Developmental algorithms for multicellular organisms: A survey of L-systems

Abstract

Multicellular organisms are construed as arrays of symbols, each symbol standing for a cell. Their development is modelled by algorithmic rules which provide the allowed substitutions of new arrays for each symbol in the previous array. These substitutions stand for cell divisions, or cell death, or for changes of cellular states. The substitutions may depend on inputs from neighbouring cells (development with cellular interactions), or only on the state of the cell itself (development without interactions). By repeated use of a system of algorithms one obtains a developmental sequence of arrays, or a set of arrays (a developmental language). Additional control mechanisms may be applied to the arrays generated by a system, thus defining a hierarchy of language families. This article presents a survey of biologically relevant mathematical results available on these algorithmic systems.