# The Follicular Automaton Model: Effect of Stochasticity and of Synchronization of Hair Cycles

#### Model Structure

Human scalp hair is made up of a set of about 10^{5} hair follicles which progress continually and independently through developmental cycles. Each follicle successively goes through a period of growth - the anagen phase (A), a period where it ceases to grow and involutes - the catagen phase (C), but still remains on the scalp - the telogen phase (T), before the follicle is shed (M) or is in latency (L) before entering a new cycle. These successive phases constitute a follicular cycle. The duration of this cycle varies from months to years. Each follicle can undergo several cycles before it dies or miniturises (M). A comprehensive study carried out on ten men has provided a complete data set for the dynamics of the human hair cycle. Over a period of 14 years, about 9000 hair cycles were recorded and characterised for a total of about 930 hair follicles followed monthly.

This large body of data was used by J. Halloy, B.A. Bernard, G. Loussouarn and A. Goldbeter in order to develop their follicular automaton model to describe the dynamics of the human hair cycle. In this model, the hair cycle is represented as the succession of the anagen (A), telogen (T) and latency (L) phases. Follicular death or miniturisation (M) removes a follicle from the cycle and it was included in the model by an additional transition from T. The catagen phase is relatively short (less than one month) and it is difficult to distinguish, therefore it has been included in the T phase. The follicular automaton (see the figure below), remains in a given state for a variable period of time before it moves onto the next phase in the cycle. The automaton completes a cycle when it enters a new A phase.

The complete original paper reference is cited below:

The Follicular Automaton Model: Effect of Stochasticity and of Synchronization of Hair Cycles, J. Halloy, B.A. Bernard, G. Loussouarn and A. Goldbeter, 2002,
*Journal of Theoretical Biology*
, 214, 469-479. (A PDF version of the article is available to subscribers on the Journal of Theoretical Biology website.) PubMed ID: 11846603

The above diagram represents the transition of a model hair follicle from anagen (A) to telogen (T) to latency (L) phase, successively. After phase T, the follicle may either die or miniaturise (transition to M; this usually occurs after a critical number of cycles), or complete a cycle by entering a new A phase. |

The raw CellML descriptions of the model can be downloaded in various formats as described in . This version of the follicular automaton model is deterministic. Currently CellML 1.0 can only handle deterministic models, therefore the authors' stochastic version of the follicular automaton model remains uncoded. In the stochastic model, each follicle in a cluster of hair follicles is characterised by: a) its spatial position; b) its state; c) the time to the next transition; and d) the number of cycles performed since entering the first A phase. In the deterministic version of the follicular automaton model encoded here, the variation in the duration of the different phases is ignored. Only the mean durations of the phases are considered. The transition from one phase to the next is governed by a kinetic constant that is inversely proportional to the duration of the phase from which the transition occurs.

Following model simulations, Hallot *et al.* demonstrated that only the stochastic model was capable of reproducing the fluctuations of the fractions of hair follicles in each of the different phases.