AGGREGATION OF BURKITT LYMPHOMA CELLS IN STATIONARY CULTURE: EXPERIMENTAL AND THEORETICAL ANALYSIS

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1 J. Cell Sci. io, (1972) 749 Printed in Great Britain AGGREGATION OF BURKITT LYMPHOMA CELLS IN STATIONARY CULTURE: EXPERIMENTAL AND THEORETICAL ANALYSIS E. MAYHEW Department of Experimental Pathology AND L. E. BLUMENSON Department of Biostatistics Roswell Park Memorial Institute, Buffalo, N.Y , U.S.A. SUMMARY Cellular motility plays an important role in natural aggregative phenomena but previously has been difficult to quantitate. We here describe a general method which can be used to determine the importance of cell motility in cell aggregation behaviour. When actively moving Burkitt lymphoma cells cultured in microtest plate wells come into contact they adhere to one another forming an aggregate. The aggregate increases in size when more cells come in contact with it. Thefinalsize and number of aggregates per well was found to be dependent on the number of cells added per well. With increasing cell numbers added per well the number of aggregates formed increased until it reached a peak of aggregates per well 20 h after the addition of cells per well. At higher cell concentrations the number of aggregates formed decreased. The system was analysed theoretically by programming a computer to simulate the experimental system. This simulation showed it was probable that the experimental results obtained were due to (a) random dropping of the cells at zero time and (b) the adhesion of the cells when they made contact and (c) unrestricted random movement of cells in the well when they reached the well surface. The computer simulation is such that given the experimentally determined cell concentration per well and rate of cell movement we can predict the number of aggregates formed for different probabilities that the adhesions formed after the cells come in contact are permanent. This experimental approach along with the computer simulation can be used to quantitate the role of cell motility and permanence of contact in cell aggregation. INTRODUCTION Model systems for the study of the mechanism of aggregation of dispersed mammalian cells usually use methods where aggregates are formed after collision of suspended cells (Curtis & Greaves, 1965; Steinberg & Roth, 1964; Gasic & Galanti, 1966; Moscona, 1959; Kemp, Jones & Groschel-Stewart, 1971). However, in most types of natural aggregation active cellular movement (Abercrombie, 1965; Weiss, 1964) is an important factor which cannot be studied using suspension techniques, and Moscona (1959) has pointed out that quantitative studies of cells aggregating under their own locomotive pressure are difficult to make. We suggest that the role of cell motility in cell aggregation can be quantitated by the combined use of model experimental systems together with computational models, such as described in this report.

2 750 E. Mayhew and L. E. Blumenson Cells obtained from Burkitt's lymphomas adhere to one another when cultured and form aggregates, which can be separated into single cells by gentle agitation (Pulvertaft, 1965). Burkitt lymphoma cells maintained in long-term stationary culture or in microtest plate wells also form aggregates. We have made observations on the formation of these aggregates from separate, actively moving cells, and have detected an unexpected relationship between the initial number of single cells inoculated into a culture and the number of aggregates formed. It also appeared from preliminary observations that cells moved in a random although restricted manner, i.e. actively moving cells seemed to remain restricted to within a few microns of their original dropping positions. However, when separate actively moving cells did come into contact they tended to remain in contact forming an aggregate and, as other cells came into contact with the aggregate, it became larger. When we attempted to simulate this aggregative behaviour with a computational model the apparent observation that single cells were restricted in their movements became open to question. The aggregative system was therefore analysed in some detail, and the data compared with alternative computational models: (1) with restricted movement of cells, and (2) with unrestricted random movement of cells. MATERIALS AND METHODS Burkitt lymphoma (Ogum) cells (Wakefield, Thorbecke, Old & Boyse, 1967) were maintained in flat-bottomed 500-ml bottles in stationary culture or in i-l. cylindrical bottles on rollers at 1 rev/min. RPMI 1640 (Moore, Sandberg & Ulrich, 1966) supplemented with 20 % foetal calf serum was used both as a medium for maintenance and for experimental situations and the cell numbers were maintained at x io s /ml. Cells from stationary and roller cultures behaved similarly in the experiments. In well-maintained cultures the viability as assessed by trypan blue staining was over 95 %, but the mean doubling time of the cells varied between 18 and 60 h Aggregation Burkitt cells form aggregates to some extent under maintenance conditions and virtually pure single cell suspensions were obtained by pipetting the cells up and down in a Pasteur pipette or in a syringe fitted with a 22-gauge needle or smaller. Burkitt cells were added to individual wells on microtest II plates (Falcon plastics) using 1- or 2-ml syringes fitted with 27-gauge needles. Microtest plate wells are ideal for observation of aggregative behaviour as known numbers of cells can be added to a small surface area. All the cells added can be observed and counted and very few cells adhere to the sides of the wells. The numbers of cells added were determined by use of a Coulter Counter or by haemocytometer count. The cells in microtest plates were incubated at 37 C under 95 % air, 5 % COj atmosphere. The plates were not moved after adding the cells in order to eliminate possible adhesion by collision of cells. An inverted phasecontrast microscope was used to count the total number of cells in a fixed area of the well (055 mm s ) at zero time. The numbers of single cells and multicellular particles were determined at intervals after the initial drop; 8-12 wells were counted for each cell number and time. Cell size The diameters of 200 Burkitt lymphoma cells were measured using an eyepiece micrometer and the mean calculated.

3 Cell locomotion Burkitt cell aggregation 751 Time-lapse, phase-contrast, cine micrographs were made of Burkitt cells at 4 or 8 frames/min. Analyses were made of the rate of movement using an analytical projector. Rate of movement was determined by measuring the distance travelled by the centre of 100 cells in 1- or 2-min intervals. Short times are necessary to determine rate of movement as these cells change direction frequently. Although shorter time intervals would give figures nearer to the rate of movement, the distances moved are so small as to be difficult to measure with any accuracy. Theoretical analysis A computer program was written to simulate the cell aggregation experiments.* For this purpose the computer had to simulate (a) the dropping of cells randomly into the well at zero time, (6) adhesion of cells and aggregates to form larger aggregates when they made contact, and (c) the movement of cells and aggregates at zero time. The method used here is the so-called Monte Carlo method (Metropolis & Ulam, 1949; Hoffman, Metropolis & Gardiner, 1955, 1956; McCracken, 1955), which, in this case, uses very long sequences of random numbers to build up a calculational model to predict the possible outcomes of the experiment. In order to accomplish this, it must be possible to describe the outcome of each step (a), (b) and (c) of the experiment numerically, either as a deterministic number or as a population of numbers with a known frequency distribution. The approximation of the experimental procedure by such a calculation therefore requires that certain assumptions be made concerning the mechanism of the cellular movements. However, the advantage here is that the results of these calculations, e.g. the prediction of the number of multicellular aggregates at 20 h, can be compared with the experimental data, and this comparison can then lead to a test of whether or not the original assumptions concerning mechanism of cell movement conflict with these data. The complete cell aggregation experiment, including (a), (b) and (c) above, was simulated as one program on the computer. In the calculation a cell is approximated by a disk of radius r = 65 /im. The zero time position of a cell is calculated by using 2 random numbers to calculate a point selected at random inside a circle whose radius is the radius of the well. After all the co-ordinates of the dropping positions are calculated it can be immediately determined whether any of the disks (of radius r) are overlapping. If 2 disks overlap they are replaced by a new disk which represents a 2-celled aggregate. The centre of the new disk is located at the arithmetic mean of the two original centres and its radius is taken as 2'.r. Observation of the multicellular aggregates suggested that the square root gave a good, simple approximation for the calculation of their area, i.e. a multicellular aggregate of N cells was approximated in the calculations as a disk of radius r x JV'. The cellular random movement was calculated on a 'minute-by-minute' basis. The location of the centre of the disk (cell) at the end of 1 min was calculated as a point randomly selected within the circle of radius 2 fim whose centre was the centre of the disk at the beginning of the 1-min interval; 2 fim were chosen as the radius of the circle as it was found experimentally that this was the maximum distance cells moved in 1 min (see Results). Thus the calculation of the path of a single cell during a 20-h period required 1200 such calculations (if the cell was not absorbed into an aggregate before this time). The movements of multicellular particles were simulated by the same type of random walk as that used for single cells. The movements of these larger particles were more difficult to classify than those of single cells and it was technically extremely difficult to simulate the movements of an aggregate in any more detail. The computer was programmed to simulate the experiments under 2 alternative hypotheses. The first was that the cells were doing a restricted random walk, which meant that a cell 'explored' its environment only within a restricted distance from the position where it fell at zero time. For example, if this distance was taken as a cell diameter (13 fim) then the computer had to check each of the minute-by-minute random movements described above to make sure that the centre of the disk was not taken outside a circle of radius 13 fim whose centre was the centre Complete details of the theoretical analysis and computer programs may be obtained directly from Dr L. Blumenson, Department of Biostatistics, Roswell Park Memorial Institute, Buffalo, N.Y , U.S.A.

4 752 E. Mayhem and L. E. Blumenson o Z Total no. cells Fig. i. The relationship between number of cells added to wells and number of multicellular particles at 20 h after drop., experimental; A A, computer simulation (free random walk); O O> computer simulation (restricted random walk). of the disk at zero time. If it was outside the circle the calculation of the random movement for this minute was repeated until the new position was not beyond the maximum distance. The alternative hypothesis was that the cells were doing a free random walk with no limitation (other than the edge of the well) for the distance between the cell and its position at zero time. The random-number generator on the computer requires that a number be given initially in order to start the random sequence. Each simulation was initiated by selecting this initial number from a table of random numbers (Snedecor & Cochran, 1967). The cell aggregation experiment was simulated on a Control Data Corporation 6400 computer. At various times during a simulation the computer was instructed to punch cards which gave the locations and sizes of the various particles. These cards were then used to plot the centres and radii of the various disks using an IBM 1627 plotter connected to an IBM 113 computer. RESULTS Burkitt cells were found to have a mean diameter of /6m and a radius of 6-5 /tm was used in the computer simulation. Most Burkitt cells move at 1-2 /tm/min; 2 /tm was taken as the maximal distance a cell moves per min in the computer simulation. It was observed that some fully viable cells did not move perceptibly for several hours, and there were a few cells (less than 1 %) in the cell population which moved at approximately 10/tm/min. Fig. 1 shows data obtained from experiments and computer simulation relating the number of cells per field in the well to the number of multicellular particles (aggregates) found 20 h after addition of the cells. The standard errors of the means of the points were calculated and ranged from 5-20% of mean. The

5 Burkitt cell aggregation ".. : o ' \ -v J) :, ' "N 0 :/ o ' \ ' ''11.., c: 1 i " Fig. 2. Plots of computer simulation-free random walk. 1-4,100 cells added; 5-8,250 cells added; 9-12, 500 cells added; 1, 5, 9, cells immediately after dropping; 2, 6, 10, cells immediately after dropping, but with cells adhering to one another formed into aggregates; 3, 7, n, aggregates and cells at 8 h; 4, 8, 12, aggregates and cells at 20 h.

6 754 E- Mayhew and L. E. Blumenson Table i. Relationship between total number of cells at 20 h and number of multicellular particles, total particles and multicellular particle size Total no. cells/field at 20 h Mean no. multicellular particles Total particles No. cells/ multicellular particle 2700 I7SO mo no ' S2-o ' i number of multicellular particles formed was a function of cell number present. When few cells were added few aggregates were formed. With increasing cell numbers, the number of multicellular particles increased until it reached a plateau after cells were added. When more than 710 cells were added the number of aggregates formed declined again. The computer simulations showed the same general shaped curves but some differences were present. At low numbers of cells there were only slight differences between the free random walk, the restricted (to a i3-/tm distance) random walk, and the experimental data. With more than 170 cells per well the restricted random-walk simulation deviated from the experimental data considerably; more aggregates were predicted than in the experimental situation. The free random-walk curve is similar to that of the experimental data except possibly at high cell numbers. From this comparison it became clear that our original short-term direct observations on limited numbers of cells were not sufficient to decide whether cell movements remain restricted over a period of hours. The deviation of the free random-walk computer simulation from the experimental results at high cell numbers probably is not due to an error in the simulation but due to an experimental error at high cell numbers where counting was difficult. Fig. 3 shows photomicrographs of cells 20 h after start of the stationary culture. Changes in aggregate size and number with different cell numbers can be seen clearly. Fig. 2 shows computer plots of cells at zero time and at 20 h for 3 different numbers of cells. The outer circle represents the edge of the microtest plate well and the inner rectangle represents the area of the plate counted in the experimental situations. The smallest circles in these plots represent single cells. /, 5 and 9 show the positions of the cells after dropping; overlapping cells can be seen particularly in plot 9. 2, 6 and 10 also show the cells after dropping but overlapping cells (multicellular particles or aggregates) are now represented by larger circles of various sizes. The circle area is proportional to the number of cells in the aggregate. The rest of the plots show cells in the microtest plate wells at 8 h (3, 7, //) and 20 h (4, 8, 12). The aggregates become larger and the number of single cells decreases.

7 Burkitt cell aggregation 755 Table 2. Data from experiments and computer simulation (440 cells /well at 20 h) Experiment v. simulation P (from Student's Experiment Simulation t test) Mean no. multicellular 57'i7 ± i'97 (12) 6027 ± 187 (11) 0-3 > P > 02 particles Mean no. cells/multicellular 6-68 ±0-24 (12) 711 ±022 (11) 02 > P > o-i particle Means are stated ± S.E. with the number of experiments in parentheses. Table 1 shows the number of multicellular particles, total particles and number of cells/multicellular particle 20 h after the addition of different number of cells to the wells. Few aggregates were formed at low cell numbers but with increasing cell numbers the number of aggregates increases until it reaches a plateau at about cells/well then declines at m o cells/well and above. The same pattern can be seen for the total particles/well. The number of cells/aggregate remains low up to about 275 cells/well then increases markedly at higher cell numbers/well. Table 2 shows the results at 20 h for 12 experiments and 11 computer simulations for 440 cells. There were no significant differences between (a) number of multicellular particles and (b) number of cells per multicellular particle in experiment and simulation. DISCUSSION In order to use this system reliably for quantitative studies of cells aggregating under their own locomotive pressure it was necessary to establish that the number of aggregates counted at 20 h was simply the result of (a) the random dropping of the cells, (b) the adhesion of cells when they make contact, and (c) the (free or restricted) random movement of all cells. At first this seemed improbable since the number of multicellular aggregates counted at 20 h remained practically constant (47-57) when the number of single cells plated at zero time varied 4-fold ( cells). The question thus arose: Is this narrow range in the number of aggregates found at 20 h simply the logical result of (a), (b) and (c) or is it necessary to introduce some further ad hoc assumptions to explain this phenomenon? One way to try to answer this question is to construct a non-biological analogue of the experiment which only incorporates (a), (b) and (c), and then see how the counts for the quantities which are the analogues of the multicellular aggregates at 20 h compares with the experimental counts. The conceptual development of such analogues is based on a simple physical model in which the analogues of cells and aggregates are disks of various sizes, placed on a large circular board; the initial positions of the disks are decided by randomly throwing imaginary darts at the board. The random movement of each disk is then selected by throwing a second dart at another board using the landing position of this dart to select the length and direction of disk move-

8 756 E. Mayheva and L. E. Blumenson ment for a i-min interval. However, it would take an inordinate length of time to perform enough of these physical simulations in order to make a meaningful comparison with the experimental data. Thus we turned to a computational model, the Monte Carlo method, which can be regarded as a speeded-up analogue of the ' disk and dart' model. Furthermore, the use of the model system permits one to distinguish whether the cells are making free or restricted random movements. Cell movements are such that fairly long periods of observation are necessary to distinguish between the 2 experimentally. However, Fig. 1 shows that computer simulations of the 2 types of movements clearly lead to different results at 20 h. In general, the free random walk model agrees closely with the experimental results, and the hypothesis of restricted random walk can be rejected. Thus it is not necessary to introduce further ad hoc assumptions to explain the peculiar variations in the number of aggregates, with the number of cells seeded into the cultures at zero time. Thus pretreatment of cells or medium could only affect the results through changing (1) the rate of random movement, or (2) the probability that contacting cells will remain adherent. It should be pointed out that we have observed that the rate of aggregate formation and the final aggregate size and number can differ under similar experimental conditions. The metabolic state of the cells affects the results considerably and cells which are growing more slowly tend to move more slowly. Thus both the state of the cells and cultural conditions must be extremely well controlled before meaningful quantitative statements can be made. In all instances more single cells were found in the experimental situation than in the computer simulation. This was probably due to the fact that (a) some dead, immotile cells were present in the cultures, but in the simulation we assumed that all cells were alive, and (b) we assumed in the simulation that all the cells moved randomly within a circle of radius 2 /tm during each minute, whereas some cells, although fully viable, moved much more slowly. Another source of discrepancy between the experimental observation and the simulation lies in the assumption that when cells made contact, the probability that they would remain in contact to form a multicellular particle was 1. However, time-lapse photography shows that the probability is less than 1, since cells were seen detaching from aggregates and moving to participate in the formation of other aggregates. Further, cells in small aggregates remain in motion, and the aggregates themselves were observed moving at velocities of several microns/min. However, such aggregate movement was incorporated in the computer simulation. The computer simulation is such that given the rate of cell movement we can predict the number of aggregates formed, for different probabilities that the adhesions formed after the cells come in contact are permanent. In this way it is a useful tool for elucidating the underlying mechanism of cell aggregation processes. We thank Dr L. Weiss for useful discussions and Mrs J. Ciszkowski for technical assistance. E.M. was supported in part by a June Lambert Memorial Grant from the American Cancer Society (P-403D) and L.E.B. by a Research Career Development Award, Ca 34932, from the National Cancer Institute.

9 Burkitt cell aggregation 757 REFERENCES ABERCROMBIE, M. (1965). The locomotory behavior of cells. In Cells and Tissues in Culture, vol. 1 (ed. E. N. Willmer), pp New York: Academic Press. CURTIS, A. S. G. & GREAVES, M. E. (1965). The inhibition of cell aggregation by a pure protein. J. Embryol. exp. Morph. 13, GASIC, G. J. & GALANTI, N. L. (1966). Proteins and disulfide groups in the aggregation of dissociated cells of sea sponges (Haliclona variabilis). Science, N.Y. 151, HOFFMAN, J., METROPOLIS, N. & GARDINER, V. (1955). Study of tumor cell populations by Monte Carlo Methods. Science, N. Y. 122, HOFFMAN, J. G., METROPOLIS, N. & GARDINER, V. (1956). Digital Computer studies of cell multiplication by Monte Carlo methods. J. natn. Cancer Inst. 17, KEMP, R. B., JONES, E. M. & GRSSCHEL-STEWART, U. (1971). Aggregative behaviour of embryonic chick cells in the presence of antibodies directed against actomyosins. J. Cell Sci. 9, MCCRACKEN, D. D. (1955). The Monte Carlo Method. Scient. Am. 192, METROPOLIS, N. & ULAM, S. (1949). The Monte Carlo Method. J. Am. statist. Ass. 44, MOORE, G. E., SANDBERG, A. A. & ULRICH, K. (1966). Suspension cell culture and in vivo and in vitro chromosome constitution of mouse leukemia L1210. J. natn. Cancer Inst. 36, MOSCONA, A. A. (1959). Patterns and mechanism of tissue reconstruction for dissociated cells. In Developing Cell Systems and Their Control (ed. D. Rudnick), pp New York: Ronald Press. MOSCONA, A. A. (1965). Recombination of dissociated cells and the development of cell aggregates. In Cells and Tissues in Culture, vol. 1 (ed. E. N. Willmer), pp New York: Academic Press. PuLVERTAFT, R. J. V. (1965). A study of malignant tumours in Nigeria by short term tissue culture. J. din. Path. 18, SNEDECOR, G. W. & COCHRAN, W. G. (1967). Statistical Methods, 6th edn. Iowa State: Ames. STEINBERG, M. S. & ROTH, S. A. (1964). Phases in cell aggregation and tissue reconstruction: An approach to the kinetics of cell aggregation. J. exp. Zool. 157, WAKEFIELD, J. D., THORBECKE, G. J., OLD, L. J. & BOYSE, E. A. (1967). Production of immunoglobulins and their subunits by human tissue culture cell lines. J. Imrnun. 99, WEISS, L. (1964). Cellular locomotive pressure in relation to initial cell contacts..?, theor. Biol. 6, {Received 8 October 1971)

10 E. Mayhew and L. E. Blumenson 3A Fig. 3. Aggregated cells at 20 h after dropping in well. Number of cells added to zero time were approximately n o, 180, 270, 440, 700, 1100, 1700, and 2700 for A - H respectively. Photographic field is approximately the same size as the field counted.