Energetics of Structural Transitions of the Addiction Antitoxin MazE

The Escherichia coli mazEF addiction module plays a crucial role in the cell death program that is triggered under various stress conditions. It codes for the toxin MazF and the antitoxin MazE, which interferes with the lethal action of the toxin. To better understand the role of various conformations of MazE in bacterial life, its order-disorder transitions were monitored by differential scanning calorimetry, spectropolarimetry, and fluorimetry. The changes in spectral and thermodynamic properties accompanying MazE dimer denaturation can be described in terms of a compensating reversible process of the partial folding of the unstructured C-terminal half (high mean net charge, low mean hydrophobicity) and monomerization coupled with the partial unfolding of the structured N-terminal half (low mean net charge, high mean hydrophobicity). At pH ≤ 4.5 and T < 50 °C, the unstructured polypeptide chains of the MazE dimer fold into (pre)molten globule-like conformations that thermally stabilize the dimeric form of the protein. The simulation based on the thermodynamic and structural information on various addiction modules suggests that both the conformational adaptability of the dimeric antitoxin form (binding to the toxins and DNA) and the reversible transformation to the more flexible monomeric form are essential for the regulation of bacterial cell life and death.

Programmed cell death, defined as an active process that results in cell suicide, refers to any form of cell death or stasis mediated by an intracellular death program, no matter what triggers it (1)(2)(3). In bacteria, programmed cell death is mediated through a unique genetic system. This system, called an "addiction module," consists of a pair of genes that specify for two components: a toxin and an antitoxin that interferes with the lethal action of the toxin. The toxin and the antitoxin are coexpressed. Their expression is autoregulated at the level of transcription either by the toxin-antitoxin complex or by the antitoxin alone (4 -19). Until recently, such genetic systems for programmed bacterial cell death have been found mainly in Escherichia coli on low copy number plasmids. When bacteria lose the plasmid(s) (or other extrachromosomal elements), the cured cells are selectively killed because the unstable antitoxin is degraded faster than the more stable toxin (4 -7). The cellular target of the toxin is known only in the ccdAB and kid-kis systems. In ccdAB, CcdB on plasmid F attacks the A subunit of gyrase, whereas in the kid-kis system, Kid on plasmid R1 targets DnaB (20 -22). Thus, the cells are "addicted" to the short-lived antitoxin because its presence is essential for cell survival (4).
Toxin-antitoxin systems, some of which are homologous to these extrachromosomal addiction modules, have been found on the chromosomes of several bacteria. For example, in E. coli, there are several such pairs of genes, including mazEF (23)(24)(25), chpBIK (24), relBE (26 -28), yefM-yoeB (29 -31), and dinJ-yafQ (32). The first toxin-antitoxin system contained in a bacterial chromosome that was described as regulatable and responsible for programmed cell death was the E. coli mazEF module (25), located in the relA operon (23). The product of mazF (MazF) is a stable toxin, and the product of mazE (MazE) is a labile protein, degraded by the protease ClpAP (25). Therefore, preventing MazF-mediated death requires a continuous cellular production of MazE. In contrast to the addiction modules that are triggered by the loss of the element, death mediated by chromosomal mazEF is achieved by several stressful conditions that prevent mazEF expression. Initially, the mazEF module was found to be under the control of ppGpp (25), the amino acid starvation signal molecule produced by the RelA protein (33). Overproduction of ppGpp leads to inhibition of the expression of mazEF and thereby to cell death (25,34). However, as reported recently, inhibiting the expression of mazEF and thus inducing cell death can be also achieved by several additional stressful conditions. These include the inhibition of transcription and/or translation (35)(36)(37), DNA damage (38,39), and oxidative stress (39).
In the last few years, the chromosomal mazEF toxin-antitoxin systems have attracted additional attention, in particular in the following four directions. (a) The first is studies on the mechanism of MazF action. MazF has been shown to inhibit translation by cleaving mRNAs at specific sites (40,41). How-ever, two laboratories have reported contradictory results for the mechanism of cleavage. According to one group, MazF inhibits translation by a ribosome-dependent mechanism (40), and according to a second group, MazF is a sequence-specific endoribonuclease that cleaves mRNAs at ACA sequences in a codon-and ribosome-independent manner (41). This second version was further confirmed by a more recent report from the same laboratory showing that, at least in vitro, MazF functions enzymatically in a similar manner to RNase A, although with different sequence specificity (42). (b) The second direction is studies on the mazEF-mediated cell death network. There is a "point of no return" in MazF-mediated cell death; overexpression of MazE can only reverse MazF lethality over a short window of time (43), suggesting that MazF is a mediator rather than an executioner of cell lethality (44). (c) The third direction is studies on the function of mazEF showing that it can prevent spreading of phage infection (45). (d) The fourth is molecular studies characterizing the forces that drive the unfolding (folding) of proteins (MazE, MazF) and the interactions that drive MazE-MazF, MazE-DNA, and MazE-MazF-DNA complex formation. The first step toward this goal was achieved by crystallization of the antitoxin MazE and by determination of part of its three-dimensional structure (46). The resulting structure is the first of any addiction antitoxin, the crystallization of which has been hampered because of its susceptibility to proteases and its high content of unstructured polypeptide. We circumvented this problem by crystallizing MazE in complex with the specific dromedary antibody fragment VHH. Furthermore, the energetics of MazE interactions with VHH was investigated in detail. It has been suggested that, under physiological conditions in solution, a significant part of the MazE polypeptide chain may be unstructured, as in the crystal of the MazE-VHH complex (47). Almost simultaneously, Kamada et al. (48) determined the crystal structure of the MazE-MazF complex, in which MazE chains appear to be less unstructured than in the complex with VHH.
It is known that proteins that lack intrinsic globular structure (intrinsically flexible, intrinsically unstructured, natively unfolded, pliable) are frequently involved in some of the most important regulatory functions in the cell (30, 49 -55). Numerous examples of domains that are unstructured in solution but become structured upon binding to the target have been identified. Thus, the intrinsic lack of structure can offer functional advantages to a protein, including its ability to bind several different targets (30, 49 -57).
In this study, we investigated to what extent MazE belongs to this category of proteins by studying its conformational changes induced by variation in temperature, pH, protein concentration, and urea concentration. The energetics of MazE order-disorder transitions was studied by various techniques (differential scanning calorimetry, spectropolarimetry, and fluorometry) and is discussed in terms of its three-dimensional structures (46,48). An attempt was made to predict some functional features of the addiction modules from the equilibrium thermodynamic model, which involves antitoxin and toxin molecules and DNA. To the best of our knowledge, the research described here represents for the first time a complete thermodynamic study of structural transitions of a protein with an intrinsically flexible nature.

Preparation of MazE Solutions
The expression and purification of MazE have been described previously (46). MazE solutions for calorimetric and spectroscopic measurements were prepared by diluting the stock solution of MazE in water to the appropriate concentrations in the appropriate buffer solutions. Depending on the pH, the buffer solutions used in our experiments were as follows: 50 mM HCl (pH 1.5), 50 mM citrate (pH 3.1), 50 mM acetate (pH 4.5), 50 mM cacodylate (pH 6.1), 50 mM phosphate (pH 7.1), 50 mM HEPPS 1 (pH 8.1), and 20 mM borate (pH 9.4). Unless stated otherwise, all buffer solutions contained 150 mM NaCl. For urea denaturation, 21 solutions with the same MazE concentration and varying urea concentrations (0 -8 M) were prepared from stock 10 M urea and stock MazE solutions in the same buffer. The pH of all solutions was checked and adjusted to the appropriate value by NaOH or HCl. Before each experiment (except those involving urea), the protein buffer solution was extensively dialyzed against the corresponding buffer solution and degassed for 15 min. The concentrations of the 98-residue-long His tagfused MazE protein (molecular mass of 11211.5 g mol Ϫ1 ) were determined spectrophotometrically by measuring the absorbance at 280 nm. The corresponding extinction coefficient of MazE in 6 M guanidinium chloride and 20 mM phosphate buffer (pH 6.5) was obtained from the amino acid composition by the method introduced by Gill and von Hippel (58) (available at www.expasy.ch). Finally, an extinction coefficient of 1.27 Ϯ 0.05 mg Ϫ1 ml cm Ϫ1 was calculated by combination of the measured absorbance of the guanidinium chloride-free MazE solution of the same concentration at the same wavelength (280 nm) as the one measured in guanidinium chloride.

Differential Scanning Calorimetry (DSC)
The thermally induced transitions of MazE were measured between pH 1.5 and 9.4 using a Nano-II DSC differential scanning calorimeter (Calorimetry Sciences Corp.). The heating rate was 1°C/min Ϫ1 , and the concentration of proteins in the measuring cell was ϳ1.2 mg ml Ϫ1 . To obtain the presented thermograms ((C p Ϫ C p,N ) versus temperature curves) (see Fig. 2), the heat capacity of the protein in the initial (native) state was subtracted from the raw signal corrected for buffer contribution. The transition enthalpies (⌬H cal ) were obtained by integration of the (C p Ϫ C p,N ) versus temperature curves.

CD Spectropolarimetry
CD spectra were recorded using a Model 62A DS spectropolarimeter (Aviv, Lakewood, NJ) equipped with a programmable thermoelectrically controlled cell holder. The presented mean residue ellipticities ([], degrees cm 2 dmol Ϫ1 ) were obtained from raw data (ellipticities) by subtracting the corresponding spectra of the buffer solution and taking into account the mass concentration (c), molecular mass (M w ), number of MazE amino acid residues (N), and optical path length (l) through the relation [] ϭ ⅐M w /(N⅐c⅐l).
Thermal Denaturation-Changes in MazE secondary (far-UV, 205-255 nm; 1-mm cuvette) and tertiary (near-UV, 255-310 nm; 1-cm cuvette) structure were followed by recording CD spectra at a MazE concentration of 0.5 mg ml Ϫ1 (see Fig. 3, a and b) at different temperatures with a temperature step of 3°C. At a lower concentration (0.05 mg ml Ϫ1 ), temperature scans in the far-UV region were performed also at ϭ 230 nm in a 1-cm cuvette.
Urea Denaturation-The changes in MazE secondary structure upon increasing urea concentrations (0 -8 M) were followed by measuring the ellipticity at 225 nm in a 1-cm cuvette at a MazE concentration of 0.05 mg ml Ϫ1 (see Fig. 5, b and c). The measurements were performed at a number of different temperatures.

Fluorescence Spectroscopy
Fluorescence emission spectra were recorded using a PerkinElmer Life Sciences LS 50 luminescence spectrometer equipped with a thermally controlled cell holder and a cuvette with a 1-cm path length. Thermal denaturation of MazE was followed by the emission fluorescence of the external fluorescent probe 1-anilino-8-naphthalenesulfonic acid ammonium salt (ANS; Fluka, Buchs, Switzerland). The emission spectra (415-615 nm) were recorded at different temperatures the range 8 -90°C using ex ϭ 400 nm (see Fig. 4). The concentrations of MazE and ANS in the buffer solutions were 0.05 and 0.126 mg ml Ϫ1 , respectively. Urea-induced denaturation of MazE was followed by measuring the changes in MazE intrinsic (Trp) emission fluorescence between 310 and 410 nm ( ex ϭ 280 nm) at urea concentrations of 0 -8 M. The concentration of MazE was 0.05 mg ml Ϫ1 (see Fig. 5b), and the measurements were performed at a number of different temperatures.

Model Analysis of Thermally Induced and Urea-induced Transitions
Our results reveal that the majority of the monitored structural transitions can be adequately described in terms of a reversible twostate process in which the protein molecule can exist either in macro state N or in macro state D. Such process can be presented as shown in Equation 1, where N n represents the MazE dimer (n ϭ 2) in the initial (native) state, whereas D corresponds to MazE in the final monomeric (denatured) state; K is the equilibrium constant of denaturation; ⌬G 0 is the corresponding standard Gibbs free energy change per mol of monomer; n is the number of subunits to which each protein dissociates upon denaturation; ␣ is the fraction of protein in the denatured state; and C T is the total protein concentration given in moles of monomer liter Ϫ1 . It should be noted that, under some specific conditions, two successive transitions that do not overlap significantly were observed (see "Results"). In such cases, the two transitions can be treated separately: the first one that corresponds to the transition of the native dimer N 2 into the intermediate dimer where ⌬H 0 (T1 ⁄2 ) is the standard enthalpy of denaturation at the reference temperature T1 ⁄2 (transition temperature at ␣ ϭ 0.5) and ⌬C p 0 is the corresponding standard heat capacity change assumed to be independent of temperature. According to the model (Equation 1), one can express an average of a physical property, F (in our case, F is the partial molar enthalpy of the protein, the mean residue ellipticity ([]), or the fluorescence intensity (FL)), in terms of the corresponding contributions F N and F D , which characterize states N and D (47,59), respectively (Equation 3).
In the case of transitions followed by spectroscopic methods (CD and fluorescence), F N and F D are assumed to be linear functions of temperature (thermal denaturation) or urea concentration (urea denaturation). The model function (C p Ϫ C p,N ) for the DSC signal is the partial molar heat capacity of the protein relative to state N. It can be derived from the first partial derivative of Equation 3 on temperature at constant pressure (60 -62) (Equation 4).
Taking into account Equations 1-4, the observed temperature profiles (melting curves) can be described in terms of the parameters ⌬H 0 (T1 ⁄2 ), ⌬C p 0 , and T1 ⁄2 . Their values were obtained from fitting the model function (CD ϭ Equation 3 and DSC ϭ Equation 4) to the experimental temperature profiles using the Levenberg-Marquardt nonlinear 2 regression procedure (63). In the case of urea-induced denaturation at a given temperature, the denaturation profiles were described by Equations 1 and 3 combined with the well known empirical where ⌬G o 0 is the standard Gibbs free energy in the absence of urea and m is the proportionality coefficient. At each temperature, the parameters ⌬G o 0 and m were adjusted according to the 2 regression procedure mentioned above. These values were then fitted by Equation 2 (for ⌬G 0 ϭ ⌬G o 0 ) to obtain the corresponding parameters ⌬H 0 (T1 ⁄2 ), ⌬C p 0 , and T1 ⁄2 in the absence of urea.

Structure-based Thermodynamic Calculations
The non-polar (A N ) and polar (A P ) solvent-accessible surface areas of proteins were calculated with NACCESS Version 2.1 (64). A N and A P of native MazE were obtained from the crystal structure of the MazE-VHH complex (probe size of 1.4 Å), and the unstructured residues were assumed to be exposed in the same way as they are in the extended Ala-X-Ala tripeptide. A N and A P contained by the denatured MazE were estimated as the sum of the corresponding accessibilities of the protein residues in an extended Ala-X-Ala tripeptide. ⌬C p 0 accompanying MazE denaturation and dissociation (1/2N 2 7 D) was calculated from the corresponding changes in non-polar and polar accessible areas using the expression introduced by Murphy and Freire (65) (Equation 5).
The same type of relations introduced by Makhatadze and Privalov (66) where the sum of the first two terms on the right-hand side represents the ⌬H 0 value observed with most globular proteins at their median transition temperature of 60°C. The corresponding entropy change was calculated as a sum of four contributions (69 -71) (Equation 7).
The solvation term ⌬S sol 0 , which describes the exposure of polar and non-polar groups to the solvent upon protein denaturation and dissociation, was obtained as ⌬S sol 0 ϭ ⌬C p 0 ln(T/385.15) (71, 72). The second term that reflects the change in the side chain conformational entropy upon dissociation (1/2N 2 7 N) was calculated as ⌬S sc 0 ϭ ⌺(⌬A sc S sc 0 / A Ala-X-Ala ). The sum was taken over each amino acid in the proteinprotein interface (excluding alanine, proline, and disulfide-bonded cysteine), and its side chain conformational entropy was scaled by its change in the accessible surface area (⌬A sc ) normalized to its A in the corresponding Ala-X-Ala tripeptide (70). The S sc 0 values were those reported by Lee et al. (73). The third contribution (⌬S rt 0 ) is due to mixing of the solvent and solute molecules when the number of solute molecules in the initial state differs from that in the final state. For the reaction 1/2N 2 7 N carried out in a hypothetical 1 M standard state, this contribution amounts to ⌬S rt 0 ϭ (Ϫ1/2)R ln(1/55.5) (74). There is a considerable debate in the literature whether this contribution accounts for the entropy change due to the increase in translational/ rotational degrees of freedom upon dissociation (67,70,71,(75)(76)(77)(78)(79)(80)(81)(82)(83)(84)(85). Nevertheless, its value has been found as the most appropriate for description of protein-protein rigid body dissociations (70,71,75). The fourth contribution (⌬S conf 0 ) refers to the configurational entropy change that accompanies the unfolding of the protein (N 7 D). It is estimated as where ͗N͘ is the number of amino acid residues participating in the unfolding process and 4.3 cal K Ϫ1 (mol residue) Ϫ1 is the average configurational entropy change associated with the passage of an amino acid from a buried to a solvent-exposed state (65). To correlate the energetics of denaturation of MazE with its structural features, the ⌬A N and ⌬A P values were estimated also from Equations 5 and 6 using the experimentally obtained ⌬H 0 and ⌬C p 0 values (see Fig. 8c). Moreover, ͗N͘ was estimated from Equation 7 as ͗N͘ ϭ (⌬S 0 Ϫ (⌬S sol 0 ϩ ⌬S sc 0 ϩ ⌬S rt 0 ))/4.3 cal K Ϫ1 (mol residue) Ϫ1 , where ⌬S 0 is the measured standard entropy change (see Fig. 9d).

Mean Hydrophobicity and Mean Net Charge
The hydrophobicity of each amino acid sequence was calculated by the Kyte and Doolittle approximation (86) using a window size of five amino acids. The hydrophobicity of individual residues was normalized to a scale of 0 -1 in these calculations. The mean hydrophobicity ͗H͘ b is defined as the sum of the normalized hydrophobicities of all residues divided by the number of residues in the polypeptide. The mean net charge ͗R͘ is defined as the net charge at pH 7 divided by the total number of residues. The calculations for various addiction antitoxin and toxin sequences were performed using the Swiss Institute of Bioinformatics server ExPASy (available at www.expasy.ch) (87).

Distribution of Molecular Species Involved in Addiction Modules
The model for calculation of fractions of antitoxin and toxin species is defined by the postulates that were extracted from the thermodynamic and structural information on addiction modules (10, 11, 46 -48, 88 -92) and from the physical properties of an E. coli cell (available at redpoll. pharmacy.ualberta.ca/CCDB/cgi-bin/STAT_NEW.cgi). The postulates and the details on the numerical procedure are given in the Supplemental Material.

RESULTS
As shown by its crystal structure (Fig. 1a), MazE exists in a solid state as a dimer. We have proved by gel filtration that it exists as a dimer also in buffer solutions and that its dimeric state around room temperature remains unchanged under the experimental conditions applied in our studies.
The extent of reversibility of the observed thermally induced transitions was checked by performing two consecutive temperature scans (DSC and CD) and/or by measuring spectra (CD, intrinsic, and ANS fluorescence) after cooling down the MazE sample to the pre-transitional temperature. Reversibility of urea denaturation was examined by dialyzing concentrated urea solutions against the appropriate buffer and measuring an optical property (CD and fluorescence) before and after the dialysis. The extent of reversibility of all monitored transitions (except for the high temperature one at pH 1.5) is Ͼ80% which makes the laws of reversible thermodynamics applicable for their description. By contrast, the model-dependent parameters (Equation 1) that describe the high temperature transition at pH 1.5 (reversibility of Ϸ30%) can serve only for comparative purposes (Table I).
pH Dependence of Thermally Induced Transitions DSC-Thermograms between pH 1.5 and 9.4 show one transition at T Ͼ 60°C, whereas at pH 1.5 and 3.1, we observed another transition at ϳ25°C (Fig. 2). The high temperature transitions can be described in terms of the equilibrium twostate model (Equations 1, 2, and 4) with n ϭ 2, whereas for the description of low temperature transitions, a two-state model with n ϭ 1 should be used. The low temperature transitions are characterized at pH 1.5 by the model-independent (⌬H cal ϭ 9 kcal mol Ϫ1 ) and model-dependent (⌬H 0 (T1 ⁄2 ) ϭ 9 kcal mol Ϫ1 and T1 ⁄2 ϭ 24°C) quantities, whereas at pH 3.1, the corresponding values are ⌬H cal ϭ 12 kcal mol Ϫ1 , ⌬H 0 (T1 ⁄2 ) ϭ 13 kcal mol Ϫ1 , and T1 ⁄2 ϭ 28°C. ⌬C p 0 values were too small to be determined accurately and were therefore neglected in our model analysis. The successive low and high temperature transitions of MazE observed at pH 1.5 and 3.1 were described also by a three-state model (1/2N 2 7 1/2I 2 7 D; see the Supplemental Material). The resulting ⌬H 0 (T1 ⁄2 ), ⌬C p 0 , and T1 ⁄2 values for both transitions were practically the same as those obtained when each transition was considered as an independent two-state transition. This agreement clearly indicates that the overlap of the two successive transitions is insignificant, and therefore, MazE denaturation can be discussed in terms of one or two independent two-state processes. Considering these facts, the thermodynamic stability of MazE at different conditions was described by the corresponding parameters (⌬H 0 (T1 ⁄2 ), ⌬C p 0 , and T1 ⁄2 ) derived from the model analysis of the measured DSC data (see Figs. 6 and 7 and Table I).
CD Spectropolarimetry-The far-UV CD spectra measured at pH 7.1 and T ϭ 37°C (Fig. 1c) show that the fractions of ␣-helix, ␤-sheet, and the remainder of the structure estimated according to Provencher and Glöckner (93) are consistent with those observed in the structure of MazE within the crystal of the MazE-VHH complex (Fig. 1a). Furthermore, the far-UV CD spectra of MazE (Figs. 1c and 8a) show an increase in the CD signal upon lowering the pH from 7.1 to 1.5, which is typical for intrinsically flexible proteins (51). One may speculate that the increase in the CD signal at pH 1.5 observed at Ͻ 205 nm can be ascribed to the increased amount of the coil-like conformation, whereas at Ͼ 210, the increased CD intensity may be  Bank code 1mvf). Atoms whose solvent-accessible area is not influenced upon dimer formation are shown in light gray, whereas the others are colored according to atom type (oxygen, red; nitrogen, blue; carbon, yellow; and sulfur, green), with the intensity of the color representing the amount of accessible surface area buried in the dimer (ranging from 0 Å 2 (light gray) to 55 Å 2 (most intense colors)). c, far-UV CD spectra of MazE (0.3 mg ml Ϫ1 ) measured in 50 mM HCl (pH 1.5) and 50 mM phosphate (pH 7.1) in the absence of NaCl. The fractions of conformations in the secondary structure of MazE estimated at pH 7.1 and T ϭ 37°C according Provencher and Glöckner (93) are 9% helix, 38% strand, and 53% remainder. deg, degrees. due to some other type of structuring. According to the spectra measured after dialysis of MazE solution at pH 1.5 against the appropriate buffer solution at pH 7.1, this low pH-induced transition is highly reversible (Ϸ90%). The far-UV CD intensity at Ͼ 210 nm increased with temperature at all pH values studied (Figs. 1c, 3a, and 8a). We believe that such behavior that resembles structuring observed within intrinsically flexible proteins (51) may be ascribed to the structuring of the disordered part of MazE molecules. A relatively high intensity CD signal was observed at low temperature and pH Ͼ1.5 also in the near-UV range (asymmetry of aromatic residues in MazE), which indicates the presence of a substantial amount of tertiary structure in MazE dimers (Fig. 3b). With increasing temperature, this amount decreased at all monitored pH values; however, a substantial amount of tertiary structure remains present even at high temperature (see Fig. 8b). Moreover, Fig. 3, a and b, shows that, also upon chemical denaturation (8 M urea at 25°C), neither the secondary nor tertiary structure of MazE was fully destroyed.
The far-and near-UV CD temperature profiles constructed at ϭ 230 and 280 nm, respectively, show at pH 1.5-9.4 one transition at T Ͼ 60°C, whereas at pH Յ4.5, another transition at ϳ25°C was detected (Fig. 3, c and d). The melting curves describing the high temperature transitions show concentration dependence (Fig. 3, a, c, and d), indicating that these processes are not monomolecular (n Ͼ 1; see Equations 1-3). By contrast, low temperature transitions observed at pH Յ4.5 seem to be concentration-independent and can be characterized as monomolecular (n ϭ 1). Some melting curves measured at higher concentrations do not level off at T Ͻ 100°C (limitation of the method), which made the determination of the end (denatured) state as a linear function of temperature questionable (Equation 3). Consequently, the end states determined at lower concentrations were used in the model analysis of these curves. Fig. 3c shows a typical temperature profile at pH Յ4.5 measured at two different concentrations. The analysis of the threestate model (1/2N 2 7 1/2I 2 7 D; see the Supplemental Material) confirms the observations from DSC measurements that the two transitions are rather independent (Fig. 3d). Wherever possible, the melting curves were analyzed in terms of an appropriate model (Equations 1-3: low temperature transitions, n ϭ 1; and high temperature transitions, n ϭ 2). In these cases, the model function (Equation 3) displays good agreement with experimentally measured mean residue ellipticities (Fig.  3), and the resulting ⌬H 0 (T1 ⁄2 ), ⌬C p 0 , and T1 ⁄2 values agree well with those derived from DSC experiments (Table I).
ANS Fluorescence-Changes in ANS fluorescence are frequently used to detect non-native intermediate conformations of globular proteins (94 -96). This is because such intermediates are characterized by the presence of solvent-exposed nonpolar clusters that bind ANS molecules. As a result, an increase in ANS fluorescence intensity accompanied by a pronounced blue shift of the emission maximum is observed (95,96). At pH Յ4.5, the observed changes in the intensity at T Ͻ 50°C (Fig. 4) show that, under these conditions, at least a part of the MazE molecule exists in a (pre)molten globule-like conformation (52,97). Furthermore, at pH 1.5, temperature-induced transitions at ϳ25°C (red shift of Ϸ3 nm) and 65°C (red shift of Ϸ5 nm) were observed that correspond well to the low and high temperature transitions observed with DSC and CD (Fig. 4b). At pH Ͼ4.5, no significant changes in the intensity or position of the emission maximum with increasing temperature were observed, which indicates that, at pH Ͼ4.5, neither the native dimeric state nor the denatured monomeric state of MazE contains exposed clusters of non-polar residues.

FIG. 2. Thermal denaturation of MazE monitored by DSC.
In DSC thermograms measured at various pH values, C p Ϫ C p,N is expressed in kcal K Ϫ1 mol Ϫ1 (monomeric unit). For clarity, only every tenth experimental point is presented. Solid lines represent graphs of the best fit model function (Equation 4). Inset, two typical consecutive C p versus temperature scans (pH 6.1) displaying a high degree of reversibility.

Urea-induced Transitions
Urea-induced denaturation of Maze at pH 7.1 was monitored by intrinsic fluorescence and far-UV CD. In Fig. 5a, an insert of the MazE structure is presented that shows that Trp is the only aromatic amino acid residue in the structured part of the MazE molecule (there are two more Trp residues in the unstructured part) that is exposed to a large extent to the solvent. This is reflected in the MazE fluorescence emission spectra, which display, in the measured solution, ( em ) max values that are close to those observed with pure Trp in water. Our measurements also show that urea-induced denaturation of MazE is characterized, contrary to many globular proteins, by an increase in the intrinsic fluorescence intensity accompanied by a small blue shift of ϳ3 nm (Fig. 5b). This result is consistent with the measured CD spectra of MazE in urea solutions (Fig.  3, a and b), which show that, even in 8 M urea, neither the secondary nor tertiary structure of MazE disappears (98). Moreover, the observed blue shift and increase in fluorescence intensity may be indicative of a local structuring of residues around one, two, or all three Trp residues. Interestingly, a similar blue shift was observed also with the thermal denaturation of MazE in urea-free aqueous solutions. Fig. 5b also shows that the far-UV CD intensity decreased with increasing urea concentration and that urea-induced transitions, followed by either CD or fluorescence, can be described in terms of an appropriate two-state model (Equations 1 and 3 with n ϭ 2).

DISCUSSION
Energetics of the MazE Structure-The stability curves (⌬G 0 versus temperature) of MazE at pH 7.1 obtained from thermal and urea-induced denaturation are presented in Fig. 6 together with the corresponding enthalpy and entropy contributions. At T ϭ 5-85°C, the ⌬G 0 values obtained from urea-induced denaturation (⌬G 0 ϭ ⌬G o 0 ; see "Experimental Procedures") are slightly higher than those obtained from thermal denaturation. Because, in the urea-denatured state, the fraction of secondary and tertiary structure is substantially lower than in the thermally denatured state (Fig. 3), the corresponding difference in ⌬G 0 may be ascribed mainly to the enhanced hydrophobic effect ing. In their structure-based calculations of thermodynamic quantities of unfolding, they used empirical parameterization based largely upon changes in polar (⌬A P ) and non-polar (⌬A N ) surface areas exposed to the solvent. ⌬A N and ⌬A P are usually calculated from the structural data. Thus, their values depend on the structural definition of the initial (native) and final (unfolded) states of the protein. The crystal structure of MazE (46) may be a good approximation of the free MazE dimer native form in solution because VHH does not interrupt MazE-DNA association (46,47) and does not interfere with MazF binding (see the figure in the Supplemental Material). This approximation is supported by the analysis of the far-UV CD spectra, which, under physiological conditions, predict a MazE structure (46) that is close to the one observed in the crystal of the MazE-VHH complex (Fig. 1). The final (unfolded) state of MazE may be defined as a state in which each MazE residue (X) is exposed to the solvent in the same way as in the corresponding Ala-X-Ala tripeptide. Using the described initial and final states, we obtained the thermodynamic profile (Equations 5-7) for the complete unfolding and dissociation of MazE (1/2N 2 7 D) (Fig. 6), in which all 44 structured residues are involved in the changes of the solvent-exposed surfaces (⌬A N,U ϭ 2907 Å 2 , ⌬A P,U ϭ 1498 Å 2 , and ͗N͘ U ϭ 44). This calculation leads to much too high ⌬C p 0 (0.92 kcal K Ϫ1 mol Ϫ1 ) and ⌬S conf 0 values. As a result, the calculated ⌬G 0 value is considerably lower than the experimental one. In an attempt to correlate the structural and thermodynamic data, we also used an opposite approach in which ⌬A N , ⌬A P , and ͗N͘ that accompany MazE denaturation were calculated from experimental thermodynamic data (Equations 5-7). The calculations show that, upon denaturation and monomerization of MazE induced by urea (⌬A N ϭ 1793 Å 2 , ⌬A P ϭ 1320 Å 2 , and ͗N͘ ϭ 31), more residues unfolded, and more non-polar surface was exposed to solvent than in the case of thermal denaturation (⌬A N ϭ 1113 Å 2 , ⌬A P ϭ 1035 Å 2 , and ͗N͘ ϭ 21). The estimates are in complete agreement with our explanation of the discrepancy between ⌬G 0 (urea) and ⌬G 0 (thermal) and show that, at physiological pH, both thermally denatured and ureadenatured states are far from being completely unfolded (͗N͘ Ͻ the total number of structured residues, ͗N͘ U ϭ 44). We would like to point out that these ⌬A N , ⌬A P , and ͗N͘ values comprise errors of the empirical parameterization and those of the measured quantities and can therefore be considered only as reasonably good approximations (see Fig. 8, c and d). Finally, we estimated the average number of unfolded residues (͗N͘) simply as ͗N͘ ϭ (⌬A N ϩ ⌬A P )⅐͗N͘ U /(⌬A N,U ϩ ⌬A P,U ), where ⌬A N and ⌬A P refer to the thermal or urea-induced denaturation of MazE, and ⌬A N,U , ⌬A P,U , and ͗N͘ U are defined as described above. Fig. 8d shows that ͗N͘ values determined in this way are surprisingly close to the corresponding ͗N͘ values calculated from Equation 7, in which the configurational entropy change upon actual unfolding is taken as ⌬S conf 0 ϭ ͗N͘⅐4.3 cal K Ϫ1 (mol residue) Ϫ1 (65). We believe that the observed agreement between the ͗N͘ values obtained from independent parameterization of ⌬C p 0 and ⌬H 0 on the one side and ⌬S 0 on the other strongly supports the parameterization of the experimental quantities ⌬C p 0 , ⌬H 0 , and ⌬S 0 suggested by Equations 5-7. In other words, the suggested parameterization seems to be successful provided that the "true" ⌬A N and ⌬A P values are used.
As shown in Fig. 7a, the stability of the MazE dimer conformation strongly depends on pH. In the studied temperature range, the measured ⌬G 0 versus pH curve exhibits a maximum at pH ϳ 4.5. Such behavior may be explained in terms of different structural characteristics of the final (high temperature) monomeric state and the initial (low temperature) dimeric state. At physiological pH, the low temperature dimeric state contains the unstructured C-terminal half characterized by low mean hydrophobicity and low negative mean net charge (see Fig. 10). Lowering the pH results in reduction of the net charge, and consequently, the unstructured MazE chains start organizing themselves into a sort of a compact molten globulelike conformation. This structuring effect is opposed by a simultaneous change in the conformation of the structured Nterminal half (low mean net charge and high mean hydrophobicity) (see Fig. 10), which is responsible for dimer formation. Because of the strong favorable contribution of the hydrophobic effect (mainly hydrophobic residues are involved in dimer formation) (Fig. 1b), a surplus of a positive charge on the N-terminal half at low pH does not break the dimer apart; however, it reduces the fraction of the secondary and tertiary structure. Inspection of data describing the high temperature monomeric state of MazE shows that, relative to the low temperature state, the secondary structure complexity of the high temperature state is about the same at all measured pH values (Fig. 8a). By contrast, the amount of the high temperature tertiary structure to the low temperature state is reduced to about the same extent only at pH Ն 4.5. At lower pH values, this reduction appears to be much smaller (Fig. 8b). It appears that the thermodynamic parameters of denaturation result from the compensating effect of the partial folding of the unstructured C-terminal half and monomerization coupled with the partial unfolding of the structured N-terminal half. Inspection of Table I shows that lowering the pH thermally stabilizes the dimeric form of MazE (T1 ⁄2 at a given MazE concentration increases with decreasing pH). Because, at pH 1.5-7.1, ⌬C p 0 and ⌬H 0 values decrease upon lowering the pH, the maximum stability reached at pH Ϸ4.5 is most likely due to the simultaneous lowering of ⌬S conf 0 . The suggested explanation is in full agreement with the calculations of ⌬A N , ⌬A P , and ͗N͘ (Fig. 8, c  and d) based on the experimental ⌬C p 0 , ⌬H 0 , and ⌬S 0 values. They show that the net effect of pH and temperature is such that, at high temperature, fewer residues unfold, and fewer non-polar and polar surfaces become exposed to the solvent at pH Յ 4.5 than at physiological pH. Moreover, ⌬A N , ⌬A P , and ͗N͘ values are much lower than those calculated for the complete unfolding of MazE, thus indicating that, irrespective of pH, the high temperature state of MazE is not a fully unfolded state.
Because of ϳ50% of the structured polypeptide chains that contain a substantial amount of tertiary structure at physiological temperature and pH, we cannot characterize the MazE dimer strictly as an intrinsically flexible (natively unfolded) protein (49 -55, 97). However, to describe the changes in its spectral and thermodynamic properties, we have to take into account the intrinsically flexible nature of its C-terminal half (49 -55, 97, 100). Furthermore, the flexible nature of MazE is hidden in the dimer-monomer equilibrium because the fractions of dimer and monomer depend on the total (dimer ϩ monomer) MazE concentration, C T (Fig. 7b).
Functional Stability of the Addiction Antitoxins-Addiction antitoxins and toxins can exist in the cell as free monomers and free dimers and can also form various antitoxin-toxin, antitoxin-DNA, and antitoxin-toxin-DNA complexes. If we want to know which species are important for regulation of cell death (or life), we have to understand its molecular mechanism. This can be achieved only by knowledge of the corresponding thermodynamic data on protein unfolding (folding) and specific protein-protein and protein-DNA interactions. Information of this type is rather scarce, but nevertheless, some thermodynamic characteristics common to addiction modules are available (10, 11, 47, 89 -91). For example, the measured ⌬G 0 for the MazE dimer-monomer transition is very similar to the corresponding ⌬G 0 values observed for the antitoxins CcdA (89) and ParD (91). Toxins have much higher thermodynamic stability (89). Moreover, it is known that the dimeric antitoxin (A 2 ) has two binding sites for the dimeric toxin (T 2 ) and vice versa, so they can form complexes of the type . . . A 2 T 2 A 2 T 2 . . . ϭ A 2i T 2j (46,48,90,92). The expression of the antitoxin and toxin can be inhibited either by low affinity binding of the antitoxin to the promoter/operator DNA (10,11,47,89,90) or by binding of the antitoxin-toxin complexes to the same part of the DNA with higher affinity (10,48,90,92). According to these observations, one may expect that the strength of the specific interactions (binding affinities) within various addiction modules would be of similar magnitude. This led us to the construction of the equilibrium model that is able to predict some features essential for understanding the function of addiction modules (for details, see the Supplemental Material). The first aim of its application was to estimate the total concentrations of antitoxin ([A] T ) and toxin ([T] T ) under ordinary cellular conditions (in the absence of stress). It was assumed that, under steadystate conditions (the rate of antitoxin and toxin synthesis is the same as the rate of their degradation), the total concentrations of the antitoxin and toxin are about the same and that no toxin is bound to its cellular target. Because the total concentration of DNA (encoding for the antitoxin and toxin) in the cell can be estimated as 2.5 nM, the antitoxin and toxin concentrations were varied simultaneously from 10 Ϫ8 to 10 Ϫ5 M. Fig. 9a shows that the modeled addiction module showed the highest sensitivity to the changes in  Fig. 9b shows that, in this range, the most populated antitoxin-toxin complexes contain more T 2 than A 2 molecules (A 2 T 4 and A 4 T 6 ). The A 2 T 4 form was also observed experimentally (48,90,92). By contrast, DNA is in the 10 Ϫ7 to 10 Ϫ6 M range occupied mainly by complexes in which A 2 and T 2 molecules are at a 1:1 ratio (Fig. 9c) and favors binding of longer A 2i T 2j associates, which is in accordance with recently proposed structural models (46,48). Our numerical simulation is based on the thermodynamic parameters estimated from in vitro experiments. To obtain measurable concentration-dependent signals, the number of antitoxin, toxin, and DNA molecules in the monitored systems has to be very large. Only under these conditions can we describe the system behavior in terms of macroscopic populations (fractions) of various species. Because the volume of the cell is very small (volume of the E. coli cytoplasm of 6.7 ϫ 10 Ϫ16 liter), we are at "normal conditions" ([A] T Ϸ [T] T Ϸ 2.5 ϫ 10 Ϫ7 M) dealing with ϳ100 antitoxin and ϳ100 toxin molecules. If this is the case, practically every single molecule is important. To keep the cell alive, the regulation of an addiction module has to be very precise and rapid because it must compensate for even very small fluctuations in the number of antitoxin and toxin molecules. Our model shows that, in a long enough period of time (cell division cycle of E. coli of ϳ20 min), a single antitoxin molecule spends ϳ40% of the time in complexes with toxin and FIG. 8. pH dependence of MazE structural characteristics. a, far-UV CD intensity. b, near-UV CD intensity. c, changes in non-polar (⌬A N ) and polar (⌬A P ) solvent-accessible surfaces upon MazE denaturation and monomerization estimated from experimentally obtained data (Table I) and Equations 5-7 given relative to ⌬A N,U and ⌬A P,U obtained for "complete unfolding" (transition to Ala-X-Ala denatured state, ⌬A N,U ϭ 2907 Å 2 and ⌬A P,U ϭ 1498 Å 2 ). At a given pH, ⌬A N and ⌬A P differ by about Ϯ50 Å 2 . d, number of amino acid residues participating in unfolding (͗N͘) estimated from Equation 7, using experimental ⌬C p 0 and ⌬S 0 values (Ⅺ), and simply as ͗N͘ ϭ (⌬A N ϩ ⌬A P )⅐͗N͘ U / (⌬A N,U ϩ ⌬A P,U ) (f), given per total number of structured residues in MazE (͗N͘ U ϭ 44).
DNA, ϳ50% of time as a free dimer, and ϳ10% of time in the monomeric form (Fig. 9a).
An important feature of intrinsically flexible proteins is that they undergo disorder-order transitions during or prior to their biological function (49 -57). In the case of addiction antitoxins, such conformational alterations have been observed upon both toxin and DNA binding (11,47,48,90,92). Moreover, we have shown that the antitoxin molecules may spend a significant amount of time as monomers with a higher potential for structural adaptability than the dimeric form. It seems that the rapid response of an addiction module to fluctuations in the number of antitoxin and toxin molecules is achieved not only by conformational adaptability of the dimeric antitoxin form, but also by transformation to the more flexible monomeric form. In this light, the thermodynamic characterization of the dimermonomer equilibrium and the monomeric forms themselves is essential for understanding the functioning of the addiction modules. Fig. 10 shows that, according to the criterion introduced by Uversky (51,52,54) and Uversky et al. (53), the addiction antitoxins in the monomeric form have a high tendency to be partially unstructured, whereas the corresponding toxins tend to be structured even as monomers. The prediction of structuring based on the mean hydrophobicity and mean net charge of the protein polypeptide chain is in good agreement with our observations and with recently reported results on addiction modules (11,47,89,90,102). Moreover, the large amount of the random-coil form found in free antitoxins in solutions (11,47,89,90,102) represents high vulnerability for their proteolytic cleavage (25,101,103).
To the best of our knowledge, the numerical simulation presented here is the first attempt to combine thermodynamic and structural information on addiction modules in terms of a mathematical model. We are aware that some properties defined in the model differ from module to module. From the numerical simulation point of view (convergence), it is not a problem to increase the size (number) of the A 2i T 2j complexes and the number of DNA-binding sites or/and to include more specific binding modes (more binding constants) in the model. It is also possible to include the kinetics (degradation rates for antitoxin and toxin) and the binding of the toxin to the specific target. The model has been developed to incorporate specific properties of a particular addiction module and to simulate some of its actions. At present, there are too little thermodynamic and structural data available to propagate the model. However, we believe that even this limited size of the model comprehends the basic physical meaning of the interplay between the antitoxin, toxin, and DNA.