2. (20 pts) Let's discuss about how antibodies favorably or unfavorably bind to receptors on cells with thermodynamics. First, think about the antibody binding with entropy S. (a) Say we have a cell that has the 5 proteins to bind antibodies. When 2 antibodies are added, calculate entropy by the statistical approach. Assume that one antibody binds one protein on the cell. Please change the sign of this entropy to be negative because the antibody binding reduces the disorder of antibody. (b) Now let's think about the entropy caused by the displacement of water molecules by antibodies at the binding sites of proteins on the cell. Say 3 water molecules are binding each protein on the cell. When an antibody binds a protein site, 2 water molecules are displaced (see a picture below for clarification). Calculate entropy when 2 antibodies bind 5 membrane proteins. To do this, let's simplify that you can treat like total number of waters on a cell as holes (i.e., 15 holes) and total number of waters binding to 2 protein sites as balls (i.e. 4 balls). The sign of this entropy is positive because more water molecules are released from the cell. n=422=435=15 (c) The affinity of antibody to protein can be considered as an enthalpy term of Gibbs free energy equation; G=HTS The overall entropy is the sum of (b) and (c). Typically, the enthalpy of antibody-protein binding is 9.901020J. Is this antibody favorable to bind the cells at 298K based on Gibbs free energy? Justify your result. (d) To flip the binding status obtained in (c), what do you do? Comment with the justification