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

The Current State of Realistic Heart Models for Disease Modelling and Cardiotoxicity

One of the many unresolved obstacles in the field of cardiovascular research is an uncompromising in vitro cardiac model. While primary cell sources from animal models offer both advantages and disadvantages, efforts over the past half-century have aimed to reduce their use. Additionally, obtaining a sufficient quantity of human primary cardiomyocytes faces ethical and legal challenges. As the practically unlimited source of human cardiomyocytes from induced pluripotent stem cells (hiPSC-CM) is now mostly resolved, there are great efforts to improve their quality and applicability by overcoming their intrinsic limitations. The greatest bottleneck in the field is the in vitro ageing of hiPSC-CMs to reach a maturity status that closely resembles that of the adult heart, thereby allowing for more appropriate drug developmental procedures as there is a clear correlation between ageing and developing cardiovascular diseases. Here, we review the current state-of-the-art techniques in the most realistic heart models used in disease modelling and toxicity evaluations from hiPSC-CM maturation through heart-on-a-chip platforms and in silico models to the in vitro models of certain cardiovascular diseases.

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.

A 3D Mathematical Model of Coupled Stem Cell-Nutrient Dynamics in Myocardial Regeneration Therapy

Stem cell therapy is a promising treatment for the regeneration of myocardial tissue injured by an ischemic event. Mathematical modeling of myocardial regeneration via stem cell therapy is a challenging task, since the mechanisms underlying the processes involved in the treatment are not yet fully understood. Many aspects must be accounted for, such as the spread of stem cells and nutrients, chemoattraction, cell proliferation, stages of cell maturation, differentiation, angiogenesis, stochastic effects, just to name a few. In this paper we propose a 3D mathematical model with a free boundary that aims to provide a qualitative description of some main aspects of the stem cell regenerative therapy in a simplified scenario. The paper mainly focuses on the description of the shrinking of the necrotic core during treatment. The stem cell and nutrients dynamics are described through coupled reaction-diffusion problems. Proliferation, chemoattraction, tissue regeneration and nutrient consumption are included in the model.

A mathematical modelling framework for the regulation of intra-cellular OCT4 in human pluripotent stem cells

Human pluripotent stem cells (hPSCs) have the potential to differentiate into all cell types, a property known as pluripotency. A deeper understanding of how pluripotency is regulated is required to assist in controlling pluripotency and differentiation trajectories experimentally. Mathematical modelling provides a non-invasive tool through which to explore, characterise and replicate the regulation of pluripotency and the consequences on cell fate. Here we use experimental data of the expression of the pluripotency transcription factor OCT4 in a growing hPSC colony to develop and evaluate mathematical models for temporal pluripotency regulation. We consider fractional Brownian motion and the stochastic logistic equation and explore the effects of both additive and multiplicative noise. We illustrate the use of time-dependent carrying capacities and the introduction of Allee effects to the stochastic logistic equation to describe cell differentiation. We conclude both methods adequately capture the decline in OCT4 upon differentiation, but the Allee effect model has the advantage of allowing differentiation to occur stochastically in a sub-set of cells. This mathematical framework for describing intra-cellular OCT4 regulation can be extended to other transcription factors and developed into predictive models.

Turning Nature's own processes into design strategies for living bone implant biomanufacturing: a decade of Developmental Engineering

A decade after the term developmental engineering (DE) was coined to indicate the use of developmental processes as blueprints for the design and development of engineered living implants, a myriad of proof-of-concept studies demonstrate the potential of this approach in small animal models. This review provides an overview of DE work, focusing on applications in bone regeneration. Enabling technologies allow to quantify the distance between in vitro processes and their developmental counterpart, as well as to design strategies to reduce that distance. By embedding Nature's robust mechanisms of action in engineered constructs, predictive large animal data and subsequent positive clinical outcomes can be gradually achieved. To this end, the development of next generation biofabrication technologies should provide the necessary scale and precision for robust living bone implant biomanufacturing.

Predicting pattern formation in embryonic stem cells using a minimalist, agent-based probabilistic model

The mechanisms of pattern formation during embryonic development remain poorly understood. Embryonic stem cells in culture self-organise to form spatial patterns of gene expression upon geometrical confinement indicating that patterning is an emergent phenomenon that results from the many interactions between the cells. Here, we applied an agent-based modelling approach in order to identify plausible biological rules acting at the meso-scale within stem cell collectives that may explain spontaneous patterning. We tested different models involving differential motile behaviours with or without biases due to neighbour interactions. We introduced a new metric, termed stem cell aggregate pattern distance (SCAPD) to probabilistically assess the fitness of our models with empirical data. The best of our models improves fitness by 70% and 77% over the random models for a discoidal or an ellipsoidal stem cell confinement respectively. Collectively, our findings show that a parsimonious mechanism that involves differential motility is sufficient to explain the spontaneous patterning of the cells upon confinement. Our work also defines a region of the parameter space that is compatible with patterning. We hope that our approach will be applicable to many biological systems and will contribute towards facilitating progress by reducing the need for extensive and costly experiments.

The recent advances in the mathematical modelling of human pluripotent stem cells

Human pluripotent stem cells hold great promise for developments in regenerative medicine and drug design. The mathematical modelling of stem cells and their properties is necessary to understand and quantify key behaviours and develop non-invasive prognostic modelling tools to assist in the optimisation of laboratory experiments. Here, the recent advances in the mathematical modelling of hPSCs are discussed, including cell kinematics, cell proliferation and colony formation, and pluripotency and differentiation.

Automated Design of Pluripotent Stem Cell Self-Organization

Human pluripotent stem cells (hPSCs) have the intrinsic ability to self-organize into complex multicellular organoids that recapitulate many aspects of tissue development. However, robustly directing morphogenesis of hPSC-derived organoids requires novel approaches to accurately control self-directed pattern formation. Here, we combined genetic engineering with computational modeling, machine learning, and mathematical pattern optimization to create a data-driven approach to control hPSC self-organization by knock down of genes previously shown to affect stem cell colony organization, CDH1 and ROCK1. Computational replication of the in vitro system in silico using an extended cellular Potts model enabled machine learning-driven optimization of parameters that yielded emergence of desired patterns. Furthermore, in vitro the predicted experimental parameters quantitatively recapitulated the in silico patterns. These results demonstrate that morphogenic dynamics can be accurately predicted through model-driven exploration of hPSC behaviors via machine learning, thereby enabling spatial control of multicellular patterning to engineer human organoids and tissues. A record of this paper's Transparent Peer Review process is included in the Supplemental Information.

Computational Modeling and Reverse Engineering to Reveal Dominant Regulatory Interactions Controlling Osteochondral Differentiation: Potential for Regenerative Medicine

The specialization of cartilage cells, or chondrogenic differentiation, is an intricate and meticulously regulated process that plays a vital role in both bone formation and cartilage regeneration. Understanding the molecular regulation of this process might help to identify key regulatory factors that can serve as potential therapeutic targets, or that might improve the development of qualitative and robust skeletal tissue engineering approaches. However, each gene involved in this process is influenced by a myriad of feedback mechanisms that keep its expression in a desirable range, making the prediction of what will happen if one of these genes defaults or is targeted with drugs, challenging. Computer modeling provides a tool to simulate this intricate interplay from a network perspective. This paper aims to give an overview of the current methodologies employed to analyze cell differentiation in the context of skeletal tissue engineering in general and osteochondral differentiation in particular. In network modeling, a network can either be derived from mechanisms and pathways that have been reported in the literature (knowledge-based approach) or it can be inferred directly from the data (data-driven approach). Combinatory approaches allow further optimization of the network. Once a network is established, several modeling technologies are available to interpret dynamically the relationships that have been put forward in the network graph (implication of the activation or inhibition of certain pathways on the evolution of the system over time) and to simulate the possible outcomes of the established network such as a given cell state. This review provides for each of the aforementioned steps (building, optimizing, and modeling the network) a brief theoretical perspective, followed by a concise overview of published works, focusing solely on applications related to cell fate decisions, cartilage differentiation and growth plate biology. Particular attention is paid to an in-house developed example of gene regulatory network modeling of growth plate chondrocyte differentiation as all the aforementioned steps can be illustrated. In summary, this paper discusses and explores a series of tools that form a first step toward a rigorous and systems-level modeling of osteochondral differentiation in the context of regenerative medicine.