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Abstract Cells are the fundamental units of life, and like all life forms, they change over time. Changes in cell state are driven by molecular processes; of these many are initiated when molecule numbers reach and exceed specific thresholds, a characteristic that can be described as “digital cellular logic”. Here we show how molecular and cellular noise profoundly influence the time to cross a critical threshold—the first-passage time—and map out scenarios in which stochastic dynamics result in shorter or longer average first-passage times compared to noise-less dynamics. We illustrate the dependence of the mean first-passage time on noise for a set of exemplar models of gene expression, auto-regulatory feedback control, and enzyme-mediated catalysis. Our theory provides intuitive insight into the origin of these effects and underscores two important insights: (i) deterministic predictions for cellular event timing can be highly inaccurate when molecule numbers are within the range known for many cells; (ii) molecular noise can significantly shift mean first-passage times, particularly within auto-regulatory genetic feedback circuits.

Single-cell technologies allow us to gain insights into cellular processes at unprecedented resolution. In stem cell and developmental biology snapshot data allow us to characterize how the transcriptional states of cells change between successive cell types. Here, we show how approximate Bayesian computation (ABC) can be employed to calibrate mathematical models against single-cell data. In our simulation study, we demonstrate the pivotal role of the adequate choice of distance measures appropriate for single-cell data. We show that for good distance measures, notably optimal transport with the Sinkhorn divergence, we can infer parameters for mathematical models from simulated single-cell data. We show that the ABC posteriors can be used (i) to characterize parameter sensitivity and identify dependencies between different parameters and (ii) to construct representations of the Waddington or epigenetic landscape, which forms a popular and interpretable representation of the developmental dynamics. In summary, these results pave the way for fitting mechanistic models of stem cell differentiation to single-cell data.

Here the authors show inducible genes and enhancers are regulated mainly by transcriptional burst frequency and that this is coordinated in single cells and individual alleles. Cohesin, which is important for inducible gene expression, is largely dispensable for regulating enhancer burst frequencies; however, it is required for coupling burst frequencies of inducible enhancers and promoters.

Abstract Network inference is a notoriously challenging problem. Inferred networks are associated with high uncertainty and likely riddled with false positive and false negative interactions. Especially for biological networks we do not have good ways of judging the performance of inference methods against real networks, and instead we often rely solely on the performance against simulated data. Gaining confidence in networks inferred from real data nevertheless thus requires establishing reliable validation methods. Here, we argue that the expectation of mixing patterns in biological networks such as gene regulatory networks offers a reasonable starting point: interactions are more likely to occur between nodes with similar biological functions. We can quantify this behaviour using the assortativity coefficient, and here we show that the resulting heuristic, functional assortativity, offers a reliable and informative route for comparing different inference algorithms.

Statistical physics provides a useful perspective for the analysis of many complex systems; it allows us to relate microscopic fluctuations to macroscopic observations. Developmental biology, but also cell biology more generally, are examples where apparently robust behaviour emerges from highly complex and stochastic sub-cellular processes. Here we attempt to make connections between different theoretical perspectives to gain qualitative insights into the types of cell-fate decision making processes that are at the heart of stem cell and developmental biology. We discuss both dynamical systems as well as statistical mechanics perspectives on the classical Waddington or epigenetic landscape. We find that non-equilibrium approaches are required to overcome some of the shortcomings of classical equilibrium statistical thermodynamics or statistical mechanics in order to shed light on biological processes, which, almost by definition, are typically far from equilibrium.

In many scientific and technological contexts, we have only a poor understanding of the structure and details of appropriate mathematical models. We often, therefore, need to compare different models. With available data we can use formal statistical model selection to compare and contrast the ability of different mathematical models to describe such data. There is, however, a lack of rigorous methods to compare different models a priori. Here, we develop and illustrate two such approaches that allow us to compare model structures in a systematic way by representing models as simplicial complexes. Using well-developed concepts from simplicial algebraic topology, we define a distance between models based on their simplicial representations. Employing persistent homology with a flat filtration provides for alternative representations of the models as persistence intervals, which represent model structure, from which the model distances are also obtained. We then expand on this measure of model distance to study the concept of model equivalence to determine the conceptual similarity of models. We apply our methodology for model comparison to demonstrate an equivalence between a positional-information model and a Turing-pattern model from developmental biology, constituting a novel observation for two classes of models that were previously regarded as unrelated.

Abstract Background Reverse engineering of gene regulatory networks from time series gene-expression data is a challenging problem, not only because of the vast sets of candidate interactions but also due to the stochastic nature of gene expression. We limit our analysis to nonlinear differential equation based inference methods. In order to avoid the computational cost of large-scale simulations, a two-step Gaussian process interpolation based gradient matching approach has been proposed to solve differential equations approximately. Results We apply a gradient matching inference approach to a large number of candidate models, including parametric differential equations or their corresponding non-parametric representations, we evaluate the network inference performance under various settings for different inference objectives. We use model averaging, based on the Bayesian Information Criterion (BIC), to combine the different inferences. The performance of different inference approaches is evaluated using area under the precision-recall curves. Conclusions We found that parametric methods can provide comparable, and often improved inference compared to non-parametric methods; the latter, however, require no kinetic information and are computationally more efficient.

Signalling responses are marked by substantial cell-to-cell variability. Here, the authors propose an information theoretic framework that accounts for multiple inputs and temporal dynamics to analyse how signals flow through shared network components.

Dynamical systems with intricate behaviour are all-pervasive in biology. Many of the most interesting biological processes indicate the presence of bifurcations, i.e. phenomena where a small change in a system parameter causes qualitatively different behaviour. Bifurcation theory has become a rich field of research in its own right and evaluating the bifurcation behaviour of a given dynamical system can be challenging. An even greater challenge, however, is to learn the bifurcation structure of dynamical systems from data, where the precise model structure is not known. Here, we study one aspects of this problem: the practical implications that the presence of bifurcations has on our ability to infer model parameters and initial conditions from empirical data; we focus on the canonical co-dimension 1 bifurcations and provide a comprehensive analysis of how dynamics, and our ability to infer kinetic parameters are linked. The picture thus emerging is surprisingly nuanced and suggests that identification of the qualitative dynamics—the bifurcation diagram—should precede any attempt at inferring kinetic parameters.

Within populations of cells, fate decisions are controlled by an indeterminate combination of cell-intrinsic and cell-extrinsic factors. In the case of stem cells, the stem cell niche is believed to maintain ‘stemness’ through communication and interactions between the stem cells and one or more other cell-types that contribute to the niche conditions. To investigate the robustness of cell fate decisions in the stem cell hierarchy and the role that the niche plays, we introduce simple mathematical models of stem and progenitor cells, their progeny and their interplay in the niche. These models capture the fundamental processes of proliferation and differentiation and allow us to consider alternative possibilities regarding how niche-mediated signalling feedback regulates the niche dynamics. Generalised stability analysis of these stem cell niche systems enables us to describe the stability properties of each model. We find that although the number of feasible states depends on the model, their probabilities of stability in general do not: stem cell–niche models are stable across a wide range of parameters. We demonstrate that niche-mediated feedback increases the number of stable steady states, and show how distinct cell states have distinct branching characteristics. The ecological feedback and interactions mediated by the stem cell niche thus lend (surprisingly) high levels of robustness to the stem and progenitor cell population dynamics. Furthermore, cell–cell interactions are sufficient for populations of stem cells and their progeny to achieve stability and maintain homeostasis. We show that the robustness of the niche – and hence of the stem cell pool in the niche – depends only weakly, if at all, on the complexity of the niche make-up: simple as well as complicated niche systems are capable of supporting robust and stable stem cell dynamics.

Signaling from the c-Met receptor tyrosine kinase is associated with progression and metastasis of epithelial tumors. c-Met, the receptor for hepatocyte growth factor, triggers epithelial-mesenchymal transition (EMT) of cultured cells, which is thought to drive migration of tumor cells and confer on them critical stem cell properties. Here, we employ mathematical modeling to better understand how EMT affects population dynamics in metastatic tumors. We find that without intervention, micrometastatic tumors reach a steady-state population. While the rates of proliferation, senescence and death only have subtle effects on the steady state, changes in the frequency of EMT dramatically alter population dynamics towards exponential growth. We also find that therapies targeting cell proliferation or cell death are markedly more successful when combined with one that prevents EMT, though such therapies do little when used alone. Stochastic modeling reveals the probability of tumor recurrence from small numbers of residual differentiated tumor cells. EMT events in metastatic tumors provide a plausible mechanism by which clinically detectable tumors can arise from dormant micrometastatic tumors. Modeling the dynamics of this process demonstrates the benefit of a treatment that eradicates tumor cells and reduces the rate of EMT simultaneously.

Controlling the behaviour of cells by rationally guiding molecular processes is an overarching aim of much of synthetic biology. Molecular processes, however, are notoriously noisy and frequently nonlinear. We present an approach to studying the impact of control measures on motifs of molecular interactions that addresses the problems faced in many biological systems: stochasticity, parameter uncertainty and nonlinearity. We show that our reachability analysis formalism can describe the potential behaviour of biological (naturally evolved as well as engineered) systems, and provides a set of bounds on their dynamics at the level of population statistics: for example, we can obtain the possible ranges of means and variances of mRNA and protein expression levels, even in the presence of uncertainty about model parameters.

Proteasomes are key proteases involved in a variety of processes ranging from the clearance of damaged proteins to the presentation of antigens to CD8+ T-lymphocytes. Which cleavage sites are used within the target proteins and how fast these proteins are degraded have a profound impact on immune system function and many cellular metabolic processes. The regulation of proteasome activity involves different mechanisms, such as the substitution of the catalytic subunits, the binding of regulatory complexes to proteasome gates and the proteasome conformational modifications triggered by the target protein itself. Mathematical models are invaluable in the analysis; and potentially allow us to predict the complex interactions of proteasome regulatory mechanisms and the final outcomes of the protein degradation rate and MHC class I epitope generation. The pioneering attempts that have been made to mathematically model proteasome activity, cleavage preference variation and their modification by one of the regulatory mechanisms are reviewed here.

Haematopoiesis is the complex developmental process that maintains the turnover of all blood cell lineages. It critically depends on the correct functioning of rare, quiescent haematopoietic stem cells (HSCs) and more numerous, HSC-derived, highly proliferative and differentiating haematopoietic progenitor cells (HPCs). Infection is known to affect HSCs, with severe and chronic inflammatory stimuli leading to stem cell pool depletion, while acute, non-lethal infections exert transient and even potentiating effects. Both whether this paradigm applies to all infections and whether the HSC response is the dominant driver of the changes observed during stressed haematopoiesis remain open questions. We use a mouse model of malaria, based on natural, sporozoite-driven Plasmodium berghei infection, as an experimental platform to gain a global view of haematopoietic perturbations during infection progression. We observe coordinated responses by the most primitive HSCs and multiple HPCs, some starting before blood parasitaemia is detected. We show that, despite highly variable inter-host responses, primitive HSCs become highly proliferative, but mathematical modelling suggests that this alone is not sufficient to significantly impact the whole haematopoietic cascade. We observe that the dramatic expansion of Sca-1+ progenitors results from combined proliferation of direct HSC progeny and phenotypic changes in downstream populations. We observe that the simultaneous perturbation of HSC/HPC population dynamics is coupled with early signs of anaemia onset. Our data uncover a complex relationship between Plasmodium and its host's haematopoiesis and raise the question whether the variable responses observed may affect the outcome of the infection itself and its long-term consequences on the host.

ABSTRACT Nitrogen regulation in Escherichia coli is a model system for gene regulation in bacteria. Growth on glutamine as a sole nitrogen source is assumed to be nitrogen limiting, inferred from slow growth and strong NtrB/NtrC-dependent gene activation. However, we show that under these conditions, the intracellular glutamine concentration is not limiting but 5.6-fold higher than in ammonium-replete conditions; in addition, α-ketoglutarate concentrations are elevated. We address this glutamine paradox from a systems perspective. We show that the dominant role of NtrC is to regulate glnA transcription and its own expression, indicating that the glutamine paradox is not due to NtrC-independent gene regulation. The absolute intracellular NtrC and GS concentrations reveal molecular control parameters, where NtrC-specific activities were highest in nitrogen-starved cells, while under glutamine growth, NtrC showed intermediate specific activity. We propose an in vivo model in which α-ketoglutarate can derepress nitrogen regulation despite nitrogen sufficiency. IMPORTANCE Nitrogen is the most important nutrient for cell growth after carbon, and its metabolism is coordinated at the metabolic, transcriptional, and protein levels. We show that growth on glutamine as a sole nitrogen source, commonly assumed to be nitrogen limiting and used as such as a model system for nitrogen limitation, is in fact nitrogen replete. Our integrative quantitative analysis of key molecules involved in nitrogen assimilation and regulation reveal that glutamine is not necessarily the dominant molecule signaling nitrogen sufficiency and that α-ketoglutarate may play a more important role in signaling nitrogen status. NtrB/NtrC integrates α-ketoglutarate and glutamine signaling—sensed by the UTase (glnD) and PII (glnB), respectively—and regulates the nitrogen response through self-regulated expression and phosphorylation-dependent activation of the nitrogen (ntr) regulon. Our findings support α-ketoglutarate acting as a global regulatory metabolite.