Before revision:  Finally, and most importantly, the focused analysis of the heat kernel provides us a way to yield insights on the fact that proteins have to satisfy specific structural design constraints that the other considered biochemical networks do not need to obey  .
After revision:  Finally, and most importantly, the focused analysis of the heat kernel provides us a way to yield insights on the fact that proteins have to satisfy specific structural design constraints that the other considered biochemical networks do not need to obey . Notably, the heat trace decay of the protein ensemble denotes subdiffusion, a peculiar property of proteins .