Several scaling relationships are important in cell structure. One is dimensional scaling—how the volume, surface area, and length of cells and its substructures relate to one another as the cell grows. These relationships depend both on the cell’s shape and the manner in which the cell grows. Consider the case where a cell doubles in volume before division then divides to form two daughters of similar shape (). In the ideal case of isotropic, three-dimensional growth of spherical cell (), a doubling of volume requires a roughly 60% increase in surface area and a 25% increase in diameter. There is a disparity as volume has increased two-fold but surface area has not. To achieve similarity of shape, dividing spherical cells must therefore provide more membrane surface area19,20
and/or remove volume.21
Different scaling relationships between cell dimensions can be achieved during the cell division cycle for cells with non-spherical cell shapes or polarized growth. For the roughly cylindrical fission yeast Schizosaccharomyces pombe
, growth of the cell occurs by elongation along the cylindrical axis while preserving the cross-sectional area ().22
In effect, the geometry has been reduced from three dimensions to one, and so volume increases are linearly proportional to both surface area and axial length. Thus, cell division requires no dramatic shape changes. The situation is more complicated in budding yeast, Saccharomyces cerevisiae
, where the mother cell volume remains largely constant while the bud size shows a combination of polarized (or apical) and isotropic growth ().23
Here, the shape of the mother-bud pair just before division has roughly double the original volume and surface area, similar to the case in fission yeast. However, the increases in volume and surface area during bud growth are less straightforward to correlate with one another.
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 (more ...)
Even the most basic question of how cell growth scales with time or progression along the cell cycle has also been a matter of intense study and debate. The two most prevalent models for cell growth are linear and exponential which are familiar as the solution to zeroth- and first-order rate equations. Both linear24
and exponential growth25,26
have been reported in various cell types, though these possibilities are often difficult to distinguish,27,28
and more complex growth patterns have also been reported.26,29,30
In the former, the rate at which a cell increases in size (typically measured by volume) is independent of its current size, and is hypothesized to be a result of a growth-limiting factor such as nutrient import which holds constant regardless of cell size.24
Exponential growth occurs when there is a linear relationship between growth rate and size, suggesting that the larger cell has proportionately more capacity for metabolism and growth.28
At a simple level, cells are membrane-bound structures that include smaller sub-structures or organelles. Each of these organelles performs a specific function and shows characteristic morphologies, though these vary from organism to organism. As the cell grows, generally organelles do as well to accommodate the typically greater need for their functions.31
How organelle size scales with cell size is a question garnering more attention as advances in microscopy and other imaging techniques allow for better quantification of cell and organelle size. A simple model to consider is that functional need for organelles increases with cell size, and that correspondingly organelle size increases with a straightforward linear scaling relationship. However, even in this overly basic framework, several questions arise. What is the relevant measure of size, both for the cell and for the organelle? Does the relevant cell size measure differ among the organelles? What is the relationship between organelle size and function, and how can this be measured?
Morphology can impact function in several ways. In terms of capacity, intuitively, as an organelle gets bigger, it will be able to perform more of the functions for which it is responsible, including metabolism, signaling, storage and homeostasis. Most organelles have membrane and lumenal environments to perform these functions, and these parameters are characterized by surface area and volume, respectively. The balance between two- and three-dimensional size determines the possible shapes of the organelle.
There are several transport factors that can depend on morphology. The first is transport between the organelle and other points in the cell. A centralized organelle like the nucleus will obviously sample a much more restricted region of the cell than a distributed network, and this localization can affect how long it takes to deliver cargo to and from that organelle. Further, cellular transport occurs by many mechanisms, and we will discuss two of these: diffusion and active transport using motor proteins traveling along the cytoskeleton. These modes of transport show different dependencies of average transport time vs. distance. Many signaling processes involve influx and subsequent diffusion of Ca2+
-ions or other species that are generally found at varying concentrations.32
The effective distance, d
, over which the signaling species propagates scales as the square root of time (d
), and therefore diffusion is more efficient at shorter length-scales. Motor protein-mediated transport requires input of ATP and allows the cargo to be targeted to particular destinations. Distance traveled scales linearly with time (d
t), which is more efficient than diffusion at longer length-scales. Then, there is transport of material from inside to outside the organelle (or vice versa), which is achieved by a number of passive or active mechanisms. The rate of these processes is likely limited in part by the amount of membrane or surface area in the organelle, and the surface area-to-volume ratio may be regulated to achieve the appropriate amount of transport back-and-forth between the organelle interior and cytoplasm. Such regulation would result in changes in membrane or lumen amounts and can occur somewhat independently for the two parameters, and this would be reflected in the overall shape of the organelle.
Just as cells show different growth patterns, there are several ways by which organelle size can increase: (I) Isotropic, three-dimensional expansion is generally found for larger, round organelles such as the nucleus. (II) Distributed networks—such as found for mitochondria and tubular endoplasmic reticulum (ER) in certain cells—are propagated by increasing the linear length of the network, keeping the cross-sectional dimensions roughly constant. (III) Organelles existing in multiple copies can simply be increased in number, as is the case for peroxisomes. Combinations of these scaling behaviors are also possible, as for example in the fungal vacuole, which can be found in a single, round morphology (I) as well as a fragmented collection of smaller vesicles (III).
Furthermore, each of these cases has different scaling properties as organelle and cell size increase (). Linear volume scaling between an organelle showing isotropic growth and the cell would give a constant proportion between organelle and cell dimensions (, purple sphere). With only one such organelle, it is trivial to optimize the transport distances to other places in the cell by placing it in the center. However, having two or more organelles necessarily breaks this symmetry, leaving at least one further away from some areas of the cell. This effect is well illustrated in electron tomography micrographs of the smallest known eukaryote, Ostreococcus tauri. O. tauri
cells contain only single copies of several organelles, which are tightly packed into a relatively small cell volume, with many organelles located at the cell periphery.33
Because of this organism’s size, all organelles are still within a short distance of all other points in the cell volume. However, these distances will grow longer with larger cells, and this may be a reason why in other organisms, only a small number of organelles tend to have this kind of morphology. Thus, organelle shape can affect cellular organization.
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), (more ...)
Organelles with network morphology ( and black lines) or multiple copies (, red spheres) can be more readily distributed around the cell as needed. An interesting scenario arises for linear networks that are localized to the periphery of an isotropically growing cell, as in the case of mitochondria in S. cerevisiae
Assuming linear scaling between cell volume and organelle length, as the cell grows its surface area increases as Vcell2/3
, meaning there will be proportionately less area per unit network length, and the area density of the organelle will increase. Network properties such as branching and spacing can adjust to accommodate this density scaling to a point. There is an upper limit on how much packing can be achieved, indicating a transition point at which the network is forced to enter into the cell volume to access more available space. With these general considerations in mind, we next consider the scaling and size regulation of particular organelles.