Dissecting mechanisms of mouse embryonic stem cells heterogeneity through a model-based analysis of transcription factor dynamics

Agent-based approaches for biological modeling in oncology: A literature review

CONTEXT

Computational modeling involves the use of computer simulations and models to study and understand real-world phenomena. Its application is particularly relevant in the study of potential interactions between biological elements. It is a promising approach to understand complex biological processes and predict their behavior under various conditions.

METHODOLOGY

This paper is a review of the recent literature on computational modeling of biological systems. Our study focuses on the field of oncology and the use of artificial intelligence (AI) and, in particular, agent-based modeling (ABM), between 2010 and May 2023.

RESULTS

Most of the articles studied focus on improving the diagnosis and understanding the behaviors of biological entities, with metaheuristic algorithms being the models most used. Several challenges are highlighted regarding increasing and structuring knowledge about biological systems, developing holistic models that capture multiple scales and levels of organization, reproducing emergent behaviors of biological systems, validating models with experimental data, improving computational performance of models and algorithms, and ensuring privacy and personal data protection are discussed.

Capturing Pluripotency and Beyond

During the development of a multicellular organism, the specification of different cell lineages originates in a small group of pluripotent cells, the epiblasts, formed in the preimplantation embryo. The pluripotent epiblast is protected from premature differentiation until exposure to inductive cues in strictly controlled spatially and temporally organized patterns guiding fetus formation. Epiblasts cultured in vitro are embryonic stem cells (ESCs), which recapitulate the self-renewal and lineage specification properties of their endogenous counterparts. The characteristics of totipotency, although less understood than pluripotency, are becoming clearer. Recent studies have shown that a minor ESC subpopulation exhibits expanded developmental potential beyond pluripotency, displaying a characteristic reminiscent of two-cell embryo blastomeres (2CLCs). In addition, reprogramming both mouse and human ESCs in defined media can produce expanded/extended pluripotent stem cells (EPSCs) similar to but different from 2CLCs. Further, the molecular roadmaps driving the transition of various potency states have been clarified. These recent key findings will allow us to understand eutherian mammalian development by comparing the underlying differences between potency network components during development. Using the mouse as a paradigm and recent progress in human PSCs, we review the epiblast's identity acquisition during embryogenesis and their ESC counterparts regarding their pluripotent fates and beyond.

Nuclear gene proximity and protein interactions shape transcript covariations in mammalian single cells

Single-cell RNA sequencing studies on gene co-expression patterns could yield important regulatory and functional insights, but have so far been limited by the confounding effects of differentiation and cell cycle. We apply a tailored experimental design that eliminates these confounders, and report thousands of intrinsically covarying gene pairs in mouse embryonic stem cells. These covariations form a network with biological properties, outlining known and novel gene interactions. We provide the first evidence that miRNAs naturally induce transcriptome-wide covariations and compare the relative importance of nuclear organization, transcriptional and post-transcriptional regulation in defining covariations. We find that nuclear organization has the greatest impact, and that genes encoding for physically interacting proteins specifically tend to covary, suggesting importance for protein complex formation. Our results lend support to the concept of post-transcriptional RNA operons, but we further present evidence that nuclear proximity of genes may provide substantial functional regulation in mammalian single cells.

Gene expression covariation can be studied by single-cell RNA sequencing. Here the authors analyze intrinsically covarying gene pairs by eliminating the confounding effects in single-cell experiments and observe covariation of proximal genes and miRNA-induced covariation of target mRNAs.

Agent-based modeling of morphogenetic systems: Advantages and challenges

The complexity of morphogenesis poses a fundamental challenge to understanding the mechanisms governing the formation of biological patterns and structures. Over the past century, numerous processes have been identified as critically contributing to morphogenetic events, but the interplay between the various components and aspects of pattern formation have been much harder to grasp. The combination of traditional biology with mathematical and computational methods has had a profound effect on our current understanding of morphogenesis and led to significant insights and advancements in the field. In particular, the theoretical concepts of reaction–diffusion systems and positional information, proposed by Alan Turing and Lewis Wolpert, respectively, dramatically influenced our general view of morphogenesis, although typically in isolation from one another. In recent years, agent-based modeling has been emerging as a consolidation and implementation of the two theories within a single framework. Agent-based models (ABMs) are unique in their ability to integrate combinations of heterogeneous processes and investigate their respective dynamics, especially in the context of spatial phenomena. In this review, we highlight the benefits and technical challenges associated with ABMs as tools for examining morphogenetic events. These models display unparalleled flexibility for studying various morphogenetic phenomena at multiple levels and have the important advantage of informing future experimental work, including the targeted engineering of tissues and organs.

A Novel Framework for Parameter and State Estimation of Multicellular Systems Using Gaussian Mixture Approximations

Multicellular systems play an important role in many biotechnological processes. Typically, these exhibit cell-to-cell variability, which has to be monitored closely for process control and optimization. However, some properties may not be measurable due to technical and financial restrictions. To improve the monitoring, model-based online estimators can be designed for their reconstruction. The multicellular dynamics is accounted for in the framework of population balance models (PBMs). These models are based on single cell kinetics, and each cellular state translates directly into an additional dimension of the obtained partial differential equations. As multicellular dynamics often require detailed single cell models and feature a high number of cellular components, the resulting population balance equations are often high-dimensional. Therefore, established state estimation concepts for PBMs based on discrete grids are not recommended due to the large computational effort. In this contribution a novel approach is proposed, which is based on the approximation of the underlying number density functions as the weighted sum of Gaussian distributions. Thus, the distribution is described by the characteristic properties of the individual Gaussians, like the mean and covariance. Thereby, the complex infinite dimensional estimation problem can be reduced to a finite dimension. The characteristic properties are estimated in a recursive approach. The method is evaluated for two academic benchmark examples, and the results indicate its potential for model-based online reconstruction for multicellular systems.

Pluripotency gene network dynamics: System views from parametric analysis

Multiple experimental data demonstrated that the core gene network orchestrating self-renewal and differentiation of mouse embryonic stem cells involves activity of Oct4, Sox2 and Nanog genes by means of a number of positive feedback loops among them. However, recent studies indicated that the architecture of the core gene network should also incorporate negative Nanog autoregulation and might not include positive feedbacks from Nanog to Oct4 and Sox2. Thorough parametric analysis of the mathematical model based on this revisited core regulatory circuit identified that there are substantial changes in model dynamics occurred depending on the strength of Oct4 and Sox2 activation and molecular complexity of Nanog autorepression. The analysis showed the existence of four dynamical domains with different numbers of stable and unstable steady states. We hypothesize that these domains can constitute the checkpoints in a developmental progression from naïve to primed pluripotency and vice versa. During this transition, parametric conditions exist, which generate an oscillatory behavior of the system explaining heterogeneity in expression of pluripotent and differentiation factors in serum ESC cultures. Eventually, simulations showed that addition of positive feedbacks from Nanog to Oct4 and Sox2 leads mainly to increase of the parametric space for the naïve ESC state, in which pluripotency factors are strongly expressed while differentiation ones are repressed.

A stochastic and dynamical view of pluripotency in mouse embryonic stem cells

Pluripotent embryonic stem cells are of paramount importance for biomedical sciences because of their innate ability for self-renewal and differentiation into all major cell lines. The fateful decision to exit or remain in the pluripotent state is regulated by complex genetic regulatory networks. The rapid growth of single-cell sequencing data has greatly stimulated applications of statistical and machine learning methods for inferring topologies of pluripotency regulating genetic networks. The inferred network topologies, however, often only encode Boolean information while remaining silent about the roles of dynamics and molecular stochasticity inherent in gene expression. Herein we develop a framework for systematically extending Boolean-level network topologies into higher resolution models of networks which explicitly account for the promoter architectures and gene state switching dynamics. We show the framework to be useful for disentangling the various contributions that gene switching, external signaling, and network topology make to the global heterogeneity and dynamics of transcription factor populations. We find the pluripotent state of the network to be a steady state which is robust to global variations of gene switching rates which we argue are a good proxy for epigenetic states of individual promoters. The temporal dynamics of exiting the pluripotent state, on the other hand, is significantly influenced by the rates of genetic switching which makes cells more responsive to changes in extracellular signals.

Network Features and Dynamical Landscape of Naive and Primed Pluripotency

Although the broad and unique differentiation potential of pluripotent stem cells relies on a complex transcriptional network centered around Oct4, Sox2, and Nanog, two well-distinct pluripotent states, called "naive" and "primed", have been described in vitro and markedly differ in their developmental potential, their expression profiles, their signaling requirements, and their reciprocal conversion. Aiming to determine the key features that segregate and coordinate these two states, data-driven optimization of network models is performed to identify relevant parameter regimes and reduce network complexity to its core structure. Decision dynamics of optimized networks is characterized by signal-dependent multistability and strongly asymmetric transitions among naive, primed, and nonpluripotent states. Further model perturbation and reduction approaches reveal that such a dynamical landscape of pluripotency involves a functional partitioning of the regulatory network. Specifically, two overlapping positive feedback modules, Klf4/Esrrb/Nanog and Oct4/Nanog, stabilize the naive or the primed state, respectively. In turn, their incoherent feedforward and negative feedback coupling mediated by the Erk/Gsk3 module is critical for robust segregation and sequential progression between naive and primed states before irreversible exit from pluripotency.

Programming Morphogenesis through Systems and Synthetic Biology

Mammalian tissue development is an intricate, spatiotemporal process of self-organization that emerges from gene regulatory networks of differentiating stem cells. A major goal in stem cell biology is to gain a sufficient understanding of gene regulatory networks and cell-cell interactions to enable the reliable and robust engineering of morphogenesis. Here, we review advances in synthetic biology, single cell genomics, and multiscale modeling, which, when synthesized, provide a framework to achieve the ambitious goal of programming morphogenesis in complex tissues and organoids.

Formative pluripotency: the executive phase in a developmental continuum

The regulative capability of single cells to give rise to all primary embryonic lineages is termed pluripotency. Observations of fluctuating gene expression and phenotypic heterogeneity in vitro have fostered a conception of pluripotency as an intrinsically metastable and precarious state. However, in the embryo and in defined culture environments the properties of pluripotent cells change in an orderly sequence. Two phases of pluripotency, called naïve and primed, have previously been described. In this Hypothesis article, a third phase, called formative pluripotency, is proposed to exist as part of a developmental continuum between the naïve and primed phases. The formative phase is hypothesised to be enabling for the execution of pluripotency, entailing remodelling of transcriptional, epigenetic, signalling and metabolic networks to constitute multi-lineage competence and responsiveness to specification cues.

Summary: This Hypothesis article poses that a third state of pluripotency, called formative pluripotency, exists between the naïve and primed states, and is enabling for the execution of pluripotency.

An extended model for culture-dependent heterogenous gene expression and proliferation dynamics in mouse embryonic stem cells

During development, pluripotency is a transient state describing a cell's ability to give rise to all three germ layers and germline. Recent studies have shown that, in vitro, pluripotency is highly dynamic: exogenous stimuli provided to cultures of mouse embryonic stem cells, isolated from pre-implantation blastocysts, significantly affect the spectrum of pluripotency. 2i/LIF, a recently defined serum-free medium, forces mouse embryonic stem cells into a ground-state of pluripotency, while serum/LIF cultures promote the co-existence of ground-like and primed-like mouse embryonic stem cell subpopulations. The latter heterogeneity correlates with temporal fluctuations of pluripotency markers, including the master regulator Nanog, in single cells. We propose a mathematical model of Nanog dynamics in both media, accounting for recent experimental data showing the persistence of a small Nanog Low subpopulation in ground-state pluripotency mouse embryonic stem cell cultures. The model integrates into the core pluripotency Gene Regulatory Network both inhibitors present in 2i/LIF (PD and Chiron), and feedback interactions with genes found to be differentially expressed in the two media. Our simulations and bifurcation analysis show that, in ground-state cultures, Nanog dynamics result from the combination of reduced noise in gene expression and the shift of the system towards a monostable, but still excitable, regulation. Experimental data and agent-based modelling simulations indicate that mouse embryonic stem cell proliferation dynamics vary in the two media, and cannot be reproduced by accounting only for Nanog-dependent cell-cycle regulation. We further demonstrate that both PD and Chiron play a key role in regulating heterogeneity in transcription factor expression and, ultimately, mouse embryonic stem cell fate decision.

Nanog Dynamics in Mouse Embryonic Stem Cells: Results from Systems Biology Approaches

Mouse embryonic stem cells (mESCs), derived from the inner cell mass of the blastocyst, are pluripotent stem cells having self-renewal capability and the potential of differentiating into every cell type under the appropriate culture conditions. An increasing number of reports have been published to uncover the molecular mechanisms that orchestrate pluripotency and cell fate specification using combined computational and experimental methodologies. Here, we review recent systems biology approaches to describe the causes and functions of gene expression heterogeneity and complex temporal dynamics of pluripotency markers in mESCs under uniform culture conditions. In particular, we focus on the dynamics of Nanog, a key regulator of the core pluripotency network and of mESC fate. We summarize the strengths and limitations of different experimental and modeling approaches and discuss how various strategies could be used.