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 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 neighbourhood 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 behaviour of the ABM. We see good agreement between the ABM and the macroscopic density. We also analyse 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.<br/

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

Rapid mechanosensitive migration and dispersal of newly divided mesenchymal cells aid their recruitment into dermal condensates

Embryonic mesenchymal cells are dispersed within an extracellular matrix but can coalesce to form condensates with key developmental roles. Cells within condensates undergo fate and morphological changes and induce cell fate changes in nearby epithelia to produce structures including hair follicles, feathers, or intestinal villi. Here, by imaging mouse and chicken embryonic skin, we find that mesenchymal cells undergo much of their dispersal in early interphase, in a stereotyped process of displacement driven by 3 hours of rapid and persistent migration followed by a long period of low motility. The cell division plane and the elevated migration speed and persistence of newly born mesenchymal cells are mechanosensitive, aligning with tissue tension, and are reliant on active WNT secretion. This behaviour disperses mesenchymal cells and allows daughters of recent divisions to travel long distances to enter dermal condensates, demonstrating an unanticipated effect of cell cycle subphase on core mesenchymal behaviour

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

Mesenchymal nuclei and Collagen-I align with mechanical strain.

(A) Plot showing the percentage decrease in anterior-posterior (A-P) and dorsal-ventral (Lat) length of mouse skin explants in a 30 min period (n = 5) when suspended freely in culture medium. (B) Images of E13.5 TCF/Lef::H2B-GFP mouse skin explants before and after a lateral stretch (upper panels) or a stretch along the anterior-posterior (A-P) axis of the embryo (lower panels). White dashed arrows show direction of stretch. (C) Nucleus orientation angle for relaxed (n = 3; upper), lateral stretched (n = 4; middle), and A-P stretched (n = 3; lower) skins. (D) Alignment score of nucleus orientation angle from relaxed (n = 3), laterally stretched (n = 4), and A-P stretched (n = 3) skins. (E) Single planes from confocal imaging of Collagen-I immunofluorescence in E13.5 TCF/Lef::H2B-GFP skin explants in stretched states. Dashed white line indicates direction of stretch. (F) Alignment scores of Collagen fibres from skin samples shown in E. The raw numerical values for A, C, D, and F can be found in S4 Data. (G) Single planes from confocal imaging of an A-P stretched E7 membrane GFP (mGFP) chicken skin. Daughter nucleus pairs are connected by white lines, showing coherent angles of mitosis aligned with applied tension. Error bars represent SEM. Scale bar in B = 2 mm; scale bar in E = 100 μm; scale bar in G = 50 μm. (TIF)</p

Orientation of mesenchymal mitosis and newly born cell migration by mechanical cues.

(A) E13.5 TCF/Lef::H2B-GFP mesenchymal nuclei in skin in relaxed and stretched states. Skins were stretched to approximately twice their length along a single axis. White dashed line indicates the A-P axis. (B) Nucleus length from relaxed (n = 3), laterally stretched (n = 4), and A-P stretched (n = 3) skins. (C, E) Plotted deviations of cell division angles (left) and migration angle of dividing (middle) and non-dividing (right) cell migration angle from the A-P axis and total cell displacement for each angle in skins that were (C) relaxed (n = 3, average number of dividing cells tracked/video = 67, non-dividing cells tracked/video = 50), (D) stretched laterally, (n = 4, average number of dividing cells tracked/video = 72, non-dividing cells tracked/video = 50) and (E) stretched along the A-P axis (n = 3, average number of dividing cells tracked/video = 79, non-dividing cells tracked/video = 50). (F) Global alignment scores across entire skin of mitosis angles from relaxed skins (n = 3), laterally stretched skins (n = 4), A-P stretched skins (n = 3), laterally stretched skins from LGK-974 treated embryos (n = 4), and whole embryos (n = 3). (G) Speed of tracked dividing (left panel; time 0 = point of mitosis) and non-dividing (right panel) cells in skins that were relaxed (n = 3, average number of dividing cells tracked/video = 67), stretched (n = 7, average number of dividing cells tracked/video = 78), or stretched after LGK-974 treatment (n = 4, average number of dividing cells tracked/video = 53); 50 non-dividing cells tracked/video for all conditions. *p p p B–G can be found in S4 data. Error bars represent SEM. Scale bar in A = 20 μm. A-P, anterior-posterior; SEM, standard error of the mean.</p

Newly born daughter cells migrate extensively after division.

(A) Schematic depicting the position of mesenchymal cells migrating and dividing in a planar manner, parallel to the epidermis. Orientation of view is shown. (B) Quantification of cells remaining in-plane after 3 hours of imaging (number of tracked daughter cells = 100; z-slice depth = 6 μm). (C) Mitosis plots mapping mother and daughter tracks before and after cell division, with corresponding cell speed plots over the time course of imaging below. Tracks were chosen from cells in which cell division took place within a time point of 40%–60% through the imaging, and both daughter cells were tracked until the end of the video. The raw numerical values and tracking data for B and C can be found in S1 Data. (TIF)</p

Detection of phospho-LRP6 (serine 1490) in mesenchymal and basal epidermal cells at mitosis.

(A, B) Single planes of the dermis and basal epidermis from confocal imaging of phospho-LRP6 (S1490) (A) and phospho-histone H3 (S10) (B) immunofluorescence in E13.5 mouse skin explants, stained with phalloidin (detecting F-actin) and DAPI. Phospho-histone H3 signal illustrates the morphology of nuclei undergoing mitosis. Yellow arrows indicate cells that are in mitosis and have condensed chromatin. Phospho-LRP6 (S1490) is detected at highest levels in cells undergoing division in mesenchyme and epithelium. Scale bar = 20 μm. (TIF)</p