Swapping in lattice-based cell migration models

Cell migration is frequently modeled using on-lattice agent-based models (ABMs) that employ the excluded volume interaction. However, cells are also capable of exhibiting more complex cell-cell interactions, such as adhesion, repulsion, pulling, pushing, and swapping. Although the first four of these have already been incorporated into mathematical models for cell migration, swapping has not been well studied in this context. In this paper, we develop an ABM for cell movement in which an active agent can "swap" its position with another agent in its neighborhood with a given swapping probability. We consider a two-species system for which we derive the corresponding macroscopic model and compare it with the average behavior of the ABM. We see good agreement between the ABM and the macroscopic density. We also analyze the movement of agents at an individual level in the single-species as well as two-species scenarios to quantify the effects of swapping on an agent's motility

Swapping in lattice-based cell migration models

Cell migration is frequently modelled using on-lattice agent-based models (ABMs) that employ the excluded volume interaction. However, cells are also capable of exhibiting more complex cell-cell interactions, such as adhesion, repulsion, pulling, pushing and swapping. Although the first four of these have already been incorporated into mathematical models for cell migration, swapping is an interaction that has not been well studied in this context. In this paper, we develop an ABM to describe cell movement where an active agent can `swap' its position with another agent in its neighbourhood with a given swapping probability. We consider single-species and two-species systems. In both cases, we derive the corresponding macroscopic model and compare it with the average behaviour of the ABM. We see good agreement between the ABM and the macroscopic density. We also derive an expression for the cell-level diffusion coefficient in terms of the swapping probability and cell density. We conclude by showing applications of swapping by using the ABM to represent cell movement with proliferation and cell-cell adhesion.Comment: 32 pages, 12 figures, articl

Mosaic analysis of stem cell function and wound healing in the mouse corneal epithelium

<p>Abstract</p> <p>Background</p> <p>The mouse corneal epithelium is a continuously renewing 5–6 cell thick protective layer covering the corneal surface, which regenerates rapidly when injured. It is maintained by peripherally located limbal stem cells (LSCs) that produce transient amplifying cells (TACs) which proliferate, migrate centripetally, differentiate and are eventually shed from the epithelial surface. LSC activity is required both for normal tissue maintenance and wound healing. Mosaic analysis can provide insights into LSC function, cell movement and cell mixing during tissue maintenance and repair. The present study investigates cell streaming during corneal maintenance and repair and changes in LSC function with age.</p> <p>Results</p> <p>The initial pattern of corneal epithelial patches in <it>XLacZ</it>^+/-X-inactivation mosaics was replaced after birth by radial stripes, indicating activation of LSCs. Stripe patterns (clockwise, anticlockwise or midline) were independent between paired eyes. Wound healing in organ culture was analysed by mosaic analysis of <it>XLacZ</it>^+/-eyes or time-lapse imaging of GFP mosaics. Both central and peripheral wounds healed clonally, with cells moving in from all around the wound circumference without significant cell mixing, to reconstitute striping patterns. Mosaic analysis revealed that wounds can heal asymmetrically. Healing of peripheral wounds produced stripe patterns that mimicked some aberrant striping patterns observed in unwounded corneas. Quantitative analysis provided no evidence for an uneven distribution of LSC clones but showed that corrected corneal epithelial stripe numbers declined with age (implying declining LSC function) but stabilised after 39 weeks.</p> <p>Conclusion</p> <p>Striping patterns, produced by centripetal movement, are defined independently and stochastically in individual eyes. Little cell mixing occurs during the initial phase of wound healing and the direction of cell movement is determined by the position of the wound and not by population pressure from the limbus. LSC function declines with age and this may reflect reduced LSCs numbers, more quiescent LSCs or a reduced ability of older stem cells to maintain tissue homeostasis. The later plateau of LSC function might indicate the minimum LSC function that is sufficient for corneal epithelial maintenance. Quantitative and temporal mosaic analyses provide new possibilities for studying stem cell function, tissue maintenance and repair.</p

Computer simulation of neutral drift among limbal epithelial stem cells of mosaic mice

Acknowledgements We thank Graham West for writing the software that made this study possible and Ronnie Grant for help with some of the figures. Disclosure of potential conflicts of interest The authors indicate no potential conflicts of interest. Funding information This work was supported by the UK Biotechnology and Biological Sciences Research Council (grants BB/J015172/1 and BB/J015237/1).Peer reviewedPublisher PD

Activated mutant NRasQ61K drives aberrant melanocyte signaling, survival, and invasiveness via a rac1-Dependent mechanism

Around a fifth of melanomas exhibit an activating mutation in the oncogene NRas that confers constitutive signaling to proliferation and promotes tumor initiation. NRas signals downstream of the major melanocyte tyrosine kinase receptor c-kit and activated NRas results in increased signaling via the extracellular signal–regulated kinase (ERK)/MAPK/ERK kinase/mitogen-activated protein kinase (MAPK) pathways to enhance proliferation. The Ras oncogene also activates signaling via the related Rho GTPase Rac1, which can mediate growth, survival, and motility signaling. We tested the effects of activated NRasQ61K on the proliferation, motility, and invasiveness of melanoblasts and melanocytes in the developing mouse and ex vivo explant culture as well as in a melanoma transplant model. We find an important role for Rac1 downstream of NRasQ61K in mediating dermal melanocyte survival in vivo in mouse, but surprisingly NRasQ61K does not appear to affect melanoblast motility or proliferation during mouse embryogenesis. We also show that genetic deletion or pharmacological inhibition of Rac1 in NRasQ61K induced melanoma suppresses tumor growth, lymph node spread, and tumor cell invasiveness, suggesting a potential value for Rac1 as a therapeutic target for activated NRas-driven tumor growth and invasiveness

The invasion speed of cell migration models with realistic cell cycle time distributions

Cell proliferation is typically incorporated into stochastic mathematical models of cell migration by assuming that cell divisions occur after an exponentially distributed waiting time. Experimental observations, however, show that this assumption is often far from the real cell cycle time distribution (CCTD). Recent studies have suggested an alternative approach to modelling cell proliferation based on a multi-stage representation of the CCTD. In this paper we investigate the connection between the CCTD and the speed of the collective invasion. We first state a result for a general CCTD, which allows the computation of the invasion speed using the Laplace transform of the CCTD. We use this to deduce the range of speeds for the general case. We then focus on the more realistic case of multi-stage models, using both a stochastic agent-based model and a set of reaction-diffusion equations for the cells' average density. By studying the corresponding travelling wave solutions, we obtain an analytical expression for the speed of invasion for a general N-stage model with identical transition rates, in which case the resulting cell cycle times are Erlang distributed. We show that, for a general N-stage model, the Erlang distribution and the exponential distribution lead to the minimum and maximum invasion speed, respectively. This result allows us to determine the range of possible invasion speeds in terms of the average proliferation time for any multi-stage model

Hierarchical patterning modes orchestrate hair follicle morphogenesis

Two theories address the origin of repeating patterns, such as hair follicles, limb digits, and intestinal villi, during development. The Turing reaction–diffusion system posits that interacting diffusible signals produced by static cells first define a prepattern that then induces cell rearrangements to produce an anatomical structure. The second theory, that of mesenchymal self-organisation, proposes that mobile cells can form periodic patterns of cell aggregates directly, without reference to any prepattern. Early hair follicle development is characterised by the rapid appearance of periodic arrangements of altered gene expression in the epidermis and prominent clustering of the adjacent dermal mesenchymal cells. We assess the contributions and interplay between reaction–diffusion and mesenchymal self-organisation processes in hair follicle patterning, identifying a network of fibroblast growth factor (FGF), wingless-related integration site (WNT), and bone morphogenetic protein (BMP) signalling interactions capable of spontaneously producing a periodic pattern. Using time-lapse imaging, we find that mesenchymal cell condensation at hair follicles is locally directed by an epidermal prepattern. However, imposing this prepattern’s condition of high FGF and low BMP activity across the entire skin reveals a latent dermal capacity to undergo spatially patterned self-organisation in the absence of epithelial direction. This mesenchymal self-organisation relies on restricted transforming growth factor (TGF) β signalling, which serves to drive chemotactic mesenchymal patterning when reaction–diffusion patterning is suppressed, but, in normal conditions, facilitates cell movement to locally prepatterned sources of FGF. This work illustrates a hierarchy of periodic patterning modes operating in organogenesis