A novel simulation model for stem cells differentiation

Human Stem Cells for Ophthalmology: Recent Advances in Diagnostic Image Analysis and Computational Modelling

Purpose of Review

To explore the advances and future research directions in image analysis and computational modelling of human stem cells (hSCs) for ophthalmological applications.

Recent Findings

hSCs hold great potential in ocular regenerative medicine due to their application in cell-based therapies and in disease modelling and drug discovery using state-of-the-art 2D and 3D organoid models. However, a deeper characterisation of their complex, multi-scale properties is required to optimise their translation to clinical practice. Image analysis combined with computational modelling is a powerful tool to explore mechanisms of hSC behaviour and aid clinical diagnosis and therapy.

Summary

Many computational models draw on a variety of techniques, often blending continuum and discrete approaches, and have been used to describe cell differentiation and self-organisation. Machine learning tools are having a significant impact in model development and improving image classification processes for clinical diagnosis and treatment and will be the focus of much future research.

Stability of two competing populations in chemostat where one of the population changes its average mass of division in response to changes of its population

This paper considers a novel dynamical behaviour of two microbial populations, competing in a chemostat over a single substrate, that is only possible through the use of population balance equations (PBEs). PBEs are partial integrodifferential equations that represent a distribution of cells according to some internal state, mass in our case. Using these equations, realistic parameter values and the assumption that one population can deploy an emergency mechanism, where it can change the mean mass of division and hence divide faster, we arrive at two different steady states, one oscillatory and one non-oscillatory both of which seem to be stable. A steady state of either form is normally either unstable or only attainable through external control (cycling the dilution rate). In our case no external control is used. Finally, in the oscillatory case we attempt to explain how oscillations appear in the biomass without any explicit dependence on the division rate (the function that oscillates) through the approximation of fractional moments as a combination of integer moments. That allows an implicit dependence of the biomass on the number of cells which in turn is directly dependent on the division rate function.

Mathematical Models of Pluripotent Stem Cells: At the Dawn of Predictive Regenerative Medicine

Regenerative medicine, ranging from stem cell therapy to organ regeneration, is promising to revolutionize treatments of diseases and aging. These approaches require a perfect understanding of cell reprogramming and differentiation. Predictive modeling of cellular systems has the potential to provide insights about the dynamics of cellular processes, and guide their control. Moreover in many cases, it provides alternative to experimental tests, difficult to perform for practical or ethical reasons. The variety and accuracy of biological processes represented in mathematical models grew in-line with the discovery of underlying molecular mechanisms. High-throughput data generation led to the development of models based on data analysis, as an alternative to more established modeling based on prior mechanistic knowledge. In this chapter, we give an overview of existing mathematical models of pluripotency and cell fate, to illustrate the variety of methods and questions. We conclude that current approaches are yet to overcome a number of limitations: Most of the computational models have so far focused solely on understanding the regulation of pluripotency, and the differentiation of selected cell lineages. In addition, models generally interrogate only a few biological processes. However, a better understanding of the reprogramming process leading to ESCs and iPSCs is required to improve stem-cell therapies. One also needs to understand the links between signaling, metabolism, regulation of gene expression, and the epigenetics machinery.

A novel quantitative model of cell cycle progression based on cyclin-dependent kinases activity and population balances

Cell cycle regulates proliferative cell capacity under normal or pathologic conditions, and in general it governs all in vivo/in vitro cell growth and proliferation processes. Mathematical simulation by means of reliable and predictive models represents an important tool to interpret experiment results, to facilitate the definition of the optimal operating conditions for in vitro cultivation, or to predict the effect of a specific drug in normal/pathologic mammalian cells. Along these lines, a novel model of cell cycle progression is proposed in this work. Specifically, it is based on a population balance (PB) approach that allows one to quantitatively describe cell cycle progression through the different phases experienced by each cell of the entire population during its own life. The transition between two consecutive cell cycle phases is simulated by taking advantage of the biochemical kinetic model developed by Gérard and Goldbeter (2009) which involves cyclin-dependent kinases (CDKs) whose regulation is achieved through a variety of mechanisms that include association with cyclins and protein inhibitors, phosphorylation-dephosphorylation, and cyclin synthesis or degradation. This biochemical model properly describes the entire cell cycle of mammalian cells by maintaining a sufficient level of detail useful to identify check point for transition and to estimate phase duration required by PB. Specific examples are discussed to illustrate the ability of the proposed model to simulate the effect of drugs for in vitro trials of interest in oncology, regenerative medicine and tissue engineering.

An agent-based model approach to multi-phase life-cycle for contact inhibited, anchorage dependent cells

Cellular agent-based models are a technique that can be easily adapted to describe nuances of a particular cell type. Within we have concentrated on the cellular particularities of the human Endothelial Cell, explicitly the effects both of anchorage dependency and of heightened scaffold binding on the total confluence time of a system. By expansion of a discrete, homogeneous, asynchronous cellular model to account for several states per cell (phases within a cell's life); we accommodate and track dependencies of confluence time and population dynamics on these factors. Increasing the total motility time, analogous to weakening the binding between lattice and cell, affects the system in unique ways from increasing the average cellular velocity; each degree of freedom allows for control over the time length the system achieves logistic growth and confluence. These additional factors may allow for greater control over behaviors of the system. Examinations of system's dependence on both seed state velocity and binding are also enclosed.

Regenerative orthopaedics: in vitro, in vivo...in silico

In silico, defined in analogy to in vitro and in vivo as those studies that are performed on a computer, is an essential step in problem-solving and product development in classical engineering fields. The use of in silico models is now slowly easing its way into medicine. In silico models are already used in orthopaedics for the planning of complicated surgeries, personalised implant design and the analysis of gait measurements. However, these in silico models often lack the simulation of the response of the biological system over time. In silico models focusing on the response of the biological systems are in full development. This review starts with an introduction into in silico models of orthopaedic processes. Special attention is paid to the classification of models according to their spatiotemporal scale (gene/protein to population) and the information they were built on (data vs hypotheses). Subsequently, the review focuses on the in silico models used in regenerative orthopaedics research. Contributions of in silico models to an enhanced understanding and optimisation of four key elements-cells, carriers, culture and clinics-are illustrated. Finally, a number of challenges are identified, related to the computational aspects but also to the integration of in silico tools into clinical practice.

Deconstructing stem cell population heterogeneity: single-cell analysis and modeling approaches

Isogenic stem cell populations display cell-to-cell variations in a multitude of attributes including gene or protein expression, epigenetic state, morphology, proliferation and proclivity for differentiation. The origins of the observed heterogeneity and its roles in the maintenance of pluripotency and the lineage specification of stem cells remain unclear. Addressing pertinent questions will require the employment of single-cell analysis methods as traditional cell biochemical and biomolecular assays yield mostly population-average data. In addition to time-lapse microscopy and flow cytometry, recent advances in single-cell genomic, transcriptomic and proteomic profiling are reviewed. The application of multiple displacement amplification, next generation sequencing, mass cytometry and spectrometry to stem cell systems is expected to provide a wealth of information affording unprecedented levels of multiparametric characterization of cell ensembles under defined conditions promoting pluripotency or commitment. Establishing connections between single-cell analysis information and the observed phenotypes will also require suitable mathematical models. Stem cell self-renewal and differentiation are orchestrated by the coordinated regulation of subcellular, intercellular and niche-wide processes spanning multiple time scales. Here, we discuss different modeling approaches and challenges arising from their application to stem cell populations. Integrating single-cell analysis with computational methods will fill gaps in our knowledge about the functions of heterogeneity in stem cell physiology. This combination will also aid the rational design of efficient differentiation and reprogramming strategies as well as bioprocesses for the production of clinically valuable stem cell derivatives.

Stem cell modeling: From gene networks to cell populations

Despite rapid advances in the field of stem/progenitor cells through experimental studies, relevant modeling approaches have not progressed with a similar pace. Various models have focused on particular aspects of stem cell physiology including gene regulatory networks, gene expression noise and signaling cascades activated by exogenous factors. However, the self-renewal and differentiation of stem cells is driven by the coordinated regulation of events at the subcellular, intercellular and milieu levels. Such events also span multiple time domains from the fast molecular reactions governing gene expression to the slower cell cycle and division. Thus, the development of multiscale computational frameworks for stem cell populations is highly desirable. Multiscale models are expected to aid the design of efficient differentiation strategies and bioprocesses for the generation of therapeutically useful stem cell progeny. Yet, challenges in making these models tractable and pairing those to sufficient experimental data prevent their wide adoption by the stem cell community. Here, we review modeling approaches reported for stem cell populations and associated hurdles.

Contribution of stochastic partitioning at human embryonic stem cell division to NANOG heterogeneity

Heterogeneity is an often unappreciated characteristic of stem cell populations yet its importance in fate determination is becoming increasingly evident. Although gene expression noise has received greater attention as a source of non-genetic heterogeneity, the effects of stochastic partitioning of cellular material during mitosis on population variability have not been researched to date. We examined self-renewing human embryonic stem cells (hESCs), which typically exhibit a dispersed distribution of the pluripotency marker NANOG. In conjunction with our experiments, a multiscale cell population balance equation (PBE) model was constructed accounting for transcriptional noise and stochastic partitioning at division as sources of population heterogeneity. Cultured hESCs maintained time-invariant profiles of size and NANOG expression and the data were utilized for parameter estimation. Contributions from both sources considered in this study were significant on the NANOG profile, although elimination of the gene expression noise resulted in greater changes in the dispersion of the NANOG distribution. Moreover, blocking of division by treating hESCs with nocodazole or colcemid led to a 39% increase in the average NANOG content and over 68% of the cells had higher NANOG level than the mean NANOG expression of untreated cells. Model predictions, which were in excellent agreement with these findings, revealed that stochastic partitioning accounted for 17% of the total noise in the NANOG profile of self-renewing hESCs. The computational framework developed in this study will aid in gaining a deeper understanding of how pluripotent stem/progenitor cells orchestrate processes such as gene expression and proliferation for maintaining their pluripotency or differentiating along particular lineages. Such models will be essential in designing and optimizing efficient differentiation strategies and bioprocesses for the production of therapeutically suitable stem cell progeny.

Scalable stirred-suspension bioreactor culture of human pluripotent stem cells

Advances in stem cell biology have afforded promising results for the generation of various cell types for therapies against devastating diseases. However, a prerequisite for realizing the therapeutic potential of stem cells is the development of bioprocesses for the production of stem cell progeny in quantities that satisfy clinical demands. Recent reports on the expansion and directed differentiation of human embryonic stem cells (hESCs) in scalable stirred-suspension bioreactors (SSBs) demonstrated that large-scale production of therapeutically useful hESC progeny is feasible with current state-of-the-art culture technologies. Stem cells have been cultured in SSBs as aggregates, in microcarrier suspension and after encapsulation. The various modes in which SSBs can be employed for the cultivation of hESCs and human induced pluripotent stem cells (hiPSCs) are described. To that end, this is the first account of hiPSC cultivation in a microcarrier stirred-suspension system. Given that cultured stem cells and their differentiated progeny are the actual products used in tissue engineering and cell therapies, the impact of bioreactor's operating conditions on stem cell self-renewal and commitment should be considered. The effects of variables specific to SSB operation on stem cell physiology are discussed. Finally, major challenges are presented which remain to be addressed before the mainstream use of SSBs for the large-scale culture of hESCs and hiPSCs.

Experimental analysis and modelling of in vitro proliferation of mesenchymal stem cells

OBJECTIVES

Stem cell therapies based on differentiation of adult or embryonic stem cells into specialized ones appear to be effective for treating several human diseases. This work addresses the mathematical simulation of proliferation kinetics of stem cells.

MATERIALS AND METHODS

Sheep bone marrow mesenchymal stem cells (phenotype characterized by flow cytometry analysis) seeded at different initial concentrations in Petri dishes were expanded to confluence. Sigmoid temporal profiles of total counts obtained through classic haemocytometry were quantitatively interpreted by both a phenomenological logistic equation and a novel model based on a one-dimensional, single-staged population balance approach capable of taking into account contact inhibition at confluence. The models' parameters were determined by comparison with experimental data on population expansion starting from single seeding concentration. Reliability of the models was tested by predicting cell proliferation carried out starting from different seeding concentrations.

RESULTS AND DISCUSSION

It was found that the proposed population balance modelling approach was successful in predicting the experimental data over the whole range of initial cell numbers investigated, while prediction capability of phenomenological logistic equation was more limited.

A simulation model for stem cells differentiation into specialized cells of non-connective tissues

A novel mathematical model to simulate stem cells differentiation into specialized cells of non-connective tissues is proposed. The model is based upon material balances for growth factors coupled with a mass-structured population balance describing cell growth, proliferation and differentiation. The proposed model is written in a general form and it may be used to simulate a generic cell differentiation pathway during in vitro cultivation when specific growth factors are used. Literature experimental data concerning the differentiation of central nervous stem cells into astrocytes are successfully compared with model results, thus demonstrating the validity of the proposed model as well as its predictive capability. Finally, sensitivity analysis of model parameters is also performed in order to clarify what mechanisms most strongly influence differentiation and cell types distribution.