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.
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.
•We have generated a framework for a simple discrete invasion model, which can be solved analytically providing a complete solution.•In large domain cases, such a complete solution is impractical and we provide stochastic simulations (code provided for free on Github) demonstrating how the invasion rate can be extracted from ensemble statistics.•Stochastic invasions are fundamentally different from their deterministic analogues. Specifically, stochastic population can invade faster and their invasion rate depends on the size of domain they are invading.•We have been able to extract a healthy precancerous cell elimination rate. This can be potentially used to predict if patients have impaired pancreatic functions and are, thus, at a higher risk of pancreatic cancer.
Conventional (100 ms) pan-retinal photocoagulation (PRP) laser burns are larger than short-pulse (10 ms to 20 ms) PRP burns. This study investigates the effect of PRP burns of different sizes on ...retinal oxygenation.
A mathematical model using COMSOL Multiphysics 6 was used to create a three-dimensional abstraction of the coupled biology of the choroid, photoreceptor, and retinal tissues. Laser burn sizes were varied in the model, specifically considering burn diameters of 500 μm, 250 μm, and 125 μm, while keeping the total burn area constant.
Total increase in retinal oxygenation was the same for different burn sizes, but the oxygen distribution differed. Smaller burns resulted in a more even lateral oxygen distribution but with reduced penetration into the inner retina.
Conventional and short-pulse PRP may affect retinal oxygenation differently, even when total burn area is the same. Further investigation into optimum burn size and pattern is required.
.
In this paper, we consider the zero-flux chemotaxis system
in a smooth and bounded domain Ω of
. The chemotactic sensitivity χ is a general nonnegative function from
while g, the production of the ...chemical signal v, belongs to
and satisfies
, for all
,
and
It is established that no chemotactic collapse for the cell distribution u occurs in the sense that any arbitrary nonnegative and sufficiently regular initial data
emanates a unique pair of global and uniformly bounded functions
which classically solve the corresponding initial boundary value problem. Finally, we illustrate the range of dynamics present within the chemotaxis system by means of numerical simulations.
The characteristics of night-time environments (NTEs) in which alcohol is consumed and that contribute to violence are poorly described. We explore competing explanations for violence in the NTE, ...with a particular focus on the number of patrons and its association with assault-related visits to a hospital emergency department. Other environmental features including the weather and notable events were also considered. The primary aim was to stimulate debate around the causal mechanisms responsible for violence.
Assault-related ED visits occurring between 8 pm and 4 am were recorded at the University Hospital of Wales, the single Emergency Department (ED) serving Cardiff, Wales, United Kingdom. Footfall was derived from the total number of unique MAC addresses recorded per hour collected from ten wireless fidelity monitoring tools located in the city centre. A narrative review of the literature concerning alcohol and violence informed exploratory analyses into the association between night-time footfall, sporting events, the weather, and other potential predictors of assault-related visits to the ED. We developed analytic methods from formal accounts of queueing.
International rugby matches at home, the weather (temperature), national holidays, the day of the week, and number of patrons in the NTE predicted assault-related injury (R
= 0.70), with footfall yielding a positive non-linear exponential association consistent with predictions derived from mathematical models of queueing.
Assault-related visits to the ED have a non-linear association with the number of people socialising in the night-time environment and are further influenced by the weather and notable events. Opportunities for further research that might inform policy and interventions aimed at better managing NTEs are discussed.
As we age, our tissues are repeatedly challenged by mutational insult, yet cancer occurrence is a relatively rare event. Cells carrying cancer-causing genetic mutations compete with normal neighbors ...for space and survival in tissues. However, the mechanisms underlying mutant-normal competition in adult tissues and the relevance of this process to cancer remain incompletely understood. Here, we investigate how the adult pancreas maintains tissue health in vivo following sporadic expression of oncogenic Kras (KrasG12D), the key driver mutation in human pancreatic cancer. We find that when present in tissues in low numbers, KrasG12D mutant cells are outcompeted and cleared from exocrine and endocrine compartments in vivo. Using quantitative 3D tissue imaging, we show that before being cleared, KrasG12D cells lose cell volume, pack into round clusters, and E-cadherin-based cell-cell adhesions decrease at boundaries with normal neighbors. We identify EphA2 receptor as an essential signal in the clearance of KrasG12D cells from exocrine and endocrine tissues in vivo. In the absence of functional EphA2, KrasG12D cells do not alter cell volume or shape, E-cadherin-based cell-cell adhesions increase and KrasG12D cells are retained in tissues. The retention of KRasG12D cells leads to the early appearance of premalignant pancreatic intraepithelial neoplasia (PanINs) in tissues. Our data show that adult pancreas tissues remodel to clear KrasG12D cells and maintain tissue health. This study provides evidence to support a conserved functional role of EphA2 in Ras-driven cell competition in epithelial tissues and suggests that EphA2 is a novel tumor suppressor in pancreatic cancer.
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•Competition with normal cells clears KRASG12D cells from adult pancreas•KRASG12D cells are eliminated from acinar, ductal, and endocrine compartments•Functional EPHA2 is essential to clear mutant cells and preserve tissue health•Retention of KRASG12D cells accelerates appearance of premalignant lesions
Hill et al. show that KrasG12D-expressing cells are outcompeted from adult pancreas tissues by normal neighbors in vivo. Epithelial compartments remodel to eliminate KrasG12D cells in an EphA2-dependent manner. In the absence of EphA2, KrasG12D cells are retained in tissues, increasing the early appearance of premalignant lesions.
In this paper, we study the zero‐flux chemotaxis‐system
ut=∇·((u+1)m−1∇u−u(u+1)α−1χ(v)∇v)+ku−μu2x∈Ω,t>0,0=Δv−v+ux∈Ω,t>0,
where Ω is a bounded and smooth domain of
Rn, n≥1, and where
m∈R, k,μ>0 and ...α≤1. For any v≥0, the chemotactic sensitivity function is assumed to behave as the prototype χ(v)=χ0/(1+av)2, with a≥0 and χ0>0. We prove that for any nonnegative and sufficiently regular initial data u(x,0), the corresponding initial‐boundary value problem admits a unique global bounded classical solution if α<1; indeed, for α=1, the same conclusion is obtained provided μ is large enough. Finally, we illustrate the range of dynamics present within the chemotaxis system in 1, 2, and 3 dimensions by means of numerical simulations.
This study examines whether, and how, multiple risks in early childhood are associated with an increased likelihood of a poor language or literacy outcome in early adolescence. Using data from 210 ...participants in the longitudinal Twins Early Developmental Study, we focus on the following risk factors at age 4: family risk, and poor language, speech, emergent literacy and nonverbal skills. The outcomes of interest at age 12 are language, reading fluency and reading comprehension. We contrast a ‘cumulative risk’ model, counting the presence or absence of each risk factor (breadth), with a model that also considers the severity of the early deficits (depth). A ‘cumulative risk index’ correlated modestly but significantly with outcome (r = 0.32–0.40). Odds ratios confirmed that having many risk factors (3–6) confers a higher probability of a poor outcome (OR 7.86–17.71) than having one or two (OR 3.65–7.28). Logistic regression models showed that predictive validity is not improved by including information about the severity of each deficit. Even with rich information on children's risk status at age 4, we can make only a moderately accurate prediction of the likelihood of a language or literacy disorder 8 years later (Area Under the Curve = 0.74–0.84; Positive Predictive Value = 0.33–0.55, Negative Predictive Value = 0.86–0.91). Taken together, and consistent with the idea of ‘cumulative risk’, these results suggest that the breadth of risk is a core predictor of outcome, and furthermore, that the severity of early deficits does not add significantly to this prediction.
The greater the number of risk factors in early childhood, the greater the likelihood of a poor language or literacy outcome in early adolescence. However, the severity of early deficits may not in itself be very informative: depth (severity) adds little to prediction beyond breadth (number of risk factors).
Bespoke Turing Systems Woolley, Thomas E.; Krause, Andrew L.; Gaffney, Eamonn A.
Bulletin of mathematical biology,
03/2021, Letnik:
83, Številka:
5
Journal Article
Recenzirano
Odprti dostop
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.
Pattern formation from homogeneity is well studied, but less is known concerning symmetry-breaking instabilities in heterogeneous media. It is non-trivial to separate observed spatial patterning due ...to inherent spatial heterogeneity from emergent patterning due to nonlinear instability. We employ WKBJ asymptotics to investigate Turing instabilities for a spatially heterogeneous reaction-diffusion system, and derive conditions for instability which are local versions of the classical Turing conditions. We find that the structure of unstable modes differs substantially from the typical trigonometric functions seen in the spatially homogeneous setting. Modes of different growth rates are localized to different spatial regions. This localization helps explain common amplitude modulations observed in simulations of Turing systems in heterogeneous settings. We numerically demonstrate this theory, giving an illustrative example of the emergent instabilities and the striking complexity arising from spatially heterogeneous reaction-diffusion systems. Our results give insight both into systems driven by exogenous heterogeneity, as well as successive pattern forming processes, noting that most scenarios in biology do not involve symmetry breaking from homogeneity, but instead consist of sequential evolutions of heterogeneous states. The instability mechanism reported here precisely captures such evolution, and extends Turing's original thesis to a far wider and more realistic class of systems.
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