Distinguishing between linear and exponential cell growth during the division cycle: single-cell studies, cell-culture studies, and the object of cell-cycle research

Abstract

Background: Two approaches to understanding growth during the cell cycle are single-cell studies, where growth during the cell cycle of a single cell is measured, and cell-culture studies, where growth during the cell cycle of a large number of cells as an aggregate is analyzed. Mitchison has proposed that single-cell studies, because they show variations in cell growth patterns, are more suitable for understanding cell growth during the cell cycle, and should be preferred over culture studies. Specifically, Mitchison argues that one can glean the cellular growth pattern by microscopically observing single cells during the division cycle. In contrast to Mitchison's viewpoint, it is argued here that the biological laws underlying cell growth are not to be found in single-cell studies. The cellular growth law can and should be understood by studying cells as an aggregate.

Results: The purpose or objective of cell cycle analysis is presented and discussed. These ideas are applied to the controversy between proponents of linear growth as a possible growth pattern during the cell cycle and the proponents of exponential growth during the cell cycle. Differential (pulse) and integral (single cell) experiments are compared with regard to cell cycle analysis and it is concluded that pulse-labeling approaches are preferred over microscopic examination of cell growth for distinguishing between linear and exponential growth patterns. Even more to the point, aggregate experiments are to be preferred to single-cell studies.

Conclusion: The logical consistency of exponential growth--integrating and accounting for biochemistry, cell biology, and rigorous experimental analysis--leads to the conclusion that proposals of linear growth are the result of experimental perturbations and measurement limitations. It is proposed that the universal pattern of cell growth during the cell cycle is exponential.

Figure 1

Human growth as a function of age. This chart, developed by the Center of Human Health Statistics, was obtained from a web search and shows the mean height (50^th percentile) and deviations from the mean height in percentiles.

Figure 2

Growth board for two individuals. This board has been used to record over the last 19 years the heights of Raya Cooper and Moses Cooper. At various times the child would stand against the board and their height would be measured by drawing a line and dating the line. At the left is the full board and at the right is a close-up of a portion of the board.

Figure 3

Chart of height of two individuals. The heights from the growth board from Figure 2 were determined and the heights are plotted in inches. The vertical bars are the birth dates.

Figure 4

Comparison of experimental measurements of exponential and linear growth. (a) Plotting of exponential and linear growth over one doubling shows that the lines are quite similar (circles, linear; squares, exponential). (b) Adding of small variations up and down to alternate exponential points shows that the lines for exponential and linear growth are very similar. (c) Removing the connecting line and looking at only the data for the varied exponential line shows that one cannot eliminate exponential growth by a straight line on rectangular coordinates. (d) Comparison of differential measurements of growth showing that one can distinguish between exponential growth and linear growth using differential measurements.

Figure 5

Reanalysis of the data of Kubitschek [16]. At the left is the original data of Kubitschek and at the right is a replotting on logarithmic coordinates. The details are presented in the text.

Figure 6

Cell cycle analysis of leucine uptake (and protein synthesis) during the division cycle. A100-ml amount of E. coli B/r lys mutant cells in culture medium (10⁸ cells per ml growing in minimal medium with glycerol and lysine) was labeled for 2 min with 2 uCi of [14C]leucine (450 mCi/mmol; New England Nuclear Corp.). The cells were then filtered, washed, and analyzed by assaying the radioactivity per cell eluted from the membrane-elution apparatus. The dashed line is the expected pattern for a constant rate of leucine uptake and protein synthesis during the division cycle. This constant rate is predicted by a model of linear rate of increase in mass during the division cycle. The upper cell elution curve has oscillations that are due to the initial cell age distribution of the cells at the time they were filtered. The decrease in the dashed line is placed at the end of the first division cycle as indicated by the cell elution curve. The decreasing exponential curve of radioactivity per cell indicates exponential growth.

Figure 7

Biosynthesis rates of the various components of the bacterial cell during the division cycle [48]. The curves are drawn proportional to their relative contributions to the cell, using the results of Neidhardt [54] for E. coli grown in minimal glucose medium. The percentages of dry weight are as follows: peptidoglycan, 2.5%; DNA, 3.1%; lipopolysaccharide, 3.4%; other (including polyamines, salts, glycogen, etc.), 6.4%; lipid, 9.1%; RNA, 20.5%; and protein, 55.0%. The RNA, protein, and other materials were assumed to have an exponential increase. The synthesis rates of lipid, lipopolysaccharide, and peptidoglycan were presumed to be proportional to the peptidoglycan synthesis rate [42, 44-47]. The rate for DNA synthesis was assumed to be linear with a doubling in rate in the middle of the division cycle [3, 25, 27]. The dotted line is an exponential increase; it indicates the difference between the calculated mass increase and exponential mass increase. The two panels are the same graphs but differ in scale to illustrate the biosynthesis rates of the less prominent material.

Figure 8

Growth in length of a single wild-type cell of S. pombe. The data for the cell lengths from Figure 2 of Sveiczer et al. [49] are plotted on a semi-logarithmic scale. The data are indicated by the filled squares. The straight line drawn through the points is the best fit based on a minimization of deviation of points from the straight line. A straight line on semi-logarithmic coordinates indicates exponential growth.

Figure 9

Length extension in the growing period of a single wild-type cell of Schizosaccharomyces pombe. Lower curve, cell length; upper curve, smooth rate of extension (see text). Data from article by Mitchison, Sveiczer and Novak [51]. See text for detailed analysis.