Thermodynamic Model for B-Z Transition of DNA Induced by Z-DNA Binding Proteins

Abstract

Z-DNA is stabilized by various Z-DNA binding proteins (ZBPs) that play important roles in RNA editing, innate immune response, and viral infection. In this review, the structural and dynamics of various ZBPs complexed with Z-DNA are summarized to better understand the mechanisms by which ZBPs selectively recognize d(CG)-repeat DNA sequences in genomic DNA and efficiently convert them to left-handed Z-DNA to achieve their biological function. The intermolecular interaction of ZBPs with Z-DNA strands is mediated through a single continuous recognition surface which consists of an α3 helix and a β-hairpin. In the ZBP-Z-DNA complexes, three identical, conserved residues (N173, Y177, and W195 in the Zα domain of human ADAR1) play central roles in the interaction with Z-DNA. ZBPs convert a 6-base DNA pair to a Z-form helix via the B-Z transition mechanism in which the ZBP first binds to B-DNA and then shifts the equilibrium from B-DNA to Z-DNA, a conformation that is then selectively stabilized by the additional binding of a second ZBP molecule. During B-Z transition, ZBPs selectively recognize the alternating d(CG)_n sequence and convert it to a Z-form helix in long genomic DNA through multiple sequence discrimination steps. In addition, the intermediate complex formed by ZBPs and B-DNA, which is modulated by varying conditions, determines the degree of B-Z transition.

1. Introduction

Left-handed Z-DNA is a higher energy conformation than right-handed B-DNA. Z-DNA was first found in a polymer of alternating d(CG)_n DNA duplexes observed in high salt conditions [1]; its crystal structure was reported in 1979 [2]. The Z-DNA helix is built from d(CG)-repeats, with the dC in the anti-conformation and the dG in the unusual syn-conformation, which causes the backbone to follow a zigzag path [3,4]. Z-DNA can also be stabilized by negative supercoiling generated behind a moving RNA polymerase during transcription [5].

A distinct biological function of Z-DNA is suggested by the discovery of various Z-DNA binding proteins (ZBPs). Double stranded (ds) RNA deaminase 1 (ADAR1) deaminates adenine in pre-mRNA to yield inosine, which codes as guanine [6,7,8]. ADAR1 has two left-handed Z-DNA binding domains (ZBDs), Zα and Zβ, at its NH₂-terminus [7,9]. High binding affinity of this Zα domain to Z-DNA was shown by a band-shift assay and confirmed by CD and Raman spectroscopic measurement [10,11,12]. The DNA-dependent activator of IFN-regulatory factors (DAI; also known as ZBP1 or DLM-1) also contains two tandem ZBDs (Zα and Zβ) at the NH₂-terminus, such as ADAR1 [13,14]. It has been shown that ZBDs regulate the localization of DAI and its association with stress granules [15,16]. All poxviruses have a gene called E3L that consists of two domains: An N-terminal ZBD and a C-terminal RNA binding domain [17,18]. This ZBD shows sequence homology to the Zα domains found in human ADAR1 and in the DAI of mammals (Figure 1a). The Z-DNA binding affinity of E3L protein is essential for pathogenesis in the poxviruses [17,18,19]. The RNA-dependent protein kinase (PKR) plays an important role in the innate immune response against viral infections by recognizing dsRNA in the cytosol [20,21,22]. In fish species, a functional analogue of PKR, PKZ contains two ZBDs instead of dsRNA binding domains [23,24,25,26]. Similar to PKR, the phosphorylation function of PKZ is activated by Z-DNA binding [24].

These biological data, along with the results of more recent structural studies of Z-DNA induced by various ZBPs, have provided insights into Z-DNA recognition and ZBP-induced B-Z transition carried out by the innate immune response, viral infection, and RNA editing that are influenced by the nature of the Z-DNA. Crystallographic and NMR studies have provided detailed three-dimensional (3D) structures and dynamic information of various ZBPs complexed with Z-DNA. The structural and dynamic data summarized in this review have yielded a rich understanding of the mechanisms by which ZBPs selectively recognize the d(CG)-repeat DNA sequences in genomic DNA and efficiently convert them to left handed Z-DNA to achieve their biological function.

2. Crystal Structures of ZBPs Complexed with DNA Duplexes

2.1. hZα_ADAR1-Z-DNA Complex

In 1999, Alexander Rich and his colleagues first reported the crystal structure of the Zα domain of human ADAR1 (hZα_ADAR1) complexed with a six-base-pair (bp), double-stranded (ds) DNA fragment d(TCGCGCG)₂ [7]. The monomeric hZα_ADAR1 domain binds to one strand of the palindromic dsDNA, in which the conformation of the DNA substrate is very similar to the canonical Z-DNA structure. (Figure 1b) [7]. A second monomer binds to the opposite strand of DNA yielding two-fold symmetry with respect to the DNA helical axis (Figure 1b) [7]. The hZα_ADAR1 domain has a compact α/β architecture containing a three-helix bundle (α1 to α3) and twisted antiparallel β sheets (β1 to β3) (Figure 1b). The arrangement of a β-hairpin with hydrogen-bonds (H-bonds) between the β2 (L185–A188) and β3 strands (P193–I197) is a common feature of helix-turn-helix (HTH) proteins with a/β topology [7]. Aliphatic residues from the three helices, together with the W195 in strand β3, form a hydrophobic core [7]. The NMR studies reported that the free hZα_ADAR1 protein in the solution adopts a similar fold in its complex structure [9,27].

The contact of hZα_ADAR1 with the Z-DNA strand is mediated through a single continuous recognition surface, which consists of residues from an α3 helix and a β-hairpin (β2-loop-β3, also called a β-wing) (Figure 1c) [7]. The electrostatic interactions in the complex are made between K169, K170, N173, R174, and Y177 in an α3 helix as well as between T191 and W195 in a β-hairpin and five consecutive phosphate-backbones of Z-DNA (Figure 1c) [7]. K169 and N173 form the direct and water-mediated H-bonds to the dC3pdG4 and dG2pdC3 phosphates, respectively (Figure 2a) [7]. The N173A mutant displays the most dramatic decrease in Z-DNA binding affinity, suggesting that it plays an important role in the Zα function [27,28]. Similarly, the K169A mutant also has a significantly lower Z-DNA binding affinity than a wild-type protein [27,28]. K170 forms direct H-bonds to the dG4pdC5 and dC5pdG6 phosphates (Figure 2a) [7]. The K170A mutant binds to Z-DNA with a lower affinity than wild-type protein, but better than the K169A and N173A mutants [27,28]. Interestingly, R174 and T191 bind to the furanose oxygens of dG6 and dG2, respectively (Figure 2a) [7]. However, the R174A and T191A mutations have little effect on the B-Z transition activities of hZα_ADAR1 [28].

In addition to polar interactions, the aromatic ring of Y177 and the side-chains of P192 and P193 make the important van der Waals interactions with Z-DNA (Figure 2a) [7]. Interestingly, Y177 displays CH-π interaction with the C8 position of dG4 (Figure 2a) [7]. The Y177A mutant, which is unable to form both H-bonding and hydrophobic interactions, exhibits a significantly low Z-DNA binding affinity [27]. The Y177I, and Y177F mutants, which are capable only of hydrophobic interactions, could bind better to Z-DNA than Y177A, but still worse than wild-type protein [17,27,28]. Furthermore, the aromatic ring of W195, which forms a water-mediated H-bond to the dG2pdC3 phosphate, is almost perpendicular to Y177 and positioned in the center of the hydrophobic core (Figure 1c) [7]. The W195F mutant has 2-fold lower B-Z transition activity than wild type protein [28].

The crystal structural study reported that hZα_ADAR1 is also able to bind to 6-bp Z-DNA duplexes with non-CG-repeat sequences, such as d(CACGTG)₂, d(CGTACG)₂, and d(CGGCCG)₂ [34]. In these structures, N173, Y177, P192, P193, and W195 contribute to the recognition of Z-DNA-like CG-repeat DNA [34]. However, R174 and T191 did not show intermolecular interaction with Z-DNA in most structures [34]. Similarly, K169 and K170 are only in contact with Z-DNA within some structures of these complexes [34]. Thus, these four residues might play an important role in the sequence discrimination step for the B-Z transition of DNA.

The second Z-DNA binding domain of human ADAR1 (hZβ_ADAR1) adopts a winged-HTH fold like hZα_ADAR1, with the addition of a C-terminal α4 helix (see sequence in Figure 1a) [35]. Superposition of the hZβ_ADAR1 with the hZα_ADAR1 structure reveals that A327, A332, and I335 (corresponding to K169, R174, and Y177 in hZα_ADAR1, respectively) did not perform H-bonding to the backbone of Z-DNA. Mutagenesis studies of these residues have shown that all three residues are important for Z-DNA-binding by Zα proteins [17,27,28]. This study suggested that hZβ_ADAR1 is unable to interact with nucleic acids in a manner similar to that seen in the hZα_ADAR1-Z-DNA complex [35]. Instead, this region participates in self-association protein–protein interactions [35].

2.2. mZα_DLM1-Z-DNA Complex

The amino acid sequence of the Zα domain of murine DLM-1 (mZα_DLM1) is ~35% identical to that of the hZα_ADAR1 (Figure 1a). The overall structures of the complexes with Z-DNA are very similar to each other [29]. The core of the Zα-DNA interface in both proteins consists of three identical residues: N173, Y177, and W195 in hZα_ADAR1 and N46, Y50, and W66 in mZα_DLM1, respectively (Figure 2a,b) [7,29]. K43 and Q47 form direct or water-mediated H-bonds to three phosphates of the dC3pdG4pdC5pdG6 sequence like the corresponding K170 and R174 of hZα_ADAR1 (Figure 2b) [29]. The structural differences between the two domains are found in the α1-β1 loop and the β-hairpin [29]. The β-hairpin of mZα_DLM1 is two residues shorter than that of hZα_ADAR1 (Figure 1a), indicating that the β-hairpin is apparently tolerant of greater sequence variability than the α3 helix without loss of function [29].

2.3. yabZα_E3L-Z-DNA Complex

The Zα domain of the Yaba-like disease virus E3L (yabZα_E3L) stabilizes the Z-DNA conformation in a manner similar to that of hZα_ADAR1 and mZα_DLM1 [30], although it shares only 26% sequence identity with hZα_ADAR1 (Figure 1a). The crystal structural study revealed that two yabZα_E3L domains are found in the asymmetric unit, each bound to one strand of double-stranded DNA in the Z- conformation [30]. The intermolecular interaction of one asymmetric unit with Z-DNA is summarized in Figure 2c [30]. Three residues, N47, Y51, and W69 (corresponding to N173, Y177, and W195 in hZα_ADAR1), play central roles in the interaction with Z-DNA, as with other members of the Zα family (Figure 2c). K43, K44, and Q48 also participate in DNA recognition via direct or water-mediated H-bonds to the phosphate backbone of Z-DNA (Figure 2c).

2.4. caZα_PKZ-Z-DNA Complex

The Zα domain of PKZ from Carassius auratus (caZα_PKZ), which shows limited identity with other ZBPs (28% for hZα_ADAR1, 20% for hZα_DAI, and 22% for yabZα_E3L, respectively), is able to convert d(CG)-repeat DNA from B-DNA to Z-DNA [36,37]. The interaction between caZα_PKZ and Z-DNA is mediated by five residues in the α3 helix and four residues in the β-hairpin, similar to other Zα proteins (Figure 2d) [31]. Unlike the positively charged Lys or Arg in other ZBPs, the S35 in the α3 helix forms electrostatic interaction with the dC3pdG4 phosphate (Figure 2d) [31]. Interestingly, K56 of caZα_PKZ interacts not only with dC1pdG2 but also with dT0pdC1 (Figure 2d) [31], whereas a polar residue, like Ser or Thr at the corresponding position in other mammalian ZBPs, could not form these interactions (Figure 2). Generally, the B-Z transition activity by ZBPs was decreased when the ionic strength was increased. Surprisingly, the reduction of the B-Z transition rate is more severe in caZα_PKZ than in hZα_ADAR1, suggesting that the effect of charge-charge interactions on B-to-Z transition activity plays a more critical role in the case of caZα_PKZ [31].

2.5. hZβ_DAI-Z-DNA Complex

The second ZBD of human DAI (hZβ_DAI) was also shown to bind Z-DNA based on its binding specificity for Z-DNA and its ability to convert B-DNA to Z-DNA [16]. Although hZβ_DAI also has α/β topology with three helices packed against three β-stands, like other ZBPs, hZβ_DAI has a 3₁₀ helix at the N terminus of α3, instead of the long continuous α3 helix [32]. In the hZβ_DAI-Z-DNA complex, protein-DNA interactions are mediated by the most conserved core residues, N141, Y145, and W162 (corresponding to N173, Y177, and W195) [32]. However, except for those core residues, other interactions with Z-DNA seem to be different for hZβ_DAI (Figure 2) [32]. For example, K138, located in the region between K169 and K170 of hZα_ADAR1, forms an H-bond to the dC3pdG4 phosphate of one Z-DNA strand, whereas the two Lys residues of hZα_ADAR1 contact the 4 phosphate groups of Z-DNA (Figure 2) [32]. Interestingly, K138 spans the length of the Z-DNA molecule and interacts with the dC5pdG6 phosphate on the opposite DNA strand (Figure 2e) [32]. An NMR study found that free hZβ_DAI has notable alterations in the α3 helix, the β-hairpin, and Y145 which are critical in Z-DNA recognition [38]. These results indicate that, unlike some other Zα domains, structural flexibility of hZβ_DAI is required for Z-DNA binding [38].

2.6. hZα_ADAR1-Z-RNA Complex

ADAR1 edits dsRNA in vitro at significantly higher levels when dsRNA contains the purine-pyrimidine repeat sequence in dsRNA [39]. The hZα_ADAR1 protein can bind to Z-RNA like Z-DNA [40]. It was first reported that the crystal structure of hZα_ADAR1 complexed with 6-bp dsRNA, r(UCGCGCG)₂ [33]. Interestingly, hZα_ADAR1 exhibited significantly different binding modes when bound to Z-RNA versus Z-DNA (Figure 2). First, in the Z-RNA binding conformation, Y177 showed H-bonding interaction with the rG2prC3 phosphate and the O2’ of rG2, whereas it H-bonded with only the dG2pdC3 phosphate in the Z-DNA binding structure (Figure 2) [7,33]. Second, in the Z-DNA binding structure, R174 showed a direct, water-mediated H-bonding interactions with the dC5pdG6 phosphate and the O4’ of dG6, respectively (Figure 2a) [7]. However, when binding to Z-RNA, a water-mediated H-bond with the rC5prG6 phosphate as well as an H-bond with the E171 side-chain were formed (Figure 2f) [33]. Third, in the Z-RNA binding conformation, H159 exhibited a distinct orientation due to a water-mediated H-bonding interaction with the K169 side-chain compared to the Z-DNA binding conformation [33]. Fourth, in the Z-RNA binding conformation, T191 showed H-bonding interaction with only the rC3prG4 phosphate, whereas it formed H-bonds with both the phosphate and the O4’ of dC3 in the Z-DNA binding structure (Figure 2) [7,33].

3. Molecular Mechanism of B-Z Transition of 6-bp DNA Induced by ZBPs

3.1. B-Z Transition of a 6-bp CG-Repeat DNA by hZα_ADAR1

NMR studies on the hZα_ADAR1-Z-DNA interaction first proposed the B-Z transition mechanism of a 6-bp DNA, d(CGCGCG)₂, by hZα_ADAR1, in which the hZα_ADAR1 plays two independent roles: (i) one molecule first binds to B-DNA and shifts the equilibrium from B-DNA to Z-DNA (BP to ZP, where B, Z, and P indicate B-DNA, Z-DNA, and protein); and (ii) the second molecule selectively binds to and stabilizes the Z-DNA conformation (Figure 3a) [41]. This study confirmed the existence of a one-to-one complex of Z-DNA and hZα_ADAR1 (ZP) by gel filtration chromatography, NMR dynamics data, and diffusion coefficient values as functions of the [P]_t/[N]_t molar ratio, where [P]_t and [N]_t are the total concentrations of the hZα_ADAR1 and DNA, respectively [41]. It was found that the Z-DNA produced was half the total amount of the added hZα_ADAR1 when the [P]_t/[N]_t ratio was ≤2 (that is Z_t = 1/2[P]_t), where Z_t is the total amount of the Z-DNA conformation (Figure 3b) [41]. To satisfy this relation, the BP and ZP complexes must exist as intermediate states with a correlation of [ZP] = [BP] (that is K_BZ,1 = [ZP]/[BP] ≈1). Based on this correlation, the observed exchange rate constant (k_ex) for the imino proton in the Z-DNA conformation could be expressed as a function of the [P]_t/[N]_t ratio by the following Equation:

$$k_{\mathrm{ex}}=k_{\mathrm{ex},\mathrm{ZP}2}+\frac{k_{\mathrm{ex},\mathrm{ZP}}-k_{\mathrm{ex},\mathrm{ZP}2}}{\left(1-\mathsf{\alpha }\right)\mathsf{\chi }}\left\{1-\sqrt{1-4\left(1-\mathsf{\alpha }\right)\left(\frac{\mathsf{\chi }}{2}-\frac{{\mathsf{\chi }}^2}{4}\right)}\right\}$$

(1)

where k_ex,ZP and k_ex,ZP2 are the exchange rate constants of the imino protons for the ZP and ZP₂ complexes, respectively, χ is the [P]_t/[N]_t ratio, and α (= K_d,ZP2/K_d,BP) is the ratio of the dissociation constants of BP and ZP₂ complexes [41]. The k_ex dataset was fitted using Equation (1) to obtain the α value of 1.15 × 10⁻² (

Table 1. Equilibrium constants for the ZBP-induced B-Z transition.

ZBP	DNA	α 1	KBZ,1	Kd,BP (μM)	Kd,ZP2 (μM)	Rerefences
hZαADAR1	d(CGCGCG)2	1.15 × 10−2	~1	<0.1	<0.1	[41]
hZαADAR1	d(CACGTG)2	1.42	0.4	260 ± 87	180 ± 62	[42]
hZαADAR1	d(CGTACG)2	13.9	6.3	400 ± 144	29 ± 11	[42]
yabZαE3L	d(CGCGCG)2	0.154	1.02	n.d. 2	n.d. 2	[43]

¹ α = K_d,ZP2/K_d,BP; ² n.d.: not determined.

) [41].

3.2. B-Z Transition of a 6-bp Non-CG-Repeat DNA by hZα_ADAR1

The hZα_ADAR1 protein can also convert the B-form of non-CG-repeat DNA, d(CACGTG)₂ and d(CGTACG)₂, to Z-form with lower activities compared to CG-repeat DNA, d(CGCGCG)₂ (Figure 3b) [41,42]. Equation (1) could not be used to analyze the hydrogen exchange data of these DNA complexed with hZα_ADAR1 because the non-CG-repeat DNA did not satisfy the relation, Z_t = 1/2[P]_t. Instead, the observed k_ex value for the imino proton in the B-DNA (not Z-DNA) conformation could be expressed as a function of the relative Z-DNA population (f_Z = Z_t/[N]_t) by the following equation:

$$k_{\mathrm{ex}}=k_{\mathrm{ex},\mathrm{B}}+\frac{k_{\mathrm{ex},\mathrm{BP}}-k_{\mathrm{ex},\mathrm{B}}}{2\left(1-\mathsf{\alpha }\right)\left(1-f_{\mathrm{z}}\right)}\left\{1+\left(K_{\mathrm{BZ},1}-1\right)f_{\mathrm{z}}-\sqrt{{\left(1+\left(K_{\mathrm{BZ},1}-1\right)f_{\mathrm{z}}\right)}^2-4K_{\mathrm{BZ},1}\left(1-\mathsf{\alpha }\right)f_{\mathrm{z}}\left(1-f_{\mathrm{z}}\right)}\right\}$$

(2)

where k_ex,B and k_ex,BP are the exchange rate constants of the imino protons for free B-DNA and the BP complex, respectively [42]. The NMR dynamics studies found that hZα_ADAR1 binds to non-CG-repeat DNA with weak binding affinity through the α3 helix as well as through the loop-β1-loop (151–158) and the α3-loop-β2 regions (178–191) [46]. Then, the B-form helix of non-CG-repeat DNA duplexes can be converted to a Z-conformation via these multiple intermolecular interactions with hZα_ADAR1 proteins [46]. These studies explained how hZα_ADAR1 exhibited the sequence preference of d(CGCGCG)₂ >> d(CACGTG)₂ > d(CGTACG)₂ during the B-Z transition [42,46]. First, the P binds to the B, with a sequence preference of d(CGCGCG)₂ >> d(CACGTG)₂ > d(CGTACG)₂ [42], even though the structural features of these three DNA duplexes complexed with hZα_ADAR1 are very similar to each other [34]. Second, the BP of d(CGCGCG)₂ and d(CACGTG)₂ convert to ZP. In d(CGTACG)₂, however, this process is less efficient as a way of discriminating d(TA)-containing DNA sequences from alternating pyrimidine-purine sequences [42]. Third, the ZP of d(CGCGCG)₂ and d(CACGTG)₂ binds to the P and forms the stable ZP₂ complex with a sequence preference of d(CGCGCG)₂ >> d(CACGTG)₂, which acts as the third sequence discrimination step [42]. Taken together, it was suggested that hZα_ADAR1 selectively recognizes the alternating d(CG)_n sequence and then converts it to a Z-form helix in long genomic DNA through its multiple sequence discrimination steps [42,46].

3.3. B-Z Transition of a 6-bp DNA by yabZα_E3L

The yabZα_E3L could efficiently change the B-form helix of the d(CGCGCG)₂ to left-handed Z-DNA like hZα_ADAR1 (Figure 3c) [43]. In this study, because the B-Z transition activity of yabZα_E3L did not satisfy the relation, Z_t = 1/2[P]_t, the observed k_ex value for the imino proton in the Z-DNA conformation could be expressed by the following equation instead of Equation (1):

$$k_{\mathrm{ex}}=k_{\mathrm{ex},\mathrm{ZP}2}+\frac{k_{\mathrm{ex},\mathrm{ZP}}-k_{\mathrm{ex},\mathrm{ZP}2}}{2K_{\mathrm{Bz},1}\left(1-\mathsf{\alpha }\right)f_{\mathrm{z}}}\left\{1+\left(K_{\mathrm{BZ},1}-1\right)f_{\mathrm{z}}-\sqrt{{\left(1+\left(K_{1,\mathrm{BZ}}-1\right)f_{\mathrm{z}}\right)}^2-4K_{\mathrm{BZ},1}\left(1-\mathsf{\alpha }\right)f_{\mathrm{z}}\left(1-f_{\mathrm{z}}\right)}\right\}$$

(3)

The k_ex dataset was fitted using Equation (3) to obtain the α value of 0.154 and the K_BZ,1 value of 1.02 (Table 1) [43]. This K_BZ,1 value means that yabZα_E3L and hZα_ADAR1 have the same B-Z transition efficiency [43], which is consistent with their structural similarity in complexes with Z-DNA [7,30].

3.4. B-Z Transition of a 6-bp DNA by hZβ_DAI

NMR studies have revealed that hZβ_DAI had significantly lower B-Z transition activity than hZα_ADAR1 and yabZα_E3L (Figure 3c) [44]. In addition, the imino proton and ³¹P-NMR spectra of d(CGCGCG)₂ complexed with hZβ_DAI are completely different from those of the d(CGCGCG)₂-hZα_ADAR1 complex [44]. These indicate that the base pair geometry and backbone conformation of the hZβ_DAI-induced Z-DNA helix are significantly different from those of the Z-DNA-hZα_ADAR1 complex, similar to their crystal structures [7,32]. The hydrogen exchange study of the d(CGCGCG)₂-hZβ_DAI complex found that the exchange rates of imino protons in B-DNA as well as Z-DNA conformations are not affected by complex formation [A4]. In addition, diffusion optimized spectroscopy experiments confirmed that the Z-form of d(CGCGCG)₂ complexed with hZβ_DAI exhibited one major complex state (perhaps ZP₂), even at various [P]_t/[N]_t [44]. Based on these results, they proposed the distinct B-Z transition mechanism where two molecules of hZβ_DAI initially bind directly to the B-form DNA and form the BP₂ complex; subsequently, there is a conformational change from BP₂ to ZP₂. (Figure 3a) [44].

3.5. B-Z Transition of a 6-bp DNA by caZα_PKZ

The caZα_PKZ domain can convert the dsDNA, d(CGCGCG)₂ to Z-DNA with lower activity rates than hZα_ADAR1 and yabZα_E3L (Figure 3d) [45]. Instead, caZα_PKZ exhibits full B-Z transition activity when binding to d(TCGCGCG)₂ (Figure 3d) [45]. This indicates that the H-bonding interaction of K56 with the dT0pdC1 phosphate plays an important role in the B-Z transition of DNA by caZα_PKZ [45]. In this study, instead of the k_ex value, the ¹H and ¹⁵N chemical shift changes (Δδ_obs) of amide protons of caZα_PKZ and relative Z-DNA population (f_Z) were determined as the functions of [N]_t and [P]_t expressed by the following functions, respectively:

$${\mathsf{\Delta }\mathsf{\delta }}_{\mathrm{obs}}=\frac{\left[\mathrm{BP}\right]}{{\left[\mathrm{P}\right]}_{\mathrm{t}}}{\mathsf{\Delta }\mathsf{\delta }}_{\mathrm{B}}+\frac{\left[\mathrm{ZP}\right]+2\left[{\mathrm{ZP}}_2\right]}{{\left[\mathrm{P}\right]}_{\mathrm{t}}}{\mathsf{\Delta }\mathsf{\delta }}_{\mathrm{Z}}$$

(4)

$$f_{\mathrm{Z}}=\frac{\left[\mathrm{ZP}\right]+\left[{\mathrm{ZP}}_2\right]}{{\left[\mathrm{P}\right]}_{\mathrm{t}}}$$

(5)

where Δδ_B and Δδ_Z are the ¹H and ¹⁵N chemical shift differences of the B-DNA- and Z-DNA-bound forms relative to free form, respectively, [BP], [ZP], and [ZP₂] are the concentration of the BP, ZP, and ZP₂ complex states, respectively, which are described as:

$$\left[\mathrm{BP}\right]={\left[\mathrm{N}\right]}_{\mathrm{t}}\frac{K_{\mathrm{d},\mathrm{ZP}2}\left[\mathrm{P}\right]}{K_{\mathrm{d},\mathrm{BP}}{K}_{\mathrm{d},\mathrm{ZP}2}+\left(1+K_{\mathrm{BZ},1}\right)K_{\mathrm{d},\mathrm{ZP}2}\left[\mathrm{P}\right]+K_{\mathrm{BZ},1}{\left[\mathrm{P}\right]}^2}$$

(6)

$$\left[\mathrm{ZP}\right]={\left[\mathrm{N}\right]}_{\mathrm{t}}\frac{K_{\mathrm{BZ},1}{K}_{\mathrm{d},\mathrm{ZP}2}\left[\mathrm{P}\right]}{K_{\mathrm{d},\mathrm{BP}}{K}_{\mathrm{d},\mathrm{ZP}2}+\left(1+K_{\mathrm{BZ},1}\right)K_{\mathrm{d},\mathrm{ZP}2}\left[\mathrm{P}\right]+K_{\mathrm{BZ},1}{\left[\mathrm{P}\right]}^2}$$

(7)

$$\left[{\mathrm{ZP}}_2\right]={\left[\mathrm{N}\right]}_{\mathrm{t}}\frac{K_{\mathrm{BZ},1}{\left[\mathrm{P}\right]}^2}{K_{\mathrm{d},\mathrm{BP}}{K}_{\mathrm{d},\mathrm{ZP}2}+\left(1+K_{\mathrm{BZ},1}\right)K_{\mathrm{d},\mathrm{ZP}2}\left[\mathrm{P}\right]+K_{\mathrm{BZ},1}{\left[\mathrm{P}\right]}^2}$$

(8)

and [P] is the concentration of free caZα_PKZ, solvable via the following cubic equation [45]:

$${\left[\mathrm{P}\right]}^3+a{\left[\mathrm{P}\right]}^2+b\left[\mathrm{P}\right]+c=0$$

(9)

$$a=2{\left[\mathrm{N}\right]}_{\mathrm{t}}-{\left[\mathrm{P}\right]}_{\mathrm{t}}+\left(1+\frac{1}{K_{\mathrm{BZ},1}}\right)K_{\mathrm{d},\mathrm{ZP}2}$$

(10)

$$b=\left(1+\frac{1}{K_{\mathrm{BZ},1}}\right)K_{\mathrm{d},\mathrm{ZP}2}\left({\left[\mathrm{N}\right]}_{\mathrm{t}}-{\left[\mathrm{P}\right]}_{\mathrm{t}}\right)+\frac{K_{\mathrm{d},\mathrm{BP}}{K}_{\mathrm{d},\mathrm{ZP}2}}{K_{\mathrm{BZ},1}}$$

(11)

$$c=-\frac{K_{\mathrm{d},\mathrm{BP}}{K}_{\mathrm{d},\mathrm{ZP}2}}{K_{\mathrm{BZ},1}}{\left[\mathrm{P}\right]}_{\mathrm{t}}$$

(12)

The closed-form solution of Equation (9) has been expressed by [45]:

$$\left[\mathrm{P}\right]=-\frac{a}{3}+\frac{2}{3}\sqrt{a^2-3b}\cos \frac{\mathsf{\theta }}{3}$$

(13)

where

$$\mathsf{\theta }=\arccos \left(\frac{-2a^3+9ab-27c}{2\sqrt{{\left(a^2-3b\right)}^2}}\right)$$

(14)

In order to obtain accurate K_d values, all ¹H and ¹⁵N titration curves and the f_Z data were globally fitted with Equation (4) and Equation (5), respectively. This approach successfully provides two binding constants, K_d,BP and K_d,ZP2, not the relative ratio (α) of these two constants as in previous studies.

At 10 mM NaCl, the global fitting gave a K_d,BP and a K_d,ZP2 of 28 and 350 nM, respectively, and a K_BZ,1 of 0.87 (

Table 2. Equilibrium constants for the caZα_PKZ-induced B-Z transition.

ZBP	DNA	pH	[NaCl]	KBZ,1	Kd,BP (μM)	Kd,ZP2 (μM)	Rerefences
caZαPKZ	d(TCGCGCG)2	6.0	10 mM	0.87 ± 0.03	0.028 ± 0.017	0.345 ± 0.079	[45]
caZαPKZ	d(TCGCGCG)2	6.0	100 mM	0.19 ± 0.02	16.4 ± 0.8	8.76 ± 0.67	[45]
caZαPKZ	d(TCGCGCG)2	6.0	250 mM	~0.01	64.1 ± 8.3	9.57 ± 0.85	[47]
caZαPKZ	d(TCGCGCG)2	8.0	10 mM	1.18 ± 0.03	0.157 ± 0.021	0.129 ± 0.074	[45]
caZαPKZ	d(TCGCGCG)2	8.0	100 mM	0.18 ± 0.02	5.41 ± 0.66	2.41 ± 0.37	[45]
caZαPKZ	d(CGCGCG)2	8.0	10 mM	0.11 ± 0.05	5.18 ± 2.43	1.79 ± 0.95	[45]

) [45]. As [NaCl] was increased, the K_d,BP and K_d,ZP2 values became increased, but the K_BZ,1 value became smaller (Table 2) [45,47]. The NMR dynamics studies found that increasing the ionic strength interferes more with the association of ZP with caZα_PKZ via intermolecular electrostatic interactions rather than the dissociation of ZP₂ [45]. In addition, the global fitting method using Equation (4) also provides the ¹H and ¹⁵N chemical shift differences between the free and the bound forms for both B-DNA (Δδ_B) and Z-DNA binding (Δδ_Z). At higher concentrations of NaCl, the B-DNA-bound state exhibited completely different results than at 10 mM NaCl, whereas the Z-DNA binding conformation was not affected by the change of ionic strength [45,47]. These results meant that the B-DNA binding state of caZα_PKZ exhibited distinct structural features under high and low salt conditions which might be related to reduced B-Z transition activity at higher [NaCl]. Taken together, these studies suggest that the intermediate complex formed by caZα_PKZ and B-DNA can be used as a molecular ruler to measure the degree to which DNA transitions to the Z isoform [45,47].

4. Conclusions

Z-DNA is induced by various Z-DNA binding proteins (ZBPs) that play important roles in RNA editing, innate immune response, and viral infection. We summarized the structural and dynamics data of various ZBPs complexed with Z-DNA to understand the mechanisms by which ZBPs selectively recognize d(CG)-repeat DNA sequences in genomic DNA and efficiently convert it to left handed Z-DNA to achieve their biological function. The contact of ZBPs with Z-DNA strands mediated through a single continuous recognition surface consists of an α3 helix and a β-hairpin. In the ZBP-Z-DNA complexes, three conserved identical residues of ZBPs (N173, Y177, and W195 in hZα_ADAR1) play a central role in interactions with Z-DNA. ZBPs convert a 6-bp DNA to a Z-form helix via a B-Z transition mechanism in which the ZBP first binds to B-DNA and then shifts the equilibrium from B-DNA to Z-DNA, a conformation that is then selectively stabilized by the additional binding of a second ZBP molecule. During B-Z transition, ZBPs selectively recognize the alternating d(CG)_n sequence and then convert it to a Z-form helix in long genomic DNA through its multiple sequence discrimination steps. In addition, the intermediate complex formed by ZBPs and B-DNA, which is modulated by varying conditions, determines the degree of B-Z transition.