Growth and Cell Pattern Formation on an Axis: Critique of Concepts, Terminology, and Modes of Study

The processes which generate length and cell pattern down a growing axis have traditionally been termed cell division and cell expansion; they are usually presented as alternate means of generating volume or length. But, because cell division can involve varying amounts of volume increase between mitoses, it can have no fixed units with regard to the volume-generating function This nonquantitative interlocking of the two processes renders them incapable of either precise description or quantitative prediction of the phenomenology of growth and pattern. A flexible and comprehensive framework for quantitative analysis, put forward by Goodwin, Erickson, and others, employs two independent but superimposable processes (not alternate means to the same end). Surface extension is the sole volume (length) generating process, measured as a compound interest rate; cell partitioning is the instantaneous act of completing a cross wall, also measured as an interest rate. Change in cell length is a direct function of the difference between the two processes (e.g., if the extension rate, in the sense of doubling, is not fully balanced by an equal partitioning rate, cell length will increase). Consistent independent gradients for extension and partitioning down an axis will generate a consistent pattern for mean cell length down the axis. This forms the basis of a revised growth-zone nomenclature linking histological change to well-defined measurable processes. Various traditional concepts of cell division reappear as special cases. The cell cycle is the interval between partitioning events. Using the cell-partitioning function down an axis, one can measure cell-cycle duration in two senses: (a) its duration at a given distance from the tip, as if the cells could remain at that position in the gradient for one cycle, and (b) the duration of the cycle for a given group of cells as they move down the axis. For (a), the expected agreement with the label accumulation method is limited but reasonable; the agreement with the metaphase accumulation method is poor. For (b), agreement with the labeled mitosis method is to be expected. Since, however, the method appears not to have been applied appropriately (i.e., to a specific group of moving cells), clear comparison cannot be made. The kinetic methods are indirect but intrinsically free of radiation/chemical artifact. They can serve as independent measures of total cycle time where the duration of separate cycle phases is under study by label methods.