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:

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 (6L), 
while the volume is L.   

Organism    Length    SA (m)    vol (m)    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. 


Cell Differentiation    [back to top] 
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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