The intricate dynamics of Hes expression across diverse cell types in the developing vertebrate embryonic tail have remained elusive. To address this, we have developed an endogenously tagged Hes1-Achilles mouse line, enabling precise quantification of dynamics at the single-cell resolution across various tissues. Our findings reveal striking disparities in Hes1 dynamics between presomitic mesoderm (PSM) and preneural tube (pre-NT) cells. While pre-NT cells display variable, low-amplitude oscillations, PSM cells exhibit synchronized, high-amplitude oscillations. Upon the induction of differentiation, the oscillation amplitude increases in pre-NT cells. Additionally, our study of Notch inhibition on Hes1 oscillations unveils distinct responses in PSM and pre-NT cells, corresponding to differential Notch ligand expression dynamics. These findings suggest the involvement of separate mechanisms driving Hes1 oscillations. Thus, Hes1 demonstrates dynamic behaviour across adjacent tissues of the embryonic tail, yet the varying oscillation parameters imply differences in the information that can be transmitted by these dynamics.@en

How does an organism regulate its genes? The involved regulation typically occurs in terms of a signal processing chain: an externally applied stimulus or a maternally supplied transcription factor leads to the expression of some downstream genes, which, in turn, are transcription factors for further genes. Especially during development, these transcription factors are frequently expressed in amounts where noise is still important; yet, the signals that they provide must not be lost in the noise. Thus, the organism needs to extract exactly relevant information in the signal. New experimental approaches involving single-molecule measurements at high temporal precision as well as increased precision in manipulations directly on the genome are allowing us to tackle this question anew. These new experimental advances mean that also from the theoretical side, theoretical advances should be possible. In this review, I will describe, specifically on the example of fly embryo gene regulation, how theoretical approaches, especially from inference and information theory, can help in understanding gene regulation. To do so, I will first review some more traditional theoretical models for gene regulation, followed by a brief discussion of information-theoretical approaches and when they can be applied. I will then introduce early fly development as an exemplary system where such information-theoretical approaches have traditionally been applied and can be applied; I will specifically focus on how one such method, namely the information bottleneck approach, has recently been used to infer structural features of enhancer architecture.@en

In the regulation of gene expression, information of relevance to the organism is represented by the concentrations of transcription factor molecules. To extract this information the cell must effectively “measure” these concentrations, but there are physical limits to the precision of these measurements. We use the gap gene network in the early fly embryo as an example of the tradeoff between the precision of concentration measurements and the transmission of relevant information. For thresholded measurements we find that lower thresholds are more important, and fine tuning is not required for near-optimal information transmission. We then consider general sensors, constrained only by a limit on their information capacity, and find that thresholded sensors can approach true information theoretic optima. The information theoretic approach allows us to identify the optimal sensor for the entire gap gene network and to argue that the physical limitations of sensing necessitate the observed multiplicity of enhancer elements, with sensitivities to combinations rather than single transcription factors.

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Organisms that exploit different environments may experience a stochastic delay in adjusting their fitness when they switch habitats. We study two such organisms whose fitness is determined by the species composition of the local environment, as they interact through a public good. We show that a delay in the fitness adjustment can lead to the coexistence of the two species in a metapopulation, although the faster-growing species always wins in well-mixed competition experiments. Coexistence is favored over wide parameter ranges and is independent of spatial clustering. It arises when species are heterogeneous in their fitness and can keep each other balanced.@en

How does delayed fitnesses adaptation after local habitat changes affect survival of species metapopulation? We study this question in a two-species model system, where the species composition of a local patch determines the reference fitness of all its individuals. When individuals move, this local species composition changes. As the local environment on the patch might adapt slowly to this change, we assume that individuals in turn adapt their fitness with a stochastic delay. We show that the combination of delay and spatial substructure can yield significantly different phase diagrams for the survival of these species with respect to models with immediate response. We investigate this exemplarily for the case where the two species interact via an exoproduct: thus, our population consists of a slow-growing producer species and a fast-growing dominant species. We provide a conceptual understanding of the role of delay by presenting analytic results in the well-mixed and low-mobility limit. By studying intermediate mobilities numerically, we ensure that our results are robust, and may be relevant to different ecological situations as well as microbial metapopulation experiments.@en

Multiple scales in metapopulations can give rise to paradoxical behavior: in a conceptual model for a public goods game, the species associated with a fitness cost due to the public good production can be stabilized in the well-mixed limit due to the mere existence of these scales. The scales in this model involve a length scale corresponding to separate patches, coupled by mobility, and separate time scales for reproduction and interaction with a local environment. Contrary to the well-mixed high mobility limit, we find that for low mobilities, the interaction rate progressively stabilizes this species due to stochastic effects, and that the formation of spatial patterns is not crucial for this stabilization.

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A deterministic population dynamics model involving birth and death for a two-species system, comprising a wild-type and more resistant species competing via logistic growth, is subjected to two distinct stress environments designed to mimic those that would typically be induced by temporal variation in the concentration of a drug (antibiotic or chemotherapeutic) as it permeates through the population and is progressively degraded. Different treatment regimes, involving single or periodical doses, are evaluated in terms of the minimal population size (a measure of the extinction probability), and the population composition (a measure of the selection pressure for resistance or tolerance during the treatment). We show that there exist timescales over which the low-stress regime is as effective as the high-stress regime, due to the competition between the two species. For multiple periodic treatments, competition can ensure that the minimal population size is attained during the first pulse when the high-stress regime is short, which implies that a single short pulse can be more effective than a more protracted regime. Our results suggest that when the duration of the high-stress environment is restricted, a treatment with one or multiple shorter pulses can produce better outcomes than a single long treatment. If ecological competition is to be exploited for treatments, it is crucial to determine these timescales, and estimate for the minimal population threshold that suffices for extinction. These parameters can be quantified by experiment.@en

We determine the thermodynamic properties and the spectral function for a homogeneous two-dimensional Fermi gas in the normal state using the Luttinger-Ward, or self-consistent T-matrix, approach. The density equation of state deviates strongly from that of the ideal Fermi gas even for moderate interactions, and our calculations suggest that temperature has a pronounced effect on the pressure in the crossover from weak to strong coupling, consistent with recent experiments. We also compute the superfluid transition temperature for a finite system in the crossover region. There is a pronounced pseudogap regime above the transition temperature: the spectral function shows a Bogoliubov-like dispersion with backbending, and the density of states is significantly suppressed near the chemical potential. The contact density at low temperatures increases with interaction and compares well with both experiment and zero-temperature Monte Carlo results.@en