Stochastic Partitioning of Chloroplasts at Cell Division in the Alga Olisthodiscus, and Compensating Control of Chloroplast Replication

J. Cell Sa. 70, 1-15 (1984) Printed in Great Britain © The Company of Biologists Limited 1984

STOCHASTIC PARTITIONING OF CHLOROPLASTS AT CELL DIVISION IN THE ALGA OLISTHODISCUS, AND COMPENSATING CONTROL OF CHLOROPLAST REPLICATION

ANNETTE S. HENNIS* AND C. WILLIAM BIRKY, JR Department of Genetics, The Ohio State University, Columbus, Ohio 432 JO, U.SA.

SUMMARY We asked how chloroplasts in a unicellular marine alga are replicated and partitioned at cell division so that each daughter cell will receive the appropriate number of copies. The data were obtained simply by counting chloroplasts in pairs of daughter cells immediately after cell division. The results show that chloroplast partitioning is not always equal; however, it is equal much more often than predicted by the binomial distribution of chloroplast numbers that would be expected if partitioning were strictly random. The parental chloroplasts were partitioned equally in approximately 76 % of the divisions, while in the remaining 24 % the deviations from equality were very small. To maintain a reasonable range of chloroplast numbers in the face of unequal partitioning, there must be some form of compensating control of chloroplast replication. Our data suggest that daughter cells that receive very large numbers of chloroplasts go directly to the next division without replicating their chloroplasts, while cells with very small numbers of chloroplasts go through two rounds of chloroplast replication before dividing.

INTRODUCTION When a cell divides it is essential that both daughter cells receive a complete set of genetic information, including at least one copy of each gene and chromosome. For chromosomes in the nucleus this is ensured by having each chromosome replicated exactly once and one copy delivered to each daughter cell by the mitotic or meiotic apparatus. The situation is less clear for cytoplasmic organelles that carry genes, i.e. mitochondria and chloroplasts (reviewed by Birky, 1982; Butterfass, 1979; Dyer, 1976; Heitz, 1961; Wilson, 1931). In some organisms, each cell has a single large chloroplast or mitochondrion, which is divided approximately equally in two at cytokinesis. In some animal cells with many mitochondria, those organelles are aligned along the mitotic spindle and divided more or less equally by the cleavage furrow. In other cells with many mitochondria or chloroplasts, the organelles seem to be arranged randomly in the cytoplasm and may be partitioned randomly between the two daughter cells. Certainly there is an element of randomness in the partitioning with respect to genotype of the organelles, which leads to progressive sorting out of organelle genes to produce lineages of homoplasmic cells (vegatative segregation, reviewed by Birky, 1978; Gillham, 1978; Kirk & Tilney-Bassett, 1978).

•Present address: 11872 Valley View Road, Sagamore Hills, Ohio 44067, U.S.A. 2 A. S. Hennis and C. W. Birky, Jr This genetic randomness in partitioning, coupled with the lack of any visible association of organelles with the mitotic apparatus or other device for controlling partitioning, leads to the possibility that partitioning in some organisms may be numerically strictly random. According to this hypothesis, the number of chloroplasts or mitochondria that enter a daughter cell would fit the binomial distribution. The other extreme model would be numerically uniform partitioning, in which each daughter cell would always receive a fixed proportion of the parental organelles (usually half). The only extensive data relevant to this question come from studies of the partitioning of mitochondria during spermatogenesis in scorpions (Hood, Watson, Deason&Benton, 1972; Wilson, 1916, 1931), and of chloroplasts during the divisions producing guard cells in Trifolium (Butterfass, 1969). In these cases, partitioning is intermediate between the two extreme models, being equal much more often than predicted by the binomial distribution but with some variation. However, less extensive data on plastids in meristem cell divisions of Epilobium show no deviation from random partitioning (Anton-Lamprecht, 1967). We have studied this problem in the unicellular alga Olisthodiscus luteus. This wall- less marine alga contains many small discrete chloroplasts lying around the periphery of the cell, which are easily counted (Cattolico, 1978; Leadbeater, 1969; Liittke, 1980). Cell division can be easily synchronized in this alga; the chloroplasts replicate during interphase, well before the cells divide (Cattolico, Boothroyd & Gibbs, 1976). By counting chloroplasts in the two halves of dividing cells, or in pairs of just-divided cells, one can determine the number of chloroplasts in each daughter; the sum of those numbers is the number in the parent cell after chloroplast replication. Our data show that chloroplast partitioning in Olisthodiscus, like that of mitochondria during spermatogenesis and chloroplasts in guard cell divisions, is not strictly uniform but is equal much more often than predicted by the random partitioning model. Because chloroplast partitioning is not always equal, every cell division tends to increase the variance of chloroplast numbers in the population of cells. Unless there is a compensating control of organelle replication, this increasing variance will eventu- ally result in cells that have too few or too many organelles for survival, and possibly cells with no organelles at all. We find that Olisthodiscus cultures do not accumulate aplastidic cells and, instead, maintain a constant variance in chloroplast numbers. We propose three models of compensating replication control; our data favour the model in which cells with large numbers of chloroplasts skip a round of chloroplast replication, while cells with very small numbers go through two rounds of chloroplast replication before the next cell division.

MATERIALS AND METHODS Olisthodiscus luteus Carter was stock LB2005 from the Texas Culture Collection of Algae. Growth medium O-3 was prepared as described by Mclntosh & Cattolico (1978). Cells were grown in 1-litre low-form culture flasks containing approximately 500 ml of medium or 250-ml Erlenmeyer flasks with approximately 50 ml of medium. The cultures were maintained at 16-20°C on a 12-h light/12-h dark cycle. Cultures were illuminated from above with General Electric cool white fluorescent lights to give an intensity of 400ft-candles (1 ft-candle = 10'76391x). Chloroplast partitioning at cytokinesis

Fig. 1. A dividing cell of Olisthodiscus flattened under a coverslip to permit counting of chloroplasts.

Cell counts were done to follow the growth of synchronized cell cultures. Approximately 500 fi\ of tincture of iodine was added per ml of sample. Each sample was counted three times in a haemocytometer chamber and the counts were then averaged. At low cell densities, cells were concentrated by centrifugation before counting. More than 200 cells were counted for each sample. To count chloroplasts in cells, approximately 50 jul of the culture was placed on a washed glass slide and covered with a 22mm2 coverslip. The droplet begins to desiccate almost immediately and the cells flatten into a single plane of focus, allowing the chloroplasts to be counted easily. The optimum time for counting is just before the cells burst, when all the chloroplasts are easily distin- guishable (Fig. 1). The counts were made at X400 magnification with a Zeiss phase-contrast microscope. For dividing cells, the numbers of chloroplasts on each side of the incipient cleavage furrow were recorded separately as the numbers of chloroplasts in the daughter cells. To obtain chloroplast counts in just-divided cells, as opposed to cells in the process of division, single cells were isolated in O-3 medium in glass depression slides just before the onset of cell division in a synchronized culture. The depression slides were placed in moist chambers made from Petri dishes lined with wet towelling. The depressions were periodically examined in a stereoscopic microscope at X 60 magnification for the presence of two cells, signalling that division was completed. The two daughter cells were placed on a slide and the chloroplasts were counted as described above. For statistical analysis, we asked if the numbers of chloroplasts in pairs of daughter cells differed significantly from those predicted by the binomial distribution. Let n be the number of chloroplasts in the parent cell and x and n —x the numbers in the daughter cells. In no case did we have a sufficiently large number of parent cells with the same value of n to do a Chi-square test, so it was necessary to pool all parents. The data were transformed using z, the cumulative distribution function of a standardized random variable. If % is a binomial function of «,l/2 then 2 = (2x—n)/V~« is approximately a normal function of 0,1. If the normal distribution is divided into k classes of equal size, then the expectation is that the z values will be equally distributed among the k classes. We calculated z for each observed x,n and determined the number of these transformed observations falling into each of the k classes. This was compared to the expected number, \/k, using the Chi- square test with k - 1 degrees of freedom.

RESULTS Parameters of synchronous and asynchronous cell replication Cell samples were taken every 12 h from an Olisthodiscus culture maintained on a constant light regime to determine the growth characteristics and maximum cell A. S. Hennis and C. W. Birky, Jr

• ,_—- • • 64-

32-

16- / o i -

4- / /

2- /%

1- • / /

0-5-

1 1 0 5 10 15 Time (days) Fig. 2. Growth of an Olisthodiscus culture in 0-3 medium under continuous light. densities. The culture was initiated by inoculating a sample of a stationary-phase stock culture in fresh medium to give approximately 2-5XlO3 cells/ml. The culture doubled in cell number every 24-3 h during the exponential growth phase in 0-3 medium (Fig. 2). The maximum cell density seen was 7xlO4 cells/ml, at which point the stationary phase began. These values for cultures maintained under a constant light regime parallel very closely those seen in previous studies (Cattolico et al. 1976). Two studies were made of growth parameters in cultures where cell division was synchronized by a 12-h light/12-h dark cycle. In the first study (data not shown), cell number increased 1-91-fold during the first 24-h cycle, but synchrony decreased sharply thereafter. To improve synchrony, a second experiment was done in which the cells were pelleted and 10% of the culture fluid was removed from the culture daily and replaced with an equal volume of fresh O-3 medium. This greatly improved the synchrony of the culture (Fig. 3) and cell number doubled approximately every 24 h for 5 days. The mean increase in cell number was 1-976-fold per cycle, which Chloroplast partitioning at cytokinesis 5 suggests that approximately 99% of the cells divide every cycle. Conversely, the maximum frequency of cells that might fail to divide because they have too few or too many chloroplasts is about 1 % in a cell generation. However, we cannot rule out the possibility that the daily brief concentration (at 2000 rev./min in a clinical centrifuge) killed some cells, and others divided more than once. It is also possible that some viable cells will skip one or more cycles before dividing, while others divide two or more times in a cycle. But we know of no reason why enough cells should divide more than once to compensate so precisely for cells that fail to divide. Fig. 4 shows the distribution of the number of chloroplasts per cell found in an exponentially growing synchronous Olisthodiscus culture. The cells were sampled between the third and ninth hour of the light cycle (L-3 and L-9). The mean was 15-4 chloroplasts per cell, substantially lower than reported by CattolicoeJ al. (1976) and Liittke (1980); this may be because they used 0-1 medium, which has different concentrations of salts from O-3. The range of chloroplast numbers was 6—35, and the variance was 23-2. The shape of the distribution, demonstrating a positive skewness, was similar to that reported by Cattolico et al. (1976).

o x 8

> s/m 4 1 % i 2 y

^-e

Time (days)

Fig. 3. Long-term synchronous growth of an Olisthodiscus culture maintained on an alternating 12-h light/12-h dark cycle in O-3 medium. White bars at the top represent the light phases. Daily, cells were pelleted and a small sample of old medium was withdrawn and replaced by fresh medium. A. S. Hennis and C. W. Birky, Jfr

n = 968 90 x= 16-4 chloroplasts S2 = 23 2 80

§• 50 IB 40

0 1 2 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 Chloroplast number/cell

Fig. 4. Distribution of the number of chloroplasts per cell found in an Olisthodiscus culture. Growth was synchronized as in Fig. 3; cells were sampled between L-3 and L-9 of the light cycle.

The cells sampled between hours L-3 and L-9 should be in G\ phase of the cell cycle and should not have begun replicating their chloroplasts (Cattolico et al. 1976). However, in our later experiments the mean number of chloroplasts per newly divided cell was 9-8, suggesting that the chloroplasts had already divided in some of the cells counted in this preliminary experiment.

Numerical partitioning: chloroplast counts in mother and daughter cells The problem of chloroplast partitioning at cell division was addressed simply by counting chloroplasts in the two halves of dividing cells. Specifically, the number of chloroplasts in each half cell represents the number in a newly formed daughter cell before chloroplast replication; the sum of the two halves represents the number in a mother cell after chloroplast replication but before cell division. A total of 111 dividing cells were sampled from well-synchronized cultures. These cultures were in log phase at least 2 days before being sampled. However, a few cells came from cultures approaching stationary-phase densities, at which chloroplast numbers may be depressed (Cattolico, 1978). Frequency distributions of chloroplast numbers (Fig. 5) show that chloroplast number is not stringently controlled. Parent cells immediately before division (Fig. 5A) showed a mean of 19-7 chloroplasts. The individual numbers ranged from 8 to 34 plastids per cell, and the variance was 29-4. The individual Chloroplast partitioning at cytokinesis

1 2 10 12 14 16 18 20 22 24 26 28 30 32 34 Chloroplast number/cell

= 222 = 9-8 = 7-9

8 10 12 14 16 18 20 22 24 26 28 30 32 34 Chloroplast number/cell Fig. 5. Distribution of the number of chloroplasts per dividing cell found in synchronous Olisthodiscus cultures sampled immediately before cell division. Cultures were grown as in Fig. 3; A, mother cells; B, daughter cells. chloroplast numbers in the resulting 222 daughters ranged from 4 to 17 chloroplasts per cell with a mean of 9-8 and a variance of 7-9 (Fig. 5B). Table 1 summarizes the relationship between chloroplast counts in individual mothers and their daughters. For each dividing cell, x and (n— x) are the numbers of chloroplasts in the two daughter cells; n is the number in the mother cell. Olistho- discus chloroplast partitioning during cell division is not always equal: x ^ (n— x) even when n is an even number. (When n is odd, partitioning must be considered 'equal' when one daughter has one more chloroplast than the other.) In addition, partitioning values differ significantly from a binomial distribution, which would be expected if the partitioning were strictly random. Specifically, the parental chloroplasts are partitioned equally between the daughter cells in approximately 79 % of the divisions. The deviations from equal numbers of chloroplasts in the remaining 21 % are small. In all but two cases there were more nearly equal divisions than predicted by the binomial distribution. The method of counting chloroplasts in half-cells during cytokinesis is rapid but suffers from a potential source of error. It is possible that the process of flattening the A. 5. Hennis and C. W. Birky, Jr Table 1. Chloroplast partitioning during cell division

N(n,x) N Exp. Obs.-Exp.

8 4 4 11 0-27 +0-73 9 — — — 0 — — 10 5 5 0 1 0-25 -0-25 6 4 1 0-41 +0-59 11 6 5 2 2 0-45 +0-160 12 6 6 1 1 0-23 +0-77 13 7 6 8 9 3-80 +4-20 8 5 1 2-80 -1-80 14 7 7 5 6 1-30 +3-70 8 6 1 2-20 -1-20 15 8 7 7 8 310 +3-90 9 6 1 2-40 -1-40 16 8 8 3 7 1-40 + 1-60 9 7 3 2-40 +0-60 10 6 1 1-70 -0-70 17 9 8 11 12 4-50 +6-50 3-60 -2-60 10 7 1 110 +4-90 18 9 9 6 6 2-80 +4-20 19 10 9 7 8 2-30 -1-30 11 8 1 0-88 +4-10 20 10 10 5 5 2-40 +4-60 21 11 10 7 7 0-84 +3-20 22 11 11 4 5 1-50 -0-50 12 10 1 3-20 +0-80 23 12 11 4 5 1-40 -0-40 13 10 1 0-97 + 3-00 24 12 12 4 6 1-80 +0-20 13 11 2 1-20 +2-80 25 13 12 4 4 0-79 +0-21 26 13 13 1 5 1-40 + 1-60 1-20 14 12 3 -1-20 0-79 15 11 0 +0-21 16 10 1 27 — — — 0 0-90 +2-10 28 14 14 3 6 1-70 -0-30 15 13 2 1-40 -0-40 16 12 1 0-28 +0-72 29 15 14 1 1 0-29 + 1-71 30 15 15 2 2 0-28 +0-72 31 16 15 1 2 0-50 +0-50 17 14 1 Chloroplast partitioning at cytokinesis Table 1. Continued.

n X n-x JV(«,JC) N Exp. Obs.-Exp. 32 16 16 0 1 0-14 -0-14 17 15 1 0-26 +0-74 33 — — — 0 — — 34 17 17 1 1 0-14 -0-86

For each dividing cell, x and (n-x) are the numbers of chloroplasts in the two half-cells (daughter cells). The sum, n, is the number of chloroplasts in the mother cell. JV (n,x) is the number of dividing cells that were counted for each set of values of x and (n-x). N is the total number of dividing cells tabulated for each n. Exp., the number of cells in that set predicted by the binomial distribution. Obs.-Exp., the difference between the observed number and the number predicted by the binomial distribution. dividing cell under a coverslip moves some chloroplasts from one side of the cell to the other, which would cause an apparent increase or decrease in the equality of partitioning. To avoid this problem, the slower but more rigorous method of counting chloroplasts in isolated newly divided cells was used. The data from 31 cases are given in Table 2. We found that 71 % of the divisions resulted in equal partitioning. This is not significantly different (by the Chi-square test) from the value of 79 % found by counting dividing cells. As was the case with the dividing cells, the deviations from equal partitioning were small in the remaining 29% of the divisions. To show that the deviation from a binomial distribution of chloroplasts was indeed statistically significant, we applied a Chi-square test to the transformed data as described in Materials and Methods. The deviation was highly significant: Chi- square =219 for 10 degrees of freedom, P«0-005. The data obtained by both counting methods were pooled for this analysis. The binomial distribution of chloroplast numbers was calculated assuming that each chloroplast has a probability of 1/2 of entering either daughter cell. This assumption is appropriate if cell division produces two daughter cells of equal size and there is no tendency toward asymmetric partitioning of the organelles, i.e. toward one daughter always receiving more organelles. This appears to be the case with Olistho- discus. But if the assumption were wrong, then the expected frequency of deviations from equal partitioning would be even larger than the values given. Our data do not exclude such an asymmetric division but do not support it either. They do show that partitioning is neither uniform nor strictly random. It is best described as stochastic, with a strong tendency toward equality.

Compensating replication control We can imagine four models of the replication control of organelles. These can also be viewed as four rules of counting, which relate the number of organelles after their replication (xz) to the number before replication (x\). In model 1, each cell makes a number of new chloroplasts equal to the pre-replication mean number (x\). The number of chloroplasts after replication is thus#2 = x\+x\. This rule of counting for 10 A.S. Hennis and C. W. Birky, Jr

Table 2. Chloroplast partitioning during cell division using the isolation method

n .V n-x N(n,x) N 10 5 5 0 1 6 4 1 11 — — — 0 12 6 6 1 1 13 7 6 1 2 8 5 1 14 7 7 1 2 8 6 1 15 — — — 0 16 8 8 1 1 17 9 8 1 1 18 9 9 3 3 19 11 8 1 1 20 10 10 2 2 21 -— — — 0 22 11 11 2 2 23 — — — 0 24 12 12 2 3 13 11 1 25 12 13 2 2 26 — — — 0 27 — — — 0 28 14 14 0 1 15 13 1 29 — — — 0 30 15 15 2 3 16 14 0 17 13 1 31 16 15 1 2 17 14 1 32 16 16 2 3 17 15 1 33 17 16 1 1

For each dividing cell, x and (n—x) are the numbers of chloroplasts in the two daughter cells. Their sum, n, is the number of chloroplasts in the mother cell. N(n,x) is the number of dividing cells that were counted for each set of values of x and (n-x). N is the total number of dividing cells tabulated for each n value. Chloroplast partitioning at cytokinesis 11

Table 3. Models of replication and their predictions

Model Mechanism Variance Coefficient of variation

1 X2 = 51 = 5? CV2 = cvjl

Xi if JCi > fu

2 X2 = 2x, if .Xi >_tt 52 < 4S? 4-xi if ^!

3 X2 = x, + (2x, -x.) =2x, = const. s| = o CV2 = 0

4 X2 = 2*, 5l = 4S? CV2 =

Olisthodiscus :S? == 7-89 «;, = 28-62% c2. i2- = 29-63 = 3-7fo? cw2 = 27-70% = 0-«

Symbols: x = number of chloroplasts; s2 = variance; cv = coefficient of variation. Subscript 1 represents postdivision (pre-replication) values; subscript 2 represents predivision (post- replication) values. replication has the effect of halving the coefficient of variation in chloroplast number at each chloroplast replication phase, thereby compensating for the new variance introduced by stochastic partitioning at the preceding cell division. In model 2, most cells exactly double the number of chloroplasts before dividing, so that xi = 2xi. However, cells with chloroplast numbers at or below a lower threshold (xi^Ji) double the number of chloroplasts twice before dividing, so that xi = 4x\. Cells with chloroplast numbers at or above an upper threshold (x[ ^tu) divide without replicating any chloroplasts (xz = x\). The values of the thresholds would be such as to compensate exactly for the variance introduced by stochastic partitioning. In model 3 each cell always makes precisely enough new chloroplasts to bring the number to a constant value: X2 = x\ + (2x\—x\) = constant. In model 4 each cell exactly doubles the number of chloroplasts before dividing. In this model there is no compensation by the replication mechanism for the variance introduced by stochastic partitioning. Instead, that variance must be eliminated in each generation by the death of cells with very small or very large numbers of chloroplasts. These models make very different predictions about the variances of chloroplast numbers in predivision (mother) cells (Sz) and postdivision (daughter) cells (S\) and also about the pre- and postdivision coefficients of variation (cvi and cv\, where cv = 100 S/x) (Berger, 1979). Table 3 summarizes the models of replication and their predictions regarding pre- and postdivision variances and coefficients of variation. Model 1 predicts that the variances in the pre- and postdivision cells will be equal but that the coefficient of variation in the postdivision cells is twice that of the predivision cells. Model 2 predicts that the predivision variance will be slightly less than four times the postdivision variance. Additionally, cvi will be slightly less than cv\. Model 3 predicts that predivision variance and coefficients of variation will be zero. Finally, in model 4 the predivision variance will be four times the postdivision variance and the coefficients of variation will be equal. 12 A. S. Hennis and C. W. Birky, Jr These predictions are compared to our data at the bottom of Table 3. The variance of chloroplast numbers in predivision cells was 3-76 times the postdivision variance, and the pre- and postdivision coefficients of variation were nearly equal. Model 3 can be ruled out immediately because the predivision variance is not zero. Model 1 can also be ruled out because the variances of the pre- and postdivision cells are not equal while the coefficients of variation are nearly equal. The Olisthodiscus data appear to be compatible with models 2 and 4. However, model 4 predicts that S\ = iS\. We therefore applied the F-ratio test of significance to the hypothesis that 29-63 = (4)(7-89); it was rejected at the 5 % level. Also, model 4 requires that some cells must fail to reproduce in order to limit the variance of chloroplast numbers in the population. As described above, about 1 % of the cells failed to reproduce in our synchronous culture on average. Without a more detailed mathematical analysis of this model, we cannot be certain that 1 % cell death would not suffice to compensate for the variance introduced by stochastic partitioning. But altogether the evidence strongly suggests that model 4 is not sufficient to explain the data, and that compensating replication control as in model 2 must be operating.

DISCUSSION Both the replication and partitioning of nuclear chromosomes are stringently controlled, with each being replicated exactly once per cell cycle and one copy trans- mitted to each daughter cell. This ensures perfect hereditary continuity of all the genes and at the same time provides that alleles will segregate during meiosis but not mitosis. Stringent control is necessary because each cell has only one or two copies of each chromosome or gene and any degree of randomness in partitioning or replication would result in the loss of essential genes in some cells. The partitioning of mitochondria and chloroplasts that are present in many copies per cell is under more relaxed control. Our data for Olisthodiscus chloroplasts confirm the widespread belief that daughter cells usually receive about half of the organelles in the mother cell but that, in the absence of an obvious mechanism to guarantee uniformity, there is a degree of randomness. A similar result was obtained by Butter- fass (1969) for chloroplasts in Trifolium hybridum and for partitioning of mitochondria duringspermatogenesis in scorpions (Hooded al. 1972; Wilson, 1925, 1931). The only other quantitative data of which we are aware are those of Anton-Lamprecht (1967) who counted plastids and mitochondria in serial electron microscope sections of the apical shoot meristem of Epilobium hirsutum. The mean numbers of plastids and mitochondria in the daughter cells were 21-8 and 120, respectively. We transformed the data and applied the Chi-square test as described in Materials and Methods: there was no significant deviation from binomial partitioning for either plastids or mitochondria (0-20>P>0-10 for both). Although this test did not exclude the hypothesis of strictly random partitioning, neither does it rule out the possibility of a tendency toward equal partitioning that is too small to detect with this sample size (14 dividing cells). More extensive data on meristem cells are needed before firm conclusions can be drawn. Chloroplast partitioning at cytokinesis 13 We can think of two general explanations for this tendency to partition cytoplasmic organelles equally in the absence of any obvious association with the mitotic spindle, asters, or other segregating mechanism (Birky, 1982). First, the organelles may tend to be distributed uniformly rather than randomly through the cytoplasmic volume, approximately equidistant from each other and with approximately equal numbers on both sides of the future cleavage plane (Butterfass, 1969). This could result from interactions between the organelles themselves, or because they are constrained by elements of the cytoskeleton; evidence for the latter has been reviewed by Birky (1982). A second factor that must be considered is the volume of the organelles. The binomial distribution is appropriate for calculating expected numbers of organelles when they are distributed randomly throughout the cytoplasm, but such a perfectly random distribution assumes that each organelle is a dimensionless point, occupying zero volume. If the volume of the organelles is large relative to the available cytoplasmic volume that they can occupy, they will be forced automatically into a more uniform spatial distribution (Butterfass, 1979). The binomial distribution can be modified to take cell and organelle volume into account (Birky & Skavaril, 1984). The chloroplasts of Olisthodiscus are apparently constrained to lie in a shell of cytoplasm in the very periphery of the cell (Cattolico et al. 1976; Leadbeater, 1969); we are currently attempting to measure the volume of this shell, and of the chloroplasts, during cell division, to determine if volume effects are sufficient to account for the near-equality of partitioning. Stochastic partitioning introduces variance in organelle numbers into the population. A similar problem occurs in the ciliate macronucleus, which has many copies of each genome and which divides amitotically so that the daughter macronuclei do not always receive half of the total DNA. In Paramecium, this variance of DNA content is eliminated in each cell cycle by the cell always making new DNA in precisely the mean pre-replication amount (Berger, 1979). This is the precedent for our model 1. In Tetrahymena, most of the variance is eliminated by a different form of compensating replication: cells with very much macronuclear DNA skip the S phase and go directly to the next cell division; cells with very little macronuclear DNA go through two 5 phases, with two doublings of macronuclear DNA (Doerder, 1979). This is our model 2, the rule of counting apparently used by Olisthodiscus. We know of no biological precedent for our model 3, but also know of no reason why it would be impossible. Model 4 is uniform replication, with every cell doubling the number of units; the variance in number of units per cell must be eliminated by death of cells with very many or very'few units. Our statistical analyses rule out models 1 and 3 conclusively, and fit model 2 perfectly. Our data do not fit model 4, but we hesitate to say that some variant of this model could not explain the results. A more direct test of model 2 would be to identify cells that fail to replicate chloroplasts, and other cells that quadruple the number of chloroplasts, during interphase. This direct test is not experimentally feasible. Such cells are expected to be rare and thus difficult to find. Moreover, we cannot count chloroplasts in the same cell before and after chloroplast replication, since counting 14 A. S. Hennis and C. W. Birky, Jr destroys the cell. For this same reason we cannot test a variant of model 2 in which, instead of rigid thresholds of chloroplast numbers above which there is no replication and below which the number is quadrupled, there is simply an increasing tendency to skip chloroplast replication as the number increases, and an increasing tendency for two rounds of doubling as the number of chloroplasts decreases. Note that these models do not specify how individual organelles (or macronuclear DNA molecules) are selected for replication. Under models 1 and 3 it is clearly not possible for every unit to be replicated exactly once in every cell cycle. Under models 2 and 4, it is possible that each unit is replicated once in every doubling, but not necessary. The organelles could be selected randomly for replication, as mitochondrial DNA molecules are in mouse cells (Bogenhagen & Clayton, 1977). It is interesting that our data on chloroplasts in algae, the data on chloroplasts in Trifolium and those on mitochondria in scorpion spermatocytes are in such close agreement with respect to the degree of randomness of partitioning. More quantitative studies are needed on a variety of organisms to see if this kind of behaviour is a general rule for multi-copy cytoplasmic organelles. Those same studies would provide information about the kind of replication mechanism or rule of counting used to compensate for randomness in partitioning. Knowing the counting rule at this level is a necessary prelude to working out the molecular mechanisms of replication control.

We thank P. S. Perlman and other members of the organelle genetics research group at Ohio State for numerous useful discussions and suggestions; T. J. Byers, R. Cattolico, and several reviewers for improving the manuscript; and David Blough and the Statistics Laboratory for suggesting statistical methods. These studies were submitted by A. S. Hennis in partial fulfillment of the M.Sc. degree requirements at The Ohio State University. The research was supported by National Institutes of Health grant GM19607 to C. W. Birky, Jr and P. S. Perlman. C. W. B. is part of the Interdepartmental Program in Molecular, Cellular, and Developmental Biology at Ohio State University.

REFERENCES ANTON-LAMPRECHT, I. (1967). Anzahl und Vermehrung der Zellorganellen im Scheitelmeristem von Epilobium. Ber. dt. bot. Ges. 80, 747-754. BERGER, J. B. (1979). Regulation of macronuclear content mParamecium tetraurelia.J. Protozool. 26, 18-28. BIRKY, C. W. JR (1978). Transmission genetics of mitochondria and chloroplasts. A. Rev. Gen. 12, 471-512. BIRKY, C. W. JR (1982). The partitioning of cytoplasmic organelles at cell division. Int. Rev. Cytol. (suppl.) 15, 49-89. BIRKY, C. W. JR & SKAVARIL, R. V. (1982). Random partitioning of cytoplasmic organelles at cell division: The effect of organelle and cell volume../, theor. Biol. 106, 441-447. BOGENHAGEN, D. & CLAYTON, D. A. (1977). Mouse L cell mitochondrial DNA molecules are selected randomly for replication throughout the cell cycle. Cell 11, 719-727. BUTTERFASS, T. (1969). Die Plastidenverteilung bei der Mitose der Schleisszellenmutterzellen von haploidem Schwedenklee {Trifolium hybridum L.). Planta 84, 230-234. BUTTERFASS, T. (1979). Patterns of Chloroplast Reproduction. New York: Springer-Verlag. CATTOLICO, R. A. (1978). Variation in plastid number. PL Physiol. 62, 558-562. CATTOLICO, R. A., BOOTHROYD, J. C. & GIBBS, S. P. (1976). Synchronous growth and plastid replication in the naturally wall-less alga Olisthodiscus luteus. PI. Physiol. 57, 497-503. Chloroplast partitioning at cytokinesis 15 DOERDER, F. P. (1979). Regulation of macronuclear DNA content in Tetrahymena thermophila. J. ProtozooL 26, 28-35. DYER, A. F. (1976). The visible events of mitotic cell division. In Cell Division in Higher Plants (ed. M. M. Yeoman), pp. 49-110. New York: Academic Press. GILLHAM, N. W. (1978). Organelle Heredity. New York: Raven Press Books. HEITZ, E. (1961). Vermehrung anderer Zellorganellen. In Encyclopedia of Plant Physiology, vol. 14 (ed. W. Ruhland), pp. 263-270. Berlin: Springer-Verlag. HOOD, R. D., WATSON, 0. F., DEASON, T. R. & BENTON, C. L. B. JR (1972). Infrastructure of scorpion spermatozoa. Cytobios. 5, 176-177. KIRK, J. T. O. & TILNEY-BASSETT, R. A. E. (1978). The Plastids, 2nd edn. New York: Elsevier/ North Holland Biomedical Press. LEADBEATER, B. S. C. (1969). A fine structural study of Olisthodiscus luteus Carter. Br. phycol. Bull. 4, 3-17. LfJTTKE, A. (1980). Relation between chloroplast replication and cell division in Olisthodiscus luteus. PL Sci. Lett. 18, 191-199. MCINTOSH, L. & CATTOLICO, R. A. (1978). Preservation of algal and higher plant ribosomal RNA integrity during extraction and electrophoretic quantitation. Analyt. Biochem. 91, 600-612. WILSON, E. B. (1916). The distribution of the chondriosomes to the spermatozoa in scorpions. Proc. natn. Acad. Sci. U.SA. 2, 321-324. WILSON, E. B. (1925). The Cell in Development and Heredity, 3rd edn. New York: MacMillan. WILSON, E. B. (1931). The distribution of sperm forming materials in scorpions. J. morph. Physiol. 52, 429-483.

(Received 2] December 1983- Accepted, in revised form, 6 March 1984)