The protein shown here is pyruvate kinase, one of the key enzymes in metabolism. This particular example comes from the common domestic cat (Felix domesticus).
Cartoons such as this one are intended to show how the backbone chain of amino acids is folded to produce the final three-dimensional structure of a protein. In this case the polypeptide chain is represented by a blue ribbon. There are spiral sections representing regions of secondary structure called α-helices and flattened sections called β-strands. The β-strand regions are often twisted.
This particular protein adopts a structure with three distinct parts called domains. As a general rule, each domain has a well-defined shape with a characteristic pattern of strands and helices. The pattern is called a fold and it it thought that there are only 1000 or so different folds in the protein universe. Different folds can be combined to make up all known proteins.
(For those who might be interested, the three domain folds in this protein are TIM beta/alpha barrel, PK beta-barrel, and the PK C-terminal domain.)
When proteins are first synthesized you can think of them as a long extended chain of amino acids with no particular secondary or tertiary structure. We refer to such unordered macromolecules as random coils. Within seconds, this random coil spontaneously folds itself into a highly ordered three-dimensional structure such that every single molecule of a given protein has the exact same shape. For example, every molecule of pyruvate kinase looks exactly like the one shown here.
The rapidity of this folding reaction tells us something about the mechanism of protein folding. We know that folding is rapid and spontaneous because proteins can be purified then unfolded by treating them with certain chemicals that cause them to become denatured or unfolded. These denatured proteins can then be allowed to re-fold when the chemicals are removed.
Cyrus Levinthal did some back-of-the-envelope calculations on the rate of protein folding. He assumed that a protein could randomly try all possible three-dimensional conformations until it found the correct one. Under those conditions it would take 1087 seconds to fold a protein of 100 amino acid residues. This is quite a bit longer than the age of the universe (6 x 1017 seconds).
Obviously, there's something wrong with the assumptions behind what came to be known as the Levinthal Paradox. As a matter of fact, the paradox was never really a paradox since the whole point of the calculation was to shown that proteins did not fold by randomly searching though the conceptual universe of all possible shapes.
The final structure of a protein minimizes the energy of the random coil by burying hydrophobic amino acids in the interior of the molecule. Hydrophobic (water fearing) amino acids are those that don't like to be exposed to water. Just as scattered oil droplets in your salad dressing will eventually coalesce to form a layer of oil over a layer of vinegar and water, so too will hydrophobic amino acids come together to form an "oily" globule in the middle of the protein. Water is excluded from this "molten globule" and this makes folding an entropically driven spontaneous reaction.
You can visualize the process by picturing a field of all possible energy levels of the random coil. The one representing the properly folded protein is the deepest well on the energy surface. The bottom of the well is the lowest energy level for the protein and this represents the stable three-dimensional structure. Protein folding, then, is like finding the well and falling down into it.
As mentioned above, the search for the lowest energy well is not a random search of all possible shapes. That would take far too long. Instead, folding proceeds in a cooperative stepwise manner with small regions of secondary structure forming first.
The most striking regions of secondary structure are the short α-helices. Certain stretches of amino acid residues will rapidly form α-helical regions involving local bonding between amino acids. These form extremely rapidly since the amino acids are already in close contact. Furthermore, the formation of these local secondary structures takes place simultaneously in many different parts of the random coil.
The helix and strand regions represent the minimal energy conformations of the local parts of the protein. Subsequent folding proceeds by forming the helices and strands into the appropriate three-dimensional folds that are characteristic of each domain. The possibilities here are much fewer than the total of all possible conformations because you are now combining blocks of amino acids that have already adopted some structure.
The figure below shows some hypothetical examples of folding pathways. Very few folding pathways have been worked out in detail but the basic principles are well understood. The biggest unsolved problem is predicting the three-dimensional structure of a protein from its amino acid sequence. This involves finding the predicted lowest energy level and that's turning out to be a tough problem indeed.