Mass Action And Metabolic Control

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Sucrose synthase (SuSy) provides another potential pathway for controlling cellulose production. SuSy cleaves sucrose in the presence of uridine diphosphate

(UDP) into UDP-glucose and fructose, thereby conserving the energy of the glycosidic bond:

UDP - glucose + Fructose ^ Sucrose + UDP

Considering the free energy of hydrolysis of sucrose as -6.6 Kcal'mol-1 and the energy of the a-D-glycosyl phosphate bond in UDP-glucose as -7.6 Kcal'mol-1, the estimated change in free energy for the reaction in vitro results in -1 Kcal'mol-1

in favor of sucrose synthesis (Cardini et al. 1955). The apparent equilibrium con stant (Keq) can be calculated from its relationship to the standard free energy

(AG0) by the following equation:

AG0 = -2.303 RT log10Keq

Where R equals 1.987 x 10-3 Kcal«mol-1«°K -1 and T equals 25°C (298°K), then

-1 Kcal/mol

This parameter falls within the range of values from 1.4 to 8 determined experimentally based on substrate concentrations at equilibrium (Cardini et al. 1955; Neufeld and Hassid 1963; Avigad 1964; Kruger 1997). Since this reaction is thermodynamically close to equilibrium, the net flux (v = v+1 - v-1) will represent only a fraction of the unidirectional flux the enzyme could catalyze in the absence of products. In vivo, the net carbon flux through this enzyme will be a function of the relative size of substrate and product pools at the steady state according to the mass action ratio (Hess 1963; Bucher and Russman 1964). For the reaction catalyzed by SuSy:

The net flux in vivo through SuSy can be altered by a relatively small shift in the mass action ratio away from its equilibrium position (Keq). To obtain net flux in favor of UDP-glucose formation, the reaction must be displaced from equilibrium such that r is higher than Keq. The disequilibrium ratio can be related to the change in free energy using the following equation (Rolleston 1972; Stitt 1989):

Thus, an increase in the divergence of mass action ratio in vivo will increase the change in free energy through the reaction. This disequilibrium ratio can also be linked to flux by the ratio of the forward and reverse reaction velocities according to the equation derived by Hess and Brand (1965) from a rate equation based on Michaelis-Menten kinetics:

Figure 5-1 shows the sensitivity analysis for changes in sucrose concentration and the ratio of reverse and forward reaction velocities. The parameters for Figure 5-1 were calculated using the ranges of substrate and product concentrations found in the literature. UDP-glucose was reported to vary between 1.4 to 3.2 mM (Dancer et al. 1990; Krause and Stitt 1992; Barreiro 1999). Reported fructose levels range from 0.1 to 1.5 mM (Winter et al. 1994; Krapp and Stitt 1995), however, the concentration of cytoplasmic fructose assumed in the calculations could be higher than the concentration found in vivo because of the existence of high fructokinase activity in the cytoplasm (Gardner et al. 1992; Renz and Stitt 1993; Renz et al. 1993). Cytosolic UDP concentrations vary from 0.35 to 1.3 mM (Isherwood and Selvendran 1970; Stitt 1989; Dancer et al. 1990; Barreiro 1999) and those for sucrose from 13 to 103 mM (Winter et al. 1993, 1994; Pilon-Smits 1995; Krapp and Stitt 1995; Barreiro 1999).

The cytoplasmic concentrations chosen for each metabolite are not only associated with the range found in the literature but also close to the ranges of apparent r =

[Sucrose][UDP]

[UDP - glucose][Fructose]

v+1 Keq

Figure 5-1. Sensitivity analysis of v - 1/v + 1 and change in free energy as a function of sucrose concentration. Negative values for the change in free energy indicate that the net flux of the reaction proceeds in the direction of sucrose synthesis

Km values for SuSy cited therein (Stitt and Steup 1985; Buczynski et al. 1993; Quick and Schaffer 1996; Barreiro 1999). We followed this approach since the optimal physiological concentration for substrates of a reaction displaced from equilibrium is at its Km (Rolleston 1972). For the sensitivity analysis the concentration of sucrose was varied, while the rest of the metabolites were clamped at the following concentrations: UDP-glucose 3 mM, fructose 0.1 mM, and UDP 0.4 mM.

The concentration gradient between metabolic pools on each side of the reaction could overcome the chemical bond energetic gradient, in favor of the mass action gradient, favoring sucrose hydrolysis in sink tissues. The threshold of sucrose concentration beyond which the net flux reverses is difficult to assess in a system with a dynamic equilibrium.

Under physiological conditions (assuming that the metabolite concentrations chosen for the calculations are similar at the steady state in planta), sucrose concentrations higher than ~4 mM could reverse the net flux of carbon through SuSy in favor of UDP-glucose synthesis due to mass action (Figure 5-1). If we assume that the physiological sucrose concentration within the cytoplasm remains near 50 mM (Barreiro 1999; Rohwer and Botha 2001) then the net flux of carbon through SuSy in sink tissues operates in the direction of UDP-glucose formation. This is consistent with experimental results using radioactive tracers (DeFekete and Cardini 1964; Milner and Avigad 1964; DeFekete 1969; Pavlinova 1971; Huber et al. 1996; Viola 1996; Geigenberger et al. 1997) and with simulations from a mathematical model built with a framework to simulate general pathways (Mendes 1993) and fitted with parameters determined experimentally

(Barreiro 1999). However, the reaction becomes readily reversible when the concentrations of sucrose within the enzyme microenvironment drop to values lower than ~4 mM (Figure 5-1).

Because of its proximity to equilibrium, the forward and reverse reactions catalyzed by SuSy will be affected in the same magnitude whenever the enzyme concentration is changed. As a consequence, the net direction of carbon flux through the enzyme will not be affected; therefore, increasing the expression of this enzyme per se may not increase the flux of carbon into the cellulose pool. On the other hand, decreasing the expression of SuSy, could cause a reduction of the UDP-glucose pool to the extent of limiting the cellulose synthetic rate. When this occurs in vivo, the UDP-glucose pool needs to be maintained by an alternative metabolic route that requires more energy to operate (Dhugga et al. 2002). Under stressful conditions, where SuSy expression may be severely attenuated, overexpression of the enzyme may help augment against yield losses.

An alternative metabolic route for UDP-glucose synthesis could be catalyzed by UDP-glucose pyrophosphorylase (UGPase). Both SuSy and UGPase are cytosolic enzymes and thus could contribute to the UDP-glucose pool in this compartment (Entwistle and ApRees 1988).

The metabolic path for UDP-glucose synthesis through UGPase, when considering sucrose as a precursor, has more intermediate steps than the route through SuSy. Whereas the formation of UDP-glucose through SuSy has only one step against a thermodynamic gradient, the route through UGPase has two: the phosphorylation of glucose, with a change in free energy of ~4.7 Kcal'mol-1, and the conversion of glucose 6-P through glucose-1-P into UDP-glucose with a change in free energy of ~2.9 Kcal*mol-1.

The available evidence, although scarce, suggests that the alternative route for the cytoplasmic UDP-glucose pool plays a relatively smaller role in comparison to SuSy. Carrot plants with an antisense version of the main form of SuSy had reduced SuSy activity in roots. Aside from having lower levels of UDP-glucose, these transgenic plants also had reduced levels of cellulose, starch, and total dry matter (Tang and Sturm 1999). Similarly, antisense downregulation of SuSy in potato tubers led to a reduction in cellulose formation (Haigler et al. 2001).

Figure 5-1 shows that the disequilibrium ratio (i.e., v - 1/v + 1) for the reaction catalyzed by SuSy can be influenced by a relative small shift in free energy away from equilibrium. Under normal growing conditions, manipulation of SuSy substrate levels to influence the magnitude of the net flux may therefore be a more effective way of controlling the quantity of cellulose deposited in the cell walls rather than altering its expression level.

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