Information and Inactivation of Biological Material 277 



system completely, we need to state, in some pre-arranged sequence, which 

 type of atom is present in each elementary volume and the bonds between 

 that atom and its six nearest neighbors. Our specification then consists of a 

 message giving the appropriate symbol to each elementary volume. To cal- 

 culate the average information per symbol, we consider the probability /7,y 

 of having the /th type of atom in theyth bonding state. The average information 

 is then given by 



H=-lPii\o%2Pii (1) 



a 



If the/j/s are assumed from the average composition of dry bacteria (hydrogen, 

 52.2 mole per cent; carbon, 29.9 mole per cent; nitrogen, 7.6 mole per cent; 

 oxygen, 5.8 mole per cent; phosphorus, 2.9 mole per cent; sulfur, 1.6 mole 

 per cent), and if we assume that all the types of bonding configurations have 

 equal a priori probabilities, we can then calculate that H is of the order of 

 4.0 bits per atom. Since the different bond configurations have rather different 

 probabilities, our figure is high and 3 bits would probably be a more realistic 

 estimate. 



An alternative but equivalent method of finding the information content 

 is to assume that all states of the system have equal a priori probability. If 

 there are A'^ possible states and L of these are biologically functional, the 

 probability that the system is in a functional state is LjN and the information 

 is given by 



H = -log2 LIN = log2 TV - log2 L (2) 



If the system must be completely specified, L equals one and H takes on its 

 maximum value, log2 A'^. We may then calculate A^ from the number of per- 

 mutations of the atoms in the elementary atomic volumes and the permutations 

 of the bond states (1). This leads to the same average information content 

 per atom as the previous treatment. 



However, from a point of view of biology, we would like to know the 

 actual value of H rather than //,uax- ^^ we consider a large collection of spores 

 or viruses or enzymes in contact with a thermal reservoir at temperature T 

 and allow the system to come to thermal equilibrium over a long time, we 

 may regard the collection as a Gibbsian ensemble, and the ratio of the final 

 activity to the initial activity is a measure of the a priori probability of finding 

 the system in a functional state, in general the activity decreases with time 

 in an exponential fashion. In all the experiments that have been carried out, 

 the sample is too small and thermal equilibrium is never reached. This enables 

 us to determine a lower limit of the information content, but the limit is too low 

 to be of any practical use. For example, dry Bacillus suhtilis spores show an 

 exponential inactivation over twelve decades. There is no indication that the 

 system is nearing equilibrium so we may conclude that the a priori probability 

 of finding the system in a living state is less than 10^^. H is then greater than 

 — log2 10~^^ or greater than 42. Since the upper limit (based on L = 1) for 

 this system is of the order of 10^^ bits, the thermal data do not help very much 

 in bracketing the figure. Experimentally it is not feasible to carry thermal 

 inactivation studies below an activity of 10^^^ because of difficulties in the 



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