The main processes involved in fruit growth are interrelated by feedback loops which provide a kind of internal control in the system. Fruit enlargement requires the accumulation of water and hydrocarbons. The rate of material accumulation depends on the balance of incoming and outgoing fluxes. The fluxes, in turn, are defined by thermodynamic potentials which are functions of the material concentrations. There is also feedback between the fluxes and the hydrostatic pressure: the pressure controls the fluxes and is influenced by them. All these interrelations are coupled with other physicochemical processes, such as cell wall extension, transformations of the carbohydrates, and their active transport and/or facilitated diffusion, mediated by a carrier, etc. Environmental conditions and agrotechnical treatments play important roles in the control of water and solute movement and accumulation in the fruit. These roles can be better understood and agrotechnical practice improved through the use of a model which describes the biophysical mechanisms of the processes involved in fruit growth and analyses their relationship to the external conditions.
These mechanisms have been discussed in the literature and have been used by several authors as tools to analyse physiological processes in plant cells and organs. The flux of solution into the grape berry, as governed by differences in water potentials in the stem and the berry, was considered and the hydrostatic and osmotic components of the potentials were estimated by treating the fruit as one compartment (Lang, Thorpe & Edwards 1986). The difference between the water potentials in the stem and in the fruit was considered as the driving force in a model of the water import rate into tomato fruit which also takes into consideration the role of the tomato anatomy (Bussières 1994). One-compartment fruit representation has been applied to fruit growth calculation by means of numerical integration of the equation for water balance, using empirically determined water influx and transpiration as input values (Lee 1990) or by means of phenomenological equations with statistically fitted parameters for water influx and transpiration (Génard & Huguet 1996). Movement of water in plant tissue through two distinct pathways, the symplasmic and the apoplasmic, was analysed by Molz & Ferrier (1982), who included the case of tissue composed of several cells in series. The possibility of sucrose import to sink regions via symplastic and apoplasmic paths operating in parallel or in series was reviewed by Patrick (1997). A model of solution transport to the root was elaborated and analysed by Steudle and coworkers (reviewed by Steudle 1993): the root was treated as one compartment separated from the outside medium by a composite membrane, which was considered to be built from ‘membrane-like elements arranged both in series and in parallel’. In fact, the root xylem is separated from the medium by several layers of cells, which can be crossed in different ways, so that each layer could be regarded as a different compartment. This, however, would result in a multicompartmental model with possible multiple pathways between the compartments. The transport characteristics for such a model cannot be estimated, and the composite membrane forms a convenient approximation to this complicated transport system. Uptake of solutes includes passive permeation of solute through the membrane, ‘solvent drag’ by the mass flow of the water, and active transport. The active and/or facilitated transport makes an important contribution to the uptake of dry materials by fruits, as studied in tomato (Milner, Ho & Hall 1995), in peach (Vizzotto et al. 1996) and in tobacco callus (Hunt & Loomis 1976). Influx of water and solutes into the cells leads to irreversible changes in the volume if it is accompanied by cell wall extension. Equations which relate the relative cell elongation to the turgor pressure exerted on the wall, linearly or by a threshold relationship, were suggested by Lockhart (1965), whose approach has been experimentally corroborated by a number of workers. A study of the joint action of auxin and pressure on a single rye coleoptile (Green & Cummins 1974) revealed a threshold turgor pressure below which no extension occurs, and showed a hysteresis in the relationship between growth rate and turgor. Threshold and hysteresis are phenomena usually connected with phase transitions in membrane structures (Blumenthal, Changeux & Lefever 1970; Nagle & Scott 1978). Possibly, some kind of co-operative transformations occur in the cell walls under the action of hydrostatic pressure. Biochemical changes in cell wall structures which may be connected with wall extension have been examined (Fry 1989; Cosgrove 1993; Passioura, Condon & Richards 1993), but a mathematical formalism for these structural changes has not yet been elaborated, and the Lockhart’s (1965) equation has been used as a convenient approximation in a number of recent studies: for example, it was adopted by Nonami & Boyer (1990) to describe stem growth and by Arkebauer, Norman & Sullivan (1995) for simulation of leaf expansion.
The aim of the present work was to develop a model of fruit growth, based on biophysical representation of water and dry material transport coupled with the process of extension stimulated by turgor pressure. This representation may relate fruit growth and several important quality characteristics of the fruit, such as water content and sugar concentration, on the one hand, to environmental conditions and basic agrotechnical treatments, on the other hand. The model was applied to the simulation of seasonal and daily growth of fruit under various conditions of crop load and water status in the tree. The results of simulations were compared with observations performed in our laboratory (INRA, Avignon Centre) or reported by other authors.