenitor population dynamics. We propose follow-up experiments for quantifying the imprinting influence of the environment on cellular noise regulation.

Multiway modeling and analysis in stem cell systems biology

Background

Systems biology refers to multidisciplinary approaches designed to uncover emergent properties of biological systems. Stem cells are an attractive target for this analysis, due to their broad therapeutic potential. A central theme of systems biology is the use of computational modeling to reconstruct complex systems from a wealth of reductionist, molecular data (e.g., gene/protein expression, signal transduction activity, metabolic activity, etc.). A number of deterministic, probabilistic, and statistical learning models are used to understand sophisticated cellular behaviors such as protein expression during cellular differentiation and the activity of signaling networks. However, many of these models are bimodal i.e., they only consider row-column relationships. In contrast, multiway modeling techniques (also known as tensor models) can analyze multimodal data, which capture much more information about complex behaviors such as cell differentiation. In particular, tensors can be very powerful tools for modeling the dynamic activity of biological networks over time. Here, we review the application of systems biology to stem cells and illustrate application of tensor analysis to model collagen-induced osteogenic differentiation of human mesenchymal stem cells.

Results

We applied Tucker1, Tucker3, and Parallel Factor Analysis (PARAFAC) models to identify protein/gene expression patterns during extracellular matrix-induced osteogenic differentiation of human mesenchymal stem cells. In one case, we organized our data into a tensor of type protein/gene locus link × gene ontology category × osteogenic stimulant, and found that our cells expressed two distinct, stimulus-dependent sets of functionally related genes as they underwent osteogenic differentiation. In a second case, we organized DNA microarray data in a three-way tensor of gene IDs × osteogenic stimulus × replicates, and found that application of tensile strain to a collagen I substrate accelerated the osteogenic differentiation induced by a static collagen I substrate.

Conclusion

Our results suggest gene- and protein-level models whereby stem cells undergo transdifferentiation to osteoblasts, and lay the foundation for mechanistic, hypothesis-driven studies. Our analysis methods are applicable to a wide range of stem cell differentiation models.

Insertional mutagenesis and clonal dominance: biological and statistical considerations

Improvements of (retroviral) gene transfer vectors, stem cell isolation and culture techniques as well as transduction protocols eventually resulted not only in the successful genetic modification of cells capable of reconstituting the haematopoietic system in various animal models, but also human beings. This was a conditio sine qua non for the successful application of gene therapy for inherited diseases as meanwhile achieved for severe combined immune deficiencies (SCID-X1, ADA-SCID) and chronic granulomatous disease (CGD). Unexpectedly, in long-term animal experiments as well as in the follow up of patients from the CGD trial, haematopoietic clones bearing insertions in certain gene loci became dominant, which was most apparent in the myeloid blood compartment. Accumulating data strongly suggest that this clonal dominance was due to some growth and/or survival advantage conferred by gene-activating or -suppressing effects of the integrated retroviral vector (insertional mutagenesis). Importantly, such induced clonal dominance seems not to lead to malignant transformation of affected cell clones inadvertently. The latter finding has become the basis for the concept of 'induced haematopoietic stem cells', a potentially powerful tool to investigate genes involved in the regulation of mechanisms underlying competitive advantages of stem cells, but also in the multi-step nature of malignant transformation. Here we discuss promises and open issues of this concept as well as the important question of common insertion sites statistics and its pitfalls.