Moving 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, l, 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 l/D ratio will be characterized by steep fronts, whereas systems with a low l/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.

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BackgroundThe expansion of cell colonies is driven by a delicate balance of several mechanisms including cell motility, cell–to–cell adhesion and cell proliferation. New approaches that can be used to independently identify and quantify the role of each mechanism will help us understand how each mechanism contributes to the expansion process. Standard mathematical modelling approaches to describe such cell colony expansion typically neglect cell–to–cell adhesion, despite the fact that cell–to-cell adhesion is thought to play an important role.ResultsWe use a combined experimental and mathematical modelling approach to determine the cell diffusivity, D, cell–to–cell adhesion strength, q, and cell proliferation rate, λ, in an expanding colony of MM127 melanoma cells. Using a circular barrier assay, we extract several types of experimental data and use a mathematical model to independently estimate D, q and λ. In our first set of experiments, we suppress cell proliferation and analyse three different types of data to estimate D and q. We find that standard types of data, such as the area enclosed by the leading edge of the expanding colony and more detailed cell density profiles throughout the expanding colony, does not provide sufficient information to uniquely identify D and q. We find that additional data relating to the degree of cell–to–cell clustering is required to provide independent estimates of q, and in turn D. In our second set of experiments, where proliferation is not suppressed, we use data describing temporal changes in cell density to determine the cell proliferation rate. In summary, we find that our experiments are best described using the range D=161−243μm2hour−1, q=0.3−0.5 (low to moderate strength) and λ=0.0305−0.0398hour−1, and with these parameters we can accurately predict the temporal variations in the spatial extent and cell density profile throughout the expanding melanoma cell colony.ConclusionsOur systematic approach to identify the cell diffusivity, cell–to–cell adhesion strength and cell proliferation rate highlights the importance of integrating multiple types of data to accurately quantify the factors influencing the spatial expansion of melanoma cell colonies.

Hepatic lipid synthesis from PUFAs is impaired and could contribute to deficiency in PCs and increased intrahepatic TG in TM6SF2 E167K variant carriers.

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Insulin decreases plasma ANGPTL3 by decreasing ANGPTL3 expression in the liver. Insulin markedly increases ANGPTL8 in adipose tissue and the liver but not in plasma. These data show that measurement of plasma ANGPTL3 but not -8 reflects insulin action in target tissues.

Mathematical models of collective cell movement often neglect the effects of spatial structure, such as clustering, on the population dynamics. Typically, they assume that individuals interact with one another in proportion to their average density (the mean-field assumption) which means that cell–cell interactions occurring over short spatial ranges are not accounted for. However, in vitro cell culture studies have shown that spatial correlations can play an important role in determining collective behaviour. Here, we take a combined experimental and modelling approach to explore how individual-level interactions give rise to spatial structure in a moving cell population. Using imaging data from in vitro experiments, we quantify the extent of spatial structure in a population of 3T3 fibroblast cells. To understand how this spatial structure arises, we develop a lattice-free individual-based model (IBM) and simulate cell movement in two spatial dimensions. Our model allows an individual’s direction of movement to be affected by interactions with other cells in its neighbourhood, providing insights into how directional bias generates spatial structure. We consider how this behaviour scales up to the population level by using the IBM to derive a continuum description in terms of the dynamics of spatial moments. In particular, we account for spatial correlations between cells by considering dynamics of the second spatial moment (the average density of pairs of cells). Our numerical results suggest that the moment dynamics description can provide a good approximation to averaged simulation results from the underlying IBM. Using our in vitro data, we estimate parameters for the model and show that it can generate similar spatial structure to that observed in a 3T3 fibroblast cell population.

BackgroundStandard two-dimensional (2D) cell migration assays do not provide information about vertical invasion processes, which are critical for melanoma progression. We provide information about three-dimensional (3D) melanoma cell migration, proliferation and invasion in a 3D melanoma skin equivalent (MSE) model. In particular, we pay careful attention to compare the structure of the tissues in the MSE with similarly-prepared 3D human skin equivalent (HSE) models. The HSE model is identically prepared to the MSE model except that melanoma cells are omitted. Using the MSE model, we examine melanoma migration, proliferation and invasion from two different human melanoma cell lines. One cell line, WM35, is associated with the early phase of the disease where spreading is thought to be confined to the epidermis. The other cell line, SK-MEL-28, is associated with the later phase of the disease where spreading into the dermis is expected.Methods3D MSE and HSE models are constructed using human de-epidermised dermis (DED) prepared from skin tissue. Primary fibroblasts and primary keratinocytes are used in the MSE and HSE models to ensure the formation of a stratified epidermis, with a well-defined basement membrane. Radial spreading of cells across the surface of the HSE and MSE models is observed. Vertical invasion of melanoma cells downward through the skin is observed and measured using immunohistochemistry. All measurements of invasion are made at day 0, 9, 15 and 20, providing detailed time course data.ResultsBoth HSE and MSE models are similar to native skin in vivo, with a well-defined stratification of the epidermis that is separated from the dermis by a basement membrane. In the HSE and MSE we find fibroblast cells confined to the dermis, and differentiated keratinocytes in the epidermis. In the MSE, melanoma cells form colonies in the epidermis during the early part of the experiment. In the later stage of the experiment, the melanoma cells in the MSE invade deeper into the tissues. Interestingly, both the WM35 and SK-MEL-28 melanoma cells lead to a breakdown of the basement membrane and eventually enter the dermis. However, these two cell lines invade at different rates, with the SK-MEL-28 melanoma cells invading faster than the WM35 cells.DiscussionThe MSE and HSE models are a reliable platform for studying melanoma invasion in a 3D tissue that is similar to native human skin. Interestingly, we find that the WM35 cell line, that is thought to be associated with radial spreading only, is able to invade into the dermis. The vertical invasion of melanoma cells into the dermal region appears to be associated with a localised disruption of the basement membrane. Presenting our results in terms of time course data, along with images and quantitative measurements of the depth of invasion extends previous 3D work that has often been reported without these details.