Defining and measuring complexity

What's complexity? For example, is the human genome more complex than the yeast genome (see my post on August 8th, 2010)? We intuitively answer this question with a big "OF COURSE". However, it has been surprisingly difficult to come up with an universally accepted definition of complexity. Although there is not yet a single science of complexity but rather several different sciences of complexity with different views about what complexity really means, the history of science shows us that the lack of an universally accepted definition of a central term in a new scientific field is more common than not. As an example, the modern genetics still does not have a good definition of gene at the molecular level.

The physicist Seth Lloyd proposed in 2001 three different dimensions along which to measure the complexity of a system:

1) How hard is it to describe?

2) How hard is it to create?

3) What is its degree of organization?

Another interesting proposed measure of complexity is the Shannon entropy, defined as the average information or "amount of surprise" a message source has for a receiver. Thus, using a classical example of genetics, we could say that the sequence CGTGGT has more entropy than the sequence AAAAAA and, therefore is more complex than the latter one. A completely random sequence has the maximum possible entropy. That means we could well make up an artificial genome by choosing a bunch of random As, Cs, Ts, and Gs. Using entropy as the measure of complexity, this random, almost certainly nonfunctional genome would be considered more complex than the human genome.

In conclusion: the most complex entities are not the most ordered or random ones but somewhere in between.

For further reading, see "Complexity: a guided tour" by M. Mitchell.

Why humans are different from rats?

Humans have a genome very similar to many other species. For example, more than 90% of our DNA is shared with mice and more than 95% with chimps. Why we are so different from these animals? The evolutionary developmental biology, whose nickname is Evo-Devo, proposes that morphological diversity among species is, for the most part, not due to differences in genes but in genetic switches that are used to turn genes on and off. These switches are the non-coding DNA, or the so-called "junk DNA", which are now known to be used in gene regulation. These genetic networks allow a huge number of possibilities for gene expression patterns, since there are so many possible ways in which proteins can be attached to the switches. The reason the humans share so many genes with quite different species is because, although the genes might be the same, the sequences making up switches have often evolved to be different. Small changes in switches can produce very different patterns of genes turning on and off during the development.

Are you sure this is a gene?

In 2006, a group of 500 scientists were given independently some real DNA sequences and asked whether each sequence qualified as a "gene". For many sequences, the opinion was split: about 60% answered they were confident that the sequences represented genes while 40% were confident that the sequences were not genes. The more specialized a scientist is in molecular biology, the less easy is to define what a gene actually is.

The gene concept and its context

The classical molecular concept of gene is not sufficient to explain several biological processes observed in studies performed in the last two or three decades. The idea of an one-to-one relationship between DNA and protein implies a structural and functional unity; however, the molecular biology showed us that some molecular phenomena like alternative RNA splicing, overlapping genes, and multiple transcription start sites, suggest that the one-to-one relationship is an oversimplification. This concept is no longer useful, except as a handy expression, whose meaning is dependent on the context. Among the several approaches to the multiple usages of gene, one that deserves attention is the concept of the gene as a “fuzzy unity”, which states the genomically diverse nature of the gene. Although this vagueness might have heuristic value, there’s a clear need for more precision. As stated by Eva Neumann-Held in "Cycles of contingency" , whatever the concept of gene is, it should consider the clarification of the purpose and the research context for which the concept is designed.