A preview of a paper to be published in the journal eLife was provided by phys.org on June 23. Plants do sums to get through the night researchers show, was the title given their report.

New research shows that to prevent starvation at night, plants perform accurate arithmetic division. The calculation allows them to use up their starch reserves at a constant rate so that they run out almost precisely at dawn. “This is the first concrete example in a fundamental biological process of such a sophisticated arithmetic calculation.” said mathematical modeller Professor Martin Howard from the John Innes Centre.

…During the night, mechanisms inside the leaf measure the size of the starch store and estimate the length of time until dawn. Information about time comes from an internal clock, similar to our own body clock. The size of the starch store is then divided by the length of time until dawn to set the correct rate of starch consumption, so that, by dawn, around 95% of starch is used up.

An ‘in press’ copy of the paper by Antonio Scialdone (John Innes Centre), Sam Mugford (John Innes Centre), Doreen Feike (John Innes Centre), Alastair Skeffington (John Innes Centre), Philippa Borrill (John Innes Centre), Alexander Graf (ETH Zurich), Alison Smith (John Innes Centre), and Martin Howard (John Innes Centre) can be accessed here. From the paper:

Overall, these results demonstrate that the control of starch degradation at night to achieve almost complete consumption at the expected time of dawn can accommodate unexpected variation in the time of onset of darkness, starch content at the start of the night, and patterns of starch accumulation during the preceding day. Although the rate of degradation is different in a circadian clock mutant with an altered period from that in the wild-type, the capacity to adjust starch degradation in response to an unexpectedly early night is not compromised.

It’s important to understand that the computations do seem to be actions since they accommodate variations in the length of the night as well as the amount of starch acquired. The quantities involved are established by mechanisms that operate within the plant’s structure that respond to the start and end of night, and molecular activity that encodes the amount of starch stored. “Since it is conceptually unclear how such a computation might be performed,” the authors tell us, “we turned to mathematical modeling to generate possible mechanisms.” They assumed the presence of two molecules, one whose concentration was related to the amount of starch present, and one whose concentration encodes information about the expected time to dawn. Arithmetic operations are then implemented by chemical reactions.

It is a longstanding idea that cells are able to use proteins to store and process information through networks of interactions (Bray, 1995. Understanding how such biochemical networks work and what kind of computations they perform is an ongoing challenge (see Deckard and Sauro, 2004, Lim et al., 2013). Our analysis here has underlined the utility of analog chemical kinetics in performing arithmetic computations in biology. Importantly, we have for the first time provided a concrete example of a biological system where such a computation is of fundamental importance.

There is something fascinating, I believe, about the relationship between these molecular actions and our symbolic arithmetic. At the very least, this research demonstrates that outside of our symbolic representation of a computation, the action of a computation exists. It reminds me of a discussion of mathematics I once read where it was noted that the derivative can be expressed in more than one way – as a rate of change, as the slope of the tangent to a curve, or fully arithmetically as a limit. So, the question was asked, what is the derivative? Inevitably, the careful observation of something like a plant’s performance of division will contribute fresh insight into the way one might try to answer this question.

[…] June 2013, I wrote about researchers who claimed that plants do arithmetic. All of this work not only tells us […]