A dynamic computer model of the metabolic and regulatory processes in Crassulacean acid metabolism

Abstract

The paper describes a computer model which is capable of simulating the typical phenomena of Crassulacean acid metabolism (CAM). The model is based on a simplified scheme of the metabolic processes of CAM described earlier in the literature. The evolution of the model proceeded in the following steps, namely i) a verbal description of CAM in the form of a scheme integrating the metabolic and regulatory CAM processes at the cellular level of the cell, and transcription of the scheme into a block diagram; ii) the stepwise transformation of the block diagram into a structural model, represented by a system of differential equations; this was later used as the dynamic model. In the first attempt to construct the dynamic model, it appeared to be useful to accept the following simplifications: i) All reactions involved were considered to be of the first order. ii) Sequences of reactions, in which the intermediary products appeared to be of minor importance, were summarized in a single step. iii) All reactions were considered to proceed irreversibly in the main direction. iv) The mathematical formulations, usually used in describing enzyme regulations (for instance, competitive or allosteric behaviour), were replaced in the model by a uniformly simplified equation which independent of the actual mechanism, described activation by the multiplication of the velocity constant with an activating factor, and inhibition by division of the velocity constant by an inhibiting factor. v) From the manifold interactions between the plants and their environment, at present, only two factors have been selected to act as input parameters of the model, namely, the CO₂ concentration in the air and light. Our studies showed that the model was capable of simulating not only some basic phenomena of CAM such as the diurnal rhythms of malic acid and starch, and the diurnal pattern of net CO₂ exchange, but also alterations in the pool sizes of phosphoenolpyruvate, glucose-6-phosphate and internal CO₂. The latter were of particular interest since the experimental findings were not made known to the model-building coauthors prior to the formulation of the model. Thus, the results could not influence the structure and behaviour of the model. It was also possible to simulate alterations of CAM behaviour as occurring in vivo in response to environmental signals. In all tested cases, the simulation was in very good agreement with the in-vivo behaviour of the plants documented by experiments or observations. This close agreement between the in-vivo behaviour of CAM and the simulation by the model indicated that the basic scheme of CAM contained all the major metabolic and regulatory interrelationships operating in vivo to bring about CAM.