Stomatal behavior of trees and their gas exchange can be derived from water and
assimilate transport needs
Eero Nikinmaa, Jouni Susiluoto and Teemu Hölttä
Department of Forest Sciences, University of Helsinki, Finland
Keywords: Stomatal conductance, phloem transport, xylem transport
INTRODUCTION
Trees similar to all plants move large quantities of water from even deep soil layers to
atmosphere. In that sense they have a significant role in controlling the global hydrological
cycle and have large influence on climate (Bonan 2008). In order to maintain the flow, they
need to transport large quantities of carbon that they fix in photosynthesis to build the
structures that allow the transport. In plant kingdom, trees are particular in that sense that
over their developmental cycle they may become very large and dominate the landscapes.
The large size is only possible if their growing environment is sufficiently humid. However,
the large size also imposes challenges for the transport processes.
CO2 intake in photosynthetic production requires open gas exchange channels between tree
leaves and surrounding atmosphere. This inevitably results into efflux of water from leaves as
the air vapor pressure is rarely saturated. Transpiration results into water loss from leaves. As
the water air interface within the leaves is rough and there are strong adhesive forces between
the water molecules and the surface, the water loss results into development of curved water
surfaces. Surface tension creates a pull that the cohesive forces between water molecules
propagate throughout the whole water transport system all the way to soil. The longer the
transport path, the greater the resistive forces and the larger the pressure difference, that are
needed to lift water to replace that lost in transpiration..
The water transport in plants takes place in specialized transport tissue, the xylem, which is
predominantly dead porous material in the interior of the tree stems. On the surface of the
xylem is the secondary cambium tissue that year after year makes new transport tissue on
interior and exterior of it. Exterior to cambium the new tissue formed is the phloem, that is
responsible for the assimilate transport in trees. The assimilate transport is driven by the
positive pressure gradient that is osmotically created (so called Munch flow, Taiz and Zeiger
2006). Photosynthesized assimilates are loaded into the transport tissue at the source leaves
and unloaded at the sites of their consumption. High solute concentration draws in water from
surrounding tissue (mainly xylem) at the source while the opposite takes place at the sink.
Similarly to water flow, long transport distances signify larger pressure differences and
stronger concentration differences. However, as assimilates are predominantly transported as
sucrose, very large concentration would lead to viscosity build up that would hinder the
transport.
Continuous transport of assimilates away from the leaves require, that the osmotic water pull
of the phloem tissue is able to match the water tension due to transpiration in the xylem
channel. Since stomata both regulate the transpiration that drives the xylem tension and the
CO2- intake that sets limit to the assimilate loading, it is natural to expect that stomatal
behavior could be linked to maintenance of the whole plant level transport. In our previous
paper (Nikinmaa et al. manuscript) we showed with dynamic model that stomatal behavior
that maximizes phloem bulk flow explains the observed variation in stomatal behavior in the
field conditions. In this paper we formulate a closed form mathematical expression for the
stomatal control from these premises in steady-state and show the general behavior of it
against its main variables.
MATERIAL AND METHODS
The transpiration rate of a plant can be written as H = agsw, where H is the transpiration rate,
gs is stomatal conductance to CO2, a is constant relating water vapor to CO2 flux (1.6), and w
is the vapor pressure deficit. Assuming that the solute potential s in xylem is zero, osmotic
potential of xylem can be calculated from the xylem pressure potential, in this case
where 1/kx is the resistance of xylem, 1/ks is the resistance of the roots and the soil, and soil is
the water potential (tension) in the ground. The phloem sucrose flux can be calculated from
concentration × conductivity of phloem × driving force (Nobel 2005) ,ie.
Setting phloem sugar trasport at the leaves to equal the rate of photosynthesis, ie. setting J =
P, where P is the photosynthesis rate from (Hari et al 1986)
and using s = csRT, where cs is the molality of the sugar solution, R is the gas constant, and T
is temperature in degrees Kelvin, the following equation is obtained:
The equation is quadratic in gs, and when soil is resistance is set to zero (which is a good
approximation except in the case of severe soil water deficit, Duursma et al. 2008) solving it
for gs yields the following solution where we use the positive root (negative root values gives
gs<0):
Returning to the general case, the phloem sugar flux is
and as we now have a formula in for gs, we have a formula for the total sugar flux. The
formula, however, turns out to be very complicated, so it is not written here.
Now the only unwanted variable in the formula is , the sugar volume fraction. It can be
eliminated so that we always choose a phloem sugar concentration that maximizes the total
phloem bulk flow. The stomatal behaviour is modeled with respect to the following
parameters: irradiance, xylem conductivity, phloem conductivity, soil/root water tension,
vapor pressure deficit, total tree leaf area, and ambient CO2-concentration. The parameter
values used are listed in table 1. Sugar concentrations and molalities are converted to volume
fractions using the formulas listed in the table. The values for xylem and phloem
conductivities are estimates based on the values from Hölttä et al (2006). The soil parameters
used in the models describe a typical soil type found in Hyytiälä Forestry Field Station in
Southern Finland.
RESULTS
With soil saturated with water, the stomatal conductivity value of 0.053 mol m-2s-1, results in
a water potential of -0.332 MPa. At this value, the typical sugar volume fraction is 0.13 (ie.
with the default parameter values, see the table 1). The corresponding value for s is 1.72
MPa. These values are well within the observed values in Hyytiälä stand.
The model produces the well known trends in stomatal conductance with respect to variations
in key environmental variables (irradiation, vpd, CO2) (see Figure 1)
Figure 1. Modeled leaf stomatal conductance as a function of a) irradiance, b) vapor pressure deficit and c) air
CO2 concentration.
The approach is also able to explain how whole tree properties, such as xylem or phloem
conductivities influence stomatal behavior (see Figure 2)
Figure 2. Modeled leaf stomatal conductance as a function of a) phloem conductivity, b) xylem conductivity.
DISCUSSION
Our earier work has shown that leaf stomata seem to regulate leaf gas exchange in such a
manner that maximizes bulk flow in phloem (Nikinmaa et al. (manuscript)). The results of
this study where the same principles are applied to formulate exact expression for the
stomatal conductance in steady state confirm the earlier findings with the numerical model.
Maximizing the bulk flow in phloem gives the observed response of stomatal conductance to
variation in leaf environment (Landsberg 1986, Buckley 2005). It turns out that this behavior
is very close to that predicted by optimal regulation leaf CO2 intake with regards to water
loss (Mäkelä et al. 1996).
The presented approach is superior to the traditional models of leaf gas exchange and
stomatal control in that it directly links the leaf level behavior with the whole tree and soil
properties. When the soil water potential was decreased, both the approach presented here
and the numerical dynamic version gave similar behavior as observed in the nature (results
not shown). This new approach greatly expands our ability to understand the complex
interactions of carbon and water fluxes in soil-plant-atmosphere continuum and how they are
linked to structural properties and development of vegetation.
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