## Diffusion, Osmosis, and Membranes

#### Overview:

Membranes give cells mechanical structure, protection, and regulate (either actively or passively) substances from entering it and others from leaving it. At this point we have explored diffusion as modeled by the random walks simulations and molecular dynamics as modeled by the Lennard-Jones simulation.

In order to begin to understand cellular structure and function, we first look at diffusion and osmosis quantitatively across an egg membrane. The transport of materials across the membrane is controlled passively by pore size and chemical structure. Then we will relate this experiment to computer-based models of membranes. Future Units will explore active transport across cells along with additional computer-based models.

#### Background:

Plasma membranes are characterized by their differential permeability which allows certain molecules to move through them and others to be excluded.

If we have a container with marbles sitting at one end of the box together and shake the box so that the marbles move randomly, the net movement is that the particles move from an area of high concentration to lower concentration. This is called diffusion and can be modeled using random walks. For a review of diffusion and random walks see earlier units. More accurately, diffusion is not strictly a function of concentration, but rather a function of the change in the free energy of the particles. In the hands-on example where there are marbles in the corner all clumped together unmoving, this is a ordered, low entropy state with more free energy than a more disordered state. So, we can rephrase our generalization based on concentrations: The movement of particles of a particular substance is from regions of greater to regions of less free energy of that substance.

#### Hands-On:

So how does this help us understand membranes? Consider a U-shaped tube divided by a semipermeable membrane (as in the figure below). The membrane is permeable to water but not to sugar (black balls). Side A contains only water; side B contains a sugar solution. Initially the quantity of fluid in the two sides is the same. Can you describe using both pictures and words what will happen to this system with time? Draw what will happen to the fluid levels in the tube? Show what happens to the sugar (black balls). The box in the middle represents a microscopic representation around the area of the membrane. Illustrate what the membrane "could" look like, and show particles of water and sugar in their initial concentrations.

The egg membrane is such a semipermeable membrane which is permeable to water but not to solute (say sucrose). The movement across such a membrane is called osmosis.

#### Egg Osmosis Experiment:

• Each group will be given 5 eggs from which the shell has been dissolved away. We assume that each egg has approximately the same concentration of solute insite the membrane, and based on the rate of osmosis, we will attempt to determine what the concentration must be.

• Weigh each egg separately.

• Place each egg into separate beakers containing solutions of distilled water, 10 percent sucrose, 20 percent, 30 percent, and 40 percent. At 15 minute time intervals (15, 30, 45, 60, 75) remove the eggs from the beakers, wipe off the excess liquid, and weigh each egg.

• Plot the changes in weight of each egg against time.

Distilled water 10 percent sucrose 20 percent sucrose 30 percent sucrose 40 percent sucrose
T0

T15

T30

T45

T60

T75

Some questions to ponder: What can you say about the initial concentration of sucrose solution the eggs were bathed in before the experiment? Would increasing the temperature effect the rate of osmosis? What other conclusions can you draw from the graph? Do you think the eggs reached equilibrium at t=75 minutes?

#### Membrane Simulations:

Several simulations have been developed at the Polymer Center which can help students understand membranes. We build from simple models to more complex ones. A series of simulations illustrate the concept of random walks as a model for diffusion. Universal Molecular Dynamics can simulate a wide range of phenomena.