Quantitative biology of hydrogen peroxide signaling

Abstract

Hydrogen peroxide (H₂O₂) controls signaling pathways in cells by oxidative modulation of the activity of redox sensitive proteins denominated redox switches. Here, quantitative biology concepts are applied to review how H₂O₂ fulfills a key role in information transmission. Equations described lay the foundation of H₂O₂ signaling, give new insights on H₂O₂ signaling mechanisms, and help to learn new information from common redox signaling experiments. A key characteristic of H₂O₂ signaling is that the ratio between reduction and oxidation of redox switches determines the range of H₂O₂ concentrations to which they respond. Thus, a redox switch with low H₂O₂-dependent oxidability and slow reduction rate responds to the same range of H₂O₂ concentrations as a redox switch with high H₂O₂-dependent oxidability, but that is rapidly reduced. Yet, in the first case the response time is slow while in the second case is rapid. H₂O₂ sensing and transmission of information can be done directly or by complex mechanisms in which oxidation is relayed between proteins before oxidizing the final regulatory redox target. In spite of being a very simple molecule, H₂O₂ has a key role in cellular signaling, with the reliability of the information transmitted depending on the inherent chemical reactivity of redox switches, on the presence of localized H₂O₂ pools, and on the molecular recognition between redox switches and their partners.

Graphical abstract

Highlights

• •Hydrogen peroxide signaling proceeds through oxidation of redox switches.
• •Oxidation of redox switches can be direct or mediated by highly reactive sensors.
• •Response of redox switches is controlled by their oxidability and reduction rate.
• •Localized protein interactions ensure the accuracy of information transmission.

1. Introduction

Hydrogen peroxide (H₂O₂) is a non-radical oxidant present in virtually all aerobic organisms. Viewed initially as a detrimental byproduct of oxidative metabolism, today H₂O₂ is recognized to play important roles in cellular physiology [1]. The cellular function of H₂O₂ is supported by coupling of cellular signals with its production. Many enzymatic sources have been identified that produce H₂O₂ directly or produce superoxide radical, which is subsequently dismutated into water and H₂O₂, a process that is accelerated many orders of magnitude by the action of superoxide dismutases. A particularly relevant source of H₂O₂ is NADPH oxidases because their sole function seems to be the tightly-regulated production of superoxide/H₂O₂ [2].

Production of H₂O₂ is balanced by the action of antioxidant enzymatic systems, such as catalase, glutathione peroxidases, and peroxiredoxins, that remove H₂O₂ very rapidly [3], [4]. An homeostatic steady-state level of 10⁻⁷−10⁻⁸ M results under physiological conditions [5], and changes around this background steady-state level will trigger cellular responses. If these concentration shifts are moderated, transient or localized in space, being a result of for example signaling processes, a physiological stress response – or eustress – is observed [3]. If variations in the H₂O₂ concentration are large, sustained or affect H₂O₂ bulk levels, a pathological stress with deleterious effects for the organism materializes [3]. Thus, oxidative effects are inherently non-linear and biphasic with threshold levels separating the physiological and the pathological domains [6], [7]. In addition, eustress and pathological stress can either be oxidative or reductive, depending on whether they are caused by an increase or decrease of H₂O₂ around its background steady-state level.

In this review, quantitative biology concepts are introduced to analyze the transmission of information mediated by H₂O₂ in the oxidative eustress setting.

1.1. H₂O₂ signaling

Signaling pathways are regulated by the reaction of H₂O₂ with proteins harboring redox sensitive moieties, like metal centers or cysteine residues, whose oxidation controls their activity. These proteins denominated redox switches are key players in the regulation of biochemical pathways, including protein phosphatases, kinases or transcription factors [8]. Thus, a change in the concentration of H₂O₂ is matched by a change in the oxidation state of a redox switch, regulating a downstream pathway and transducing the information encoded in the H₂O₂ concentration profile along a signaling cascade.

Chemically, most previously identified redox-controlled switches are thiol proteins [9], [10], [11], but metal switches have also been described [12], [13]. Thiol switches are proteins with cysteine residues with low pKa that favors their proton dissociation to form a thiolate at physiological pH. Thiolates have a higher reactivity towards H₂O₂, but the pKa of the cysteine residue is not the only determinant of the reactivity of the thiol protein with H₂O₂. Rather, stabilization of the transition state between H₂O₂ and the cysteine residue is critical to achieve high catalytic rates with the protein environment affecting the reactivity of the cysteine group [14]. Thus, reactivity of thiol proteins towards H₂O₂ spans several orders of magnitude, from the low 20 M⁻¹s⁻¹ for some protein tyrosine phosphatases, like PTP1B and SHP-2, to the high 10⁷ M⁻¹s⁻¹ for peroxiredoxin 2 [15].

The chemical reactivity of redox switches is a potential mechanism underlying specific biological effects caused by different concentrations of H₂O₂. At low H₂O₂ concentrations only the most reactive switches will sense H₂O₂, while less reactive switches will sense H₂O₂ at high concentrations. As will be described below, such chemical specificity based on the oxidability of the redox switch is just one of several regulatory mechanisms in H₂O₂ signaling.

2. Quantitative analysis of H₂O₂ signal processing

2.1. The steady-state approximation

The steady-state concept is central to quantitative analyses in redox biology [16], [17], [18]. As a result of continuous formation and elimination, H₂O₂ settles to a near steady-state given by Eq. 1 in Fig. 1. It is important to test the validity of the steady-state approximation during signaling events when variations of the H₂O₂ concentration are observed. In other words, does the steady-state approximation hold when H₂O₂ is not steady? When H₂O₂ production is increased, for example due to the activation of an NADPH oxidase, the steady-state approximation can be used to calculate the transient dynamics of H₂O₂ because the very fast elimination of H₂O₂ by antioxidants systems has a reaction time much quicker than the transient responses formed during signaling events (Fig. 2). Thus, the steady-state approximation is valid even when H₂O₂ levels change during signaling events.

Fig. 1.

The steady-state of H₂O₂. A steady-state is reached when the rates of formation (v_formation) are balanced by the rates of elimination (v_consumption). The rate of H₂O₂ elimination is assumed to follow first-order kinetics because in the eustress domain H₂O₂ does not overload the antioxidant systems. Thus, v_consumption= k_cons×[H₂O₂] with k_cons being the pseudo first-order rate constant for the overall consumption of H₂O₂. The steady-state Eq. 1 is deduced from the equality between the rates of formation and elimination of H₂O₂.

Fig. 2.

Application of the steady-state approximation to H₂O₂ dynamics during signaling events. To reproduce a transient H₂O₂ increase, the rate of H₂O₂ formation was assumed to peak at 5 min and to decay to zero at 20 min as observed in Ref. [19]. Three H₂O₂ profiles are shown: one was calculated according to steady-state Eq. 1 and two according to simulations reproducing the cell behavior for two values of consumption rate constants – 1.2 s⁻¹ and 12 s⁻¹. Simulated H₂O₂ profiles approach that calculated from Eq. 1 when the value of k_cons increases, and for k_cons=120 s⁻¹ or higher, simulation curves coincide with the steady-state curve (not shown). This trend is justified by the very fast time scale of the k_cons rate constant. A time scale of 0.06 s is calculated according to the formula t_1/2= ln(2)/k_cons, with ln(2) being the natural logarithm of 2, for a k_cons =12 s⁻¹, a lower limit for the value of the k_cons rate constant (see Table 1 below). A t_1/2 value of 0.06 s is much faster than the time scale associated with the variation of H₂O₂ formation during signaling events, which is in the minute range, and thus the steady-state approximation is valid. In general, the steady-state approximation is a reasonable assumption when analyzing processes in the minute range or slower because antioxidant systems are usually fast enough.

To make a quantitative analysis of H₂O₂ signal processing, the simple steady-state scheme of Fig. 1 was extended to include a signaling reaction. The formation of H₂O₂ is now balanced by two elimination reactions, one being the consumption of H₂O₂ by antioxidant systems and the other the oxidation of redox switches (Fig. 3). When first-order kinetics are assumed for these elimination processes, H₂O₂ steady-state is given by Eq. 2 in Fig. 3.

Fig. 3.

The H₂O₂ steady-state in the presence of signaling. In principle, a signal (Signal in) can modulate either the production or the removal of H₂O₂, the activation of a NADPH oxidase being a common mechanism. The subsequent change in H₂O₂ concentration is sensed by a redox switch (Target) that upon oxidation (v_signaling) transmits information downstream the signaling cascade (Signal out). Similarly to the rate of H₂O₂ consumption by antioxidant systems, the signaling reaction also follows first-order kinetics, being v_signaling=k_sign×[H₂O₂] with k_sign referring to the rate constant for the reaction of H₂O₂ with the redox target. The resulting steady-state H₂O₂ concentration is given by Eq. 2.

Eq. 2 shows the relative magnitude of k_cons and k_sign only is needed to predict whether signaling processes affect directly the H₂O₂ steady-state. According to published data, k_cons is five to six orders of magnitude higher than k_sign (Table 1), implying that antioxidant reactions vastly outcompete signaling reactions for H₂O₂. Thus, a kinetic bottleneck for H₂O₂ signaling is established [10], [14], [15], [20]. If highly efficient antioxidant systems divert more than 99.999% of H₂O₂ from signaling reactions, how are H₂O₂ variations sensed? The rate of signaling is calculated as the product of the rate constant k_sign by the concentration of H₂O₂ (Fig. 3). So, the rate of the signaling reaction will match the variations of H₂O₂, and the information encoded in the H₂O₂ concentration profile can, in principle, be transmitted downstream the signaling cascade. The key question is whether the information is transferred fast enough when v_signaling is very slow.

Table 1.

Competition between enzymatic antioxidants and redox switches for H₂O₂. k_cons and k_sign are pseudo first-order rate constants calculated as the product between k_target+H2O2, the chemical rate constant between H₂O₂ and its target protein, and the concentration of the target protein, either an enzymatic antioxidant or a redox switch. For protein concentrations and rate constant values see [15], [8]. The rather high value for catalase concentration refers to the peroxisome [21].

	ktarget+H2O2 (M−1s−1)	[protein] (µM)	ktarget+H2O2× protein (s−1)
Antioxidant			kcons
Prx	105–107	10	1–100
GPx	6×107	0.2–10	12–600
Catalase	107	103	104
Redox switch			ksign
PTP1B	24	0.01	2.4×10−7
SHP‐2	20	0.01	2.0×10−7
Keap1	140	1	1.4×10−4

Prx – Peroxiredoxin; GPx – Glutathione peroxidase 1.

2.2. Equations governing H₂O₂ signaling

The issue whether a slow chemical reaction between H₂O₂ and a redox switch ensures timely information transmission during signal processing may be addressed with the help of the minimal mathematical model shown in Fig. 4. This model is formed by the oxidation-reduction cycle of a redox switch, which may be viewed as a switch-on switch-off sequence [22] with the on state – oxidized form of the redox switch – relaying the information encoded in H₂O₂ down the signaling cascade. The solution of this model yields a master equation (Eq. 3 in Fig. 5) describing the time course of the fraction of the redox switch in the reduced form [23]. From Eq. 3 two sets of simpler equations are deduced (Fig. 5), namely (i) Eqs. 4 A and 4B describing the effect of input H₂O₂ concentrations on the signaling response, and (ii) Eqs. 5 A and 5B characterizing the time-dependent H₂O₂ signaling properties. The input H₂O₂ concentrations and the response time are two important quantitative measures of redox signaling proposed before [18].

Fig. 4.

A minimal model of H₂O₂ signaling mediated by redox switches. A redox switch (Target) is oxidized by H₂O₂ and then reduced by, for example, a member of the thioredoxin family (Trx). The rate of target oxidation is equaled to the rate of the chemical reaction between H₂O₂ and the reduced form of the target (k_target+H2O2×[H₂O₂]×[Target_rd]), and the rate of reduction is set to k_switchoff×[Target_ox], with k_switchoff being a pseudo first-order rate constant. The differential equation is built, simplified by dividing by the total concentration of target [Target_tot], and solved with a software like Maxima [24]. The resulting solution describes the time course of the target in terms of its molar fraction in the reduced state (Target_rd), thus avoiding the utilization of absolute concentrations, a measure that is difficult to measure experimentally.

Fig. 5.

Governing equations of H₂O₂ signaling. The master equation (Eq. 3) includes the dependence on the sustained H₂O₂ signaling concentration [H₂O₂] attained in the vicinity of the redox switch during the signaling process, as well as the rate constants for oxidation (k_target+H2O2) and reduction (k_switchoff) of the redox switch, and the fraction of the redox switch in the reduced form at time 0 (${{\mathrm{Target}}_{\mathrm{rd}}|}_0$). The key features of H₂O₂ signaling are described by two sets of simpler equations deduced from the master Eq. 3 [8], [23]. Eq. 4A is deduced by letting t tend to infinite and represents the steady-state fraction of the redox switch in the oxidized form (Target_ox), which is a measure of the amount of information transmitted from H₂O₂ to the redox target. Calculation of the H₂O₂ signaling concentration causing a certain steady-state value of target oxidation is done with Eq. 4B, which results from an arrangement of Eq. 4A. The second set of equations (Eqs. 5A and 5B) calculates the response time of the redox switch to H₂O₂, giving the time (t_1/2) needed for oxidizing half of the target present initially, i.e., indicating whether transmission of information proceeds rapid enough. Eq. 5A is deduced by replacing ${{\mathrm{Target}}_{\mathrm{rd}}|}_t$ by ${{\mathrm{Target}}_{\mathrm{rd}}|}_0/2$ and t by t_1/2 in Eq. 3 and calculates t_1/2 as a function of H₂O₂ concentration. Eq. 5B is deduced by replacing Eq. 4B in Eq. 5A and calculates t_1/2 as a function of the steady-state fraction of the redox switch in the oxidized form and on the value of k_switchoff.

2.3. H₂O₂ dynamic range

The input dynamic range, i.e. the range of H₂O₂ concentrations for which redox switches act as sensors of H₂O₂, depends on the reactivity of the redox switch towards H₂O₂, being inversely proportional to k_target+H2O2 (Fig. 6A). One source of uncertainty in the plot of Fig. 6A is the k_target+H2O2 value because, among other factors, H₂O₂ reactivity increases several orders of magnitude upon reaction with phosphate and carbon dioxide yielding peroxymonophosphate [25] and peroxymonocarbonate [26], [27], respectively. The reactivity of PTP1B with peroxymonophosphate is 7000-fold higher than with H₂O₂ itself [25], and at pH 7, the presence of carbonate at 25 mM, a physiological level, accelerates the reaction between PTP1B and H₂O₂ from 24 M⁻¹s⁻¹ to 202 M⁻¹s⁻¹ at 25 °C and to 396 M⁻¹s⁻¹ at 37 °C. The formation of these derivatives is not immediate, taking 5–8 min to reach an equilibrium with H₂O₂ [25], [27]. Nevertheless, for peroxymonocarbonate, PTP1B accelerates this equilibration to a few seconds or faster [26]. This effect was attributed to oxidation of the active-site cysteine by peroxymonocarbonate possibly formed in the active center of the enzyme [26]. Zn(II) complexes and other Lewis acids increase the rate of peroxymonocarbonate formation [27], and one may speculate that Arg221, being present in the active site of PTP1B and being essential for catalysis [28], can act as a Lewis acid catalyzing the formation of peroxymonocarbonate. Therefore, in Fig. 6A the input dynamic range was also calculated for PTP1B in the presence of CO₂.

Fig. 6.

H₂O₂ input dynamic range for redox switches. Plots of Eq. 4A show the range of H₂O₂ concentrations to which thiol proteins with different reactivity respond. The following k_target+H2O2 values were used: peroxiredoxin 2 (Prx2) – 1×10⁷ M⁻¹s⁻¹; peroxiredoxin 5 (Prx5) – 3×10⁵ M⁻¹s⁻¹; Kelch-like ECH-associated protein 1 (Keap1) – 140 M⁻¹s⁻¹; cell division cycle 25B (cdc25B) – 140 M⁻¹s⁻¹; protein tyrosine phosphatase 1B (PTP1B) – 24 M⁻¹s⁻¹; PTP1B in presence of bicarbonate (PTP1B + CO₂) – 396 M⁻¹s⁻¹; and, src-homology 2 containing tyrosine phosphatase (SHP-2) – 20 M⁻¹s⁻¹. In (A) k_switchoff value was 2×10⁻³ s⁻¹, while in (B) the influence of a range of k_switchoff values is shown for peroxiredoxin 5. Input H₂O₂ concentrations sustaining information transmission by redox switches are shown in green and were defined as the input eliciting a 10–90% oxidation of the protein. Below 10% oxidation, redox switch response is considered too weak to transmit efficiently the H₂O₂ signal, while above 90% oxidation, the response is near saturated to further increase in the H₂O₂ concentration.

In addition to the reactivity of the redox protein towards H₂O₂, the input dynamic range also depends on the rate of reduction of the redox switch, increasing for high k_switchoff rate constants, as shown in Fig. 6B. Thus, according to Eqs. 4A and 4B the reduction of the redox switch inhibits the transmission of H₂O₂ signals, as it is observed for the reductions of OxyR by glutaredoxin 1 [29], of Yap1 by thioredoxins 1 and 2 [30], of Pap1 by thioredoxins 1 and 3 [31], [32], of PTP1B by redoxin TRP14 and thioredoxin 1 [33], [34], of PTEN by thioredoxin 1 [34], and of the NRF2/KEAP1 system by the thioredoxin system [35].

k_switchoff values for protein phosphatases PTP1B and SHP-2 – 2×10⁻³ s⁻¹ – [23] are about three orders of magnitude lower than for peroxiredoxins – 2 s⁻¹ [36]. This large difference reflects the value of the rate constant for the reduction of phosphatases – 700 M⁻¹s⁻¹ for PTP1B (estimated from [37]) – being much lower than the rate constant for the reduction of peroxiredoxins by thioredoxin – 2.1×10⁵ M⁻¹s⁻¹ [38], 2.2×10⁵ M⁻¹s⁻¹ (estimated from [39]) and (2–8)×10⁵ M⁻¹s⁻¹ (estimated from [40]) for peroxiredoxins 2, 3, and 5, respectively. Thus, the input dynamic range for peroxiredoxins is not as low as it could be expected from their high reactivity towards H₂O₂, and may even overlap with that of less reactive proteins. For example, input dynamic ranges for PTP1B and peroxiredoxin 5 are predicted to overlap (Table 2).

Table 2.

H₂O₂ dynamic range and response time for thiol proteins. Calculation of H₂O₂ dynamic range was done with Eq. 4B, assuming 10% and 90% of target oxidation, respectively for the lower and upper limit. Calculation of the response time to H₂O₂ was done with Eq. 5B, assuming 50% of target oxidation. For PTP1B and SHP-2 data for the reactivity obtained in the presence of CO₂[26] is also shown.

Redox target	ktarget+H2O2(M−1s−1)	kswitchoff(s−1)	H2O2dynamic range (µM)	Response time to H2O2(s)
PTP1B	24	2×10−3	9–750	173
+CO2	396	2×10−3	0.6–45	173
SHP‐2	20	2×10−3	11–900	173
+CO2	167	2×10−3	1.3–108	173
Prx5	3×105	2	0.7–60	0.2
Prx2	1×107	2	0.02–1.8	0.2

Table 2 shows the input dynamic range predicted according to published kinetic data. For H₂O₂ signaling concentrations lower than 1 µM, signaling is probably intermediated by a high reactive protein such as peroxiredoxin 2. For H₂O₂ concentrations higher than 1 µM, mediation of signaling by proteins with different reactivity towards H₂O₂ is feasible, but mediation by a high or by a low reactive protein is not equivalent as the response time is different (see below).

Not considered here is the hyperoxidation of peroxiredoxins, which also mediates transmission of information encoded in H₂O₂ [41], [42], [43]. Having different input dynamic ranges depending on modified forms of the same protein gives adaptability to signaling systems [44].

2.4. Response time to H₂O₂

Similarly to the input range, the response time also depends on the reactivity of proteins towards H₂O₂ and on the value of k_switchoff (Eqs. 5A and 5B). But contrary to the input dynamic range, the response does not depend on the ratio of the rate constant values for these processes, but rather on their sum. Therefore, between two proteins with similar input dynamic ranges, the one with higher reactivity towards H₂O₂ displays a faster response time for a given H₂O₂ concentration. For example, PTP1B will respond with a time of approximately 3 min, while peroxiredoxin 5 responds in less than 1 s, even if they have similar input dynamic ranges (Table 2). The response time for PTP1B calculated here is much faster than published estimations [8], [26], [36] because previous analyses considered only the oxidation of the redox switch, neglecting the impact of its reduction in the acceleration of the response time.

Response time values shown in Table 2 were calculated with Eq. 5 B, which hides the influence of H₂O₂ concentration and k_target+H2O2. For example, in spite of very different reactivity towards H₂O₂, peroxiredoxins 2 and 5 have a similar response time – 0.2 s. Implicit H₂O₂ concentrations used are, however, different for peroxiredoxins 2 and 5, being those that induce 50% of peroxiredoxin oxidation, as calculated by Eq. 4B. For the same H₂O₂ concentration, peroxiredoxin 2 has a much faster response time than peroxiredoxin 5, as shown in Fig. 7A.

Fig. 7.

Response time of redox switches to H₂O₂. Plots of Eq. 5A show the time needed to reach 50% of the overall response of sensors to H₂O₂. Values of rate constants are the same as those used in Fig. 6. In (A) k_switchoff value was 2×10⁻³ s⁻¹, while in (B) the influence of a range of k_switchoff values is shown for peroxiredoxin 5. Input H₂O₂ concentrations supporting rapid information transmission by redox switches are shown in green and were defined as the input eliciting responses faster than 10 min. Nonetheless, some processes may be compatible with longer responses times to H₂O₂, including for example apoptosis [45] or adaptation pathways [46], [47].

2.5. Analyzing typical experiments

In addition to provide new insights on the mechanisms of H₂O₂ signaling, the two sets of Eqs. 4 and 5 may be applied to learn new information from typical redox signaling experiments that measure the oxidation time course of redox switches. To this end, three experimental measurements are useful: (i) the fraction of the redox target in the oxidized form, (ii) the response time, and (iii) the H₂O₂ input dynamic range. The oxidation levels of the redox target and the response time can be estimated from the time course of the oxidation profile of the target under analysis. The measurement of the input dynamic range is more difficult. When H₂O₂ is added externally, the intracellular concentration of H₂O₂ is lower than that applied extracellularly, and a gradient across the plasma membrane is established [48]. The magnitude of this gradient is unknown and depends on the cell type and whether peroxiredoxins are active at the external H₂O₂ concentration applied in the experimental set up. The presence of active peroxiredoxins increases gradients by approximately two orders of magnitude, from values under 10 [48], [49], [50] to values in the 650–1000 range [51], [52]. Thus, uncertainties in the values of intracellular H₂O₂ concentrations impact the determination of the input dynamic range when H₂O₂ is added extracellularly. Alternatively, if endogenous production of H₂O₂ is stimulated with a signaling molecule, like a growth factor, the intracellular H₂O₂ concentration is also unknown. Even if the intracellular H₂O₂ level is followed with a probe, the conversion of the signal measured to H₂O₂ concentrations values is usually not done. In spite of these caveats, useful information can still be obtained from the concentration of H₂O₂ applied in experiments as exemplified below.

Stat3 is inhibited by 5 µM extracellular H₂O₂ [53], which corresponds to an intracellular concentration in the range of 0.5–0.005 µM if gradients are considered. In spite of this wide range of possible H₂O₂ concentrations, the involvement of a sensor with reactivity similar to peroxiredoxin 2 can be predicted (Table 2). In addition, the response time observed experimentally is below 60 s, for an extracellular H₂O₂ concentration of 50 µM [53]. A peroxiredoxin-like sensor is needed to attain such rapid response according to Eqs. 5 A and 5B. In fact, peroxiredoxin 2 acts as a sensor, reacting with H₂O₂ and then relaying the oxidation to form disulfide links between Stat3 monomers [53]. Of note, when oxidation relays are involved response times are slower than those indicated in Table 2 as the oxidation relay step introduces an additional delay not considered in the minimal model of Fig. 4.

In another example, a response time of about 4–5 min is estimated from the PTP1B oxidation profile observed when the endogenous production of H₂O₂ is triggered by EGF in A431 cells [54]. This slow response time is compatible with the direct reaction of H₂O₂ with PTP1B (see Table 2). In addition, in this case the H₂O₂ signaling concentration attained in the vicinity of PTP1B can be estimated as rate constants for PTP1B are known: if the level of PTP1B oxidation measured experimentally – approximately 50% [54] – together with k_target+H2O2 =396 M⁻¹s⁻¹ and k_switchoff =2×10⁻³ s⁻¹, is introduced in equation 4B, a concentration of 5 µM is estimated. By a similar approach, the H₂O₂ concentration attained in the vicinity of SHP-2 during stimulation of Rat-1 cells by PDGF is calculated to be 6 µM, based on the observed SHP-2 oxidation profile [55]. H₂O₂ concentrations in the order of 5–6 µM are much higher than the bulk steady-state H₂O₂ concentration, estimated in the range 0.1–0.01 µM [5], but are still plausible as localized pools of H₂O₂ probably play an important role during signaling [13], [36], [41], [56]. The plausibility of this estimation is reinforced by noting that oxidation profiles of protein phosphatases PTP1B and SHP-2 observed with growth factors are similar to those observed with extracellular H₂O₂ concentrations close to 100 µM [23], [55], [57]. An extracellular 100 µM H₂O₂ concentration corresponds to an intracellular concentration of 5 µM if an H₂O₂ gradient across the plasma membrane of 20 is established, which is plausible taking into consideration that at this relatively high external H₂O₂ levels peroxiredoxin systems are at least partially inhibited [36], [58].

Nonetheless, H₂O₂ concentrations attained during signaling are most probably pathway dependent. As referred above, low H₂O₂ extracellular concentrations, in the order of 5 µM, are in play during the formation of disulfide-linked Stat3 oligomers [53]. On the other hand, the inhibition of protein phosphatase 1 (PP1) probably needs a high dose of H₂O₂ because an associated IC₅₀ of 67 µM was measured in vitro [13]; in fact, this inhibition is probably mediated by localized production of H₂O₂ because colocalization of NOX4 and PP1 was observed and both proteins were identified together in a complex [13].

The previous discussion illustrates how Eqs. 4 and 5 give new insights on the mechanisms of H₂O₂ signaling and how new information is learned from common experimental measures. In addition, other applications for the equations are possible, including for example their fitting to experimental data to determine rate constants [23].

3. Final remarks

The main results of the quantitative biology analysis of H₂O₂ signaling presented here are summarized in the form of Eqs. 4 and 5 and are depicted in Fig. 8. Eqs. 4 and 5 govern the biology of H₂O₂ signaling and provide a quantitative framework with predictive power. In addition, common experimental measurements, like response time and oxidation profile of redox switches, may be analyzed with these equations, giving hints on the mechanisms of signal processing underlying experimental observations. Although the analysis was focused on thiol switches, these equations also apply to other types of redox switches.

Fig. 8.

Redox signaling properties. Redox characteristics of the redox switch define the properties of the transmission of information encoded in H₂O₂. When the ratio between oxidation and reduction is similar the same information output is observed (panels A and B), but the redox switch with higher redox turnover has a faster response (panel B). If oxidation dominates over reduction, signal transduction is favored by displacing the redox switch to the oxidized form (Panel C).

The input dynamic range, i.e., the H₂O₂ concentration range to which redox switches respond, depends not only on their H₂O₂-induced oxidability but also on their rate of reduction (Fig. 8). Eq. 4 indicates that the ratio between the kinetics constants of these two processes defines the sensitivity of the redox switch to H₂O₂. Peroxiredoxins and protein phosphatases respond in ranges of H₂O₂ concentration that are not as far apart as it could be predicted based solely in their very large different reactivity towards H₂O₂, because peroxiredoxins are reduced faster than protein phosphatases (Table 2). The response time also depends on the rates of oxidation and reduction of the redox switch given by Eq. 5. In this case, it is not the ratio between oxidation and reduction that determines the response time, but their effects add up to increase the rate of response.

Redox switches transmit information along a signaling cascade after being oxidized by H₂O₂. This oxidation may be direct or, alternatively, indirect when the redox sensor is a high reactive protein, like a peroxiredoxin, that relays the oxidation to a redox switch with low reactivity towards H₂O₂ (Fig. 9) [4], [59], [60]. Examples of relay circuits already identified include the original discovery of the Gpx3/Yap1 [61], and subsequently Tpx1/Pap1 [32], [62], Tsa1/Sty1 [63], Prx1/Ask1 [64], and Prx2/Stat3 [53]. In the thioredoxin-peroxiredoxin model, thioredoxin, or another protein responsible for the reduction of the redox sensor, acts as a redox relay, mediating the oxidation of a downstream redox switch [60], [65].

Fig. 9.

Mechanisms of H₂O₂ signaling. In the direct signaling pathway, H₂O₂ reacts directly with a redox switch. In the redox relay mechanism, the sensor of H₂O₂, a high-reactive protein such as a peroxiredoxin, relays the oxidation to a redox switch. The redox relay mechanism can be made more complex by the intervention of additional intermediates, as exemplified in the thioredoxin-peroxiredoxin model in which the protein responsible for the reduction of the redox sensor acts as a redox relay.

Independently of the specific mechanism, localized interactions are probably important to attain accurate information transmission [66]. These localized interactions include (1) complexes of NOX with redox switches, favoring switch on of a specific redox sensor, and (2) the interaction of a high reactive sensor, such as a peroxiredoxin, with a target protein, sustaining a specific relay of the oxidative signal. In this second case, the peroxiredoxin will not only relay the oxidative signal downstream but also trap H₂O₂ [36], avoiding H₂O₂ diffusion outside the signal locus and, consequently, preventing either unspecific signaling messages or even some form of pathological stress.

In conclusion, the relatively weak oxidation potential of H₂O₂ is coupled to timely and accurate transmission of information by a combination of chemical reactions that balance oxidation and reduction of redox switches, together with specific protein interactions and localized H₂O₂ pools.