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.

Minimal reaction schemes for pattern formation.

We link continuum models of reaction-diffusion systems that exhibit diffusion-driven instability to constraints on the particle-scale interactions underpinning this instability. While innumerable biological, chemical and physical patterns have been studied through the lens of Alan Turing's reaction-diffusion pattern-forming mechanism, the connections between models of pattern formation and the nature of the particle interactions generating them have been relatively understudied in comparison with the substantial efforts that have been focused on understanding proposed continuum systems. To derive the necessary reactant combinations for the most parsimonious reaction schemes, we analyse the emergent continuum models in terms of possible generating elementary reaction schemes. This analysis results in the complete list of such schemes containing the fewest reactions; these are the simplest possible hypothetical mass-action models for a pattern-forming system of two interacting species.

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.

System-level consequences of synergies and trade-offs between SDGs: quantitative analysis of interlinkage networks at country level.

The Sustainable Development Goals (SDGs) present a complex system of 17 goals and 169 individual targets whose interactions can be described in terms of co-benefits and trade-offs between policy actions. We analyse in detail target-by-target interlinkage networks established by the Institute for Global Environmental Strategies (IGES) SDG Interlinkages Tool. We discuss two quantitative measures of network structure; the leading eigenvector of the interlinkage networks ('eigencentrality') and a notion of hierarchy within the network motivated by the concept of trophic levels for species in food webs. We use three interlinkage matrices generated by IGES: the framework matrix which provides a generic network model of the interlinkages at the target level, and two country-specific matrices for Bangladesh and Indonesia that combine SDG indicator data with the generic framework matrix. Our results echo, and are confirmed by, similar work at the level of whole SDGs that has shown that SDGs 1-3 (ending poverty, and providing food security and healthcare) are much more likely to be achieved than the environmentally- related SDGs 13-15 concerned with climate action, life on land and life below water. Our results here provide a refinement in terms of specific targets within each of these SDGs. We find that not all targets within SDGs 1-3 are equally well-supported, and not all targets within SDGs 13-15 are equally at risk of not being achieved. Finally, we point to the recurring issue of data gaps that hinders our quantitative analysis, in particular for SDGs 5 (gender equality) and 13 (climate action) where the huge gaps in indicator data that mean the true nature of the interlinkages and importance of these two SDGs are not fully recognised. Supplementary Information: The online version contains supplementary material available at 10.1007/s11625-022-01109-y.

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.

Novel generic models for differentiating stem cells reveal oscillatory mechanisms.

Understanding cell fate selection remains a central challenge in developmental biology. We present a class of simple yet biologically motivated mathematical models for cell differentiation that generically generate oscillations and hence suggest alternatives to the standard framework based on Waddington's epigenetic landscape. The models allow us to suggest two generic dynamical scenarios that describe the differentiation process. In the first scenario, gradual variation of a single control parameter is responsible for both entering and exiting the oscillatory regime. In the second scenario, two control parameters vary: one responsible for entering, and the other for exiting the oscillatory regime. We analyse the standard repressilator and four variants of it and show the dynamical behaviours associated with each scenario. We present a thorough analysis of the associated bifurcations and argue that gene regulatory networks with these repressilator-like characteristics are promising candidates to describe cell fate selection through an oscillatory process.

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.

Forecasting resilience profiles of the run-up to regime shifts in nearly-one-dimensional systems.

The forecasting of sudden, irreversible shifts in natural systems is a challenge of great importance, whose realization could allow pre-emptive action to be taken to avoid or mitigate catastrophic transitions, or to help systems adapt to them. In recent years, there have been many advances in the development of such early warning signals. However, much of the current toolbox is based around the tracking of statistical trends and therefore does not aim to estimate the future time scale of transitions or resilience loss. Metric-based indicators are also difficult to implement when systems have inherent oscillations which can dominate the indicator statistics. To resolve these gaps in the toolbox, we use additional system properties to fit parsimonious models to dynamics in order to predict transitions. Here, we consider nearly-one-dimensional systems-higher dimensional systems whose dynamics can be accurately captured by one-dimensional discrete time maps. We show how the nearly one-dimensional dynamics can be used to produce model-based indicators for critical transitions which produce forecasts of the resilience and the time of transitions in the system. A particularly promising feature of this approach is that it allows us to construct early warning signals even for critical transitions of chaotic systems. We demonstrate this approach on two model systems: of phosphorous recycling in a shallow lake, and of an overcompensatory fish population.

Demographic noise slows down cycles of dominance.

We study the phenomenon of cyclic dominance in the paradigmatic Rock-Paper-Scissors model, as occurring in both stochastic individual-based models of finite populations and in the deterministic replicator equations. The mean-field replicator equations are valid in the limit of large populations and, in the presence of mutation and unbalanced payoffs, they exhibit an attracting limit cycle. The period of this cycle depends on the rate of mutation; specifically, the period grows logarithmically as the mutation rate tends to zero. We find that this behaviour is not reproduced in stochastic simulations with a fixed finite population size. Instead, demographic noise present in the individual-based model dramatically slows down the progress of the limit cycle, with the typical period growing as the reciprocal of the mutation rate. Here we develop a theory that explains these scaling regimes and delineates them in terms of population size and mutation rate. We identify a further intermediate regime in which we construct a stochastic differential equation model describing the transition between stochastically-dominated and mean-field behaviour.

Meandering instability of a viscous thread.

A viscous thread falling from a nozzle onto a surface exhibits the famous rope-coiling effect, in which the thread buckles to form loops. If the surface is replaced by a belt moving with speed U , the rotational symmetry of the buckling instability is broken and a wealth of interesting states are observed [see S. Chiu-Webster and J. R. Lister, J. Fluid Mech. 569, 89 (2006)]. We experimentally studied this "fluid-mechanical sewing machine" in a more precise apparatus. As U is reduced, the steady catenary thread bifurcates into a meandering state in which the thread displacements are only transverse to the motion of the belt. We measured the amplitude and frequency omega of the meandering close to the bifurcation. For smaller U , single-frequency meandering bifurcates to a two-frequency "figure-8" state, which contains a significant 2omega component and parallel as well as transverse displacements. This eventually reverts to single-frequency coiling at still smaller U . More complex, highly hysteretic states with additional frequencies are observed for larger nozzle heights. We propose to understand this zoology in terms of the generic amplitude equations appropriate for resonant interactions between two oscillatory modes with frequencies omega and 2omega . The form of the amplitude equations captures both the axisymmetry of the U=0 coiling state and the symmetry-breaking effects induced by the moving belt.