The rates of molecular motions can be measured by a variety of spectroscopic techniques. A large globular protein is constantly tumbling, rotating about its axis about a million times per second. Molecules are also in constant translational motion, which causes them to explore the space inside the cell very efficiently by wandering through it—a process called diffusion. In this way, every molecule in a cell collides with a huge number of other molecules each second. As the molecules in a liquid collide and bounce off one another, an individual molecule moves first one way and then another, its path constituting a random walk (Figure 2–26). In such a walk, the average net distance that each molecule travels (as the “crow flies”) from its starting point is proportional to the square root of the time involved: that is, if it takes a molecule 1 second on average to travel 1 μm, it takes 4 seconds to travel 2 μm, 100 seconds to travel 10 μm, and so on.
The inside of a cell is very crowded (Figure 2–27). Nevertheless, experiments in which fluorescent dyes and other labeled molecules are injected into cells show that small organic molecules diffuse through the watery gel of the cytosol nearly
Figure 2–25 How enzymes work. each enzyme has an active site to which one or more substrate molecules bind, forming an enzyme–substrate complex. a reaction occurs at the active site, producing an enzyme–product complex. The product is then released, allowing the enzyme to bind further substrate molecules.
as rapidly as they do through water. A small organic molecule, for example, takes only about one-fifth of a second on average to diffuse a distance of 10 μm. Diffusion is therefore an efficient way for small molecules to move the limited distances in the cell (a typical animal cell is 15 μm in diameter).
Since enzymes move more slowly than substrates in cells, we can think of them as sitting still. The rate of encounter of each enzyme molecule with its substrate will depend on the concentration of the substrate molecule. For example, some abundant substrates are present at a concentration of 0.5 mM. Since pure water is 55.5 M, there is only about one such substrate molecule in the cell for every 105 water molecules. Nevertheless, the active site on an enzyme molecule that binds this substrate will be bombarded by about 500,000 random collisions with the substrate molecule per second. (For a substrate concentration tenfold lower, the number of collisions drops to 50,000 per second, and so on.) A random collision between the active site of an enzyme and the matching surface of its substrate molecule often leads immediately to the formation of an enzyme–substrate complex. A reaction in which a covalent bond is broken or formed can now occur extremely rapidly. When one appreciates how quickly molecules move and react, the observed rates of enzymatic catalysis do not seem so amazing.
Two molecules that are held together by noncovalent bonds can also dissociate. The multiple weak noncovalent bonds that they form with each other will persist until random thermal motion causes the two molecules to separate. In general, the stronger the binding of the enzyme and substrate, the slower their rate of dissociation. In contrast, whenever two colliding molecules have poorly matching surfaces, they form few noncovalent bonds and the total energy of association will be negligible compared with that of thermal motion. In this case, the two molecules dissociate as rapidly as they come together, preventing incorrect and unwanted associations between mismatched molecules, such as between an enzyme and the wrong substrate.
The free-energy Change for a Reaction, ∆G, Determines Whether it Can occur spontaneously