The developmental basis of fingerprint pattern formation and variation.

Fingerprints are complex and individually unique patterns in the skin. Established prenatally, the molecular and cellular mechanisms that guide fingerprint ridge formation and their intricate arrangements are unknown. Here we show that fingerprint ridges are epithelial structures that undergo a truncated hair follicle developmental program and fail to recruit a mesenchymal condensate. Their spatial pattern is established by a Turing reaction-diffusion system, based on signaling between EDAR, WNT, and antagonistic BMP pathways. These signals resolve epithelial growth into bands of focalized proliferation under a precociously differentiated suprabasal layer. Ridge formation occurs as a set of waves spreading from variable initiation sites defined by the local signaling environments and anatomical intricacies of the digit, with the propagation and meeting of these waves determining the type of pattern that forms. Relying on a dynamic patterning system triggered at spatially distinct sites generates the characteristic types and unending variation of human fingerprint patterns.

Gap junctions in Turing-type periodic feather pattern formation.

Periodic patterning requires coordinated cell-cell interactions at the tissue level. Turing showed, using mathematical modeling, how spatial patterns could arise from the reactions of a diffusive activator-inhibitor pair in an initially homogeneous 2D field. Most activators and inhibitors studied in biological systems are proteins, and the roles of cell-cell interaction, ions, bioelectricity, etc. are only now being identified. Gap junctions (GJs) mediate direct exchanges of ions or small molecules between cells, enabling rapid long-distance communications in a cell collective. They are therefore good candidates for propagating nonprotein-based patterning signals that may act according to the Turing principles. Here, we explore the possible roles of GJs in Turing-type patterning using feather pattern formation as a model. We found 7 of the 12 investigated GJ isoforms are highly dynamically expressed in the developing chicken skin. In ovo functional perturbations of the GJ isoform, connexin 30, by siRNA and the dominant-negative mutant applied before placode development led to disrupted primary feather bud formation. Interestingly, inhibition of gap junctional intercellular communication (GJIC) in the ex vivo skin explant culture allowed the sequential emergence of new feather buds at specific spatial locations relative to the existing primary buds. The results suggest that GJIC may facilitate the propagation of long-distance inhibitory signals. Thus, inhibition of GJs may stimulate Turing-type periodic feather pattern formation during chick skin development, and the removal of GJ activity would enable the emergence of new feather buds if the local environment were competent and the threshold to form buds was reached. We further propose Turing-based computational simulations that can predict the sequential appearance of these ectopic buds. Our models demonstrate how a Turing activator-inhibitor system can continue to generate patterns in the competent morphogenetic field when the level of intercellular communication at the tissue scale is modulated.

Bat Motion can be Described by Leap Frogging.

We present models of bat motion derived from radio-tracking data collected over 14 nights. The data presents an initial dispersal period and a return to roost period. Although a simple diffusion model fits the initial dispersal motion we show that simple convection cannot provide a description of the bats returning to their roost. By extending our model to include non-autonomous parameters, or a leap frogging form of motion, where bats on the exterior move back first, we find we are able to accurately capture the bat's motion. We discuss ways of distinguishing between the two movement descriptions and, finally, consider how the different motion descriptions would impact a bat's hunting strategy.

The embryonic trunk neural crest microenvironment regulates the plasticity and invasion of human neuroblastoma via TrkB signaling.

Mistakes in trunk neural crest (NC) cell migration may lead to birth defects of the sympathetic nervous system (SNS) and neuroblastoma (NB) cancer. Receptor tyrosine kinase B (TrkB) and its ligand BDNF critically regulate NC cell migration during normal SNS development and elevated expression of TrkB is correlated with high-risk NB patients. However, in the absence of a model with in vivo interrogation of human NB cell and gene expression dynamics, the mechanistic role of TrkB in NB disease progression remains unclear. Here, we study the functional relationship between TrkB, cell invasion and plasticity of human NB cells by taking advantage of our validated in vivo chick embryo transplant model. We find that LAN5 (high TrkB) and SHSY5Y (moderate TrkB) human NB cells aggressively invade host embryos and populate typical NC targets, however loss of TrkB function significantly reduces cell invasion. In contrast, NB1643 (low TrkB) cells remain near the transplant site, but over-expression of TrkB leads to significant cell invasion. Invasive NB cells show enhanced expression of genes indicative of the most invasive host NC cells. In contrast, transplanted human NB cells down-regulate known NB tumor initiating and stem cell markers. Human NB cells that remain within the dorsal neural tube transplant also show enhanced expression of cell differentiation genes, resulting in an improved disease outcome as predicted by a computational algorithm. These in vivo data support TrkB as an important biomarker and target to control NB aggressiveness and identify the chick embryonic trunk neural crest microenvironment as a source of signals to drive NB to a less aggressive state, likely acting at the dorsal neural tube.

The association of neurodevelopmental abnormalities, congenital heart and renal defects in a tuberous sclerosis complex patient cohort.

BACKGROUND: Tuberous sclerosis complex (TSC) is a rare multi-system genetic disorder characterised by the presence of benign tumours throughout multiple organs including the brain, kidneys, heart, liver, eyes, lungs and skin, in addition to neurological and neuropsychiatric complications. Intracardiac tumour (rhabdomyoma), neurodevelopmental disorders (NDDs) and kidney disorders (KD) are common manifestations of TSC and have been linked with TSC1 and TSC2 loss-of-function mutations independently, but the dynamic relationship between these organ manifestations remains unexplored. Therefore, this study aims to characterise the nature of the relationship specifically between these three organs' manifestations in TSC1 and TSC2 mutation patients. METHODS: Clinical data gathered from TSC patients across South Wales registered with Cardiff and Vale University Health Board (CAV UHB) between 1990 and 2020 were analysed retrospectively to evaluate abnormalities in the heart, brain and kidney development. TSC-related abnormalities such as tumour prevalence, location and size were analysed for each organ in addition to neuropsychiatric involvement and were compared between TSC1 and TSC2 mutant genotypes. Lastly, statistical co-occurrence between organ manifestations co-morbidity was quantified, and trajectories of disease progression throughout organs were modelled. RESULTS: This study found a significantly greater mutational frequency at the TSC2 locus in the cohort in comparison to TSC1. An equal proportion of male and female patients were observed in this group and by meta-analysis of previous studies. No significant difference in characterisation of heart involvement was observed between TSC1 and TSC2 patients. Brain involvement was seen with increased severity in TSC2 patients, characterised by a greater prevalence of cortical tubers and communication disorders. Renal pathology was further enhanced in TSC2 patients, marked by increased bilateral angiomyolipoma prevalence. Furthermore, co-occurrence of NDDs and KDs was the most positively correlated out of investigated manifestations, regardless of genotype. Analysis of disease trajectories revealed a more diverse clinical outcome for TSC2 patients: however, a chronological association of rhabdomyoma, NDD and KD was most frequently observed for TSC1 patients. CONCLUSIONS: This study marks the first empirical investigation of the co-morbidity between congenital heart defects (CHD), NDDs, and KDs in TSC1 and TSC2 patients. This remains a unique first step towards the characterisation of the dynamic role between genetics, heart function, brain function and kidney function during the early development in the context of TSC.

Feather arrays are patterned by interacting signalling and cell density waves.

Feathers are arranged in a precise pattern in avian skin. They first arise during development in a row along the dorsal midline, with rows of new feather buds added sequentially in a spreading wave. We show that the patterning of feathers relies on coupled fibroblast growth factor (FGF) and bone morphogenetic protein (BMP) signalling together with mesenchymal cell movement, acting in a coordinated reaction-diffusion-taxis system. This periodic patterning system is partly mechanochemical, with mechanical-chemical integration occurring through a positive feedback loop centred on FGF20, which induces cell aggregation, mechanically compressing the epidermis to rapidly intensify FGF20 expression. The travelling wave of feather formation is imposed by expanding expression of Ectodysplasin A (EDA), which initiates the expression of FGF20. The EDA wave spreads across a mesenchymal cell density gradient, triggering pattern formation by lowering the threshold of mesenchymal cells required to begin to form a feather bud. These waves, and the precise arrangement of feather primordia, are lost in the flightless emu and ostrich, though via different developmental routes. The ostrich retains the tract arrangement characteristic of birds in general but lays down feather primordia without a wave, akin to the process of hair follicle formation in mammalian embryos. The embryonic emu skin lacks sufficient cells to enact feather formation, causing failure of tract formation, and instead the entire skin gains feather primordia through a later process. This work shows that a reaction-diffusion-taxis system, integrated with mechanical processes, generates the feather array. In flighted birds, the key role of the EDA/Ectodysplasin A receptor (EDAR) pathway in vertebrate skin patterning has been recast to activate this process in a quasi-1-dimensional manner, imposing highly ordered pattern formation.

Accounting for dimensional differences in stochastic domain invasion with applications to precancerous cell removal.

We consider a specific form of domain invasion that is an abstraction of pancreatic tissue eliminating precancerous mutant cells through juxtacrine signalling. The model is explored discretely, continuously, stochastically and deterministically, highlighting unforeseen nonlinear dependencies on the dimension of the solution domain. Specifically, stochastically simulated populations invade with a dimension dependent wave speed that can be over twice as fast as their deterministic analogues. Although the wave speed can be analytically derived in the cases of small domains, the probabilistic state space grows exponentially and, thus, we use numeric simulation and curve fitting to predict limiting dynamics.

Boundary Conditions Cause Different Generic Bifurcation Structures in Turing Systems.

Turing's theory of morphogenesis is a generic mechanism to produce spatial patterning from near homogeneity. Although widely studied, we are still able to generate new results by returning to common dogmas. One such widely reported belief is that the Turing bifurcation occurs through a pitchfork bifurcation, which is true under zero-flux boundary conditions. However, under fixed boundary conditions, the Turing bifurcation becomes generically transcritical. We derive these algebraic results through weakly nonlinear analysis and apply them to the Schnakenberg kinetics. We observe that the combination of kinetics and boundary conditions produce their own uncommon boundary complexities that we explore numerically. Overall, this work demonstrates that it is not enough to only consider parameter perturbations in a sensitivity analysis of a specific application. Variations in boundary conditions should also be considered.

Bespoke Turing Systems.

Reaction-diffusion systems are an intensively studied form of partial differential equation, frequently used to produce spatially heterogeneous patterned states from homogeneous symmetry breaking via the Turing instability. Although there are many prototypical "Turing systems" available, determining their parameters, functional forms, and general appropriateness for a given application is often difficult. Here, we consider the reverse problem. Namely, suppose we know the parameter region associated with the reaction kinetics in which patterning is required-we present a constructive framework for identifying systems that will exhibit the Turing instability within this region, whilst in addition often allowing selection of desired patterning features, such as spots, or stripes. In particular, we show how to build a system of two populations governed by polynomial morphogen kinetics such that the: patterning parameter domain (in any spatial dimension), morphogen phases (in any spatial dimension), and even type of resulting pattern (in up to two spatial dimensions) can all be determined. Finally, by employing spatial and temporal heterogeneity, we demonstrate that mixed mode patterns (spots, stripes, and complex prepatterns) are also possible, allowing one to build arbitrarily complicated patterning landscapes. Such a framework can be employed pedagogically, or in a variety of contemporary applications in designing synthetic chemical and biological patterning systems. We also discuss the implications that this freedom of design has on using reaction-diffusion systems in biological modelling and suggest that stronger constraints are needed when linking theory and experiment, as many simple patterns can be easily generated given freedom to choose reaction kinetics.

Vitrifying multiple embryos in different arrangements does not alter the cooling rate.

Vitrification is the most common method of cryopreservation of gametes in fertility clinics due to its improved survival rates compared to slow freezing techniques. For the Open Cryotop® vitrification device, the number of oocytes, or embryos, mounted onto a single device can vary. In this work, a mathematical model is developed for the cooling of oocytes and embryos (samples). The model is solved computationally, to investigate whether varying the number of samples mounted onto the Open Cryotop® affects the cooling rates, and consequently the survival rates, of vitrified samples. Several realistic spatial arrangements of samples are examined, determining their temperature over time. In this way we quantify the effect of spatial arrangement on the cooling rate. Our results indicate that neither the spatial arrangement nor the number of mounted samples has a large effect on cooling rates, so long as the volume of the cryoprotectant remains minimal. The time taken for cooling is found to be on the order of half a second, or less, regardless of the spatial arrangement or number of mounted samples. Hence, rapid cooling can be achieved for any number or arrangement of samples, as long as device manufacturer guidelines are adhered to.

Coloured Noise from Stochastic Inflows in Reaction-Diffusion Systems.

In this paper, we present a framework for investigating coloured noise in reaction-diffusion systems. We start by considering a deterministic reaction-diffusion equation and show how external forcing can cause temporally correlated or coloured noise. Here, the main source of external noise is considered to be fluctuations in the parameter values representing the inflow of particles to the system. First, we determine which reaction systems, driven by extrinsic noise, can admit only one steady state, so that effects, such as stochastic switching, are precluded from our analysis. To analyse the steady-state behaviour of reaction systems, even if the parameter values are changing, necessitates a parameter-free approach, which has been central to algebraic analysis in chemical reaction network theory. To identify suitable models, we use tools from real algebraic geometry that link the network structure to its dynamical properties. We then make a connection to internal noise models and show how power spectral methods can be used to predict stochastically driven patterns in systems with coloured noise. In simple cases, we show that the power spectrum of the coloured noise process and the power spectrum of the reaction-diffusion system modelled with white noise multiply to give the power spectrum of the coloured noise reaction-diffusion system.

Turing Patterning in Stratified Domains.

Reaction-diffusion processes across layered media arise in several scientific domains such as pattern-forming E. coli on agar substrates, epidermal-mesenchymal coupling in development, and symmetry-breaking in cell polarization. We develop a modeling framework for bilayer reaction-diffusion systems and relate it to a range of existing models. We derive conditions for diffusion-driven instability of a spatially homogeneous equilibrium analogous to the classical conditions for a Turing instability in the simplest nontrivial setting where one domain has a standard reaction-diffusion system, and the other permits only diffusion. Due to the transverse coupling between these two regions, standard techniques for computing eigenfunctions of the Laplacian cannot be applied, and so we propose an alternative method to compute the dispersion relation directly. We compare instability conditions with full numerical simulations to demonstrate impacts of the geometry and coupling parameters on patterning, and explore various experimentally relevant asymptotic regimes. In the regime where the first domain is suitably thin, we recover a simple modulation of the standard Turing conditions, and find that often the broad impact of the diffusion-only domain is to reduce the ability of the system to form patterns. We also demonstrate complex impacts of this coupling on pattern formation. For instance, we exhibit non-monotonicity of pattern-forming instabilities with respect to geometric and coupling parameters, and highlight an instability from a nontrivial interaction between kinetics in one domain and diffusion in the other. These results are valuable for informing design choices in applications such as synthetic engineering of Turing patterns, but also for understanding the role of stratified media in modulating pattern-forming processes in developmental biology and beyond.

A mathematical insight into cell labelling experiments for clonal analysis.

Studying the progression of the proliferative and differentiative patterns of neural stem cells at the individual cell level is crucial to the understanding of cortex development and how the disruption of such patterns can lead to malformations and neurodevelopmental diseases. However, our understanding of the precise lineage progression programme at single-cell resolution is still incomplete due to the technical variations in lineage-tracing approaches. One of the key challenges involves developing a robust theoretical framework in which we can integrate experimental observations and introduce correction factors to obtain a reliable and representative description of the temporal modulation of proliferation and differentiation. In order to obtain more conclusive insights, we carry out virtual clonal analysis using mathematical modelling and compare our results against experimental data. Using a dataset obtained with Mosaic Analysis with Double Markers, we illustrate how the theoretical description can be exploited to interpret and reconcile the disparity between virtual and experimental results.

Self-organizing hair peg-like structures from dissociated skin progenitor cells: New insights for human hair follicle organoid engineering and Turing patterning in an asymmetric morphogenetic field.

Human skin progenitor cells will form new hair follicles, although at a low efficiency, when injected into nude mouse skin. To better study and improve upon this regenerative process, we developed an in vitro system to analyse the morphogenetic cell behaviour in detail and modulate physical-chemical parameters to more effectively generate hair primordia. In this three-dimensional culture, dissociated human neonatal foreskin keratinocytes self-assembled into a planar epidermal layer while fetal scalp dermal cells coalesced into stripes, then large clusters, and finally small clusters resembling dermal condensations. At sites of dermal clustering, subjacent epidermal cells protruded to form hair peg-like structures, molecularly resembling hair pegs within the sequence of follicular development. The hair peg-like structures emerged in a coordinated, formative wave, moving from periphery to centre, suggesting that the droplet culture constitutes a microcosm with an asymmetric morphogenetic field. In vivo, hair follicle populations also form in a progressive wave, implying the summation of local periodic patterning events with an asymmetric global influence. To further understand this global patterning process, we developed a mathematical simulation using Turing activator-inhibitor principles in an asymmetric morphogenetic field. Together, our culture system provides a suitable platform to (a) analyse the self-assembly behaviour of hair progenitor cells into periodically arranged hair primordia and (b) identify parameters that impact the formation of hair primordia in an asymmetric morphogenetic field. This understanding will enhance our future ability to successfully engineer human hair follicle organoids.

Time to change your mind? Modelling transient properties of cortex formation highlights the importance of evolving cell division strategies.

The successful development of the mammalian cerebral neocortex is linked to numerous cognitive functions such as language, voluntary movement, and episodic memory. Neocortex development occurs when neural progenitor cells divide and produce neurons. Critically, although the progenitor cells are able to self-renew they do not reproduce themselves endlessly. Hence, to fully understand the development of the neocortex we are faced with the challenge of understanding temporal changes in cell division strategy. Our approach to modelling neuronal production uses non-autonomous ordinary differential equations and allows us to use a ternary coordinate system in order to define a strategy space, through which we can visualise evolving cell division strategies. Using this strategy space, we fit the known data and use approximate Bayesian computation to predict the founding progenitor population sizes, currently unavailable in the experimental literature. Counter-intuitively, we show that humans can generate a larger number of neurons than a macaque's even when starting with a smaller number of progenitor cells. Accompanying the article is a self-contained piece of software, which provides the reader with immediate simulated results that will aid their intuition. The software can be found at www.dpag.ox.ac.uk/team/noemi-picco.

Likely equilibria of the stochastic Rivlin cube.

The problem of the Rivlin cube is to determine the stability of all homogeneous equilibria of an isotropic incompressible hyperelastic body under equitriaxial dead loads. Here, we consider the stochastic version of this problem where the elastic parameters are random variables following standard probability laws. Uncertainties in these parameters may arise, for example, from inherent data variation between different batches of homogeneous samples, or from different experimental tests. As for the deterministic elastic problem, we consider the following questions: what are the likely equilibria and how does their stability depend on the material constitutive law? In addition, for the stochastic model, the problem is to derive the probability distribution of deformations, given the variability of the parameters. This article is part of the theme issue 'Rivlin's legacy in continuum mechanics and applied mathematics'.

Mathematical Modeling of Cortical Neurogenesis Reveals that the Founder Population does not Necessarily Scale with Neurogenic Output.

The mammalian cerebral neocortex has a unique structure, composed of layers of different neuron types, interconnected in a stereotyped fashion. While the overall developmental program seems to be conserved, there are divergent developmental factors generating cortical diversity amongst species. In terms of cortical neuronal numbers, some of the determining factors are the size of the founder population, the duration of cortical neurogenesis, the proportion of different progenitor types, and the fine-tuned balance between self-renewing and differentiative divisions. We develop a mathematical model of neurogenesis that, accounting for these factors, aims at explaining the high diversity in neuronal numbers found across species. By framing our hypotheses in rigorous mathematical terms, we are able to identify paths of neurogenesis that match experimentally observed patterns in mouse, macaque and human. Additionally, we use our model to identify key parameters that would particularly benefit from accurate experimental investigation. We find that the timing of a switch in favor of symmetric neurogenic divisions produces the highest variation in cortical neuronal numbers. Surprisingly, assuming similar cell cycle lengths in primate progenitors, the increase in cortical neuronal numbers does not reflect a larger size of founder population, a prediction that has identified a specific need for experimental quantifications.

Prehospital tranexamic acid shortens the interval to administration by half in Major Trauma Networks: a service evaluation.

INTRODUCTION: Tranexamic acid (TXA) reduces bleeding and mortality. Recent trials have demonstrated improved survival with shorter intervals to TXA administration. The aims of this service evaluation were to assess the interval from injury to TXA administration and describe the characteristics of patients who received TXA pre-hospital and in-hospital. METHODS: We reviewed Trauma and Audit Research Network records and local trauma registries to identify patients of any age that received TXA at all London Major Trauma Centres and Queen's Medical Centre, Nottingham, during 2017. We used the 2016 NICE Guidelines (NG39) which state that TXA should be given within 3 hours of injury. RESULTS: We identified 1018 patients who received TXA, of whom 661 (65%) had sufficient data to assess the time from injury to TXA administration. The median interval was 74 min (IQR: 47-116). 92% of patients received TXA within 3 hours from injury, and 59% within 1 hour. Half of the patients (54%) received prehospital TXA. The median time to TXA administration when given prehospital was 51 min (IQR: 39-72), and 112 min (IQR: 84-160) if given in-hospital (p<0.001). In-hospital TXA patients had less haemodynamic derangement and lower base deficit on admission compared with patients given prehospital TXA. CONCLUSION: Prehospital administration of TXA is associated with a shorter interval from injury to drug delivery. Identifying a proportion of patients at risk of haemorrhage remains a challenge. However, further reinforcement is needed to empower pre-hospital clinicians to administer TXA to trauma patients without overt signs of shock.

Global contraction or local growth, bleb shape depends on more than just cell structure.

When the plasma membrane of a cell locally delaminates from its actin cortex the membrane is pushed outwards due to the cell׳s internal fluid pressure. The resulting spherical protrusion is known as a bleb. A cell׳s ability to function correctly is highly dependent on the production of such protrusions with the correct size and shape. Here, we investigate the nucleation of large blebs from small, local neck regions. A mathematical model of a cell׳s membrane, cortex and interconnecting adhesions demonstrates that these three components are unable to capture experimentally observed bleb shapes without the addition of further assumptions. We have identified that combinations of global cortex contraction and localised membrane growth are the most promising methods for generating prototypical blebs. Currently, neither proposed mechanism has been fully tested experimentally and, thus, we propose experiments that will distinguish between the two methods of bleb production.