This section of the AP Biology curriculum focuses on cell size and shape. More specifically, it looks at how the surface-area-to-volume ratio of a cell helps determine how efficient that cell is at exchanging macromolecules with the external environment. Cells fall within specific limits, based on the surface-area-to-volume ratio, due to specific constraints of the cell membrane and the functions of the cell itself. Plus, this section looks at how organisms manipulate cell size and shape to create various functions and complete difficult tasks!

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ENDURING UNDERSTANDING
ENE-1
The highly complex organization of living systems requires a constant input of energy and the exchange of macromolecules.

LEARNING OBJECTIVE
ENE-1.B
Explain the effect of surface area-to-volume ratios on the exchange of materials between cells or organisms and the environment.

ENE-1.C
Explain how specialized structures and strategies are used for the efficient exchange of molecules to the environment.

ESSENTIAL KNOWLEDGE
ENE-1.B.1
Surface area-to-volume ratios affect the ability of a biological system to obtain necessary resources, eliminate waste products, acquire or dissipate thermal energy, and otherwise exchange chemicals and energy with the environment.

ENE-1.B.2
The surface area of the plasma membrane must be large enough to adequately exchange materials –

1. These limitations can restrict cell size and shape. Smaller cells typically have a higher surface area-to-volume ratio and more efficient exchange of materials with the environment.
2. As cells increase in volume, the relative surface area decreases and the demand for internal resources increases.
3. More complex cellular structures (e.g. membrane folds) are necessary to adequately exchange materials with the environment.
4. As organisms increase in size, their surface area-to-volume ratio decreases, affecting properties like rate of heat exchange with the environment.

ENE-1.C.1
Organisms have evolved highly efficient strategies to obtain nutrients and eliminate wastes. Cells and organisms use specialized exchange surfaces to obtain and release molecules from or into the surrounding environment.

RELEVANT EQUATIONS

Volume of a Sphere: V = (4/3)πr³
Volume of a Cube: V = s³
Volume of a Rectangular Solid: V = lwh
Volume of a Cylinder: V = πr²h

Surface Area of a Sphere: SA = 4πr²
Surface Area of a Cube: SA = 6s²
Surface Area of a Rectangular Solid: SA = 2lh + 2lw + 2wh
Surface Area of a Cylinder: SA = 2πrh + 2πr²

r = radius
l = length
h = height
w = width
s = length of one side of a cub

2.2 Cell Structure and Function Overview

The big picture of section 2.3 is that the complex organization of living systems requires constant energy and the exchange of macromolecules. To understand how cells accomplish these tasks, we must first look at the size and shape of cells. Surface area-to-volume ratios are incredibly important to cells, as they affect the ability of cells to obtain nutrients and gather energy from the environment.

In fact, the smallest known cells are about 1 micrometer. These bacterial cells are similar in size to chloroplasts and mitochondria. Bacterial cells can get slightly bigger, up to about 100 micrometers. However, with their simple construction and lack of internal organelles, this is about the maximum size of a bacterial cell. To become larger, cells need an endomembrane system that helps efficiently distribute nutrients and excrete waste products. Eukaryotic cells can get up to 1 centimeter – though the large majority of eukaryotic cells are closer to 100 micrometers.

In fact, if you look at the blood cells in an elephant and a mouse, you will find that they are the exact same size. That is because blood cells are maximally efficient at this particular size. Other cells may be bigger in the elephant – such as nerve cells that must span much larger distances – but in general, cells reach a maximum size based on one factor: their surface area-to-volume ratio. Let’s take a look at this concept!

All cells, from bacterial cells to the cells in your body, must exchange macromolecules, gases, and water with the outside environment. The cell membrane is composed of many phospholipid molecules. These phospholipids hold a high number of proteins, many of which are responsible for importing or exporting substances to or from the cell. As a cell gets larger, the volume of the cell increases much faster than the surface area. Therefore, the cell would need more membrane proteins in order to fulfill the needs of the internal cytosol. At a certain point, a cell would need more proteins than it can reasonably pack into the cell membrane. This is why cells have an upper limit.

Likewise, as a cell gets smaller it limits the number of phospholipid molecules that surround it, and therefore the number of proteins that can be held within the membrane. This forms the lower limit of cell size. This is why the surface area-to-volume ratio of a cell is so important – it is an effective way to measure how efficiently a cell can exchange the substances it needs to survive!

A surface area-to-volume ratio is exactly what it sounds like. It is the total surface area of a cell, divided by the total volume of the cell. In order to calculate the surface area-to-volume ratio for a cell, first, we have to find an appropriate model for the cell.

Most plant cells have a cuboid shape. If we pretend that a plant cell has a height of 2 millimeters, and a width and depth of 1 millimeter each, we can easily calculate both the volume and the surface area using simple geometric formulas. The volume is 2, while the surface area is 10. So, the surface area-to-volume ratio is 10 divided by 2 – which reduces to 5.

If we consider a similar-sized single-cell organism, only with a spherical shape, let’s see what we get. If the diameter of this cell is 2 millimeters, the radius is 1 millimeter. Therefore, the volume is about 4.2 mm³. The surface area is about 12.6 mm². Therefore, the surface area-to-volume ratio is 12.6 divided by 4.2. This reduces to 3. So, this cell has a slightly smaller surface area-to-volume ratio, simply because it is spherical in shape! This tells us that not only does size matter, but shape can also increase or decrease the SA-to-V ratio!

The limits imposed by the surface area-to-volume ratio of cells can be seen through several examples. Let’s start with the largest cells in nature – eggs!

At this end of the spectrum, the cell has much more volume than it has surface area. In fact, if these were normal cells they would likely not be functional because processes carried out in their volume would far outweigh the amount of surface area that the cell has available to exchange macromolecules. However, eggs are not normal cells. At the time they are laid, they are not actively creating products, excreting wastes, or otherwise exchanging macromolecules with the environment. That’s because eggs are packed full of nutrients when they are formed. Then, the single-cell inside rapidly divides many times to become an organism. The cells get consecutively smaller with each division, becoming more efficient each time. Thus, by the time they hatch as a fully-formed organism, the average cell size in an egg has decreased by orders of magnitude!

By contrast, these bacteria are at the other end of the size spectrum. They are just large enough to house their DNA and carry out the basic functions of life. Compared to their volume, their surface area is much higher, giving them a very high surface area-to-volume ratio. In fact, if they were any smaller these cells would not have the volume to allow DNA to replicate properly, and their lipid bilayer may not have enough room for all of the proteins needed to import and export macromolecules!

While these surface area-to-volume constraints apply to single cells, there are many ways organisms can increase the efficiency of obtaining nutrients within a larger organism. The most common theme in cells that need to absorb a lot of nutrients or substances from the external environment is simply folding cells and cell membranes in ways that increase the surface area. In turn, this increases the surface area-to-volume ratio and allows the cells to be as efficient as possible. Let’s consider a couple of examples.

Alveoli are small sacs – located in the lungs – which are responsible for both absorbing oxygen and expelling carbon dioxide. Instead of one large cell at the end of each airway, these small sacs are lined with hundreds of tiny, rectangular cells. If oxygen and carbon dioxide had to diffuse through only 1 large cell, it would take a lot of time and be much less efficient. By contrast, the many endothelial cells that create the alveoli can quickly transfer oxygen into the capillaries and carbon dioxide out of the body.

Similar to the folding pattern seen in alveoli is the massive surface area increase of cells in the small intestine. In fact, there are three levels of folding that happen to dramatically increase the surface area available to absorb important nutrients from food. First, the intestine lining itself is folded, doubling the surface area of each fold. On top of these folds are more tiny projections – called villi – that also double the surface area available. Each villus is covered in cells. If we look closely at these cells, we can see that each cell has its own microvilli. These tiny extensions of the cell membrane massively increase the surface area available to take in nutrients. Altogether, the folds of this system increase the efficiency of the intestinal lining hundreds of times over!

Similarly, the excretory system of humans also works by making convoluted folds in tissues, cells, and individual cellular membranes that drastically increase their surface area. For example, let’s take a look at the kidneys – the body’s main excretory organ.

The kidney is an organ made up of many identical structures. Each medulla is packed with cells and has both arteries and veins – taking in blood from the heart, filtering out nitrogenous wastes, and sending the blood back to the heart.

Inside each medulla are the Malpighian tubules. These tubules are made of many smaller cells, which have different functions in different parts of the fold. Like the cells in alveoli, each of these cells is small, rectangular, and pretty flat – allowing for the maximum efficiency! In fact, a single kidney can filter half a cup of blood every minute. Since you have about 20 cups of blood in your body, that means your kidneys can filter all of the blood in your body every 40 minutes. That kind of efficiency is necessary for large organisms with trillions of cells that are constantly creating waste products!

While importing and exporting substances is the main reason why certain cells have surface area-to-volume ratio limits, there are many other functions that need cells of a certain size. For instance, certain organisms need to dissipate heat. They do so with many small cells on the skin and in the lungs that can transfer heat out of the body. By contrast, seals that swim in the frigid waters of the Arctic are covered in a layer of very large fat cells. These cells hold in heat, allowing them to live in water that would quickly give a human hypothermia.