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Diffusion is one of the fundamental behaviors in physics, chemistry, and
biology. In short, it is the spontaneous “spreading” of particles from a
region of high concentration to one of lower concentration. In chemistry,
for example, we define diffusion as the movement of ions from a region of
higher
chemical potential
to a lower
one. In biology, diffusion is sometimes referred to as a form of
passive transport in which substances or
material cross
membranes. It is also
an excellent way to observe
random
motion as well as use
Monte Carlo
methods to predict long-term or large-scale behavior.
Diffusion plays a critical
role in biology; most biological systems are designed around diffusion
behaviors. For example, it is necessary for cells to exchange gases
(usually CO2 and O2), take in food and water, and
eliminate wastes. In order to accomplish this, molecules must move through
the membrane that surrounds the cell. The cell membrane is an amazingly
complex structure that is responsible for separating the contents of the
cell from its surroundings, for controlling the movement of materials into
and out of the cell, and for interacting with the environment surrounding
the cell.
Molecules move through the cell membrane in only two ways: by passive
transport and
active transport.
Active transport requires that the cell use
energy that it has
obtained from food to move the molecules (or larger particles) through the
cell membrane. Passive transport – on the other hand – does not require
such an energy expenditure and occurs the process occurs spontaneously. The
principle means of passive transport is diffusion.
However,
modeling diffusion at the cellular level is difficult, since the cell
membrane is so complex. In order to understand how this transport mechanism
works, we must better understand the process of diffusion first. Diffusion occurs when a system is not at
equilibrium. For example, suppose you release one drop of a
chemical dye into a glass of water (as shown on Figure 1 below).
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| Figure 1:
Chemical dye diffusing in water. |
Initially, the
molecules of the dye are found in a small volume of space. They move around
in what is known as a
random walk. Each
molecule moves in essentially a straight line and changes direction only
when it collides with another molecule or a surrounding water molecule. In
a short period of time, most of the molecules of the dye near the outside of
the drop move away from the center of the drop. Given enough time –
depending upon the size of each molecule and the surrounding water molecule
as well as the amount of energy each has – the dye becomes thoroughly mixed
in the water and the dye is diffused throughout. So, in order to play with
this idea, we will start with a simple example and add complexity until we
can develop a more complete
model.
Activity.
Write a
simple program that explores diffusion (also known as
Brownian motion). One such program is
given below (in a language called
NetLogo™).
Make modifications in the program in order to study the behavior of
diffusion.
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to setup
ca
;; clear everything
ask patches [
setup-cells ]
;; this sets up the position of the
setup-balls
;; cells,
balls, and patches.
setup-plotting
end
to setup-cells
;; this splits the screen in half
ifelse ( pxcor <= 100 )
[ set pcolor
blue ] ;;
and colors them.
[ set pcolor
yellow ]
end
to setup-balls
create-turtles total-number-of-balls ;;
create balls
ask turtles
;;
put them in each half
[set size
3 ;; and
count them.
set shape "circle"
ifelse who <
(balls-in-blue-container)
[ set color white setxy random 100 random-ycor ]
[ set color black setxy random (100) + 101 random-ycor
]]
set counter
(balls-in-blue-container)
end
to
go
;; randomly switch them from
ask turtle (random
total-number-of-balls) ;; side to side and count.
[ ifelse
pcolor = blue [ setxy random (100) + 101 random-ycor set counter counter - 1
]
[ setxy random 100 random-ycor
set counter counter + 1 ]]
do-plot
end |
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This program
runs a Monte Carlo simulation of two types of particles moving between a
membrane. By changing several parameters (the number of balls to start with
and the number of balls on a particular side of the screen), you can better
recognize how diffusion works in a simple 2-D model (Figure 2). Enjoy!
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|
Figure 2: Screenshot of the diffusion
program |
It
should be clear now that diffusion is the foundation to modeling much of
biological behavior at the cellular level. The next step – after testing
several diffusion simulations – is to see how to actually use the concepts
in diffusion to further our understanding of the mechanisms driving biology. |
