Differential versus Integral

I’ve been thinking about how information arises and grows in an origin-of-life context. I recently started reading From Matter to Life, a compilation of essays on Information and Causality, mainly authored by scientists although a couple of contributions are from philosophers. One essay that caught my attention was “Digital and Analogue Information in Organisms” by the systems biologist Denis Noble.

Scientific essays can be dense and difficult to understand, particularly when dealing with complex matter (pun intended). Noble’s essay is refreshingly clear in its presentation, especially since I am not a systems biologist. He begins by clearly outlining the main issue:

Are organisms encoded as purely digital molecular descriptions in their gene sequences? By analyzing the genome alone, could we then solve the forward problem of computing the behaviour of the system from this information? I argue that the first is incorrect and the second is impossible. We therefore need to replace the gene-centric digital view of the relation between genotype and phenotype with an integrative view that also recognises the importance of analogue information in organisms and its contribution to inheritance across generations. Nature and nurture must interact. Either on its own can do nothing.

Evidence is provided by analyzing the relative importance of inherited non-DNA components found in egg and sperm cells. Unlike the digitally-encoded information of DNA, these components provide information in analogue form. The living cell isn’t just a bag of chemicals, but is full of structural organization within – a microcosm packed into a micron. Representing the analogue complexity is no easy feat. Replicating this information is no easy feat either. It’s much easier to copy digital information and store it in compressed form. 

DNA is popularly described as the blueprint of life. The builder reading it can construct everything from the blueprint! Except that you also need the builder. And the tools or equipment. And the raw materials. And scaffolding. And energy sources. The idea that life can be fundamentally reduced to a Dawkins-esque selfish gene that autonomously directs its own replication is a fantasy. Fantastic sounding, but a fantasy nevertheless. Noble calls this the differential view of genetics. It’s a bottom-up gene-centric reductionist view of biology, still prevalently transmitted through biology classes in high school and college, not to mention the popular press.

If you remove DNA from the cell of one organism and inject DNA from a different organism into it, you might end up with a strange hybrid but more often than not the cell simply becomes non-viable. DNA and its analogue counterparts must interact compatibly, and it turns out that you can’t just build the latter solely from the former. Easy examples illustrating the power of alleles that significantly influence phenotype are useful for introducing basic concepts in genetics, but there are very few cases where a single gene wields such influence. In most cases, many genes and epigenetic factors contribute. In humans, there is no single gene for intelligence, or even something very measurable such as height.

It also turns out that evolutionary change can take place through mechanisms other than DNA mutation. Noble advocates an integral view relating genotype and phenotype that encompasses both the digital and the analogue. He favorably quotes Andreas Wagner’s recent book for examples of how evolution can be accelerated through other mechanisms beyond DNA mutation. Genetic digital information should not necessarily be privileged over the vast analogue information – the two work in tandem, and there might even be more information from the analogue contribution.

As I’ve been steeped in answering P-Chem questions with the final exam approaching, I was particularly struck by an analogy Noble makes between the two views and the dreaded Calculus. I must admit that I’ve mainly thought about calculus operationally – what I can do with it – and not as much about what it means. I also never took the standard college calculus class and likely missed chunks of the theory in my scientific education. I close this post with Noble’s analogy and summary. Who would have thought that solving integrals is what life does!

Restricting ourselves to the differential view of genetics is rather like working only at the level of differential equations in mathematics, as though the integral sign had never been invented. This is a good analogy, since the constants of integration, the initial and boundary conditions, restrain the possible solutions possible in a way comparable to that by which the cell and tissue structures restrain whatever molecular interactions are possible… Multilevel interactions are important both in development and in evolutionary change… [and] are analogue in nature because they depend on constraints of lower (e.g., molecular) levels by higher-level processes that are formed as dynamic patterns. These patterns represent continuous variation in expression levels of genes and many other factors.