MadSci Network: Cell Biology Query:

### Re: How would overall cell size affect processes like osmosis, diffusion,

Date: Wed Jan 12 06:58:19 2005
Posted By: Ian WHITE, Secondary School Teacher, Biology 11-19, Godalming College
Area of science: Cell Biology
ID: 1105485120.Cb
Message:
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Dear Cathy,
This is a question of 'supply and demand'!

This is a 'central concept' in biology!
Surface area is where all exchanges take place between 'inside'
and 'outside', whether this be the cell (membrane and cytoplasm) or
lungs/gut (outside world and body) or skin/fur and the rest of the
universe!

In economic terms, surface = supply; inside = demand.

Think of a series of cubes.
Side 1x1x1 gives surface area of (1x1) x6 = 6; volume of 1x1x1 = 1. Thus
SA/V = 6

Side 2, gives SA of (2x2) x6 = 24; vol of 2x2x2 = 8. SA/V of 3
Side 3 gives Sa of (3x3) x 6 = 54; vol of 3x3x3 = 27. SA/V of 2
Side 4, 5 and 6 give ratios of 1.5, 1.25 and 1.0

Thus, the larger the organism, the smaller the SA/Vol ratio!

If a cell gets TOO big, then the mechanical forces on the membrane will
break it; however, if the cell is smaller, but very active, then it may be
unable to absorb enough oxygen/glucose to meet its requirements.  The
normal solution to this is to change shape!  Spheres have the smallest
possible surface area/vol ratio (bad for cells).  A cube is almost as bad,
but long, thin, cells (such as nerve cells), or wide, flat cells (such as
those lining your cheek) have a LARGE surface area/vol ratio (good for
cells).  A third option is to fill the whole of the centre of the cell
(furthest from the outside) with water, leaving the living bit (cytoplasm)
as a thin layer just inside the membrane.  Plant cells do this!

Hence big cells tend to be 'passive' (fat cells, plant storage cells);
active cells tend to be long and thin (nerves, muscles).

For WHOLE organs/organisms, the same principles apply:

Lungs/guts/Red Blood Cell's have a large surface area to allow rapid
exchange (gas or food); small organisms don't need a blood supply, nor
specialised gas exchange surfaces, but are limited in size; insects can
never be bigger than they are; large animals keep warm easily, but may
have problems keeping cool (elephants, hippos); small organisms have
problems keeping warm, thus hibernate in the cold.

The biggest bear - polar bears; the biggest penguin - Emperor penguins,
living in the Antarctic in winter (brrrrrrr!)!
The smallest bear - Koalas - living in Australia (130F+ ...phew!); the
smallest penguins - Rock-Hopper penguins that live on the Galapagos (=
tortoise in Spanish!), which are right on the equator!

Big animals = cold regions, small animals = hot regions.

Other answers are on www.biologymad.com - then search under 'surface area
to volume ratios'

See below:

Diffusion and the Problem of Size

All organisms need to exchange substances such as food, waste, gases and
heat with their surroundings. These substances must diffuse between the
organism and the surroundings. The rate at which a substance can diffuse
is given by Fick's law:

Rate of Diffusion a
surface area  x concentration difference

distance

The rate of exchange of substances therefore depends on the organism's
surface area that is in contact with the surroundings. The requirements
for materials depends on the volume of the organism, so the ability to
meet the requirements depends on the surface area : volume ratio. As
organisms get bigger their volume and surface area both get bigger, but
volume increases much more than surface area.. This can be seen with some
simple calculations for different-sized organisms. In these calculations
each organism is assumed to be cube-shaped to make the calculations
easier. The surface area of a cube with length of side L is LxL X6 (6L²),
while the volume is L³.

Organism    Length    SA (m²)    vol (m³)    SA/vol (m-1)
bacterium    1 mm        (10-6 m)      6 x 10-12      10-18
6,000,000
amoeba    100 mm    (10-4 m)     6 x 10-8      10-12    60,000
fly    10 mm      (10-2 m)      6 x 10-4    10-6    600
dog    1 m           (100 m)      6 x 100    100    6
whale    100 m       (102 m)    6 x 104      106    0.06

So as organisms get bigger their surface area/volume ratio gets smaller.
A bacterium is all surface with not much inside, while a whale is all
insides with not much surface. This means that as organisms become bigger
it becomes more difficult for them to exchange materials with their
surroundings. In fact this problem sets a limit on the maximum size for a
single cell of about 100 mm. In anything larger than this materials simply
cannot diffuse fast enough to support the reactions needed for life. Very
large cells like birds' eggs are mostly inert food storage with a thin
layer of living cytoplasm round the outside.

Organisms also need to exchange heat with their surroundings, and here
large animals have an advantage in having a small surface area/volume
ratio: they lose less heat than small animals. Large mammals keep warm
quite easily and don't need much insulation or heat generation. Small
mammals and birds lose their heat very readily, so need a high metabolic
rate in order to keep generating heat, as well as thick insulation. So
large mammals can feed once every few days while small mammals must feed
continuously. Human babies also loose heat more quickly than adults, which
is why they need woolly hats.

So how do organisms larger than 100 mm exists? All organisms larger than
100 mm are multicellular, which means that their bodies are composed of
many small cells, rather than one big cell. Each cell in a multicellular
organism is no bigger than about 30mm, and so can exchange materials
quickly and independently. Humans have about 1014 cells.

Multicellular organisms have another difference from unicellular ones:
their cells are specialised, or differentiated to perform different
functions. So the cells in a leaf are different from those in a root or
stem, and the cells in a brain are different from those in skin or muscle.
In a unicellular organism (like bacteria or yeast) all the cells are
alike, and each performs all the functions of the organism.

Cell differentiation leads to higher levels of organisation:

A tissue is a group of similar cells performing a particular function.
Simple tissues are composed of one type of cell, while compound tissues
are composed of more than one type of cell. Some examples of animal
tissues are: epithelium (lining tissue), connective, skeletal, nerve,
muscle, blood, glandular. Some examples of plant tissues are: epithelium,
meristem, epidermis, vascular, leaf, chollenchyma, sclerenchyma,
parenchyma.

An organ is a group of physically-linked different tissues working
together as a functional unit. For example the stomach is an organ
composed of epithelium, muscular, glandular and blood tissues.

A system is a group of organs working together to carry out a specific
complex function. Humans have seven main systems: the circulatory,
digestive, nervous, respiratory, reproductive, urinary and muscular-
skeletal systems.

A multicellular organism like a human starts off life as a single cell
(the zygote), but after a number of cell divisions cells change and
develop in different ways, eventually becoming different tissues. This
process of differentiation is one of the most fascinating and least-
understood areas of modern biology. For some organisms differentiation is
reversible, so for example we can take a leaf cell and grow it into a
complete plant with roots, stem, leaf and vascular tissue. However for
humans and other mammals differentiation appears to be irreversible, so we
cannot grow new humans from a few cells, or even grow a new arm.

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