A robust method for designing multistable systems by embedding bistable subsystems

Although multistability is an important dynamic property of a wide range of complex systems, it is still a challenge to develop mathematical models for realising high order multistability using realistic regulatory mechanisms. To address this issue, we propose a robust method to develop multistable mathematical models by embedding bistable models together. Using the GATA1-GATA2-PU.1 module in hematopoiesis as the test system, we first develop a tristable model based on two bistable models without any high cooperative coefficients, and then modify the tristable model based on experimentally determined mechanisms. The modified model successfully realises four stable steady states and accurately reflects a recent experimental observation showing four transcriptional states. In addition, we develop a stochastic model, and stochastic simulations successfully realise the experimental observations in single cells. These results suggest that the proposed method is a general approach to develop mathematical models for realising multistability and heterogeneity in complex systems

High-dimensional switches and the modeling of cellular differentiation

Many genes have been identified as driving cellular differentiation, but because of their complex interactions, the understanding of their collective behaviour requires mathematical modelling. Intriguingly, it has been observed in numerous developmental contexts, and particularly hematopoiesis, that genes regulating differentiation are initially co-expressed in progenitors despite their antagonism, before one is upregulated and others downregulated. We characterise conditions under which 3 classes of generic "master regulatory networks", modelled at the molecular level after experimentally-observed interactions (including bHLH protein dimerisation), and including an arbitrary number of antagonistic components, can behave as a "multi-switch", directing differentiation in an all-or-none fashion to a specific cell-type chosen among more than 2 possible outcomes. bHLH dimerisation networks can readily display coexistence of many antagonistic factors when competition is low (a simple characterisation is derived). Decision-making can be forced by a transient increase in competition, which could correspond to some unexplained experimental observations related to Id proteins; the speed of response varies with the initial conditions the network is subjected to, which could explain some aspects of cell behaviour upon reprogramming.The coexistence of antagonistic factors at low levels, early in the differentiation process or in pluripotent stem cells, could be an intrinsic property of the interaction between those factors, not requiring a specific regulatory system

Gene Networks of Fully Connected Triads with Complete Auto-Activation Enable Multistability and Stepwise Stochastic Transitions

Fully-connected triads (FCTs), such as the Oct4-Sox2-Nanog triad, have been implicated as recurring transcriptional motifs embedded within the regulatory networks that specify and maintain cellular states. To explore the possible connections between FCT topologies and cell fate determinations, we employed computational network screening to search all possible FCT topologies for multistability, a dynamic property that allows the rise of alternate regulatory states from the same transcriptional network. The search yielded a hierarchy of FCTs with various potentials for multistability, including several topologies capable of reaching eight distinct stable states. Our analyses suggested that complete auto-activation is an effective indicator for multistability, and, when gene expression noise was incorporated into the model, the networks were able to transit multiple states spontaneously. Different levels of stochasticity were found to either induce or disrupt random state transitioning with some transitions requiring layovers at one or more intermediate states. Using this framework we simulated a simplified model of induced pluripotency by including constitutive overexpression terms. The corresponding FCT showed random state transitioning from a terminal state to the pluripotent state, with the temporal distribution of this transition matching published experimental data. This work establishes a potential theoretical framework for understanding cell fate determinations by connecting conserved regulatory modules with network dynamics. Our results could also be employed experimentally, using established developmental transcription factors as seeds, to locate cell lineage specification networks by using auto-activation as a cipher

Gene Networks of Fully Connected Triads with Complete Auto-Activation Enable Multistability and Stepwise Stochastic Transitions

abstract: Fully-connected triads (FCTs), such as the Oct4-Sox2-Nanog triad, have been implicated as recurring transcriptional motifs embedded within the regulatory networks that specify and maintain cellular states. To explore the possible connections between FCT topologies and cell fate determinations, we employed computational network screening to search all possible FCT topologies for multistability, a dynamic property that allows the rise of alternate regulatory states from the same transcriptional network. The search yielded a hierarchy of FCTs with various potentials for multistability, including several topologies capable of reaching eight distinct stable states. Our analyses suggested that complete auto-activation is an effective indicator for multistability, and, when gene expression noise was incorporated into the model, the networks were able to transit multiple states spontaneously. Different levels of stochasticity were found to either induce or disrupt random state transitioning with some transitions requiring layovers at one or more intermediate states. Using this framework we simulated a simplified model of induced pluripotency by including constitutive overexpression terms. The corresponding FCT showed random state transitioning from a terminal state to the pluripotent state, with the temporal distribution of this transition matching published experimental data. This work establishes a potential theoretical framework for understanding cell fate determinations by connecting conserved regulatory modules with network dynamics. Our results could also be employed experimentally, using established developmental transcription factors as seeds, to locate cell lineage specification networks by using auto-activation as a cipher.The article is published at http://journals.plos.org/plosone/article?id=10.1371/journal.pone.010287

Bridging Time Scales in Cellular Decision Making with a Stochastic Bistable Switch

Cellular transformations which involve a significant phenotypical change of the cell's state use bistable biochemical switches as underlying decision systems. In this work, we aim at linking cellular decisions taking place on a time scale of years to decades with the biochemical dynamics in signal transduction and gene regulation, occuring on a time scale of minutes to hours. We show that a stochastic bistable switch forms a viable biochemical mechanism to implement decision processes on long time scales. As a case study, the mechanism is applied to model the initiation of follicle growth in mammalian ovaries, where the physiological time scale of follicle pool depletion is on the order of the organism's lifespan. We construct a simple mathematical model for this process based on experimental evidence for the involved genetic mechanisms. Despite the underlying stochasticity, the proposed mechanism turns out to yield reliable behavior in large populations of cells subject to the considered decision process. Our model explains how the physiological time constant may emerge from the intrinsic stochasticity of the underlying gene regulatory network. Apart from ovarian follicles, the proposed mechanism may also be of relevance for other physiological systems where cells take binary decisions over a long time scale.Comment: 14 pages, 4 figure

Modeling cell differentiation using dynamical systems on graphs

La cellula vivente è un sistema complesso governato da molti processi che non sono ancora stati compresi: il processo di differenziazione cellulare è uno di questi. La differenziazione cellulare è il processo in cui le cellule di un tipo specifico si riproducono e danno origine a diversi tipi di cellule. La differenziazione cellulare è regolata dai cosiddetti Gene Regulatory Networks (GRN). Un GRN è una raccolta di regolatori molecolari che interagiscono tra loro e con altre sostanze nella cellula per governare i livelli di espressione genica di mRNA e proteine. Kauffman propose per la prima volta nel 1969 di modellare GRN attraverso le cosiddette Random Boolean Networks (RBN). I RBN sono reti in cui ogni nodo può avere solo due possibili valori: 0 o 1, dove ogni nodo rappresenta un gene in GRN che può essere ”on” oppure ”off”. Queste reti possono modellizzare i GRN perchè l’attività di un nodo rappresenta il livello di espressione di un gene nell’intera regolazione. In questo lavoro di tesi ci avvaliamo di un modello matematico per sviluppare e riprodurre una possibile rete di regolazione genica per il processo di differenziazione cellulare

A novel 4-valued discrete network for the analysis of signalling events integrating protein interaction and gene expression data applied on hematopoietic diefferentiation

Signaltransduction is an important process, that is crucial for the interplay of cells in multicellular organisms and controls among other things cellular proliferation and cellular differentiation. The complexity of signalling networks and the absence of comprehensive and accurate quantitative data make a precise mathematical description of such networks difficult. This work deals with the questions, if and how predications about signalling processes for specific cellular models can be made with the aid of interaction databases and gene expression profiles. Starting from molecular interaction-databases complex networks are generated comprising all known cellular signalling paths. But, not all of them play a role in a specific cellular model. The specific adaptation of the networks to a specific cellular system is achieved by additional integration of data obtained from gene expression profiles. Thereby, 1. the information about expression or non-expression of a gene and 2. the change of gene expression in time (increase, decrease or unchanged) is used. 1. Information about the expression is included in the calculations, by removing unexpressed elements from the network and thus changing its topology. 2. Chronological changes in expression are integrated in the estimations by a four-valued, discrete network containing statistical elements, that was developed in this work. This network is able to deal with contradicting data and pays attention to the importance of feedback loops for differentiation processes. This enables an extraction of subnetworks having a dynamic that approximates the measured data best. Hematopoietic processes, playing among other things a role in development of leukaemias, were examined with a sensitivity analysis. The analysis revealed central molecules of EpoR induced hematopoesis, like AKT, PIP3, Pi3K, Lyn, ERK

Computational Integrative Models for Cellular Conversion: Application to Cellular Reprogramming and Disease Modeling

The groundbreaking identification of only four transcription factors that are able to induce pluripotency in any somatic cell upon perturbation stimulated the discovery of copious amounts of instructive factors triggering different cellular conversions. Such conversions are highly significant to regenerative medicine with its ultimate goal of replacing or regenerating damaged and lost cells. Precise directed conversion of damaged cells into healthy cells offers the tantalizing prospect of promoting regeneration in situ. In the advent of high-throughput sequencing technologies, the distinct transcriptional and accessible chromatin landscapes of several cell types have been characterized. This characterization provided clear evidences for the existence of cell type specific gene regulatory networks determined by their distinct epigenetic landscapes that control cellular phenotypes. Further, these networks are known to dynamically change during the ectopic expression of genes initiating cellular conversions and stabilize again to represent the desired phenotype. Over the years, several computational approaches have been developed to leverage the large amounts of high-throughput datasets for a systematic prediction of instructive factors that can potentially induce desired cellular conversions. To date, the most promising approaches rely on the reconstruction of gene regulatory networks for a panel of well-studied cell types relying predominantly on transcriptional data alone. Though useful, these methods are not designed for newly identified cell types as their frameworks are restricted only to the panel of cell types originally incorporated. More importantly, these approaches rely majorly on gene expression data and cannot account for the cell type specific regulations modulated by the interplay of the transcriptional and epigenetic landscape. In this thesis, a computational method for reconstructing cell type specific gene regulatory networks is proposed that aims at addressing the aforementioned limitations of current approaches. This method integrates transcriptomics, chromatin accessibility assays and available prior knowledge about gene regulatory interactions for predicting instructive factors that can potentially induce desired cellular conversions. Its application to the prioritization of drugs for reverting pathologic phenotypes and the identification of instructive factors for inducing the cellular conversion of adipocytes into osteoblasts underlines the potential to assist in the discovery of novel therapeutic interventions

Computational Integrative Models for Cellular Conversion: Application to Cellular Reprogramming and Disease Modeling

The groundbreaking identification of only four transcription factors that are able to induce pluripotency in any somatic cell upon perturbation stimulated the discovery of copious amounts of instructive factors triggering different cellular conversions. Such conversions are highly significant to regenerative medicine with its ultimate goal of replacing or regenerating damaged and lost cells. Precise directed conversion of damaged cells into healthy cells offers the tantalizing prospect of promoting regeneration in situ. In the advent of high-throughput sequencing technologies, the distinct transcriptional and accessible chromatin landscapes of several cell types have been characterized. This characterization provided clear evidences for the existence of cell type specific gene regulatory networks determined by their distinct epigenetic landscapes that control cellular phenotypes. Further, these networks are known to dynamically change during the ectopic expression of genes initiating cellular conversions and stabilize again to represent the desired phenotype. Over the years, several computational approaches have been developed to leverage the large amounts of high-throughput datasets for a systematic prediction of instructive factors that can potentially induce desired cellular conversions. To date, the most promising approaches rely on the reconstruction of gene regulatory networks for a panel of well-studied cell types relying predominantly on transcriptional data alone. Though useful, these methods are not designed for newly identified cell types as their frameworks are restricted only to the panel of cell types originally incorporated. More importantly, these approaches rely majorly on gene expression data and cannot account for the cell type specific regulations modulated by the interplay of the transcriptional and epigenetic landscape. In this thesis, a computational method for reconstructing cell type specific gene regulatory networks is proposed that aims at addressing the aforementioned limitations of current approaches. This method integrates transcriptomics, chromatin accessibility assays and available prior knowledge about gene regulatory interactions for predicting instructive factors that can potentially induce desired cellular conversions. Its application to the prioritization of drugs for reverting pathologic phenotypes and the identification of instructive factors for inducing the cellular conversion of adipocytes into osteoblasts underlines the potential to assist in the discovery of novel therapeutic interventions

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