of his legs. He died "held in the greatest affection by more than a hundred scientific descendants all over the world". Cooperativity of protein binding and enzyme kinetics Although Hill's work in muscle physiology is probably the most important, and certainly responsible for his Nobel Prize, he is also very well known in biochemistry for the Hill equation, which he used to quantify binding of oxygen to haemoglobin, written here as a kinetic equation, as it is mainly used for that: Here is the rate of reaction at concentration of substrate, is the rate at saturation, is the value of that gives , and the exponent is a parameter that expresses the degree of departure from Michaelis-Menten kinetics: positive cooperativity for , no cooperativity for , and negative cooperativity for . Note that there is no implication that is an integer, and in most experimental cases, apart from the trivial case of , it is not. Although many authors use or rather than these symbols are misleading if taken to imply that it shows the number of binding sites on the protein. Hill himself avoided any such interpretation. The equation can be rearranged as follows: This shows that when the Hill equation is accurately obeyed (which usually it is not) a plot of gives a straight line of slope . This is called a Hill plot. Muscle physiology Hill made many exacting measurements of the heat released when skeletal muscles contract and relax. A key finding was that heat is produced during contraction, which requires investment of chemical energy, but not during relaxation, which is passive. His earliest measurements used equipment left behind by the Swedish physiologist Magnus Blix, Hill measured a temperature rise of only 0.003 °C. After publication he learned that German physiologists had already reported on heat and muscle contraction and he went to Germany to learn more about their work. He continually improved his apparatus to make it more sensitive and to reduce the time lag between the heat released by the preparation and its recording by his thermocouple. Hill is regarded, along with Hermann Helmholtz, as one of the founders of biophysics. Hill returned briefly to Cambridge in 1919 before taking the chair in physiology at the Victoria University of Manchester in 1920 in succession to William Stirling. Using himself as the subject he ran every morning from 7:15 to 10:30 he showed that running