The logic of kinetic regulation in the thioredoxin system

Abstract

Background: The thioredoxin system consisting of NADP(H), thioredoxin reductase and thioredoxin provides reducing equivalents to a large and diverse array of cellular processes. Despite a great deal of information on the kinetics of individual thioredoxin-dependent reactions, the kinetic regulation of this system as an integrated whole is not known. We address this by using kinetic modeling to identify and describe kinetic behavioral motifs found within the system.

Results: Analysis of a realistic computational model of the Escherichia coli thioredoxin system revealed several modes of kinetic regulation in the system. In keeping with published findings, the model showed that thioredoxin-dependent reactions were adaptable (i.e. changes to the thioredoxin system affected the kinetic profiles of these reactions). Further and in contrast to other systems-level descriptions, analysis of the model showed that apparently unrelated thioredoxin oxidation reactions can affect each other via their combined effects on the thioredoxin redox cycle. However, the scale of these effects depended on the kinetics of the individual thioredoxin oxidation reactions with some reactions more sensitive to changes in the thioredoxin cycle and others, such as the Tpx-dependent reduction of hydrogen peroxide, less sensitive to these changes. The coupling of the thioredoxin and Tpx redox cycles also allowed for ultrasensitive changes in the thioredoxin concentration in response to changes in the thioredoxin reductase concentration. We were able to describe the kinetic mechanisms underlying these behaviors precisely with analytical solutions and core models.

Conclusions: Using kinetic modeling we have revealed the logic that underlies the functional organization and kinetic behavior of the thioredoxin system. The thioredoxin redox cycle and associated reactions allows for a system that is adaptable, interconnected and able to display differential sensitivities to changes in this redox cycle. This work provides a theoretical, systems-biological basis for an experimental analysis of the thioredoxin system and its associated reactions.

Figure 1

Modelling the thioredoxin system in E. coli. A kinetic model of the thioredoxin system in E. coli was developed that included reactions for the reduction of oxidized thioredoxin (TrxSS) by thioredoxin reductase (TR), the thioredoxin-dependent reductions of methionine sulfoxide (Met-S-SO) by methionine sulfoxide reductase (MsrA) and 3'-phosphoadenosine-5'-phosphosulfate (PAPS) by PAPS reductase (PR) and the Tpx-dependent reduction of hydrogen peroxide. In other systems biology approaches, electron flow pathways have been used to model this system (blue arrows). However, in our model, thioredoxin-dependent reactions were modeled as a series of moiety conserved cycles (see text for details).

Figure 2

Parameter portraits of the systemic behavior of a computational model of the E. coli thioredoxin system. Changes in the thioredoxin reductase (TR) concentration affected the fluxes of thioredoxin-dependent reactions (A) and the steady state thioredoxin (blue, •) and oxidized thioredoxin concentrations (red, -) (B) in the model. Similarly, changes in the protein disulfide (C), PAPS (D), methionine sulfoxide (E) and hydrogen peroxide (F) concentrations also affected the fluxes through the system. The PAPS reductase reaction was modeled with mass action kinetics (Figures 2 A-C, E-F) or with ping-pong kinetics (Figure 2D) (see Methods for details). The fluxes shown are thioredoxin reductase (black, •••), protein disulfide reduction (red, ---), methionine sulfoxide reductase (blue, •••), PAPS reductase (green, -•-) and Tpx (magenta, -). Parameters are summarized in Table 1. This figure was generated using 'Logic_Figure 2_and Figure 4.psc' (Additional file 1) and 'Logic_Figure 2 D.psc' (Additional file 2). SBML versions of these models, 'Logic_Figure 2_and Figure 4.xml' (Additional file 5) and 'Logic_Figure 2 D.xml' (Additional file 6), are provided as well.

Figure 3

The effect of changes in the concentration of the components of the thioredoxin system on the kinetic profile of the system. In a kinetic model of the thioredoxin system, the concentrations of NADPH (A), thioredoxin reductase (B) and thioredoxin (C) were changed over the range 0.1 (black, •••), 1 (red, --), 2 (blue, -) and 10 (green, -•-) and the response of the flux through the thioredoxin reductase reaction towards changes in the PSS concentration monitored. Parameters were as in Table 2, except where indicated otherwise. This figure was generated using 'Logic_Figure 3.psc' (Additional file 3). A SBML version of this model ('Logic_Figure 3.xml') is available as Additional file 7.

Figure 4

Ultrasensitive changes in the steady state concentrations of the redox couples in the thioredoxin and Tpx redox cycles are dependent on the kinetics of the Tpx redox cycle. In each of these simulations, the ratio of the second order rate constants for Tpx oxidation and reduction (i.e. k_H2O2/k_trxsh, Table 1) were varied from 0.015 (black, •••), 0.05 (red, ---), 0.10 (blue, solid line) to 1.00 (green, -•-) and the effect on the steady state concentrations of reduced thioredoxin (TrxSH), oxidized thioredoxin (TrxSS), reduced Tpx (TpxSH) and oxidized Tpx (TpxSS) monitored. Parameters were as in Table 2, except where indicated otherwise. This figure was generated using 'Logic_Figure 2_and_Figure 4.psc' (Additional file 1). A SBML version of this model ('Logic_Figure 2_and_Figure 4.xml') is available as Additional file 5.

Figure 5

Thioredoxin oxidation reactions can affect each other. In (A), the flux through the thioredoxin-dependent reduction reaction of a substrate (PSS) at varying concentrations of a second thioredoxin substrate (RSS, Scheme II) was monitored in a kinetic model of the thioredoxin system (Scheme II). The concentrations of RSS were 0.1 (black, •••), 1 (red, --), 2 (blue, -) and 10 (green, -•-). In (B), the flux through the thioredoxin-dependent reduction of PSS with increasing concentrations of RSS was monitored over a range of thioredoxin reductase concentrations: 0.1 (black, •••), 1 (red, --), 2 (blue, -) and 10 (green, -•-). Parameters were as in Table 2, except where indicated otherwise. This figure was generated using 'Logic_Figure 5.psc' (Additional file 4). A SBML version of this model ('Logic_Figure 5.xml') is available as Additional file 8.