October 20, 2023 | David F. Coppedge

Plants Do Calculus

A simple shoot emerging from the soil can add, subtract,
and integrate multiple dynamic signals over time


The first seed leaf emerging from a grass seed, called a coleoptile, is a mathematical genius. Faced with constantly varying signals of temperature, wind, gravity and moisture, it calculates the information needed to continue growing upright. Two biologists at Tel Aviv University reverse-engineered what the tiny plants are able to do without a brain or central nervous system. They found that plants not only do arithmetic (23 June 2013), they can do calculus.

Plants sum and subtract stimuli over different timescales (Mathieu Rivière and Yasmine Meroz, PNAS, 10 Oct 2023). A glance through this Darwin-free scientific paper shows differential equations, integrals and derivations. The title of the paper mentions addition and subtraction, but the ability to integrate multiple input signals in a time-varying manner is the work of calculus. Here’s what the authors say about their measurements and experiments with wheat seed sprouts:

Plants are sessile decentralized systems with no brain or neural system, and very little is known regarding how they quantify external stimuli. We experimentally probe the dependence of gravitropic responses of wheat coleoptiles on the presence of previous stimuli, revealing how coleoptiles integrate multiple stimuli over time. We report quantitative evidence that plants effectively respond not only to sums of stimuli but also to differences between stimuli, over different timescales. This finding advances our understanding of how plants negotiate their environment since the ability of organisms to subtract stimuli over time is crucial in order to compare signals and is at the basis of navigation and active sensing.

A humble little seedling without a brain can add, subtract, compare values over time, and navigate with active sensing? Who taught it to do such things? There’s more. It’s calculator has a memory function.

We quantitatively show that coleoptiles respond not only to sums but also to differences between stimuli over different timescales, constituting evidence that plants can compare stimuli—crucial for search and regulation processes. These timescales also coincide with oscillations observed in gravitropic responses of wheat coleoptiles, suggesting shoots may combine memory and movement in order to enhance posture control and sensing capabilities.

Where is this memory located, if there is no brain? Don’t let the abstruse terms diminish your wonder at the discovery of a calculator with memory in a humble little seed. These authors proved its existence with quantitative results:

Here, the memory kernel represents the dynamics of a hierarchy of stochastic processes underpinning gravitropic responses, the details of which are currently not well understood, such as statolith sedimentation in gravity-sensing cells, and the ensuing asymmetrical redistribution of PIN proteins and the growth hormone auxin. Previous studies adopting a response theory approach to model tropic responses assumed an arbitrary form of the memory kernel and showed that the model qualitatively reproduced observations of temporal integration of multiple stimuli over limited timescales; however, they could not make quantitative predictions, or explain negative responses observed for transient stimuli at longer times. To obtain a quantitative picture of plants’ computational capabilities, in terms of quantifying and processing sensory information, it is necessary to extract the mathematical form of the memory kernel.

… which they proceeded to do, using experiments and measurements to figure out how the memory works.

Accordingly, in the first phase of this study, we sought to extract the memory kernel by probing the dependence of gravitropic responses on the history of stimuli. To this end, we exposed wheat coleoptiles to transient gravistimulation protocols. Coleoptiles were placed vertically on a platform, which inclined horizontally for a stimulus duration , then rotated back to the vertical (shown schematically in Fig. 1B). We recorded the gravitropic responses of coleoptiles to different values of stimulus duration…

… measuring the effects of rotation from 6 minutes (the minimum time needed to witness a response) to 10 hours, which is indistinguishable from time = infinity. Math whizzes will enjoy the calculus integrals and derivations. Here, in summary, is what they discovered:

Together, these findings provide quantitative evidence that plants respond to the sum and difference of stimuli over different timescales, framed within a general mathematical framework. These computational processes can be identified as fundamental elements of natural search algorithms, common across diverse biological organisms. In the context of signal processing or control theory, the memory kernel may be interpreted as a band-pass filter. The summation of stimuli is effectively a moving average, improving the signal-to-noise ratio of an environmental signal. Subtraction of stimuli, which has never been reported before in plants, is required in order to compare signals over time, a strategy commonly used by a variety of living organisms in order to detect and climb signal gradients.

Observed oscillations in the gravitropic reorientation of wheat coleoptiles have been conjectured to speed up the regulation of posture control. … Within this context, our findings suggest that shoots may enhance regulation of posture control by comparing the relative inclination of the organ sensed at either side of an oscillation or circumnutation period, or equivalently detect a light gradient by comparing measured light intensities. Furthermore, as the ability of plants to integrate stimuli has been observed for a range of species and tropisms, it suggests that these computational abilities might be general.

Put together, our study provides the backdrop for understanding how plants may combine memory and movement in order to enhance movement control and sensing capabilities in the face of weak signals and fluctuating environments.

Emerging leaves from a broadleaf plant (left) and grass (right). Credit: State of Nevada.

So while this is an amazing ability of plants, previously unreported, it also appears to be a general ability of all organisms. In fact, they cite research by others showing that bacteria use similar algorithms to sense and climb chemical gradients.

All this goes on in a little green shoot emerging from a humble seed into the first light of its new world.

We love to highlight Darwin-free science done rigorously with logical conclusions and mathematical analysis. This is way beyond any experiments you may have done with bean sprouts in middle school, watching them bend toward the light. Plants do calculus? Wow. The Creator of life is amazing; he implanted some of his wisdom into all he created. We owe him our humble adoration and thanks.

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