In Shannon's communication model (Appendix 20), long delay periods are required to encode and decode the signal. The delay increases the dimensionality of the space (because more numbers are used to describe the signal), so that the spheres become more sharply defined. Sharp-edged high dimensional spheres overlap less than fuzzy low dimensional ones, and this reduces the error rate. Therefore, a long coding period can be used to protect against noise. Surprisingly, this allows a communication system to operate at the channel capacity and yet have arbitrarily few errors [Shannon, 1949]. A well known example of this kind of coding is the parity check [Hamming, 1986,Gersting, 1986].
A simple molecular machine can reach high dimensionality only by using spatial mechanisms since it is not possible for them to remember more than one item at a time (Appendix 23). In a time-encoding, the parts of a communications signal that are spread out in time are combined to form a code to protect against errors [Sloane, 1984,Conway & Sloane, 1988,Gilbert, 1966]. In a space-encoding, the information from a set of parallel channels is combined to form the code. The simplest molecular machines are obliged to use space-encoding, so their parts must interact during the operation. Indeed, cooperative interactions within a single molecule were recently proposed to explain the high accuracy of the restriction enzyme EcoRI [McClarin et al., 1986,Rosenberg et al., 1987b,Rosenberg et al., 1987a,Rosenberg et al., 1987c,] and the specific binding of sugars by cell surface receptors [Vyas et al., 1988], while the cooperative nature of DNA and RNA hybridization [Britten & Kohne, 1968] and oxygen binding by hemoglobin [Perutz, 1970] are well known. The frequent appearance of lock-and-key [Rastetter, 1983,Gilbert & Greenberg, 1984] and allosteric mechanisms [Monod et al., 1965] in molecular biology suggests that space-encoding is used by most if not all molecular machines. Instead of paying for accuracy by using long time periods, molecular machines use large numbers of interacting atoms.
Shannon's channel capacity theorem states that as long as the rate of communication is less than the channel capacity, the error rate may be made arbitrarily small. This theorem also applies to molecular machines because the proof is based only on the geometry of the spheres, and this is the same for both models (see Appendix 21). In terms of molecular machines, the theorem says that:
The degree to which this happens during evolution depends, of course, on the requirements for function, the current design, and the evolutionary paths available to the machine. If a good code is found (i.e. if there is a good way to have the molecular machine's motions in one state be distinct from the motions when it is in another state), then the molecular machine can operate close to its machine capacity. In other words, the enormous complexity of molecular machines allows them to be accurate, and coding theory should help us to understand the mechanisms, accuracy, and evolution of molecular machines.