1 - Information Theory and the Thermodynamic Efficiency of Biological Sorting Systems: Case Studies of the Kidney and of Mitochondrial ATP-Synthase

Abstract

It occurs that the kidney, an organ, and the mitochondrion, an organelle, are both physical realizations of a Maxwell demon. To understand how this occurs, a detailed analysis of the operation of the demon construct and of organ and organelle is given. The focus of attention in this chapter is upon the energetic cost of gathering information, as occurs in the biological function of both the kidney and mitochondrion. We give the mathematical definition of the cost of information. Horton A. Johnson and Knud D. Knudsen pioneered the use of this expression in calculating the efficiency of the kidney, solving a paradox long held, to the effect that the kidney efficiency was an order of magnitude less than that of comparable organs. By accounting for the cost of information gathered by the kidney in its biological function, its efficiency was shown to be of a magnitude similar to other such organs. Here we follow the reasoning of Johnson and Knudsen, but apply it to the biological function of the mitochondrion. In this way, we arrive at an efficiency for the mitochondrial oxidative phosphorylation that is approaching 90%, considerably higher than the corresponding textbook value of some 60%. This increase in the efficiency of the mitochondria parallels precisely the increase in the efficiency of the kidney achieved by Johnson, and for the same reason, viz., recognizing explicitly that there is an energy cost of information that must be paid for by whatever is the ultimate source of energy that is driving the process. Remarkably, information is not free but must be accounted for. The minimal energetic cost of one binary decision is kT ln2, irrespective of the precise mechanism at play. The parallel of the kidney and the mitochondrion, as two realizations of Maxwell's demon of substantially different size, is a biological illustration of an almost poetic observation of Feynman, to the effect that nature's patterns in the small are to be found repeated in the large, reminiscent as we might say of the repetitions characteristic of fractals.