Raw egg white contains avidin. As dietary protein is digested, the presence of avidin can bind to biotin tightly preventing its absorption into the body (1). Because biotin is used as a prosthetic group in acetyl CoA carboxylase, a biotin deficiency can then inhibit the carboxylation reaction catalyzed by acetyl CoA carboxylase that converts malonyl CoA from acetyl CoA and CO2 (2). The conversion to malonyl CoA is ultimately the reaction by which carbons of a fatty acid are contributed to by acetyl CoA (2). Cooking destroys the avidin, which is a good thing.
But wait, an article in the latest Journal of Nutrition explains that Maillard reaction products (result of heating proteins and sugars) may alter amino acid availability and reduce digestibility of certain proteins (3). It would lead to believe that you'd want your protein raw or microfiltered versus fried or treated with ultra-high temperatures. Sure enough, you'll get more protein from a raw egg, plus enzymes and vitamins.
In the end, if you're going to eat eggs at all (see next post on cholesterol), it's probably best to cook the egg minimally and take a quality multi-vitamin and an enzymes supplement. That way you don't accidentally get salmonella.
Reference List
1. Brody T. Nutritional Biochemistry. San Diego: Academic Press, 1999.
2. Gropper SS, Smith JL, Groff JL. Advanced Nutrition and Human Metabolism. Belmont, CA: Thomson Wadsworth, 2009.
3. Lacroix M, Bon C, Bos C et al. Ultra high temperature treatment, but not pasteurization, affects the postprandial kinetics of milk proteins in humans. J Nutr 2008;138:2342-7.