1.1.B SA/V ratio

Learning outcomes:

1.1.U3 Cell Surface to volume is an important limitation to cell size.

1.1.NOS1 Looking for trends and discrepancies- although most organisms conform to cell theory, there are exceptions.

(U - understanding; A - applications; NOS - nature of science; S - skills)

Cell membrane (plasma membrane)

The cell membrane, also called the plasma membrane, is found in all cells and separates the interior of the cell from the outside environment. The cell membrane consists of a lipid bilayer that is semipermeable (selectively permeable). The cell membrane regulates the transport of materials entering and exiting the cell.

The fluid mosaic model is used to describe the structure and function of the cell membrane.

Fluid mosaic model

Cell membranes are represented according to a fluid-mosaic model, due to the fact that they are:

Fluid – the phospholipid bilayer is viscous and individual phospholipids can move position.
Mosaic – the phospholipid bilayer is embedded with proteins, resulting in a mosaic of components.

Membrane transport

The cell membrane is selectively permeable to ions and organic molecules and controls the movement of substances in and out of cells.

The transport of substances across the cell membrane is carried out in an active and passive manner. Passive transport most often occurs through simple diffusion and facilitated diffusion.

Diffusion

Diffusion is a net movement of particles (for example, an atom, ions or molecules) from a region with a high concentration to a region with a low concentration, leading to spontaneous alignment (equilibrium) of concentrations throughout the occupied volume.

The rate of diffusion is proportional to the cross-sectional area of the sample, as well as the difference in concentrations, temperatures or charges.

Surface area (S, SA)

The space occupied by a two-dimensional flat surface is called the area. It is measured in square units. The area occupied by a three-dimensional object by its outer surface is called the surface area. It is also measured in square units.

The surface area of a cube is equal to the square of the length of its face multiplied by six.

The formula for calculating the area of a cube:

SA = 6 a2

Where:

S is the area of the cube,
a is the length of the face of the cube.

Volume (V)

Volume is the space occupied within the boundaries of an object in three-dimensional space. It is also known as the capacity of the object.

The volume of a cube can be calculated by knowing only the length of its edge. Since all its edges are equal to each other. Simply put, the volume of a cube is equal to the cube of the length of its edge.

The formula for calculating the volume of a cube:

V = a3

Where:

V is the volume of the cube,
a is the length of the face of the cube.

Surface area to volume ratio (S/V, SA/V, SA:V)

The SA/V ratio is the amount of surface area per unit volume of an object or group of objects.

Surface area is of great importance for metabolism because it is related to the diffusion of oxygen and nutrients.

The formula for calculating the ratio of the surface area to the volume of a cube is:

SA/V

Where:

S is the surface area of the cube,
V is the volume of the cube.

SA = 6 a2

V = a3

As linear dimensions increase, the surface area increases squared and volume cubed.

Dynamics of SA/V to increase in volume and surface area

As the size of the cube (green line) grows:

The surface area (yellow line) gradually increases;
The volume of the cube (blue line) also increases.

Everyone is growing, but the volume is growing faster than the surface.

SA/V ratio (red line) decreases as the size of the cubes increases.

Surface area of a cuboid

The formula for calculating the surface area of a cuboid is shown below:

SA = 2 * (a*b + b*c + a*c)

The formula for calculating the volume of a cuboid is shown below:

V = a*b*c

SA= 16 SA=2*(2*2+2*1+2*1)

V = 4 V=2*2*1

SA/V= 4 SA/V=16/4

SA= 18 SA=2*(1*4+4*1+1*1)

V = 4 V=1*4*1

SA/V= 4.5 SA/V=18/4

SA= 24 SA=6*22

V = 8 V=2*2*2

SA/V= 3 SA/V=24/7

SA= 34 S=2*(1*8+8*1+1*1)

V = 8 V=8*1*1

SA/V= 4.25 S/V=34/8

The importance of SA/V ratio for life processes in the cell

For more efficient (fast) gas exchange, cells must have the largest surface area while maintaining the same volume. The figure above shows how the surface area of the cell increases significantly with a slight decrease in volume. Which in turn leads to an increase in the SA/V ratio.

Amoeba

A large number of pseudopodia increase the surface area of the amoeba. Due to this, the exchange of gas and substances is very efficient for her.

Alveoli

Due to the cellular structure, the alveoli have a large surface area. Due to this, gas exchange between the atmosphere and blood vessels is very efficient.

Villi

There are a lot of villi in the intestines, where each cell has its own microvilli. As a result, they have a very large surface area. Which is very effective in absorbing particles from digested food.

Why are almost all unicellular organisms small?

A large volume with a small surface area does not allow gas exchange to occur efficiently. Gas exchange in living organisms proceeds by diffusion, and its rate is a very important factor.

For example, one large cell has a low SA/V ratio and another group of cells of the same volume has a higher SA/V ratio in sum. Therefore, diffusion is most efficient in cells with a high SA/V ratio.

The figure shows that a small cell has a high SA/V ratio, the same as a group of cells, but much larger than a single cell of a huge volume.

An exception to the rule

Single-celled organisms cannot be large, however, there is an exception to the rule. Below are two examples, these are fairly large single-celled organisms.

Syringammina fragilissima

Syringammina reaches large sizes due to its folded structure, and its SA/V ratio is very high.

Valonia ventricosa

Valonia is spherical in structure and this clearly reduces its SA/V ratio. However, it has a huge central vacuole inside. Due to it, the entire cytoplasm with organelles is close to the outer surface.

Form matters

For unicellular organisms, the shape is of great importance. For example, there are different forms of bacteria: cocci (spherical) bacilli (rod-shaped) spirilla (long and spiral).

Larger SA/V ratio allows bacilli and spirilla to be larger than cocci.

A high SA/V ratio also has much biological importance. For example, you can observe the size of the ears of the arctic and desert fox, as well as the ears of the mammoth and the African elephant.

Large ears are necessary for animals living in hot climates. Since through such large ears, there is a large loss of heat and the body is cooled.

Illustration of the woolly mammoth (left) and modern African elephant (right). Artwork by Alexa R. Stephenson.

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