Describing life as information can clarify questions about sequences, inheritance and prediction. It can also hide important differences. A count of possible sequences, a physical copying mechanism and a biological function are distinct subjects that need to be connected explicitly.
Counting possibilities
Consider strings of eight symbols drawn from an alphabet of four symbols. There are 4⁸ = 65,536 possible strings. Specifying one among equally likely alternatives requires log₂(65,536) = 16 bits. This is a statement about an ensemble and its coding, not a measurement of biological function.
Now restrict the strings to contain exactly two of each symbol. There are 8!/(2!)⁴ = 2,520 distinct arrangements. Selecting one from this equally weighted set corresponds to log₂(2,520), approximately 11.30 bits. A constraint on composition reduces the number of alternatives without selecting one arrangement.
For example, AABBCCDD and ABCDABCD have identical one-symbol frequencies and different ordering. A description that records only the frequencies loses that distinction. Whether the lost distinction matters depends on the process that uses or responds to the sequence.
Function needs a context
Imagine a device that responds only when two adjacent symbols are both A. It distinguishes our example strings: AABBCCDD contains AA, while ABCDABCD does not. A different device might respond only to total composition and treat them alike.
The example makes a limited point: the same sequence description can be sufficient for one task and insufficient for another. In biology, a functional claim likewise needs a specified system and consequence. Calling a sequence information does not identify the machinery, interactions or environmental conditions that make the consequence occur.
Nor should the largest number of bits automatically be read as the greatest biological value. A highly variable sequence can carry little information about a particular outcome. The appropriate question is which distinctions improve a specified prediction or support a specified operation.
Inheritance is physical
Meselson and Stahl investigated DNA replication using nitrogen isotopes to distinguish material histories. After bacteria grown with heavy nitrogen were supplied with light nitrogen, their 1958 experiment found intermediate-density DNA after one generation. After two generations, intermediate and light DNA were present in approximately equal amounts. These observations constrained how parental material was distributed during replication and agreed with semiconservative copying.
The original paper and Caltech archive show how a claim about inheritance was tested through physical separation and measurement. The observation was not merely that a message remained readable; it concerned how old and newly incorporated material were related.
Follow two kinds of continuity
For a simplified semiconservative bookkeeping example, start with one double-stranded molecule whose two strands carry an old label. After one ideal copying round there are two molecules, each with one old strand. After two rounds there are four molecules, two with an old strand and two without one. After three rounds, two of eight molecules retain an original strand.
This construction assumes copying without label recycling, degradation or sequence error. The number of original strands stays two while the number of molecules doubles each round. The fraction of molecules carrying an original strand after n ≥ 1 rounds is 2/2ⁿ. Sequence continuity and constituent continuity therefore need not have the same numerical description.
The turnover model tracks a different history: loss from a constant stock. The two models should not be merged merely because both contain changing proportions. Their assumptions about growth, replacement and what is labelled differ.
Information and prediction
A biological description is useful when it retains distinctions relevant to the question. A sequence may be needed to predict one response, a population distribution to predict another, and an environmental record to predict a third. “The information” is incomplete unless we identify the variables, alternatives and task.
This is the theme of memory for prediction. A compressed description can be adequate for current observations and inadequate after a change in conditions. Discovering that limitation tells us which additional state distinctions the model needs.
For Duality of Time, a corresponding question is how an observer's retained description relates to the proposed generative state. A biological application would have to preserve the distinctions required for real inheritance and response. An analogy between DNA and a programme does not supply that mapping by itself.
Sources and further reading
- Meselson, M. and Stahl, F. W. (1958), The replication of DNA in Escherichia coli, PNAS 44, 671–682. Published paper; published text.
- The sequence-counting and ideal strand-bookkeeping examples are teaching constructions, not estimates of the information content of an organism.
- Adaptation and history; Duality of Time: book contents.