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Computer modeling of multicellular systems has been a valuable tool forinterpreting and guiding in vitro experiments relevant to embryonicmorphogenesis, tumor growth, angiogenesis and, lately, structure formationfollowing the printing of cell aggregates as bioink particles. Computersimulations based on Metropolis Monte Carlo (MMC) algorithms were successful inexplaining and predicting the resulting stationary structures (corresponding tothe lowest adhesion energy state). Here we present two alternatives to the MMCapproach for modeling cellular motion and self-assembly: (1) a kinetic MonteCarlo (KMC), and (2) a cellular particle dynamics (CPD) method. Unlike MMC,both KMC and CPD methods are capable of simulating the dynamics of the cellularsystem in real time. In the KMC approach a transition rate is associated withpossible rearrangements of the cellular system, and the corresponding timeevolution is expressed in terms of these rates. In the CPD approach cells aremodeled as interacting cellular particles (CPs) and the time evolution of themulticellular system is determined by integrating the equations of motion ofall CPs. The KMC and CPD methods are tested and compared by simulating twoexperimentally well known phenomena: (1) cell-sorting within an aggregateformed by two types of cells with different adhesivities, and (2) fusion of twospherical aggregates of living cells.

Kinetic Monte Carlo and Cellular Particle Dynamics Simulations of Multicellular Systems