Understanding the regulation of aspartate metabolism using a model based on measured kinetic parameters

Abstract

The aspartate-derived amino-acid pathway from plants is well suited for analysing the function of the allosteric network of interactions in branched pathways. For this purpose, a detailed kinetic model of the system in the plant model Arabidopsis was constructed on the basis of in vitro kinetic measurements. The data, assembled into a mathematical model, reproduce in vivo measurements and also provide non-intuitive predictions. A crucial result is the identification of allosteric interactions whose function is not to couple demand and supply but to maintain a high independence between fluxes in competing pathways. In addition, the model shows that enzyme isoforms are not functionally redundant, because they contribute unequally to the flux and its regulation. Another result is the identification of the threonine concentration as the most sensitive variable in the system, suggesting a regulatory role for threonine at a higher level of integration.

Figure 1

The central enzymes of the Asp-derived amino-acid pathway in chloroplasts and allosteric regulation. (A) The amino acids Lys, Met, Thr and Ile, and the methylating agent AdoMet are synthesized from aspartate. Simple and double arrows indicate reactions treated as irreversible and reversible, respectively. Enzyme names are indicated in italics. (B) Regulatory map of the Asp-derived amino-acid pathway in Arabidopsis leaf mesophyll cell. The 13 enzymes constituting the core of the system are co-expressed in Arabidopsis mesophyll cell chloroplasts. Isoforms exist for monofunctional AKs (AK1, AK2), bifunctional AKs (AKI–HSDH I and AKII–HSDH II) and DHDPS (DHDPS1 and 2). AK3 and TS2 are not expressed in mesophyll cell chloroplasts (see Supplementary data). Genes for ASADH, HSK, CGS and allosteric TD are present as single copies in the Arabidopsis genome. Enzymes shown against a white background are non-allosteric, and those with a yellow background are allosteric. Bifunctional AK–HSDH proteins are symbolized with a linker between the two domains. Continuous lines symbolize interactions of high apparent affinity, and broken lines symbolize interactions of low apparent affinity. Boxed metabolites appear explicitly in the enzyme equation models. Other metabolite concentrations were taken into account but are subsumed in the apparent rate constants (see Supplementary data).

Figure 2

Parameter adjustment. External metabolite concentrations were as indicated in Table IV. (A) In the absence of a demand for the amino-acid end products (limiting rate V^AaRS of lysyl, threonyl and isoleucyl-tRNA synthetases set at 0) no steady state could be obtained. The inset shows the same curves on an expanded scale. (B) Time-dependent evolution of the low-abundance metabolites AspP, ASA, Hser for V^AaRS=0.43 μM s⁻¹ (see text). (C) Time-dependent evolution of the end products Lys, Thr and Ile and the intermediate metabolite PHser for V^AaRS=0.43 μM s⁻¹ (see text). The half-time is about 400 s and the figure shows that an apparent steady state is reached in about 2 h. Independent determination of the steady state with COPASI confirmed that the state reached satisfies the criteria for a true and stable steady state (with all eigen-values negative or complex with negative real parts). For other steady-state values, see Figure 3.

Figure 3

Reference steady state. Each enzyme is represented by a green disk of sizes that roughly indicate the abundance of the corresponding protein (Table V). Each flux is symbolized by a gray line of thickness proportional to its magnitude, its value in μM s⁻¹ being shown in blue. Metabolites shown against a yellow background (Asp, AdoMet, Val, Cys) have fixed concentrations; those with white backgrounds have the steady-state concentrations indicated, which were obtained by the simulation. The limiting rate V^AaRS for lysyl, threonyl and isoleucyl tRNA synthetases was set at 0.43 μM s⁻¹. The concentrations of pyruvate, ATP, ADP, NADPH, NADP, P_i, all set at physiological values (see Materials and methods), are omitted from the scheme for the sake of clarity. Histograms for the common flux (ASADH), the demand flux for AdoMet, and the demand fluxes for the three aminoacyl-tRNA synthetases indicate the flux control coefficients for these fluxes (see Table II for numerical values). In each histogram the ordinate range is from –1 to +1, and the black bar (not visible in the ASADH histogram because the control coefficient concerned is very small) refers to the enzyme that catalyzes the reaction concerned. Most other control coefficients are very small, but non-trivial ones are labeled with the corresponding enzymes.

Figure 4

Modulation of the demand for Met–AdoMet. An increase in [AdoMet] simulates decreased demand in the Met branch. Steady-state variables were calculated as functions of [AdoMet], with V^AaRS=0.43 μM s⁻¹ as in Figure 3. Curves do not extend below [AdoMet]=2 μM because the equation used for TS is not valid below this value. Panels are arranged in the order in which they are discussed in the text. (A) Fluxes in the Lys, Thr → protein and Met branches. (B) Fluxes through the four AK isoforms. (C) Concentration of ASA. (D) Concentrations of Thr, Ile, Lys and PHser. Notice that the vertical scales in (C) and (D) are very different. The bell-shaped form of [Thr] dependence may be explained in terms of a TS activity that is virtually proportional to [PHser] but sigmoidal with respect to [AdoMet]. As the curves cross, the net effect of varying [AdoMet] changes sign at 10 μM: below this value, increasing [AdoMet] more than compensates for the decrease in [PHser] and the result is an increase in TS activity; above it the opposite occurs.

Figure 5

Modulation of the demand for Lys. (A) Steady-state fluxes of Lys and Thr to protein synthesis and flux of Lys degradation (v_LKR) as a function of [LKR] (protein concentration). (B) [Lys]_ss with normal inhibition of DHDPS1-2 by Lys (‘regulated') and in an uncoupled version of the model with this interaction suppressed (‘unregulated') as described in the text. (C) [ASA]_ss as a function of [LKR] (with a greatly expanded vertical scale). The inset shows the same dependence with a normal scale. (D) Dependence of [Thr]_ss for the regulated and unregulated models. (E) The almost flat curve in (D) redrawn with a greatly expanded vertical scale. (F) Thr flux (shown with an expanded scale). The bell-shaped curves are due to the fact that for [Lys]>57 μM ([LKR]<10 μM) changes in [Lys] (Figure 5B) have more effect on Lys-sensitive AK than on DHDPS, but the opposite occurs when [Lys]<57 μM.

Figure 6

Modulation of the demand for Thr. (A) Fluxes of Lys and Thr to protein synthesis and flux of Thr degradation (v_THA) as a function of [THA] (protein concentration). (B) Steady-state [Lys], [Thr] and [Ile] concentrations.

Figure 7

Modulation of the demand for Lys, Thr and Ile for protein synthesis. Change in V^AaRS simulates modification of the demand for Lys, Thr and Ile for protein synthesis (these being changed simultaneously). The shaded area in each figure indicates V^AaRS values for which no steady state is possible, and the arrow indicates the level of demand in the reference state. (A) [Thr]_ss as a function of V^AaRS. (B) [Lys]_ss and [Ile]_ss. (C) Fluxes in the Lys, Thr and Ile to protein branches. When V^AaRS >0.6 μM s⁻¹, the Ile flux fails to follow the demand and then decreases with further increases in demand. The reason is that [Thr]_ss and [Ile]_ss both decrease (B) when demand is increased. The decrease in Ile concentration relaxes the inhibitory effect on TD activity but at one point the relaxation of the inhibitory effect ceases to compensate for the decrease in [Thr] (the substrate of TD), and the flux in the Ile branch decreases. (D) Time for [Thr] to reach 0.5[Thr]_ss, starting from 0.