Novel generic models for differentiating stem cells reveal oscillatory mechanisms

Tipping in Stuart-Landau oscillators induced by higher-order repulsive interactions

Tipping phenomena in complex systems represent abrupt transitions in the system behavior due to incremental changes in parameters. Here, we report the emergence of an abrupt transition from an oscillatory to a death state in coupled limit cycle oscillators with higher-order repulsive interactions. This transition contrasts with the typical continuous transitions observed with pairwise repulsive links. It is notable that higher-order interactions introduce more complexity to the system dynamics, thereby leading to the transition to the death state at lower coupling strengths compared to pairwise coupled systems. Importantly, there exists a sudden revival of the oscillation from the death state with increasing the pairwise coupling strength despite the detrimental effect of pairwise couplings. The results are also robust for nonidentical systems. Furthermore, the analytical determination of the critical coupling strength for the tipping point aligns closely with the results obtained from numerical simulations.

Myron Gordon Award Lecture 2023: Painting the neural crest: How studying pigment cells illuminates neural crest cell biology

It has been 30 (!!) years since I began working on zebrafish pigment cells, as a postdoc in the laboratory of Prof. Christiane Nüsslein-Volhard. There, I participated in the first large-scale mutagenesis screen in zebrafish, focusing on pigment cell mutant phenotypes. The isolation of colourless, shady, parade and choker mutants allowed us (as a postdoc in Prof. Judith Eisen's laboratory, and then in my own laboratory at the University of Bath since 1997) to pursue my ambition to address long-standing problems in the neural crest field. Thus, we have studied how neural crest cells choose individual fates, resulting in our recent proposal of a new, and potentially unifying, model which we call Cyclical Fate Restriction, as well as addressing how pigment cell patterns are generated. A key feature of our work in the last 10 years has been the use of mathematical modelling approaches to clarify our biological models and to refine our interpretations. None of this would have been possible without a hugely talented group of laboratory members and other collaborators from around the world-it has been, and I am sure will continue to be, a pleasure and privilege to work with you all!

Biological computations: Limitations of attractor-based formalisms and the need for transients

Living systems, from single cells to higher vertebrates, receive a continuous stream of non-stationary inputs that they sense, for e.g. via cell surface receptors or sensory organs. By integrating these time-varying, multi-sensory, and often noisy information with memory using complex molecular or neuronal networks, they generate a variety of responses beyond simple stimulus-response association, including avoidance behavior, life-long-learning or social interactions. In a broad sense, these processes can be understood as a type of biological computation. Taking as a basis generic features of biological computations, such as real-time responsiveness or robustness and flexibility of the computation, we highlight the limitations of the current attractor-based framework for understanding computations in biological systems. We argue that frameworks based on transient dynamics away from attractors are better suited for the description of computations performed by neuronal and signaling networks. In particular, we discuss how quasi-stable transient dynamics from ghost states that emerge at criticality have a promising potential for developing an integrated framework of computations, that can help us understand how living system actively process information and learn from their continuously changing environment.

Ghost Channels and Ghost Cycles Guiding Long Transients in Dynamical Systems

Dynamical descriptions and modeling of natural systems have generally focused on fixed points, with saddles and saddle-based phase-space objects such as heteroclinic channels or cycles being central concepts behind the emergence of quasistable long transients. Reliable and robust transient dynamics observed for real, inherently noisy systems is, however, not met by saddle-based dynamics, as demonstrated here. Generalizing the notion of ghost states, we provide a complementary framework that does not rely on the precise knowledge or existence of (un)stable fixed points, but rather on slow directed flows organized by ghost sets in ghost channels and ghost cycles. Moreover, we show that the appearance of these novel objects is an emergent property of a broad class of models typically used for description of natural systems.

Oscillatory differentiation dynamics fundamentally restricts the resolution of pseudotime reconstruction algorithms

The challenge to understand differentiation and cell lineages in development has resulted in many bioinformatics software tools, notably those working with gene expression data obtained via single-cell RNA sequencing obtained at snapshots in time. Reconstruction methods for trajectories often proceed by dimension reduction, data clustering and then computation of a tree graph in which edges indicate closely related clusters. Cell lineages can then be deduced by following paths through the tree. In the case of multi-potent cells undergoing differentiation, this trajectory reconstruction involves the reconstruction of multiple distinct lineages corresponding to commitment to each of a set of distinct fates. Recent work suggests that there may be cases in which the cell differentiation process involves trajectories that explore, in a dynamic and oscillatory fashion, propensity to differentiate into a number of possible cell fates before commitment finally occurs. Here, we show theoretically that the presence of such oscillations provides intrinsic constraints on the quality and resolution of the trajectory reconstruction process, even for idealized noise-free data. These constraints point to inherent common limitations of current methodologies and serve both to provide additional challenge in the development of software tools and also may help to understand features observed in recent experiments.

Zebrafish pigment cells develop directly from persistent highly multipotent progenitors

Neural crest cells are highly multipotent stem cells, but it remains unclear how their fate restriction to specific fates occurs. The direct fate restriction model hypothesises that migrating cells maintain full multipotency, whilst progressive fate restriction envisages fully multipotent cells transitioning to partially-restricted intermediates before committing to individual fates. Using zebrafish pigment cell development as a model, we show applying NanoString hybridization single cell transcriptional profiling and RNAscope in situ hybridization that neural crest cells retain broad multipotency throughout migration and even in post-migratory cells in vivo, with no evidence for partially-restricted intermediates. We find that leukocyte tyrosine kinase early expression marks a multipotent stage, with signalling driving iridophore differentiation through repression of fate-specific transcription factors for other fates. We reconcile the direct and progressive fate restriction models by proposing that pigment cell development occurs directly, but dynamically, from a highly multipotent state, consistent with our recently-proposed Cyclical Fate Restriction model.

Cell Fate Decisions in the Neural Crest, from Pigment Cell to Neural Development

The neural crest shows an astonishing multipotency, generating multiple neural derivatives, but also pigment cells, skeletogenic and other cell types. The question of how this process is controlled has been the subject of an ongoing debate for more than 35 years. Based upon new observations of zebrafish pigment cell development, we have recently proposed a novel, dynamic model that we believe goes some way to resolving the controversy. Here, we will firstly summarize the traditional models and the conflicts between them, before outlining our novel model. We will also examine our recent dynamic modelling studies, looking at how these reveal behaviors compatible with the biology proposed. We will then outline some of the implications of our model, looking at how it might modify our views of the processes of fate specification, differentiation, and commitment.

Cyclical fate restriction: a new view of neural crest cell fate specification

Neural crest cells are crucial in development, not least because of their remarkable multipotency. Early findings stimulated two hypotheses for how fate specification and commitment from fully multipotent neural crest cells might occur, progressive fate restriction (PFR) and direct fate restriction, differing in whether partially restricted intermediates were involved. Initially hotly debated, they remain unreconciled, although PFR has become favoured. However, testing of a PFR hypothesis of zebrafish pigment cell development refutes this view. We propose a novel 'cyclical fate restriction' hypothesis, based upon a more dynamic view of transcriptional states, reconciling the experimental evidence underpinning the traditional hypotheses.