Scaling properties of cell and organelle size

Abstract

How size is controlled is a fundamental question in biology. In this review, we discuss the use of scaling relationships-for example, power-laws of the form y∝x(α)-to provide a framework for comparison and interpretation of size measurements. Such analysis can illustrate the biological and physical principles underlying observed trends, as has been proposed for the allometric dependence of metabolic rate or limb structure on organism mass. Techniques for measuring size at smaller length-scales continue to improve, leading to more data on the control of size in cells and organelles. Size scaling of these structures is expected to influence growth patterns, functional capacity and intracellular transport. Furthermore, organelles such as the nucleus, mitochondria and endoplasmic reticulum show widely varying morphologies that affect their scaling properties. We provide brief summaries of these issues for individual organelles, and conclude with a discussion on how to apply this concept to better understand the mechanisms of size control in the cellular environment.

Keywords: allometry; cell; organelle; power law; scaling relationships; size control.

Figure 1

Illustration of the use of log-log plots to analyze power-law scaling relationships. Functions of the form y = Cx^α, where the prefactor C is used to normalize the plots to the desired range. The function is plotted for α = 1/2 (blue), 1 (red), 3/2 (green), and 2 (yellow) in linear coordinates (left) and log-log coordinates (right). In log-log coordinates, the lines have slope = α and y-intercept = log C.

Figure 2

The following cartoons illustrate three cell growth patterns. In each case, the cell (left purple) grows as illustrated by the grey arrows until total cell volume (V) increases to twice its original value (middle purple) with some increase in surface area (A). Division creates two daughters (right purple and yellow) with V and A equal to the original value. (I) A spherical cell grows isotropically in three-dimensions. Volume scales differently than surface area, leaving a discrepancy of the two sizes during division. (II) In fission yeast, the cell grows along the long axis, so V and A both scale as the length, L. (III) In budding yeast, the cell first experiences polarized growth to form a bud, then the bud grows until it reaches roughly the size of the mother cell.

Figure 3

Cartoon illustration of the scaling of organelles with cell size. The cell on the right is twice the diameter of the left. The eight-fold increase in cell volume is correlated to a proportionate increase in: (I) volume for a centralized organelle (purple), (II) total network length of tubular organelles (black lines), (III) copy number for organelles with multiple copies (red). The yellow organelle shows the effect of an eight-fold increase in surface area rather than volume for a centralized organelle.