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13 p.-1 fig.-2 tab., A proliferating population of cells may be considered complex when its proliferative or growth fraction P is lower than 1 and/or when it is formed by subpopulations with different mean cycle times. The present paper shows that in such complex populations exponential growth is consistent with a steady-state distribution of cells. Obviously, when P = 1 then cell distribution is only a function of cell age. An analytical model has been developed to study complex populations including both quiescent fractions formed by cells with unreplicated genome (G0 cells) and cells with fully duplicated chromosomes (Q2 cells). The model also considers those quasi-quiescent cells in their last transit through G1 and S (Q1 and Qs cells) before becoming quiescent. In order to solve the difficulties of a direct analysis of the whole population, its kinetic parameters have been obtained by studying the negative exponential distribution of two subpopulations: one formed by the proliferating cells and another formed by the quasi-quiescent cells. Additionally, the model could be applied when quiescence is initiated at any other cycle phase different from G1 and G2, for instance, cells in the process of replicating their DNA or being at any other mitotic phases. The utility of the method was illustrated in populations which constitute the root meristems of both Allium cepa L. and Pisum sativum L. Three facts should be stressed: (1) the method seems to be rather powerful because it can be carried out from different sets of experimentally measured parameters; (2) the rate of division and, therefore, the population doubling time can be easily estimated by this method; and (3) it also allows the determination of the amount of cells that had become quiescent either before they had replicated their DNA (G0) or after having completed their replication (Q2), as well as those quasi-quiescent cells which are progressing throughout their last pre-replicative and replicative periods (thus Q1 and Qs, respectively). © 2002 Elsevier Science Ltd. All rights reserved., This work has been partially supported by the Direccio! n General de Ensen* anza Superior e Investigacio! n Cient!ıfica del Ministerio de Educacio! n y Cultura from Spain (Projects PB96-0909 and PB97-0909, by the CSIC-Universidad de Chile joint Project (99 CL-0009) and by the European Union (BIO6-CT96-0275). We thank Mr J. L. Marcilla and Ms M. Carrascosa for excellent technical assistance.

The distribution of cell surface area projection (cell size) has been measured at birth and at initiation of DNA synthesis in steady-state populations of Allium cepa root meristems. The conditional probability, P( I G 1 ) , that initiation occurs given that the event of being in g1 also occurs has been estimated from these data. p( I G 1 ) was found to increase when cells became larger. The distribution of G1 duration has been constructed from indicated cell size distributions. The absolute frequencies of G1 times showed a maximum in the zone of cells with short G1 periods; about 14% of cells appear to enter into S with G1 ∼- 1 h. These results suggest that the increase of p( I G 1 ) was due to cell enlargement and not to cell aging. By comparing the cell size distribution at initiation of S and at the end of this period, a drastic reduction of cell size variability during DNA replication was observed and both curves were seen as rather similar in shape although they obviously had different modal points. These observations support that there is a negative correlation between the initiation size and the duration of genome duplication, and that cells which initiate DNA synthesis with the same size have a similar replication time. From this hypothesis, a plot of S duration versus cell size at initiation of this period was constructed by comparing the distributions of cell size at start and end of replication; this plot was also consistent with the existence of a negative correlation between cell initiation size and S length.

6 p.-1 fig.-2 tab., The rates of cell entrance into three cell cycle periods, G1, S and metaphase, have been measured in meristems of Allium cepa L. roots. The objective was to study, in a direct way, the question of cell age distribution in a tissue formed by proliferating cells with different average generation times. Entrance rates significantly changed from one period to another: the number of cells entering into G1 per unit time almost doubled the entry rate into metaphase. These data rules out a linear cell age distribution. The ratio of entry rates into different pairs of cell cycle periods was calculated, by assuming negative exponential cell age distribution, from the frequency of cell number between birth and the initiation of each period. Comparison of expected values with experimental ones strongly supports a negative exponential age distribution similar to that found in cell cultures with a single cell cycle average time., This work was supported by a grant from the CICYT (Spain). M.I. Gimenez-Abian is the recipient of a postdoctoral fellowship from the CSIC. Secretarial and technical work carried out by respectively, Ms. M.O. Partearroyo and Ms. M. Carrascosa, is acknowledged.

Meristematic cells from Allium cepa L roots can attain a steady-state of growth at both 15 and 25 °C in the presence of drugs, hydroxyurea and 5-amino-uracil, which reduce the rate of DNA synthesis. These drugs, at used concentrations, significantly lengthen the S period without altering the cell growth rate, as indicated by the maintenance of the generation time. It has been observed that steady-state populations respond to a gradual increase in S by a reduction of G2 until a minimum value; with larger lengthening of S, both G1 and G2 are reduced. Natural synchronous populations have been used to study cell cycle parameters during transition from the physiological steady-state to the new one created by the presence of the drug. G2 (but not G1) is reduced during transition even in the presence of maximum drug concentrations that do not alter the cell growth rate. Both the S period and the division time are lengthened during transition. These observations support the concept that certain fractions of G1 and G2 are expendable, because they have no role in the DNA-division sequence of cell cycle events. We conclude that cell size regulates the length of these fractions by means of a negative correlation.

The variability of (1) surface area projection (size) at which cells terminate DNA replication, (2) the area at which they initiate mitosis, (3) the area at which they divide, (4) the duration of G2, and (5) the duration of G2 plus mitosis (in fact, prophase + metaphase + anaphase) has been estimated in steady-state cell populations of Allium cepa root meristems. The coefficient of variation of cell area at termination of DNA synthesis was found to be 14% while the coefficient of variation of cell area at mitosis initiation was 13%. As there is also a substantial variability of G2 (the coefficient of variation was estimated to be 38%), the combination of these data indicates that cell size regulation of G2 contributes to maintaining cell size variability (and therefore DNA concentration) within certain limits. Mitosis also varies but less than G2 (the coefficient of variation of G2 + mitosis was found to be 31%). As the coefficient of variation of cell area at division (14%) is hardly larger than the coefficient of variation of cell area at initiation of mitosis, it can be suggested that coordination between cell size and mitosis duration helps to avoid a significant increase in the variability of cell size at the end of the division cycle.