2.2 Surface area to volume ratio

2.2

Surface area to volume ratio

KEY IDEAS

Cells can be many different shapes and sizes, but very few are large enough to be seen by the human eye without the aid of a microscope. For cells to stay alive, their cytoplasm must exchange nutrients and waste with the external environment. This exchange occurs across the plasma membrane. Prokaryotic cells are much smaller than eukaryotic cells because they do not contain specialised organelles for specific tasks. Eukaryotic cells have compartmentalised organelles with specific roles so that the cell can carry out cellular processes efficiently.

Surface area and volume

Biologists compare the surface area to volume ratio (SA:V) of cells when they compare cell surface area size. Surface area refers to the surface area of the plasma membrane, the area surrounding the total area of the the cell that is exposed to the external environment. Volume refers to the space taken up by plasma membrane that diffusion occurs the internal contents or cytoplasm. across As a cell grows, both the surface area and the volume of the cell increase; however, the cell volume volume increases more than the surface area. This means that the bigger the cell, the more the total amount of difficult it is for the cell to exchange nutrients and waste between the centre of the cell and the space in a contained external environment. Small cells have a larger surface area to volume ratio than large cells. area As a result, small cells are better at taking in nutrients and removing waste than large cells. The surface area to volume ratio limits how big a cell can grow.

In this topic, you will learn that: ✚ surface area to volume ratio limits cell size ✚ organelles are needed for specific cellular functions. FIGURE 1 The irregular shape of this unicellular organism (called a desmid) maximises the surface area to volume ratio. DRAFT ONLY - NOT FOR SALE

a

0.1 nm 1 nm 10 nm 100 nm 1 μm 10 μm 100 μm 1 mm 1 cm 0.1 m 1 m 10 m 100 m 1 km Unaided eye Light microscope Electron microscope Lipid Atom Small Protein molecule

Fish egg Chloroplast Plant and animal cells Most bacteria T2 phage (virus)

Blue whale Human White-lipped tree frog

Giant pine tree metres (m) Range of sizes for organisms Ångstrom units (Å) 10 × 1000 × 1000 × 1000 Å = 1 m 1 Å = 10 –10 m nanometres (nm) 1000 × 1000 × 1000 nm = 1 m 1 nm = 10 –9 m micrometres (μm) 1000 × 1000 μm = 1 m 1 μm = 10 –6 m millimetres (mm) 1000 mm = 1 m 1 mm = 10 –3 m centimetres (cm) 100 cm = 1 m 1 cm = 10 –2 m Range of sizes for atoms, molecules and viruses Range of sizes for cells Range of sizes for organs and tissues b Units of measurement FIGURE 2 Most cells are so small that you need a microscope to see them. DRAFT ONLY - NOT FOR SALE

Cell size limitations

As cells grow, their volume increases at a much greater rate than their surface area. Therefore, there is more cytoplasm volume than plasma membrane surface. There are several consequences of increasing cell size. • The DNA within the nucleus (controlling activities such as protein production) is under higher demand because more cytoplasm and organelles need to be produced, maintained and replaced. • Growing cells have increased metabolism (cellular reactions), which means they produce more waste than smaller cells do. Waste can become toxic if it is not quickly removed from the cell. Large cells have more difficulty removing waste than small cells do. • Nutrients must be able to reach all regions of the cell and move across the plasma membrane fast enough to accommodate the needs of the entire cell. Small cells with large surface area to volume ratios can move nutrients from their membrane to the centre of the cell much faster than large cells with small surface area to volume ratios. Having more smaller cells or long, thin cells is more efficient than having a single large cell (Figure 3). Most cells reach a particular size and then divide to form more cells. metabolism all the chemical processes occurring within a cell Cut Change shape Cube 10 × 10 × 10 units Volume = 1000 units3 Surface area = 600 units2 SA:V = 6:10 Volume of each = 125 units3 Surface area of each = 150 units2 Total volume = 1000 units3 Total surface area = 1200 units2 Total SA:V = 12:10 8 cubes each 5 × 5 × 5 units Rectangular prism 5 × 5 × 40 units Volume = 1000 units3 Surface area = 850 units2 SA:V = 8.5:10 DRAFT ONLY - NOT FOR SALE

FIGURE 3 Cutting a large cube into smaller cubes demonstrates how an increased number of smaller cells is more efficient than a single large cell because they have an increased surface area to volume ratio.

WORKED EXAMPLE 2.2 CALCULATING SURFACE AREA TO VOLUME RATIO

Video Worked example 2.2: Calculating surface area to volume ratio

Consider Figure 4. For each cube, calculate: a the surface area (mm2 ) b the volume (mm3 ) c SA:V. SOLUTION a Calculate the surface area for each cube. Surface area (mm2) = length × width × number of sides (cube faces) Cube length 1 mm: Surface area = 1 × 1 × 6 = 6 mm 2 Cube length 2 mm: Surface area = 2 × 2 × 6 = 24 mm 2 Cube length 3 mm: Surface area = 3 × 3 × 6 = 54 mm2 b Calculate the volume for each cube. Volume (mm3) = length × width × height Cube length 1 mm: Volume = 1 × 1 × 1 = 1 mm 3 Cube length 2 mm: Volume = 2 × 2 × 2 = 8 mm3 Cube length 3 mm: Volume = 3 × 3 × 3 = 27 mm 3 c Calculate SA:V. Simplify the ratios by dividing by the highest common factor. Cube length 1 mm: 6 : 1 Cube length 2 mm (simplify by dividing by the highest common factor = 8) 24 : 8 = 3 : 1 (the second ratio is a simplification of the first ratio) Cube length 3 mm (simplify by dividing by the highest common factor = 27) 1 mm 2 mm 3 mm FIGURE 4 As cell size increases, the SA:V decreases because the volume increases more than the surface area. DRAFT ONLY - NOT FOR SALE 54 : 27 = 2 : 1

TABLE 1 Surface area to volume ratios for each cube

Cell length (mm) Surface area (mm2) Volume (mm3) 1 6 1

2 24 8 SA:V

6:1

3:1

3 54 27 2:1

Organelles in eukaryotic cells

Eukaryotic cells have membrane-bound organelles. A membrane enables an organelle to carry out a specialised cellular function; for example, chloroplasts carry out photosynthesis. Organelles contain enzymes and molecules in a unique internal environment that may be different from the surrounding fluid or of any other organelle. Diffusion The greater the area taken up by the plasma membrane, the more places there are for substances (e.g. oxygen, carbon dioxide and amino acids) to move randomly across it. However, as the volume of the cell increases, the organelles become spread further apart, increasing the time taken for nutrients to be transported to where they are needed. Organelles that are closer to the plasma membrane surface use these substances before they reach the centre of a cell. Therefore, the size of these cells is limited so that all regions of the cell, including the nucleus, can obtain the substances required for metabolic reactions.

Study tip

Cells that require rapid diffusion are often long and thin rather than square. They have adapted to having a large plasma membrane, increasing surface area without compromising the cytoplasmic volume.

Diffusion pathways

In small cells with a large SA:V, substances can move efficiently into the centre and waste can move out. Most of these substances move by a process of random movement, bumping into diffusion each other until they spread evenly across the cellular space. These diffusion pathways allow the random materials to reach all regions of the cell as rapidly as possible.movement of substances Larger cells (with a small SA:V) require more resources than can be provided by their across the plasma limited surfaces. There is a longer diffusion pathway and the central area of the cell does not membrane from an area of receive the substances it needs to function correctly. Ultimately, this means the cell is unable high substance to survive. concentration to an area of low substance You will learn more about diffusion in Topic 2.4. concentration

FIGURE 5 Diffusion across a cell membrane DRAFT ONLY - NOT FOR SALE

Cells are adapted for increasing SA:V

As multicellular organisms become larger and more complex, their cells become specialised to carry out one key function. For example, red blood cells are specialised to transport oxygen around the body. They do not pass on messages as nerve cells do, or contract like muscle cells. Specialisiation enables the multicellular organisms to become larger and more complex. This is different from unicellular organisms, which are much more inefficient and in which all cell processes are completed by a single cell. CASE STUDY 2.2 Cytoplasmic streaming The cytoplasm of larger eukaryotic plant and animal cells circulates within the cell in a process known as cytoplasmic streaming. The organelles and other components of the cytoplasm flow in a circular motion around the cell. Organelles such as chloroplasts circulate close to the cell wall where gases diffuse into and out of the cell. In this way, carbon dioxide that enters the cell reaches the chloroplasts rapidly for the process of photosynthesis. Often, in larger cells the nucleus does not circulate, but is situated towards the cell membrane rather than centrally within the cell (Figure 6). FIGURE 6 In epidermal cells of the aquatic plant Elodea, chloroplasts circulate by cytoplasmic streaming. Nucleus Chloroplasts DRAFT ONLY - NOT FOR SALE

CHALLENGE 2.2

SA:V in different shapes

Describe and explain

1 Define ‘diffusion’. 2 Explain the significance of surface area to volume ratio for cell size. 3 Draw a cell diagram to represent Figure 8 and label the regions of the Paramecium that relates to surface area and the area that relates to volume. 4 ‘Cell size is limited.’ Explain what is meant by this statement in terms of surface area to volume ratio. Consider the two shapes in Figure 7. 1 Calculate the SA:V of each shape. 2 Explain which shape has the larger SA:V and what this means for the cell. 2 mm 2 mm

CHECK YOUR LEARNING 2.2 Apply, analyse and compare

5 A student used modelling clay to make models of different ‘cells’ in the shape of a sphere, a rectangular prism and a flat sheet. All the models had the same volume. Predict which shape(s) would have the: a largest surface area to volume ratio b smallest surface area to volume ratio. 6 Apply your understanding of cell size to explain why single-celled protists are generally microscopic in size. 7 Read Case study 2.2. a Explain the purpose of cytoplasmic streaming. b Explain why the nucleus in larger cells is often located towards the cell membrane and not in the centre of the cell.

Design and discuss

FIGURE 8 A micrograph of a Paramecium cell 8 Discuss how different cell types are adapted to maximise surface area without increasing cell volume. Use examples in your discussion. 9 Design a simple experiment to demonstrate how increasing cell size can lead to a longer diffusion pathway. Remember to identify independent, dependent and (at least two) controlled variables for your experiment.

6 mm 2 mm 2 mm 1 mm FIGURE 7 Calculate the SA:V of each shape. DRAFT ONLY - NOT FOR SALE