Deriving nutrition information using mathematical estimation: the example of phenylalanine in sweets with gelatin

Phenylketonuria (PKU) is a protein metabolism disorder characterized by high blood levels of the amino acid phenylalanine. This results from a mutation in the gene responsible for phenylalanine hydroxylase, an enzyme that converts phenylalanine into tyrosine. When this enzyme is deficient, phenylalanine builds up in the blood, leading to symptoms such as vomiting, rashes, seizures, growth deficiency, and severe mental retardation. An early diagnosis and a diet restricting phenylalanine intake...

Sugar (a simple carbohydrate) metabolism (chemical reactions) is a classic example of the many cellular processes that use and produce energy. Living things consume sugar as a major energy source because sugar molecules have considerable energy stored within their bonds. Consumed carbohydrates have their origins in photosynthesizing organisms like plants. During photosynthesis, plants use the energy of sunlight to convert carbon dioxide gas into sugar molecules, like glucose. Because this...

The fundamental mathematical principles, such as calculus and graphs, play crucial roles in analyzing drug movement and determining pharmacokinetic parameters. Differential calculus examines rates of change and helps to determine the dissolution rate of drugs in biofluids, as well as how drug concentrations change over time. For instance, it can help calculate the rate of elimination of a drug from the body based on its concentration-time profile.
On the other hand, integral calculus focuses on...

Imagine adding a small amount of sugar to a glass of water, stirring until all the sugar has dissolved, and then adding a bit more. You can repeat this process until the sugar concentration of the solution reaches its natural limit, a limit determined primarily by the relative strengths of the solute-solute, solute-solvent, and solvent-solvent attractive forces. You can be certain that you have reached this limit because, no matter how long you stir the solution, undissolved sugar remains. The...