Spatial and vacancy effects on the stabilising mechanisms of two-dimensional free growth

A Monte-Carlo simulation technique is introduced to study the spatial considerations of cellular distribution that affect the overall asynchronous process of population growth. The stochastic nature of cellular characteristics such as mitotic time, loss rate and direction of growth is considered. The fluctuation of these values from one generation to the next and from one cell to the other, is illustrated. Cells are assumed to grow in a two-dimensional honeycomb-like network such that a central cell is always surrounded with six equally distant sites. The modes of cellular growth are controlled mainly and simply by the existence of a definite number of neighbouring vacancies. An IBM-compatible PC-AT computer was used and a program written in Pascal is employed to simulate and follow up the growth of a single stem cell in a 40,000-sites network. The results of the proposed stochastic model illustrate the importance of the spatial interaction among growing cellular modes such that vacancies act as local sensors for a negative feedback mechanism regulating the overall growth pattern. The role of the resting mode (G0) in stabilising the overall growth pattern is discussed.