The maximum size of cell-aggregates is determined by the competition between the strain energy and the binding energy of cells

The development of tissues and organs is affected by how cells interact with each other to form aggregates. Such an interaction is in turn determined by several different factors, such as inter-cellular attractive forces, cell motility, and the strain energy of cells. Here, we have used mathematical modelling and numerical simulations to explore how the interplay between these factors can influence the formation and stability of 2D cell aggregates. Cell aggregates were created by incrementally accumulating cells over an initial seed. The binding energy density of these aggregates was determined using the harmonic approximation and was integrated into a probabilistic model to estimate the maximum cluster size, beyond which the aggregate becomes unstable and breaks into smaller fragments. Our simulations reveal that the ratio of strain energy to internal adhesive energy ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow><mml:msub><mml:mi>U</mml:mi> <mml:mi>s</mml:mi></mml:msub> <mml:mo>/</mml:mo> <mml:msub><mml:mi>U</mml:mi> <mml:mi>b</mml:mi></mml:msub> </mml:mrow> </mml:math> ) critically impacts cell aggregation; smaller ratios allow for larger cluster sizes. These findings have significant implications for tissue engineering, in-vitro modeling, the study of neurodegenerative diseases, and tissue regeneration, providing insights into how physical and biological characteristics of cells influence their aggregation and stability.