Biology 131 The Movement of Solutes and Water Across Biological Membranes (Including Problem Set 2). Introduction As we have discussed in class, all cells are surrounded by a lipid bilayer membrane. This membrane is quite permeable to hydrophobic (“water fearing”) molecules (e.g. steroid hormones), is somewhat permeable to uncharged polar molecules (e.g., water) and is virtually impermeable to ions (e.g., K+). The permeability of cell membranes to small ions is provided by highly specialized proteins called ion channels. Ion channels typically have a hydrophobic portion that allows them to insert themselves into the lipid bilayer, and a hydrophilic region that forms a water-filled pore. The pore is formed from the aggregation of three or more alpha helices. The pore also has charged groups (provided by the amino acid R groups that extend out from the helix) that regulate what ions (K+or Na+or Ca2+, for example) are allowed to pass through the pore. As a consequence, cells have definite and variable permeability to ions that determines the overall membrane permeability to small ions. This overall permeability has profound consequences for the electrical state of cells. As this matter is so important to understanding the physiology of organisms, it is necessary that we develop a quantitative way of talking about it. The following discussion is intended to present a fundamental relationship of physiology, the Nernst equation, in an intuitive way. It is also easy to derive the Nernst equation from elementary considerations of energy relationships. In order to arrive at the Nernst equation, we first need to develop some basic understanding of the movement of solute molecules and water molecules. A similar, but non-quantitative, discussion of these matters is found in Chapter 5 as well as pp.848-850 of Life. You should carefully read that material as you think about the lectures and read these notes. Diffusion The diffusion of molecules is a manifestation of the dynamic nature of a “Restless Universe” as Max Born put it. The molecules of a solution (or gas or solid, for that matter) are in constant, incessant motion. They are continually colliding with each other and with the walls of their container. While their motion is random, we can predict the average distance that a molecule will move from some initial starting point in a given period of time. This distance depends on both the nature of the molecule itself and surrounding medium through which it moves, as well as the temperature, which determines the average kinetic energy (and thus the speed) of the molecules. This characteristic distance can be summarized by a constant that is specific for a given molecule in a given medium at a particular temperature. That constant is called the diffusion coefficient, D, and it has the units of area per unit time. For example, D for a potassium ion in an aqueous medium at 25oC is about 2.1 x 10-5cm2/s. By contrast, the diffusion coefficient of a protein molecule in a lipid bilayer membrane might be 10-91
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