A new mechanism for stomatal responses to humidity and temperature is proposed. Unlike previously-proposed mechanisms, which rely on liquid water transport to create water potential gradients within the leaf, the new mechanism assumes that water transport to the guard cells is primarily through the vapour phase. Under steady-state conditions, guard cells are assumed to be in near-equilibrium with the water vapour in the air near the bottom of the stomatal pore. As the water potential of this air varies with changing air humidity and leaf temperature, the resultant changes in guard cell water potential produce stomatal movements. A simple, closed-form, mathematical model based on this idea is derived. The new model is parameterized for a previously published set of data and is shown to fit the data as well as or better than existing models. The model contains mathematical elements that are consistent with previously-proposed mechanistic models based on liquid flow as well as empirical models based on relative humidity. As such, it provides a mechanistic explanation for the realm of validity for each of these approaches.

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 CO2 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.A lthough biological and computational systems appear to share many analogous structures and processes (1), rigorous, nontrivial connections between life and computation remain elusive. One difficulty is that the biological systems that have been most actively investigated for evidence of computation (macroscopic organisms with neuronal networks, on the one hand, and proteins and nucleic acids participating in tangled webs of chemical reactions, on the other) are built from elements that interact irreducibly with vast numbers of each other. Such highly interconnected systems are notoriously hard to adequately describe mathematically. Support for the existence of sophisticated computation in biology (if it exists) is probably more likely to be found in systems in which the relevant elements interact sparsely. We propose that plants may be ideal for this purpose. Plants solve a gas exchange problem by using apparatus whose structure is reminiscent of cellular automata (CA), computerbased simulations of locally connected networks (2). Results of experiments we performed involving transient gas exchange and photosynthesis in intact, living leaves are remarkably similar to dynamical behavior observed in some CA that perform specific computational tasks. As we discuss below, these results are consistent with the hypothesis that plants engage in a form of emergent, distributed computation. Our argument is based on ideas drawn, in part, from plant biology and, in part, from computer science and physics. Because most readers will not be conversant with all of these, we first summarize the relevant (and well established) notions from each area. Salient Facts About PlantsIn bright light, a plant's stomata [variable aperture pores distributed over its leaves (and other parts) at densities of tens to hundreds per mm 2 (Fig. 1a)] tend to open. This creates a dilemma. The plant benefits from the opening because it is able to take in CO 2 , which it uses in photosynthetic energy storage. At the same time, it also experiences the detriment of increased water evaporation and the consequent ...

Use of polar coordinates is examined in performing summation over all Feynrnan histories. Several relationships for the Lagrangian path integral and the Hamiltonian path integral are derived in the central-force problem. Applications are made for a harmonic oscillator, a charged particle in a uniform magnetic field, a particle in an inverse-square potential, and a rigid rotator. Transformations from Cartesian to polar coordinates in path integrals are rather different from those in ordinary calculus and this complicates evaluation of path integrals in polars. However, it is observed that for systems of central symmetry use of polars is often advantageous over Cartesians.

Stomatal responses to leaf temperature (Tl) and to the mole fractions of water vapour in the ambient air (wa) and the leaf intercellular air spaces (wi) were determined in darkness to remove the potential effects of changes in photosynthesis and intercellular CO2 concentration. Both the steadystate and kinetic responses of stomatal conductance (gs) to wa in darkness were found to be indistinguishable from those in the light. gs showed a steep response to the difference (Dw) between wa and wi when wa was varied. The response was much less steep when wi was varied. Although stomatal apertures responded steeply to Tl when Dw was held constant at 17 mmol mol . These results are discussed in the context of mechanisms for the stomatal response to humidity.