Evidence for complex, collective dynamics and emergent, distributed computation in plants

Abstract

It has been suggested that some biological processes are equivalent to computation, but quantitative evidence for that view is weak. Plants must solve the problem of adjusting stomatal apertures to allow sufficient CO(2) uptake for photosynthesis while preventing excessive water loss. Under some conditions, stomatal apertures become synchronized into patches that exhibit richly complicated dynamics, similar to behaviors found in cellular automata that perform computational tasks. Using sequences of chlorophyll fluorescence images from leaves of Xanthium strumarium L. (cocklebur), we quantified spatial and temporal correlations in stomatal dynamics. Our values are statistically indistinguishable from those of the same correlations found in the dynamics of automata that compute. These results are consistent with the proposition that a plant solves its optimal gas exchange problem through an emergent, distributed computation performed by its leaves.

Fig. 1.

(a) Confocal micrograph of a 0.56-μm² region of a leaf surface showing a field of (bean-shaped) stomata. (b) Near-infrared image of a 6.25-cm² region of a leaf surface showing patchy chlorophyll fluorescence. The image is brighter where the leaf's stomata are more closed.

Fig. 2.

Space–time diagrams of the 1D GKL classifier CA. The top line in each case has 75 white sites and 74 black sites. (a) “Easy problem” in which the space correctly becomes all white at t = 140. (b) “Hard problem” created by randomly interchanging the states of two sites in the starting configuration of a. Relaxation to a (wrong, in this case) uniform black state does not occur until t = 290.

Fig. 3.

State trend images. (Top) A 15 × 15 sandpile CA. Red sites have more grains than they did six time steps in the past, yellow sites have fewer grains, and black sites have the same number of grains. The activity in the avalanche spreads in a typically irregular fashion. (Middle) A 15 × 15, nonuniform density classifier CA. Red sites have a higher state value than six time steps in the past, yellow sites have a lower state value, and black sites have the same state value. The activity contains triangular structures that propagate coherently from left to right at constant speed. (Bottom) A 25-mm² portion of a leaf during dynamical patchiness. Red pixels have a higher fluorescence intensity than they did eight minutes earlier, yellow pixels have a decreased intensity, and black pixels have the same intensity. As in the classifier CA, a coherent, nondispersive (yellow) structure propagates at constant speed (≈8 μm/s) from the upper left to the lower right.

Fig. 4.

Stomatal aperture [or stomatal conductance (SC)], as measured by gas exchange, is inversely correlated with chlorophyll fluorescence [or pixel intensity (PI)]. Data demonstrate that fluorescence is an accurate surrogate for aperture.

Fig. 5.

Waiting-time (squares) and event-size (circles) distributions for fluorescence intensity “events” during stomatal patchiness. (Inset) A small portion of the event data used to determine the distributions.