Statistical properties of Poisson-Voronoi tessellation cells in bounded regions

Gezer, Fatih; Aykroyd, Robert G.; Barber, Stuart

doi:10.1080/00949655.2020.1836184

Cited by 6 publications

(7 citation statements)

References 19 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…S2), which should depend only on the area and be independent of the perimeter. Thus, the λ P -independence of µ validates the phenomenological implementation [57,58] of this constraint. Second, these results can provide crucial insights regarding the model parameters.…”

Section: Comparison With Simulationssupporting

confidence: 64%

See 1 more Smart Citation

The origin of universal cell shape variability in a confluent epithelial monolayer

Sadhukhan

Nandi

2021

Preprint

View full text Add to dashboard Cite

Cell shape is fundamental in biology. The average cell shape can influence crucial biological functions, such as cell fate and division orientation. But cell-to-cell shape variability is often regarded as noise. In contrast, recent works reveal that shape variability in diverse epithelial monolayers follows a nearly universal distribution. However, the origin and implications of this universality are unclear. Here, assuming contractility and adhesion are crucial for cell shape, characterized via aspect ratio (AR), we develop a mean-field analytical theory for shape variability. We find that a single parameter, α, containing all the system-specific details, describes the probability distribution function (PDF) of AR; this leads to a universal relation between the standard deviation and the average of AR. The PDF for the scaled AR is not strictly but almost universal. The functional form is not related to jamming, contrary to common beliefs, but a consequence of a mathematical property. In addition, we obtain the scaled area distribution, described by the parameter µ. We show that α and µ together can distinguish the effects of changing physical conditions, such as maturation, on different system properties. The theory is verified in simulations of two distinct models of epithelial monolayers and agrees well with existing experiments. We demonstrate that in a confluent monolayer, average shape determines both the shape variability and dynamics. Our results imply the cell shape variability is inevitable, where a single parameter describes both statics and dynamics and provides a framework to analyze and compare diverse epithelial systems.

show abstract

Section: Comparison With Simulationssupporting

confidence: 64%

“…S2), Eq. ( 6), together with the constraint of confluency [57,58], give the distribution for the scaled area a = A/Ā, whereĀ is the average of area, A. It is a Gamma distribution, with a single parameter µ,…”

Section: Analytical Theory For the Shape Variabilitymentioning

confidence: 99%

The origin of universal cell shape variability in a confluent epithelial monolayer

Sadhukhan

Nandi

2021

Preprint

View full text Add to dashboard Cite

show abstract

“…Additionally, as detailed in ‘Distribution for area’, Equation 18 together with the constraint of confluency ( Weaire, 1986 ; Gezer et al, 2021 ), give the distribution for the scaled area

, where

is the average of area. It is a Gamma distribution, with a single parameter μ,

…”

Section: Resultsmentioning

confidence: 99%

On the origin of universal cell shape variability in confluent epithelial monolayers

Sadhukhan

Nandi

2022

eLife

View full text Add to dashboard Cite

Cell shape is fundamental in biology. The average cell shape can influence crucial biological functions, such as cell fate and division orientation. But cell-to-cell shape variability is often regarded as noise. In contrast, recent works reveal that shape variability in diverse epithelial monolayers follows a nearly universal distribution. However, the origin and implications of this universality remain unclear. Here, assuming contractility and adhesion are crucial for cell shape, characterized via aspect ratio (r), we develop a mean-field analytical theory for shape variability. We find that all the system-specific details combine into a single parameter α that governs the probability distribution function (PDF) of r; this leads to a universal relation between the standard deviation and the average of r. The PDF for the scaled r is not strictly but nearly universal. In addition, we obtain the scaled area distribution, described by the parameter μ, α and μ together can distinguish the effects of changing physical conditions, such as maturation, on different system properties. We have verified the theory via simulations of two distinct models of epithelial monolayers and with existing experiments on diverse systems. We demonstrate that in a confluent monolayer, average shape determines both the shape variability and dynamics. Our results imply that cell shape distribution is inevitable, where a single parameter describes both statics and dynamics and provides a framework to analyze and compare diverse epithelial systems. In contrast to existing theories, our work shows that the universal properties are consequences of a mathematical property and should be valid in general, even in the fluid regime.

show abstract

“…In particular Koufos and Dettmann (2019) considered PV cells located close to the boundaries of the quadrant R + and obtained that the gamma distribution, with location-dependent parameters, provides a reasonably good approximation to the distribution of cell area. Gezer et al (2021) compared the statistical properties of the area of PV cells in the infinite plane and of clipped cells in two bounded regions: the unit square and the convex hull of the points; they found that the generalized gamma distribution provides a good fit with parameters varying according to the location of the cell seed in the bounded region. It should be noted that, as the number of the points increases, the vast majority of cells are not affected by the imposition of boundaries; indeed Devroye et al (2017) have shown that the asymptotic distribution of the Voronoi cell area is independent of the location of the seed and of the intensity measure underlying the Poisson point process.…”

Section: Introductionmentioning

confidence: 99%

Temporal variations of the probability distribution of voronoi cells generated by earthquake epicenters

Rotondi

Varini

2022

Front. Earth Sci.

View full text Add to dashboard Cite

The area of the cells of Voronoi tessellations has been modelled through different probability distributions among which the most promising are the generalized gamma and tapered Pareto distributions. In particular the latter has been used to model times and distances between successive earthquakes besides area and perimeter of cells generated by earthquake epicenters. In the framework of nonextensive statistical mechanics applied in geophysics, variables like seismic moment, inter-event time or Euclidean distance between successive earthquakes or length of faults in a given region have been studied through the so-called q-exponential distributions obtained by maximizing the Tsallis entropy under suitable conditions. These distributions take also the name of generalized Pareto distributions in the context of the limit distributions of excesses. In this work we consider the spatial distribution of a set of earthquakes and its temporal variations by modelling the area of Voronoi cells generated by the epicenters through a generalized Pareto distribution. Following the Bayesian paradigm we analyze the recent seismicity of the central Italy and we compare the posterior marginal likelihood of the aforementioned distributions in shifting time windows. We point out that the best fitting distribution varies over time and the trend of all three distributions converges to that of the exponential distribution in the preparatory phase for the mainshock.

show abstract

Statistical properties of Poisson-Voronoi tessellation cells in bounded regions

Cited by 6 publications

References 19 publications

The origin of universal cell shape variability in a confluent epithelial monolayer

The origin of universal cell shape variability in a confluent epithelial monolayer

On the origin of universal cell shape variability in confluent epithelial monolayers

Temporal variations of the probability distribution of voronoi cells generated by earthquake epicenters

Contact Info

Product

Resources

About