A common molecular logic determines embryonic stem cell self-renewal and reprogramming.

During differentiation and reprogramming, new cell identities are generated by reconfiguration of gene regulatory networks. Here, we combined automated formal reasoning with experimentation to expose the logic of network activation during induction of naïve pluripotency. We find that a Boolean network architecture defined for maintenance of naïve state embryonic stem cells (ESC) also explains transcription factor behaviour and potency during resetting from primed pluripotency. Computationally identified gene activation trajectories were experimentally substantiated at single-cell resolution by RT-qPCR Contingency of factor availability explains the counterintuitive observation that Klf2, which is dispensable for ESC maintenance, is required during resetting. We tested 124 predictions formulated by the dynamic network, finding a predictive accuracy of 77.4%. Finally, we show that this network explains and predicts experimental observations of somatic cell reprogramming. We conclude that a common deterministic program of gene regulation is sufficient to govern maintenance and induction of naïve pluripotency. The tools exemplified here could be broadly applied to delineate dynamic networks underlying cell fate transitions.

How computational models contribute to our understanding of the germ line.

Computational models are an invaluable tool in modern biology. They provide a framework within which to summarize existing knowledge, enable competing hypotheses to be compared qualitatively and quantitatively, and to facilitate the interpretation of complex data. Moreover, models allow questions to be investigated that are difficult to approach experimentally. Theories can be tested in context, identifying the gaps in our understanding and potentially leading to new hypotheses. Models can be developed on a variety of scales and with different levels of mechanistic detail, depending on the available data, the biological questions of interest, and the available mathematical and computational tools. The goal of this review is to provide a broad picture of how modeling has been applied to reproductive biology. Specifically, we look at four uses of modeling: (i) comparing hypotheses; (ii) interpreting data; (iii) exploring experimentally challenging questions; and (iv) hypothesis evaluation and generation. We present examples of each of these applications in reproductive biology, drawing from a range of organisms-including Drosophila, Caenorhabditis elegans, mouse, and humans. We aim to describe the data and techniques used to construct each model, and to highlight the benefits of modeling to the field, as complementary to experimental work. Mol. Reprod. Dev. 83: 944-957, 2016 © 2016 Wiley Periodicals, Inc.

Chaste: an open source C++ library for computational physiology and biology.

Chaste - Cancer, Heart And Soft Tissue Environment - is an open source C++ library for the computational simulation of mathematical models developed for physiology and biology. Code development has been driven by two initial applications: cardiac electrophysiology and cancer development. A large number of cardiac electrophysiology studies have been enabled and performed, including high-performance computational investigations of defibrillation on realistic human cardiac geometries. New models for the initiation and growth of tumours have been developed. In particular, cell-based simulations have provided novel insight into the role of stem cells in the colorectal crypt. Chaste is constantly evolving and is now being applied to a far wider range of problems. The code provides modules for handling common scientific computing components, such as meshes and solvers for ordinary and partial differential equations (ODEs/PDEs). Re-use of these components avoids the need for researchers to 're-invent the wheel' with each new project, accelerating the rate of progress in new applications. Chaste is developed using industrially-derived techniques, in particular test-driven development, to ensure code quality, re-use and reliability. In this article we provide examples that illustrate the types of problems Chaste can be used to solve, which can be run on a desktop computer. We highlight some scientific studies that have used or are using Chaste, and the insights they have provided. The source code, both for specific releases and the development version, is available to download under an open source Berkeley Software Distribution (BSD) licence at http://www.cs.ox.ac.uk/chaste, together with details of a mailing list and links to documentation and tutorials.

The Nucleosome Remodelling and Deacetylation complex coordinates the transcriptional response to lineage commitment in pluripotent cells.

As cells exit the pluripotent state and begin to commit to a specific lineage they must activate genes appropriate for that lineage while silencing genes associated with pluripotency and preventing activation of lineage-inappropriate genes. The Nucleosome Remodelling and Deacetylation (NuRD) complex is essential for pluripotent cells to successfully undergo lineage commitment. NuRD controls nucleosome density at regulatory sequences to facilitate transcriptional responses, and also has been shown to prevent unscheduled transcription (transcriptional noise) in undifferentiated pluripotent cells. How these activities combine to ensure cells engage a gene expression program suitable for successful lineage commitment has not been determined. Here, we show that NuRD is not required to silence all genes. Rather, it restricts expression of genes primed for activation upon exit from the pluripotent state, but maintains them in a transcriptionally permissive state in self-renewing conditions, which facilitates their subsequent activation upon exit from naïve pluripotency. We further show that NuRD coordinates gene expression changes, which acts to maintain a barrier between different stable states. Thus NuRD-mediated chromatin remodelling serves multiple functions, including reducing transcriptional noise, priming genes for activation and coordinating the transcriptional response to facilitate lineage commitment.

A two-dimensional model of the colonic crypt accounting for the role of the basement membrane and pericryptal fibroblast sheath.

The role of the basement membrane is vital in maintaining the integrity and structure of an epithelial layer, acting as both a mechanical support and forming the physical interface between epithelial cells and the surrounding connective tissue. The function of this membrane is explored here in the context of the epithelial monolayer that lines the colonic crypt, test-tube shaped invaginations that punctuate the lining of the intestine and coordinate a regular turnover of cells to replenish the epithelial layer every few days. To investigate the consequence of genetic mutations that perturb the system dynamics and can lead to colorectal cancer, it must be possible to track the emerging tissue level changes that arise in the crypt. To that end, a theoretical crypt model with a realistic, deformable geometry is required. A new discrete crypt model is presented, which focuses on the interaction between cell- and tissue-level behaviour, while incorporating key subcellular components. The model contains a novel description of the role of the surrounding tissue and musculature, based upon experimental observations of the tissue structure of the crypt, which are also reported. A two-dimensional (2D) cross-sectional geometry is considered, and the shape of the crypt is allowed to evolve and deform. Simulation results reveal how the shape of the crypt may contribute mechanically to the asymmetric division events typically associated with the stem cells at the base. The model predicts that epithelial cell migration may arise due to feedback between cell loss at the crypt collar and density-dependent cell division, an hypothesis which can be investigated in a wet lab. This work forms the basis for investigation of the deformation of the crypt structure that can occur due to proliferation of cells exhibiting mutant phenotypes, experiments that would not be possible in vivo or in vitro.

Entropy sorting of single-cell RNA sequencing data reveals the inner cell mass in the human pre-implantation embryo.

A major challenge in single-cell gene expression analysis is to discern meaningful cellular heterogeneity from technical or biological noise. To address this challenge, we present entropy sorting (ES), a mathematical framework that distinguishes genes indicative of cell identity. ES achieves this in an unsupervised manner by quantifying if observed correlations between features are more likely to have occurred due to random chance versus a dependent relationship, without the need for any user-defined significance threshold. On synthetic data, we demonstrate the removal of noisy signals to reveal a higher resolution of gene expression patterns than commonly used feature selection methods. We then apply ES to human pre-implantation embryo single-cell RNA sequencing (scRNA-seq) data. Previous studies failed to unambiguously identify early inner cell mass (ICM), suggesting that the human embryo may diverge from the mouse paradigm. In contrast, ES resolves the ICM and reveals sequential lineage bifurcations as in the classical model. ES thus provides a powerful approach for maximizing information extraction from high-dimensional datasets such as scRNA-seq data.

The Reasoning Engine: A Satisfiability Modulo Theories-Based Framework for Reasoning About Discrete Biological Models.

We present a framework called the Reasoning Engine, which implements Satisfiability Modulo Theories (SMT)-based methods within a unified computational environment to address diverse biological analysis problems. The Reasoning Engine was used to reproduce results from key scientific studies, as well as supporting new research in stem cell biology. The framework utilizes an intermediate language for encoding partially specified discrete dynamical systems, which bridges the gap between high-level domain-specific languages and low-level SMT solvers. We provide this framework as open source together with various biological case studies, illustrating the synthesis, enumeration, optimization, and reasoning over models consistent with experimental observations to reveal novel biological insights.

Modelling the role of the basement membrane beneath a growing epithelial monolayer.

The role of the basement membrane is vital in maintaining the integrity and structure of an epithelial layer, acting as both a mechanical support and forming the physical interface between epithelial cells and the surrounding connective tissue. The function of this membrane is explored here in the context of a growing epithelial monolayer, defined such that the epithelial cells divide and migrate along a deformable substrate. A discrete, off-lattice cell-centre modelling approach is undertaken, which permits definition of a basement membrane component, separating the epithelial cells from the tissue stroma whilst responding to forces from both that arise due to cell division, migration and apoptosis. This model is applicable to a range of biological epithelia, including the self-renewing interfollicular epidermis, the olfactory epithelium and the intestinal crypts of Lieberkühn, to inform response and recovery of such tissues following injury. Model simulations show that homeostasis of the growing monolayer can be achieved and sustained, and the necessary balance of interactive cell forces, cell migration and cell death is presented. This work is proposed as a novel extension to the body of discrete models of biological epithelia, permitting investigation of the growth and migration of epithelial cells in a deformable environment.

Formal Analysis of Network Motifs Links Structure to Function in Biological Programs.

A recurring set of small sub-networks have been identified as the building blocks of biological networks across diverse organisms. These network motifs are associated with certain dynamic behaviors and define key modules that are important for understanding complex biological programs. Besides studying the properties of motifs in isolation, current algorithms typically evaluate the occurrence frequency of a specific motif in a given biological network compared to that in random networks of similar structure. However, it remains challenging to relate the structure of motifs to the observed and expected behavior of the larger, more complex network they are contained within. This problem is compounded as even the precise structure of most biological networks remains largely unknown. Previously, we developed a formal reasoning approach enabling the synthesis of biological networks capable of reproducing some experimentally observed behavior. Here, we extend this approach to allow reasoning over the requirement for specific network motifs as a way of explaining how these behaviors arise. We illustrate the approach by analyzing the motifs involved in sign-sensitive delay and pulse generation. We demonstrate the scalability and biological relevance of the approach by studying the previously defined networks governing myeloid differentiation, the yeast cell cycle, and naïve pluripotency in mouse embryonic stem cells, revealing the requirement for certain motifs in these systems.

Computational Stem Cell Biology: Open Questions and Guiding Principles.

Computational biology is enabling an explosive growth in our understanding of stem cells and our ability to use them for disease modeling, regenerative medicine, and drug discovery. We discuss four topics that exemplify applications of computation to stem cell biology: cell typing, lineage tracing, trajectory inference, and regulatory networks. We use these examples to articulate principles that have guided computational biology broadly and call for renewed attention to these principles as computation becomes increasingly important in stem cell biology. We also discuss important challenges for this field with the hope that it will inspire more to join this exciting area.

Automated Formal Reasoning to Uncover Molecular Programs of Self-Renewal.

The Reasoning Engine for Interaction Networks (RE:IN) is a tool that was developed initially for the study of pluripotency in mouse embryonic stem cells. A set of critical factors that regulate the pluripotent state had been identified experimentally, but it was not known how these genes interacted to stabilize self-renewal or commit the cell to differentiation. The methodology encapsulated in RE:IN enabled the exploration of a space of possible network interaction models, allowing for uncertainty in whether individual interactions exist between the pluripotency factors. This concept of an "abstract" network was combined with automated reasoning that allows the user to eliminate models that are inconsistent with experimental observations. The tool generalizes beyond the study of stem cell decision-making, allowing for the study of interaction networks more broadly across biology.

A protein phosphatase network controls the temporal and spatial dynamics of differentiation commitment in human epidermis.

Epidermal homeostasis depends on a balance between stem cell renewal and terminal differentiation. The transition between the two cell states, termed commitment, is poorly understood. Here, we characterise commitment by integrating transcriptomic and proteomic data from disaggregated primary human keratinocytes held in suspension to induce differentiation. Cell detachment induces several protein phosphatases, five of which - DUSP6, PPTC7, PTPN1, PTPN13 and PPP3CA - promote differentiation by negatively regulating ERK MAPK and positively regulating AP1 transcription factors. Conversely, DUSP10 expression antagonises commitment. The phosphatases form a dynamic network of transient positive and negative interactions that change over time, with DUSP6 predominating at commitment. Boolean network modelling identifies a mandatory switch between two stable states (stem and differentiated) via an unstable (committed) state. Phosphatase expression is also spatially regulated in vivo and in vitro. We conclude that an auto-regulatory phosphatase network maintains epidermal homeostasis by controlling the onset and duration of commitment.

A Method to Identify and Analyze Biological Programs through Automated Reasoning.

Predictive biology is elusive because rigorous, data-constrained, mechanistic models of complex biological systems are difficult to derive and validate. Current approaches tend to construct and examine static interaction network models, which are descriptively rich but often lack explanatory and predictive power, or dynamic models that can be simulated to reproduce known behavior. However, in such approaches implicit assumptions are introduced as typically only one mechanism is considered, and exhaustively investigating all scenarios is impractical using simulation. To address these limitations, we present a methodology based on automated formal reasoning, which permits the synthesis and analysis of the complete set of logical models consistent with experimental observations. We test hypotheses against all candidate models, and remove the need for simulation by characterizing and simultaneously analyzing all mechanistic explanations of observed behavior. Our methodology transforms knowledge of complex biological processes from sets of possible interactions and experimental observations to precise, predictive biological programs governing cell function.

Automated Synthesis and Analysis of Switching Gene Regulatory Networks.

Studying the gene regulatory networks (GRNs) that govern how cells change into specific cell types with unique roles throughout development is an active area of experimental research. The fate specification process can be viewed as a biological program prescribing the system dynamics, governed by a network of genetic interactions. To investigate the possibility that GRNs are not fixed but rather change their topology, for example as cells progress through commitment, we introduce the concept of Switching Gene Regulatory Networks (SGRNs) to enable the modelling and analysis of network reconfiguration. We define the synthesis problem of constructing SGRNs that are guaranteed to satisfy a set of constraints representing experimental observations of cell behaviour. We propose a solution to this problem that employs methods based upon Satisfiability Modulo Theories (SMT) solvers, and evaluate the feasibility and scalability of our approach by considering a set of synthetic benchmarks exhibiting possible biological behaviour of cell development. We outline how our approach is applied to a more realistic biological system, by considering a simplified network involved in the processes of neuron maturation and fate specification in the mammalian cortex.

Computational models reveal a passive mechanism for cell migration in the crypt.

Cell migration in the intestinal crypt is essential for the regular renewal of the epithelium, and the continued upward movement of cells is a key characteristic of healthy crypt dynamics. However, the driving force behind this migration is unknown. Possibilities include mitotic pressure, active movement driven by motility cues, or negative pressure arising from cell loss at the crypt collar. It is possible that a combination of factors together coordinate migration. Here, three different computational models are used to provide insight into the mechanisms that underpin cell movement in the crypt, by examining the consequence of eliminating cell division on cell movement. Computational simulations agree with existing experimental results, confirming that migration can continue in the absence of mitosis. Importantly, however, simulations allow us to infer mechanisms that are sufficient to generate cell movement, which is not possible through experimental observation alone. The results produced by the three models agree and suggest that cell loss due to apoptosis and extrusion at the crypt collar relieves cell compression below, allowing cells to expand and move upwards. This finding suggests that future experiments should focus on the role of apoptosis and cell extrusion in controlling cell migration in the crypt.

Oligodendrocyte dynamics in the healthy adult CNS: evidence for myelin remodeling.

Oligodendrocyte precursors (OPs) continue to proliferate and generate myelinating oligodendrocytes (OLs) well into adulthood. It is not known whether adult-born OLs ensheath previously unmyelinated axons or remodel existing myelin. We quantified OP division and OL production in different regions of the adult mouse CNS including the 4-month-old optic nerve, in which practically all axons are already myelinated. Even there, all OPs were dividing and generating new OLs and myelin at a rate higher than can be explained by first-time myelination of naked axons. We conclude that adult-born OLs in the optic nerve are engaged in myelin remodeling, either replacing OLs that die in service or intercalating among existing myelin sheaths. The latter would predict that average internode length should decrease with age. Consistent with that, we found that adult-born OLs elaborated much shorter but many more internodes than OLs generated during early postnatal life.

Modeling alveolar volume changes during periodic breathing in heterogeneously ventilated lungs.

A simplified model of periodic breathing, proposed by Whiteley et al. (Math. Med. Biol. 20:205-224, 2003), describes a non-uniform breathing pattern for a lung with an inhomogeneous gas distribution, such as that observed in some subjects suffering from respiratory disease. This model assumes a constant alveolar volume, and predicts incidence of irregular breathing caused by small, poorly ventilated regions of the lung. Presented here is an extension to this work which, by allowing variable lung volume, facilitates the investigation of pulmonary collapse in poorly ventilated compartments. A weakness of the original model is that a very small alveolar volume is required for periodic breathing to occur. The model presented within, which removes the assumption of constant compartment volume and allows alveolar volume to vary with time, predicts periodic breathing at higher, more realistic alveolar volumes. Furthermore, the predicted oscillations in ventilation match experimental data more closely. Thus the model that allows for alveolar collapse has improved upon these earlier results, and establishes a theoretical link between periodic breathing and atelectasis.