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Abstract T-cell development provides an excellent model system for studying lineage commitment from a multipotent progenitor. The intrathymic development process has been thoroughly studied. The molecular circuitry controlling it has been dissected and the necessary steps like programmed shut off of progenitor genes and T-cell genes upregulation have been revealed. However, the exact timing between decision-making and commitment stage remains unexplored. To this end, we implemented an agent-based multi-scale model to investigate inheritance in early T-cell development. Treating each cell as an agent provides a powerful tool as it tracks each individual cell of a simulated T-cell colony, enabling the construction of lineage trees. Based on the lineage trees, we introduce the concept of the last common ancestors (LCA) of committed cells and analyse their relations, both at single-cell level and population level. In addition to simulating wild-type development, we also conduct knockdown analysis. Our simulations predicted that the commitment is a three-step process that occurs on average over several cell generations once a cell is first prepared by a transcriptional switch. This is followed by the loss of the Bcl11b-opposing function approximately two to three generations later. This is when our LCA analysis indicates that the decision to commit is taken even though in general another one to two generations elapse before the cell actually becomes committed by transitioning to the DN2b state. Our results showed that there is decision inheritance in the commitment mechanism.

Quantum annealing has shown promise for finding solutions to difficult optimization problems, including protein folding. Recently, we used the D-Wave Advantage quantum annealer to explore the folding problem in a coarse-grained lattice model, the HP model, in which amino acids are classified into two broad groups: hydrophobic (H) and polar (P). Using a set of 22 HP sequences with up to 64 amino acids, we demonstrated the fast and consistent identification of the correct HP model ground states using the D-Wave hybrid quantum-classical solver. An equally relevant biophysical challenge, called the protein design problem, is the inverse of the above, where the task is to predict protein sequences that fold to a given structure. Here, we approach the design problem by a two-step procedure implemented and executed on a D-Wave machine. In the first step, we perform a pure sequence-space search by varying the type of amino acid at each sequence position, and seek sequences which minimize the HP-model energy of the target structure. After mapping this task onto an Ising spin-glass representation, we employ a hybrid quantum-classical solver to deliver energy-optimal sequences for structures with 30–64 amino acids, with a 100% success rate. In the second step, we filter the optimized sequences from the first step according to their ability to fold to the intended structure. In addition, we try solving the sequence optimization problem using only the quantum processing unit (QPU), which confines us to sizes ≤20, due to exponentially decreasing success rates. To shed light on the pure QPU results, we investigate the effects of control errors caused by an imperfect implementation of the intended Hamiltonian on the QPU, by numerically analyzing the Schrödinger equation. We find that the simulated success rates in the presence of control noise semiquantitatively reproduce the modest pure QPU results for larger chains.

Quantum annealing is a promising approach for obtaining good approximate solutions to difficult optimization problems. Folding a protein sequence into its minimum-energy structure represents such a problem. For testing new algorithms and technologies for this task, the minimal lattice-based [hydrophobic (H) or polar (P) beads] HP model is well suited, as it represents a considerable challenge despite its simplicity. The HP model has favorable interactions between adjacent, not directly bound hydrophobic residues. Here, we develop a novel spin representation for lattice protein folding tailored for quantum annealing. With a distributed encoding onto the lattice, it differs from earlier attempts to fold lattice proteins on quantum annealers, which were based upon chain growth techniques. With our encoding, the Hamiltonian by design has the quadratic structure required for calculations on an Ising-type annealer, without having to introduce any auxiliary spin variables. This property greatly facilitates the study of long chains. The approach is robust to changes in the parameters required to constrain the spin system to chainlike configurations, and performs very well in terms of solution quality. The results are evaluated against existing exact results for HP chains with up to N=30 beads with 100% hit rate, thereby also outperforming classical simulated annealing. In addition, the method allows us to recover the lowest known energies for N=48 and N=64 HP chains, with similar hit rates. These results are obtained by the commonly used hybrid quantum-classical approach. For pure quantum annealing, our method successfully folds an N=14 HP chain. The calculations were performed on a D-Wave Advantage quantum annealer.

Summary: Intrathymic development of committed progenitor (pro)-T cells from multipotent hematopoietic precursors offers an opportunity to dissect the molecular circuitry establishing cell identity in response to environmental signals. This transition encompasses programmed shutoff of stem/progenitor genes, upregulation of T cell specification genes, proliferation, and ultimately commitment. To explain these features in light of reported cis-acting chromatin effects and experimental kinetic data, we develop a three-level dynamic model of commitment based upon regulation of the commitment-linked gene Bcl11b. The levels are (1) a core gene regulatory network (GRN) architecture from transcription factor (TF) perturbation data, (2) a stochastically controlled chromatin-state gate, and (3) a single-cell proliferation model validated by experimental clonal growth and commitment kinetic assays. Using RNA fluorescence in situ hybridization (FISH) measurements of genes encoding key TFs and measured bulk population dynamics, this single-cell model predicts state-switching kinetics validated by measured clonal proliferation and commitment times. The resulting multi-scale model provides a mechanistic framework for dissecting commitment dynamics.

Modern vibrational spectroscopy techniques enable the rapid collection of thousands of spectra in a single hyperspectral image, allowing researchers to study spatially heterogeneous samples at micrometer resolution. A number of algorithms have been developed to correct for effects such as atmospheric absorption, light scattering by cellular structures and varying baseline levels. After preprocessing, spectra are commonly decomposed and clustered to reveal informative patterns and subtle spectral changes. Several of these steps are slow, labor-intensive and require programming skills to make use of published algorithms and code. We here present a free and platform-independent graphical toolbox that allows rapid preprocessing of large sets of spectroscopic images, including atmospheric correction and a new algorithm for resonant Mie scattering with improved speed. The software also includes modules for decomposition into constituent spectra using the popular Multivariate Curve Resolution–Alternating Least Squares (MCR-ALS) algorithm, augmented by region-of-interest selection, as well as clustering and cluster annotation.

We explore cell heterogeneity during spontaneous and transcription-factor-driven commitment for network inference in hematopoiesis. Since individual genes display discrete OFF states or a distribution of ON levels, we compute and combine pairwise gene associations from binary and continuous components of gene expression in single cells. Ddit3 emerges as a regulatory node with positive linkage to erythroid regulators and negative association with myeloid determinants. Ddit3 loss impairs erythroid colony output from multipotent cells, while forcing Ddit3 in granulo-monocytic progenitors (GMPs) enhances self-renewal and impedes differentiation. Network analysis of Ddit3-transduced GMPs reveals uncoupling of myeloid networks and strengthening of erythroid linkages. RNA sequencing suggests that Ddit3 acts through development or stabilization of a precursor upstream of GMPs with inherent Meg-E potential. The enrichment of Gata2 target genes in Ddit3-dependent transcriptional responses suggests that Ddit3 functions in an erythroid transcriptional network nucleated by Gata2.

Depicting developmental processes as movements in free energy genetic landscapes is an illustrative tool. However, exploring such landscapes to obtain quantitative or even qualitative predictions is hampered by the lack of free energy functions corresponding to the biochemical Michaelis–Menten or Hill rate equations for the dynamics. Being armed with energy landscapes defined by a network and its interactions would open up the possibility of swiftly identifying cell states and computing optimal paths, including those of cell reprogramming, thereby avoiding exhaustive trial-and-error simulations with rate equations for different parameter sets. It turns out that sigmoidal rate equations do have approximate free energy associations. With this replacement of rate equations, we develop a deterministic method for estimating the free energy surfaces of systems of interacting genes at different noise levels or temperatures. Once such free energy landscape estimates have been established, we adapt a shortest path algorithm to determine optimal routes in the landscapes. We explore the method on three circuits for haematopoiesis and embryonic stem cell development for commitment and reprogramming scenarios and illustrate how the method can be used to determine sequential steps for onsets of external factors, essential for efficient reprogramming.

Although the plant and animal kingdoms were separated more than 1,6 billion years ago, multicellular development is for both guided by similar transcriptional, epigenetic and posttranscriptional machinery. One may ask to what extent there are similarities and differences in the gene regulation circuits and their dynamics when it comes to important processes like stem cell regulation. The key players in mouse embryonic stem cells governing pluripotency versus differentiation are Oct4, Sox2 and Nanog. Correspondingly, the WUSCHEL and CLAVATA3 genes represent a core in the Shoot Apical Meristem regulation for plants. In addition, both systems have designated genes that turn on differentiation. There is very little molecular homology between mammals and plants for these core regulators. Here, we focus on functional homologies by performing a comparison between the circuitry connecting these players in plants and animals and find striking similarities, suggesting that comparable regulatory logics have been evolved for stem cell regulation in both kingdoms. From in silico simulations we find similar differentiation dynamics. Further when in the differentiated state, the cells are capable of regaining the stem cell state. We find that the propensity for this is higher for plants as compared to mammalians. Our investigation suggests that, despite similarity in core regulatory networks, the dynamics of these can contribute to plant cells being more plastic than mammalian cells, i.e. capable to reorganize from single differentiated cells to whole plants-reprogramming. The presence of an incoherent feed-forward loop in the mammalian core circuitry could be the origin of the different reprogramming behaviour.

BACKGROUND:Living organisms need to regulate their gene expression in response to environmental signals and internal cues. This is a computational task where genes act as logic gates that connect to form transcriptional networks, which are shaped at all scales by evolution. Large-scale mutations such as gene duplications and deletions add and remove network components, whereas smaller mutations alter the connections between them. Selection determines what mutations are accepted, but its importance for shaping the resulting networks has been debated. METHODOLOGY:To investigate the effects of selection in the shaping of transcriptional networks, we derive transcriptional logic from a combinatorially powerful yet tractable model of the binding between DNA and transcription factors. By evolving the resulting networks based on their ability to function as either a simple decision system or a circadian clock, we obtain information on the regulation and logic rules encoded in functional transcriptional networks. Comparisons are made between networks evolved for different functions, as well as with structurally equivalent but non-functional (neutrally evolved) networks, and predictions are validated against the transcriptional network of E. coli. PRINCIPAL FINDINGS:We find that the logic rules governing gene expression depend on the function performed by the network. Unlike the decision systems, the circadian clocks show strong cooperative binding and negative regulation, which achieves tight temporal control of gene expression. Furthermore, we find that transcription factors act preferentially as either activators or repressors, both when binding multiple sites for a single target gene and globally in the transcriptional networks. This separation into positive and negative regulators requires gene duplications, which highlights the interplay between mutation and selection in shaping the transcriptional networks.

BACKGROUND/OBJECTIVES:A cascade of gene activations under the control of Notch signalling is required during T-cell specification, when T-cell precursors gradually lose the potential to undertake other fates and become fully committed to the T-cell lineage. We elucidate how the gene/protein dynamics for a core transcriptional module governs this important process by computational means. METHODS:We first assembled existing knowledge about transcription factors known to be important for T-cell specification to form a minimal core module consisting of TCF-1, GATA-3, BCL11B, and PU.1 aiming at dynamical modeling. Model architecture was based on published experimental measurements of the effects on each factor when each of the others is perturbed. While several studies provided gene expression measurements at different stages of T-cell development, pure time series are not available, thus precluding a straightforward study of the dynamical interactions among these genes. We therefore translate stage dependent data into time series. A feed-forward motif with multiple positive feed-backs can account for the observed delay between BCL11B versus TCF-1 and GATA-3 activation by Notch signalling. With a novel computational approach, all 32 possible interactions among Notch signalling, TCF-1, and GATA-3 are explored by translating combinatorial logic expressions into differential equations for BCL11B production rate. RESULTS:Our analysis reveals that only 3 of 32 possible configurations, where GATA-3 works as a dimer, are able to explain not only the time delay, but very importantly, also give rise to irreversibility. The winning models explain the data within the 95% confidence region and are consistent with regard to decay rates. CONCLUSIONS:This first generation model for early T-cell specification has relatively few players. Yet it explains the gradual transition into a committed state with no return. Encoding logics in a rate equation setting allows determination of binding properties beyond what is possible in a Boolean network.

Molecular mechanisms employed by individual multipotent cells at the point of lineage commitment remain largely uncharacterized. Current paradigms span from instructive to noise-driven mechanisms. Of considerable interest is also whether commitment involves a limited set of genes or the entire transcriptional program, and to what extent gene expression configures multiple trajectories into commitment. Importantly, the transient nature of the commitment transition confounds the experimental capture of committing cells. We develop a computational framework that simulates stochastic commitment events, and affords mechanistic exploration of the fate transition. We use a combined modeling approach guided by gene expression classifier methods that infers a time-series of stochastic commitment events from experimental growth characteristics and gene expression profiling of individual hematopoietic cells captured immediately before and after commitment. We define putative regulators of commitment and probabilistic rules of transition through machine learning methods, and employ clustering and correlation analyses to interrogate gene regulatory interactions in multipotent cells. Against this background, we develop a Monte Carlo time-series stochastic model of transcription where the parameters governing promoter status, mRNA production and mRNA decay in multipotent cells are fitted to experimental static gene expression distributions. Monte Carlo time is converted to physical time using cell culture kinetic data. Probability of commitment in time is a function of gene expression as defined by a logistic regression model obtained from experimental single-cell expression data. Our approach should be applicable to similar differentiating systems where single cell data is available. Within our system, we identify robust model solutions for the multipotent population within physiologically reasonable values and explore model predictions with regard to molecular scenarios of entry into commitment. The model suggests distinct dependencies of different commitment-associated genes on mRNA dynamics and promoter activity, which globally influence the probability of lineage commitment.

Mammalian embryogenesis is a dynamic process involving gene expression and mechanical forces between proliferating cells. The exact nature of these interactions, which determine the lineage patterning of the trophectoderm and endoderm tissues occurring in a highly regulated manner at precise periods during the embryonic development, is an area of debate. We have developed a computational modeling framework for studying this process, by which the combined effects of mechanical and genetic interactions are analyzed within the context of proliferating cells. At a purely mechanical level, we demonstrate that the perpendicular alignment of the animal-vegetal (a-v) and embryonic-abembryonic (eb-ab) axes is a result of minimizing the total elastic conformational energy of the entire collection of cells, which are constrained by the zona pellucida. The coupling of gene expression with the mechanics of cell movement is important for formation of both the trophectoderm and the endoderm. In studying the formation of the trophectoderm, we contrast and compare quantitatively two hypotheses: (1) The position determines gene expression, and (2) the gene expression determines the position. Our model, which couples gene expression with mechanics, suggests that differential adhesion between different cell types is a critical determinant in the robust endoderm formation. In addition to differential adhesion, two different testable hypotheses emerge when considering endoderm formation: (1) A directional force acts on certain cells and moves them into forming the endoderm layer, which separates the blastocoel and the cells of the inner cell mass (ICM). In this case the blastocoel simply acts as a static boundary. (2) The blastocoel dynamically applies pressure upon the cells in contact with it, such that cell segregation in the presence of differential adhesion leads to the endoderm formation. To our knowledge, this is the first attempt to combine cell-based spatial mechanical simulations with genetic networks to explain mammalian embryogenesis. Such a framework provides the means to test hypotheses in a controlled in silico environment.

Hematopoietic stem cell lineage choices are decided by genetic networks that are turned ON/OFF in a switch-like manner. However, prior to lineage commitment, genes are primed at low expression levels. Understanding the underlying molecular circuitry in terms of how it governs both a primed state and, at the other extreme, a committed state is of relevance not only to hematopoiesis but also to developmental systems in general. We develop a computational model for the hematopoietic erythroid-myeloid lineage decision, which is determined by a genetic switch involving the genes PU.1 and GATA-1. Dynamical models based upon known interactions between these master genes, such as mutual antagonism and autoregulation, fail to make the system bistable, a desired feature for robust lineage determination. We therefore suggest a new mechanism involving a cofactor that is regulated as well as recruited by one of the master genes to bind to the antagonistic partner that is necessary for bistability and hence switch-like behavior. An interesting fallout from this architecture is that suppression of the cofactor through external means can lead to a loss of cooperativity, and hence to a primed state for PU.1 and GATA-1. The PU.1-GATA-1 switch also interacts with another mutually antagonistic pair, C/EBPalpha-FOG-1. The latter pair inherits the state of its upstream master genes and further reinforces the decision due to several feedback loops, thereby leading to irreversible commitment. The genetic switch, which handles the erythroid-myeloid lineage decision, is an example of a network that implements both a primed and a committed state by regulating cooperativity through recruitment of cofactors. Perturbing the feedback between the master regulators and downstream targets suggests potential reprogramming strategies. The approach points to a framework for lineage commitment studies in general and could aid the search for lineage-determining genes.

Recent studies have associated the transcription factors, Oct4, Sox2 and Nanog as parts of a self-regulating network which is responsible for maintaining embryonic stem cell properties: self renewal and pluripotency. In addition, mutual antagonism between two of these and other master regulators have been shown to regulate lineage determination. In particular, an excess of Cdx2 over Oct4 determines the trophectoderm lineage whereas an excess of Gata-6 over Nanog determines differentiation into the endoderm lineage. Also, under/over-expression studies of the master regulator Oct4 have revealed that some self-renewal/pluripotency as well as differentiation genes are expressed in a biphasic manner with respect to the concentration of Oct4.We construct a dynamical model of a minimalistic network, extracted from ChIP-on-chip and microarray data as well as literature studies. The model is based upon differential equations and makes two plausible assumptions; activation of Gata-6 by Oct4 and repression of Nanog by an Oct4-Gata-6 heterodimer. With these assumptions, the results of simulations successfully describe the biphasic behavior as well as lineage commitment. The model also predicts that reprogramming the network from a differentiated state, in particular the endoderm state, into a stem cell state, is best achieved by over-expressing Nanog, rather than by suppression of differentiation genes such as Gata-6.The computational model provides a mechanistic understanding of how different lineages arise from the dynamics of the underlying regulatory network. It provides a framework to explore strategies of reprogramming a cell from a differentiated state to a stem cell state through directed perturbations. Such an approach is highly relevant to regenerative medicine since it allows for a rapid search over the host of possibilities for reprogramming to a stem cell state.

BACKGROUND: Transcriptional regulation of the genes in metabolic pathways is a highly successful strategy, which is virtually universal in microorganisms. The lac operon of E. coli is but one example of how enzyme and transporter production can be made conditional on the presence of a nutrient to catabolize. METHODOLOGY: With a minimalist model of metabolism, cell growth and transcriptional regulation in a microorganism, we explore how the interaction between environmental conditions and gene regulation set the growth rate of cells in the phase of exponential growth. This in silico model, which is based on biochemical rate equations, does not describe a specific organism, but the magnitudes of its parameters are chosen to match realistic values. Optimizing the parameters of the regulatory system allows us to quantify the fitness benefit of regulation. When a second nutrient and its metabolic pathway are introduced, the system must further decide whether and how to activate both pathways. CONCLUSIONS: Even the crudest transcriptional network is shown to substantially increase the fitness of the organism, and this effect persists even when the range of nutrient levels is kept very narrow. We show that maximal growth is achieved when pathway activation is a more or less steeply graded function of the nutrient concentration. Furthermore, we predict that bistability of the system is a rare phenomenon in this context, but outline a situation where it may be selected for.

Recent ChIP experiments of human and mouse embryonic stem cells have elucidated the architecture of the transcriptional regulatory circuitry responsible for cell determination, which involves the transcription factors OCT4, SOX2, and NANOG. In addition to regulating each other through feedback loops, these genes also regulate downstream target genes involved in the maintenance and differentiation of embryonic stem cells. A search for the OCT4-SOX2-NANOG network motif in other species reveals that it is unique to mammals. With a kinetic modeling approach, we ascribe function to the observed OCT4-SOX2-NANOG network by making plausible assumptions about the interactions between the transcription factors at the gene promoter binding sites and RNA polymerase (RNAP), at each of the three genes as well as at the target genes. We identify a bistable switch in the network, which arises due to several positive feedback loops, and is switched on/off by input environmental signals. The switch stabilizes the expression levels of the three genes, and through their regulatory roles on the downstream target genes, leads to a binary decision: when OCT4, SOX2, and NANOG are expressed and the switch is on, the self-renewal genes are on and the differentiation genes are off. The opposite holds when the switch is off. The model is extremely robust to parameter changes. In addition to providing a self-consistent picture of the transcriptional circuit, the model generates several predictions. Increasing the binding strength of NANOG to OCT4 and SOX2, or increasing its basal transcriptional rate, leads to an irreversible bistable switch: the switch remains on even when the activating signal is removed. Hence, the stem cell can be manipulated to be self-renewing without the requirement of input signals. We also suggest tests that could discriminate between a variety of feedforward regulation architectures of the target genes by OCT4, SOX2, and NANOG.

In recent years, the advent of experimental methods to probe gene expression profiles of cancer on a genome-wide scale has led to widespread use of supervised machine learning algorithms to characterize these profiles. The main applications of these analysis methods range from assigning functional classes of previously uncharacterized genes to classification and prediction of different cancer tissues. This article surveys the application of machine learning algorithms to classification and diagnosis of cancer based on expression profiles. To exemplify the important issues of the classification procedure, the emphasis of this article is on one such method, namely artificial neural networks. In addition, methods to extract genes that are important for the performance of a classifier, as well as the influence of sample selection on prediction results are discussed.