Integrating Gene Regulatory Network Dynamics with Heterogeneous Stem Cell Regeneration

BackgroundThe emergent dynamics of complex gene regulatory networks govern various cellular processes. However, understanding these dynamics is challenging due to the difficulty of parameterizing the computational models for these networks, especially as the network size increases. Here, we introduce a simulation library, Gene Regulatory Interaction Network Simulator (GRiNS), to address these challenges.ResultsGRiNS integrates popular parameter-agnostic simulation frameworks, RACIPE and Boolean Ising formalism, into a single Python library capable of leveraging GPU acceleration for efficient and scalable simulations. GRiNS extends the ordinary differential equations (ODE) based RACIPE framework with a more modular design, allowing users to choose parameters, initial conditions, and time-series outputs for greater customisability and accuracy in simulations. For large networks, where ODE-based simulation formalisms do not scale well, GRiNS implements Boolean Ising formalism, providing a simplified, coarse-grained alternative, significantly reducing the computational cost while capturing key dynamical behaviours of large regulatory networks.ConclusionGRiNS enables parameter-agnostic modeling of gene regulatory networks to study their dynamic and steady-state behaviors in a scalable and efficient manner. The documentation and installation instructions for GRiNS can be found at https://moltenecdysone09.github.io/GRiNS/.

Cell fate determination is usually described as the result of the stochastic dynamics of gene regulatory networks (GRNs) reaching one of multiple steady-states each of which corresponds to a specific decision. However, the fate of a cell is determined in finite time suggesting the importance of transient dynamics in cellular decision making. Here we consider cellular decision making as resulting from first passage processes of regulatory proteins and examine the effect of transient dynamics within the initial lysis-lysogeny switch of phage λ. Importantly, the fate of an infected cell depends, in part, on the number of coinfecting phages. Using a quantitative model of the phage λ GRN, we find that changes in the likelihood of lysis and lysogeny can be driven by changes in phage co-infection number regardless of whether or not there exists steady-state bistability within the GRN. Furthermore, two GRNs which yield qualitatively distinct steady state behaviors as a function of phage infection number can show similar transient responses, sufficient for alternative cell fate determination. We compare our model results to a recent experimental study of cell fate determination in single cell assays of multiply infected bacteria. Whereas the experimental study proposed a “quasi-independent” hypothesis for cell fate determination consistent with an observed data collapse, we demonstrate that observed cell fate results are compatible with an alternative form of data collapse consistent with a partial gene dosage compensation mechanism. We show that including partial gene dosage compensation at the mRNA level in our stochastic model of fate determination leads to the same data collapse observed in the single cell study. Our findings elucidate the importance of transient gene regulatory dynamics in fate determination, and present a novel alternative hypothesis to explain single-cell level heterogeneity within the phage λ lysis-lysogeny decision switch.

Regulation of gene expression is a fundamental mechanism allowing the existence of complex living systems. This regulation takes shape in the form of hierarchical gene regulatory networks (GRNs), culminating in the binding of transcription factors (TFs) to regulatory elements (REs). Uncovering the structures of these GRNs has shed light on the mechanistic basis of complex spatiotemporal processes like embryonic development. The reconstruction of such GRN, for any biological process, is therefore the ultimate goal for its understanding. The planarian Schmidtea mediterranea is an important model organism for the study of adult stem cell systems, cell differentiation and regeneration. However, very little is known about the structure of GRNs in this organism due to the historical lack of adequate tools to study regulatory elements. At the beginning of my thesis, I developed a robust Start-seq protocol to study RE activity in S. mediterranea by probing for transcription initiation events. Following this, I characterized the identified putative REs on the basis of their distribution, chromatin context as well as motif content. Putative REs identified using Start-seq possess characteristic epigenomic signatures as they are situated within regions of open chromatin and are enriched for active epigenetic marks such as H3K27Ac, H3K4me3 and H3k4me1. I next showed that both planarian putative enhancers and promoter are enriched for core promoter motifs that are mostly situated at the expected position. Interestingly, the DPE motif was enriched at the transcription initiation site in both types of REs instead of its described position at ± +30 nt. Following this, I showed that most of the identified REs showed sign of bidirectional transcription initiation which is considered as a characteristic feature of REs. After characterizing the REs, I leveraged the existence of two naturally occurring biotypes within S. mediterranea (sexual and asexual) to investigate gene regulatory networks (GRNs) responsible for the development and maintenance of the planarian reproductive system. These biotypes are genetically similar, but one fails to develop sexual organs. Comparing their transcription initiation landscapes allowed me to identify multiple transcription factors potentially part of in these GRNs. Notably, the majority of the selected TF candidates exhibited expression in sexual organs, with half of the candidates being specifically expressed in these tissues. Knockdown of three candidates (tead 1, thap and cebp 4 ) showed dysregulation of many reproductive genes. In situ hybridizations on sexual markers after RNAi of the three candidates confirmed the abrogation of sexual tissues in these conditions. The results indicated that tead 1 produced a severe phenotype, where most sexual organs were absent, except for the ovaries. The thap candidate exhibited a defect in shell gland formation and yolk tissue patterning, while the cebp 4 candidate displayed an impairment in sperm differentiation. Overall, this study was not able to recreate a GRN governing the development and maintenance of the reproductive tissue in S. mediterranea. However, it lays a foundation for further research on GRNs in planaria as it shows that identification of differentially active REs using the established protocol was successful in obtaining important regulators the planarian reproductive system.

Cells in an organism interact with each other and with the environment through a complex set of signals, which triggers responses and activates cellular regulation mechanisms. Models obtained by computational mathematics for cellular signaling dynamics are used to understand factors and causes of deregulation of internal biological processes, which is a relevant knowledge in a disease such as cancer. Gene regulatory networks describe gene interactions and how these relationships control cellular processes such as growth and cell division, which relate this disease to the regulatory network. Despite its simplicity, Boolean networks may accurately model some biological phenomena, such as gene regulatory network dynamics. Indeed, several reports in the literature show that they are accurate enough to build models of regulatory networks of cell lines related to breast cancer. In this chapter, we present a methodology for building cellular regulatory networks based on the Boolean paradigm, which uses entropy as a criterion for selecting genes that are included in the network. The main objective is to understand dynamical behaviors related to situations that cause breast cancer and tumor lineages and to suggest experimentations to verify the outcome of interventions in networks, in order to support the identification of new therapeutic targets.

How gene regulatory networks (GRNs) encode gene expression dynamics and how GRNs evolve are not well understood, although these problems have been studied extensively. We created a digital twin that accurately reproduces expression dynamics of 13 genes that initiate expression in 32-cell ascidian embryos. We first showed that gene expression patterns can be manipulated according to predictions by this digital model. Next, to simulate GRN rewiring, we changed regulatory functions that represented their regulatory mechanisms in the digital twin, and found that in 55 of 100 cases, removal of a single regulator from a conjunctive clause of Boolean functions did not theoretically alter qualitative expression patterns of these genes. In other words, we found that more than half the regulators gave theoretically redundant temporal or spatial information to target genes. We experimentally substantiated that the expression pattern of Nodal was maintained without one of these factors, Zfpm, by changing the upstream regulatory sequence of Nodal. Such robust buffers of regulatory mechanisms may provide a basis of enabling developmental system drift, or rewiring of GRNs without changing expression patterns of downstream genes, during evolution.

A new phenotypic variant may appear first in organisms through plasticity, that is, as a response to an environmental signal or other nongenetic perturbation. If such trait is beneficial, selection may increase the frequency of alleles that enable and facilitate its development. Thus, genes may take control of such traits, decreasing dependence on nongenetic disturbances, in a process called genetic assimilation. Despite an increasing amount of empirical studies supporting genetic assimilation, its significance is still controversial. Whether genetic assimilation is widespread depends, to a great extent, on how easily mutation and recombination reduce the trait's dependence on nongenetic perturbations. Previous research suggests that this is the case for mutations. Here we use simulations of gene regulatory network dynamics to address this issue with respect to recombination. We find that recombinant offspring of parents that produce a new phenotype through plasticity are more likely to produce the same phenotype without requiring any perturbation. They are also prone to preserve the ability to produce that phenotype after genetic and nongenetic perturbations. Our work also suggests that ancestral plasticity can play an important role for setting the course that evolution takes. In sum, our results indicate that the manner in which phenotypic variation maps unto genetic variation facilitates evolution through genetic assimilation in gene regulatory networks. Thus, we contend that the importance of this evolutionary mechanism should not be easily neglected.

How can cells shape and utilize dynamic gene regulation to enable complex cellular behaviors? I study this question in natural and synthetic contexts. The first project studies how a natural genetic network can imbue cells with a sense of ‘time’. It has long been known that environmental signals induce diverse cellular differentiation programs. In certain systems, cells defer differentiation for extended time periods after the signal appears, proliferating through multiple rounds of cell division before committing to a new fate. How can cells set a deferral time much longer than the cell cycle? Here we study Bacillus subtilis cells that respond to sudden nutrient limitation with multiple rounds of growth and division before differentiating into spores. A well characterized genetic circuit controls the concentration and phosphorylation of the master regulator Spo0A, which rises to a critical concentration to initiate sporulation. However, it remains unclear how this circuit enables cells to defer sporulation for multiple cell cycles. Using quantitative time-lapse fluorescence microscopy of Spo0A dynamics in individual cells, we observed pulses of Spo0A phosphorylation at a characteristic cell cycle phase. Pulse amplitudes grew systematically and cell-autonomously over multiple cell cycles leading up to sporulation. This pulse growth required a key positive feedback loop involving the sporulation kinases, without which the deferral of sporulation became ultrasensitive to kinase expression. Thus, deferral is controlled by a pulsed positive feedback loop in which kinase expression is activated by pulses of Spo0A phosphorylation. This pulsed positive feedback architecture provides a more robust mechanism for setting deferral times than constitutive kinase expression. Finally, using mathematical modeling, we show how pulsing and time delays together enable ‘polyphasic’ positive feedback, in which different parts of a feedback loop are active at different times. Polyphasic feedback can enable more accurate tuning of long deferral times. Together, these results suggest that Bacillus subtilis uses a pulsed positive feedback loop to implement a timer that operates over time scales much longer than a cell cycle. The second project proposes a method to rapidly generate and test complex genetic network dynamics in living cells. Existing microorganisms have evolved genetic circuitry to meet diverse challenges and maximize their survival and fitness. These challenges arise from external environmental pressures, or internal evolved constraints. Furthermore, these challenges may be either static or dynamic in nature. While existing circuits have likely evolved to be ‘good enough’ to respond to historical challenges, it remains unclear if they can be improved upon, and whether they respond well to novel situations. Synthetic biology seeks to engineer organisms with complex novel phenotypes, both to harness these novel organisms for a function and to understand their underlying biology. Dynamic gene expression strategies may be necessary to successfully generate these phenotypes. Unfortunately, generating novel dynamic gene expression patterns with conventional genetic engineering remains a challenge. Here I propose and describe progress towards a computerized feedback control setup to enable the programming and rapid testing of dynamic gene regulatory patterns in living cells. Small sets of genes will be regulated optogenetically based on programmed control laws, and past and present cellular state. This setup will enable us to explore the functions and limits of engineered dynamic gene regulation, while hopefully, in the process, providing lessons about the underlying biology.

Models of Gene Regulatory Networks (GRNs) capture the dynamics of the regulatory processes that occur within the cell as a means to understand the variability observed in gene expression between different conditions. Arguably the simplest mathematical construct used for modeling is the Boolean network, which dictates a set of logical rules for transition between states described as Boolean vectors. Due to the complexity of gene regulation and the limitations of experimental technologies, in most cases knowledge about regulatory interactions and Boolean states is partial. In addition, the logical rules themselves are not known a-priori. Our goal in this work is to create an algorithm that finds the network that fits the data optimally, and identify the network states that correspond to the noise-free data. We present a novel methodology for integrating experimental data and performing a search for the optimal consistent structure via optimization of a linear objective function under a set of linear constraints. In addition, we extend our methodology into a heuristic that alleviates the computational complexity of the problem for datasets that are generated by single-cell RNA-Sequencing(scRNA-Seq). We demonstrate the effectiveness of these tools using a public scRNA-Seq dataset and the GRN that is associated with it. Our methodology wm enable researchers to obtain a better understanding of the dynamics of gene regulatory networks and their biological role.

Gene regulatory networks are essential for understanding the mechanisms underlying genetic disorders. However, traditional models based on deterministic Hill functions (without fluctuations) often fail to capture critical stochastic effects, particularly in small systems in which molecular fluctuations play a significant role. In this study, we introduced a modified Hill function derived from the stochastic dynamics of ligand–receptor interactions. By performing a second-order expansion of the chemical master equation, we derived a set of ordinary differential equations governing the mean concentrations and covariances. This framework allows the identification of effective reaction rates using Hill functions that include stochastic correction terms that account for fluctuations in ligand–receptor binding. We applied this approach to canonical models, such as the Toggle Switch, Repressilator, and Activator–Repressor Clock, and showed that the Hill function with stochastic corrections provides a more accurate description of system dynamics with intrinsic fluctuations. Moreover, the proposed method offers substantial computational advantages over direct stochastic simulations using the Gillespie algorithm. Our results demonstrate that this approximation captures the essential features of stochastic biochemical systems more accurately than models that use deterministic Hill functions, offering a powerful tool for studying the role of fluctuations in complex reaction networks and uncovering potential emergent behaviors driven by intrinsic fluctuations in the system.

Cell-machine interfaces for characterizing gene regulatory network dynamics

A strategy for estimating structure of gene regulatory networks (GRNs) is proposed on basis of time series experimental data in this paper. This strategy is an essential for transforming the problem of identifying a GRN into that of sparse reconstruction whose measurement matrix is composed of the nonlinear functions of a GRN. Differently from tradition methods, this method is well suitable for a large scale network identification, and may avoid both linearized inaccuracy and limitation of the length of time series data. We utilize an algorithm of the stagewise modified orthogonal matching pursuit (SmOMP) to estimate the sparse vector that denote a gene regulated by other genes. Compared with robust state estimator (RSE), the well known extended Kalman filter (EKF) and unscented Kalman filter (UKF) based method, the efficiency of this method has been verified by numerical simulations. Actual results show that this suggested method not only has better convergence speed and higher estimate accuracy, but also can significantly reduce the computational complexity in GRN inferences.

A general mathematical framework for understanding the behavior of heterogeneous stem cell regeneration

Bridging social evolution theory and emerging empirical approaches to social behavior

A key topic in systems biology is to understand the intricate relations between molecular network structures, dynamic properties and biological function. In this context, gene regulatory networks (GRNs) describing the regulatory interactions between genes and their products are of crucial importance. The general goal of this thesis is to explore the relationship between the structure and dynamics of GRNs. This is done in a discrete modelling framework using the Thomas formalism. A GRN is represented by a discrete model which includes an interaction graph (IG) and a logical parameter function that characterise the regulatory interactions. The dynamics of a GRN is modelled by an asynchronous state transition graph (ASTG), where the states of the system can only be changed by asynchronous and unitary updates. In 2011, T. Lorenz proposed two reverse engineering algorithms for inferring from a given ASTG models satisfying specific properties. In the first part of the thesis, the focus is on the explanation, implementation, and generalisation of the Lorenz algorithms. In order to handle general inputs, three necessary and sufficient conditions are presented to characterise ASTGs among all graphs on a given state space. Furthermore, a fourth condition is derived which is necessary and sufficient for an ASTG to admit a realistic model. These four ASTG conditions provide the basis for a generalisation of Lorenz algorithms and several applications. Multistationarity and homeostasis are two important dynamical properties of high biological relevance, which can be represented by attractors in the ASTG. In the second part of the thesis, two discrete modelling workflows are developed for exploring all those GRNs that are able to realise a given functionality. The forward modelling workflow includes enumerating all possible models and searching for those models whose ASTG exhibits the desired properties. The reverse engineering workflow starts from enumerating all graphs on the state space satisfying the dynamic properties and then infers all models of these graphs using the generalised Lorenz algorithms. To analyse the resulting functional IGs, a logical analysis method is developed, which encodes IGs by Boolean expressions, and then uses Boolean function minimisation to obtain a compact representation. The same logical analysis method can also be applied to the logical parameters. In the last part of the thesis, the discrete modelling workflows are applied to explore the space of GRNs realising some typical dynamic behaviours of biological interest. Three case studies are presented. The first one concerns homeostasis in a simplified MAPK cascade, the second one multistationarity in cell differentiation, and the third one single-stripe forming in the embryogenesis of the fruit fly Drosophila melanogaster.

We present CellLine, a simulator of the dynamics of gene regulatory networks (GRN) in the cells of a lineage. From user-defined reactions and initial substance quantities, it generates cell lineages, i.e. genealogic pedigrees of cells related through mitotic division. Each cell's dynamics is driven by a delayed stochastic simulation algorithm (delayed SSA), allowing multiple time delayed reactions. The cells of the lineage can be individually subject to 'perturbations', such as gene deletion, duplication and mutation. External interventions, such as adding or removing a substance at a given moment, can be specified. Cell differentiation lineages, where differentiation is stochastically driven or externally induced, can be modeled as well. Finally, CellLine can generate and simulate the dynamics of multiple copies of any given cell of the lineage. As examples of CellLine use, we simulate the following systems: cell lineages containing a model of the P53-Mdm2 feedback loop, a differentiation lineage where each cell contains a 4 gene repressilator (a bistable circuit), a model of the differentiation of the cells of the retinal mosaic required for color vision in Drosophila melanogaster, where the differentiation pathway depends on one substance's concentration that is controlled by a stochastic process, and a 9 gene GRN to illustrate the advantage of using CellLine rather than simulating multiple independent cells, in cases where the cells of the lineage are dynamically correlated. The CellLine program, instructions and examples are available at www.ucalgary.ca/~aribeiro/CellLine/CellLine.html