Protein Folding

Proteins are long biological molecules that are found in each living cell. A protein is made of a long chain (~10-1000) of short molecules called AMINO ACID. The function of a protein in the cell is determine by the type of amino acid that it is made of, the number of amino acids and the precise position of each amino acid.

The same protein can function differently depended on the arrangement of its amino acid.

When a protein is immersed in a water solution (like the biological cell) it is first look like this:
 



 


Then, very rapidly it start folding. The folding occur in a way that keeps the bond angles between the amino acid as a constant. The forces that determine the folding are van der Waals.
 


The numerical simulation


 


We use a monte-carlo simulation to find the final position of the protein. In each cycle one of the amino acid is randomly chosen and its bond angle is being flipped. The flipping of the bond angle is in a way that keep the angle absolute value. If the protein after the angle flipping reach a lower energy, it stays in the new position. Else if the new protein energy is higher then before, it will randomly stay in the new position. The higher the temperature is the more likely the protein will stay in the higher new position. By using this procedure the protein will fold and form symmetric forms which depend on the forces between the amino acid and the bond angles. The below figure shows the same protein as before after folding:
 



 


In the simulation we can keep track on the folding process by drawing the protein energy and spatial extent as the monte-carlo cycles proceed: