Biochemical Models for Assimilation

14.8 Biochemical Models for Assimilation

To investigate more detailed questions related to response of assimilation to the leaf environment a more detailed model is needed that addresses temperature sensitivity of enzymes and limitations by light,

and the of products of photosynthesis. The model we present here is from Collatz et al. (1991). The model considers the gross assimilation rate A, in units of

to be the minimum of three potential capacities:

where the light-limited assimilation rate, is the Rubisco-limited rate, and is the rate imposed by sucrose synthesis.

The light-limited assimilation rate can be computed from:

where is the absorptivity of the leaf for PAR, is the maximum quan- tum efficiency (maximum number of

molecules fixed per quantum of radiation absorbed),

is the PAR photon flux density incident on the leaf

concentration. The light compensation point is the

and

is the intercellular

concentration at which assimilation is zero. It is computed from:

where is the oxygen concentration in air (210000 and is a ratio describing the partitioning of

to the carboxylase or oxygenase reactions of Rubisco. In C3 species, oxygen competes with and is a measure of this competition. The Rubisco-limited assimilation rate is computed from:

where is the Rubisco capacity per unit leaf area s -1 ),

is the Michaelis constant for fixation, and is the Michaelis constant for oxygen inhibition. Equation (14.20) is a

rectangular hyperbola, typical of enzyme catalyzed reactions. At low concentrations of

shows a linear increase with increasing concen- tration, but when

is large, becomes almost constant, approaching the value

The oxygen concentration influences the initial slope of the relationship, but not the

value reached at high concentra- tions. At normal atmospheric

concentrations, decreasing the oxygen concentration around a C3 leaf dramatically increases the photosynthetic rate in light, but at high

levels the effect of oxygen concentration is negligible.

240 Plants and Plant Communities

The final constraint is the one imposed by the export and use of the products of photosynthesis. As in any chemical reaction, when the concentration of products builds up, the reaction slows. Sucrose synthe- sis is considered the most likely rate limiting step. The sucrose-limited assimilation rate is assumed, by Collatz et al. (1991) to be just

Equation (14.17) implies a sharp transition from one rate limiting process to another. In reality there is a more gradual transition, with some

imitation when two rates are nearly equal. This colimitation is modeled empirically using quadratic functions. The minimum of

and is first computed from:

where 8 represents a number between and 1 that controls the abruptness of the transition from one limitation to the other. Measurements tend to give values of around 0.95. The second limitation is imposed by computing the minimum of

(from Eq. (14.22) with

where performs the same function in Eq. (14.23) that 8 did in Eq. (14.22). A typical value for is 0.98, indicating a sharp transition between

and J,. The net assimilation rate is the gross assimilation given by Eq. (14.23)

minus the respiration rate for the leaf:

Collatz, et al. (1991) compute

as 0.015

The temperature response ofphotosynthesis is modeled by considering the temperature dependence of the model parameters. Five parameters need adjustment for temperature:

and The first three temperature adjustments take the same form, namely:

where k represents the value of any of the parameters at leaf temperature is the value of that parameter at

C, and q is the tempera-

ture coefficient for that parameter. In addition to this adjustment,

and need a high temperature cutoff. The temperature response for these parameters is:

Control of Conductance

or rapidly at temperatures above 41 or

reduces the value of

C, respectively.

It is, of course, not practical to use this photosynthesis model for hand calculations. It can be a

matter, though, to make a computer which solves these equations. Table 14.1 gives values for the model parameters, as supplied by Collatz et al. (1991). Figure 14.5 shows the temperature response predicted by the model, Fig. 14.6 shows the light response, and Fig. 14.7 shows the

response. It is important to note, in the table and in all of the figures, that our values are per unit total leaf surface area. Collatz et al. (1991) and most other researchers compute photosynthesis on a per unit projected leaf area basis. Our values are therefore half those typically found in the photosynthesis literature.