Large-scale simulations of biological cell sorting driven by differential adhesion follow diffusion-limited domain coalescence regime

Abstract

Cell sorting, whereby a heterogeneous cell mixture segregates and forms distinct homogeneous tissues, is one of the main collective cell behaviors at work during development. Although differences in interfacial energies are recognized to be a possible driving source for cell sorting, no clear consensus has emerged on the kinetic law of cell sorting driven by differential adhesion. Using a modified Cellular Potts Model algorithm that allows for efficient simulations while preserving the connectivity of cells, we numerically explore cell-sorting dynamics over very large scales in space and time. For a binary mixture of cells surrounded by a medium, increase of domain size follows a power-law with exponent n = 1/4 independently of the mixture ratio, revealing that the kinetics is dominated by the diffusion and coalescence of rounded domains. We compare these results with recent numerical studies on cell sorting, and discuss the importance of algorithmic differences as well as boundary conditions on the observed scaling.

Cluster size distribution of cells disseminating from a primary tumor

“…At very high value of p 0 ( p 0 > 30), the individual cells can actually start to break apart (see S13(G) and S13(K) Fig for p 0 = 36), which is an artifact of the Potts model [ 52 ]. We note that this does not appear to directly affect our results in the range of parameters that we have considered, as we do not see any significant change in mean cluster size ( ) as we increase p 0 for p 0 > 30 compared to at p 0 = 30.…”

Is cell segregation like oil and water: Asymptotic versus transitory regime

“…One of the earliest attempts of simulating cell segregation is the Cellular-Potts-Model (CPM) of Glazier and Graner [ 12 , 13 ], in which segregation results from differential adhesion. While the observed segregation indices display a logarithmic decay, successive studies concluded that the segregation indices actually follow a logarithmic decay only initially and settle to an algebraic one for longer times [ 16 – 18 , 32 , 34 , 35 ]. Nakajima and Ishihara [ 17 ] used the CPM to study the effects of even and uneven cell type ratios on the segregation process.…”

“…He measured the segregation indices over time, which showed a maximal algebraic decay with exponent of 1/4. Durand [ 32 ] used a CPM with modified update algorithm, which allows for simulation of larger number of cells over longer times while preserving cell connectivity. He observed an asymptotic algebraic decay with an exponent of 1/4 and concluded that the previously reported scaling with exponent 1/3 is only transitory.…”

“…The analysis of the asymptotic behavior in these theoretical models, in a steady regime and for large numbers of cells, is primarily used to discriminate between models. However, it is unclear whether this asymptotic regime is relevant for biological cell segregation processes and the corresponding in-vitro experiments [ 32 ]. Moreover, for both experiments and numerical simulations, the algebraic decay of the segregation indices is usually only observed during the last two orders of magnitude of time [ 17 , 18 , 31 , 33 ] or on an even shorter time interval [ 20 , 38 ].…”

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“…At very high value of p 0 (p 0 > 30), the individual cells can actually start to break apart (see S13(G) and S13(K) Fig for p 0 = 36), which is an artifact of the Potts model [52]. We note that this does not appear to directly affect our results in the range of parameters that we have considered, as we do not see any significant change in mean cluster size (N ) as we increase p 0 for p 0 > 30 compared to at p 0 = 30.…”