3,371 research outputs found
Quantifying spatial structure in experimental observations and agent-based simulations using pair-correlation functions
No full textWe define a pair-correlation function that can be used to characterize spatiotemporal patterning in experimental images and snapshots from discrete simulations. Unlike previous pair-correlation functions, the pair-correlation functions developed here depend on the location and size of objects. The pair-correlation function can be used to indicate complete spatial randomness, aggregation, or segregation over a range of length scales, and quantifies spatial structures such as the shape, size, and distribution of clusters. Comparing pair-correlation data for various experimental and simulation images illustrates their potential use as a summary statistic for calibrating discrete models of various physical processes.Benjamin J. Binder, Matthew J. Simpso
Spectral analysis of pair-correlation bandwidth: application to cell biology images
No full textPublished 11 February 2015Images from cell biology experiments often indicate the presence of cell clustering, which can provide insight into the mechanisms driving the collective cell behaviour. Pair-correlation functions provide quantitative information about the presence, or absence, of clustering in a spatial distribution of cells. This is because the pair-correlation function describes the ratio of the abundance of pairs of cells, separated by a particular distance, relative to a randomly distributed reference population. Pair-correlation functions are often presented as a kernel density estimate where the frequency of pairs of objects are grouped using a particular bandwidth (or bin width), Δ>0. The choice of bandwidth has a dramatic impact: choosing Δ too large produces a pair-correlation function that contains insufficient information, whereas choosing Δ too small produces a pair-correlation signal dominated by fluctuations. Presently, there is little guidance available regarding how to make an objective choice of Δ. We present a new technique to choose Δ by analysing the power spectrum of the discrete Fourier transform of the pair-correlation function. Using synthetic simulation data, we confirm that our approach allows us to objectively choose Δ such that the appropriately binned pair-correlation function captures known features in uniform and clustered synthetic images. We also apply our technique to images from two different cell biology assays. The first assay corresponds to an approximately uniform distribution of cells, while the second assay involves a time series of images of a cell population which forms aggregates over time. The appropriately binned pair-correlation function allows us to make quantitative inferences about the average aggregate size, as well as quantifying how the average aggregate size changes with time.Benjamin J. Binder and Matthew J. Simpso
Assessing the role of spatial correlations during collective cell spreading
No full textSpreading cell fronts are essential features of development, repair and disease processes. Many mathematical models used to describe the motion of cell fronts, such as Fisher's equation, invoke a mean-field assumption which implies that there is no spatial structure, such as cell clustering, present. Here, we examine the presence of spatial structure using a combination of in vitro circular barrier assays, discrete random walk simulations and pair correlation functions. In particular, we analyse discrete simulation data using pair correlation functions to show that spatial structure can form in a spreading population of cells either through sufficiently strong cell-to-cell adhesion or sufficiently rapid cell proliferation. We analyse images from a circular barrier assay describing the spreading of a population of MM127 melanoma cells using the same pair correlation functions. Our results indicate that the spreading melanoma cell populations remain very close to spatially uniform, suggesting that the strength of cell-to-cell adhesion and the rate of cell proliferation are both sufficiently small so as not to induce any spatial patterning in the spreading populations.Katrina K. Treloar, Matthew J. Simpson, Benjamin J. Binder, D. L. Sean McElwain, Ruth E. Bake
“Chieftain, Farewell”: Bishop Matthew Simpson’s Funeral Address to Abraham Lincoln
No full textThis article reflects back on the historic oration by Methodist Bishop Matthew Simpson at the funeral of Abraham Lincoln in Springfield, Illinois in 1865. Matthew Simpson was one of the most prominent orators of his day and had built up political connections during the Lincoln Presidency. Bishop Simpson in many ways represents the rising respectability of Methodism in the United States as its influence grew and Methodism became more acceptable among society and in political circles. Simpson even represents a form of Christian nationalism which emerges from his funeral address and the way he portrays the “martyred” president
Modeling proliferative tissue growth: a general approach and an avian case study
No full textDuring development, tissues often undergo rapid physical expansion due to cell proliferation. Continuous and discrete models of one- and two-dimensional tissue growth are developed and applied to observational data of the developing avian gut, where the gut tissue cells undergo dramatic proliferation. The discrete cellular automata model provides results at the level of individual cells that reflect a realistic stochasticity and nonuniformity expected in cellular systems. Averaging the discrete results predicts population-level properties of the system, which match those of the continuous model. This dual approach provides an understanding of the interaction between the individual-level and population-level aspects of a developmental growth process. Both models are applied to a case study involving the developing intestinal tract of a quail embryo. A nonuniform growth model accurately predicts the positions of measurable biological landmarks within the growing tissue. Furthermore, the discrete model provides a framework for modeling the interactions between growing tissues and other biological mechanisms, such as cell motility and proliferation on an expanding tissue.Benjamin J. Binder, Kerry A. Landman, Matthew J. Simpson, Michael Mariani and Donald F. Newgree
Interpreting scratch assays using pair density dynamics and approximate Bayesian computation
No full textQuantifying the impact of biochemical compounds on collective cell spreading is an essential element of drug design, with various applications including developing treatments for chronic wounds and cancer. Scratch assays are a technically simple and inexpensive method used to study collective cell spreading; however, most previous interpretations of scratch assays are qualitative and do not provide estimates of the cell diffusivity, D, or the cell proliferation rate, λ. Estimating D and λ is important for investigating the efficacy of a potential treatment and provides insight into the mechanism through which the potential treatment acts. While a few methods for estimating D and λ have been proposed, these previous methods lead to point estimates of D and λ, and provide no insight into the uncertainty in these estimates. Here, we compare various types of information that can be extracted from images of a scratch assay, and quantify D and λ using discrete computational simulations and approximate Bayesian computation. We show that it is possible to robustly recover estimates of D and λ from synthetic data, as well as a new set of experimental data. For the first time, our approach also provides a method to estimate the uncertainty in our estimates of D and λ. We anticipate that our approach can be generalized to deal with more realistic experimental scenarios in which we are interested in estimating D and λ, as well as additional relevant parameters such as the strength of cell-to-cell adhesion or the strength of cell-to-substrate adhesion.Stuart T. Johnston, Matthew J. Simpson, D. L. Sean McElwain, Benjamin J. Binder, Joshua V. Ros
Quantifying the roles of cell motility and cell proliferation in a circular barrier assay
No full textMoving fronts of cells are essential features of embryonic development, wound repair and cancer metastasis. This paper describes a set of experiments to investigate the roles of random motility and proliferation in driving the spread of an initially confined cell population. The experiments include an analysis of cell spreading when proliferation was inhibited. Our data have been analysed using two mathematical models: a lattice-based discrete model and a related continuum partial differential equation model. We obtain independent estimates of the random motility parameter, D, and the intrinsic proliferation rate, λ, and we confirm that these estimates lead to accurate modelling predictions of the position of the leading edge of the moving front as well as the evolution of the cell density profiles. Previous work suggests that systems with a high λ/D ratio will be characterized by steep fronts, whereas systems with a low λ/D ratio will lead to shallow diffuse fronts and this is confirmed in the present study. Our results provide evidence that continuum models, based on the Fisher–Kolmogorov equation, are a reliable platform upon which we can interpret and predict such experimental observations.Matthew J. Simpson, Katrina K. Treloar, Benjamin J. Binder, Parvathi Haridas, Kerry J. Manton, David I. Leavesley, D. L. Sean McElwain and Ruth E. Bake
Presidential Election Tally Sheet, Carroll County, Indiana, 1860
No full textOn the tally sheet there are four sections, each with thirteen men's names across the top. Each section represents one of the four parties on the ballot. In order of appearance: Northern Democrat with 1,446 votes, Constitutional Union with 5 votes, Republican with 1,590 votes, and Southern Democrat with 14 votes. Voters cast their vote on the electors, who in turn would vote for their party. Lincoln and his running mate Hannibal Hamlin received 39% of the total vote, but were able to win 180 electoral votes from the more densely populated Northern, free states, and therefore won the election.The tally sheet is signed by Matthew Simpson, Clerk of the Carroll Circuit Court and by thirteen judges and inspectors from throughout the county: Francis Thomson, Jonathan Bonnard, Harrison Gwinn, C. Robinson, John Minkle, George Zinn, John Roop, Charles Oliver, C. J. Daggett, John Cook, John Bridge, and A. H. Evans. An accompanying letter, signed by John S. Williams certifies that he received the tally sheet from Matthew Simpson and that he will deliver it to the secretary of state
Beauty for the Present: Mill, Arnold, Ruskin and Aesthetic Education
No full textThe present thesis examines the idea of aesthetic education of three eminent Victorians: John Stuart Mill, Matthew Arnold and John Ruskin. By focusing on the essence of what they meant with ‘the cultivation of the beautiful’ and, more importantly, the way their ideas of beauty informed their criticism of society, my study aims to contribute to our understanding of the idea of aesthetic education in the Victorian context and, further, to participate in a recent debate about the nature of beauty and aesthetic education.
Chapter One focuses on John Stuart Mill’s concept of ‘feeling’ in a series of essays. I will demonstrate how Mill’s idea of ‘aesthetic education’ was an ‘education of feelings,’ and moreover, how this idea was integrated into his literary criticism, his later critique of democratisation, his description of an ideal liberal society and even his own style of writing. Chapter Two contains a comparative study of Matthew Arnold and Friedrich Schiller. Through a rereading of Arnold, I will argue that his idea of aesthetic education is essentially Schillerian and that their resemblance consists primarily in their stress on the importance of aesthetic unity for modern life, which was becoming increasingly fragmentary and multitudinous. Chapter Three examines John Ruskin’s idea of aesthetic education and concentrates particularly on the cultivation of perception. Perception, as I shall show, was pivotal in Ruskin’s idea of aesthetic education. Just as what happened in Mill and Arnold, the emphasis on the education of seeing continued from his early writings well into his art and social criticisms. It not only differentiated him from his fellow art critics; the conviction that people should perceive with a pure heart also enabled him to link observation of artistic details with moral criticism of contemporary society and, thereby, to turn the cultivation of the beautiful into a moral-aesthetic experience
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