Effective molarity in a nucleic acid-controlled reaction

Abstract

Positioning of reactive functional groups within a DNA duplex can enable chemical reactions that otherwise would not occur to an appreciable extent. However, few studies have quantitatively defined the extent to which the enforced proximity of reaction partners in duplex DNA can favor chemical processes. Here, we measured substantial effective molarities (as high as 25 M) afforded by duplex DNA to a reaction involving interstrand cross-link formation between 2′-deoxyadenosine and a 2-deoxyribose abasic (Ap) site.

Graphical Abstract

The idea that enforced proximity can increase reaction rates and equilibria is pervasive in cell biology,^1–4 enzymology,^5–8 chemical catalysis,^9–11 and physical organic chemistry.¹² The concept of “effective molarity” provides a quantitative method for expressing the extent to which enforced proximity favors a given unimolecular process over the corresponding bi-molecular counterpart.^3,9,12 Mathematically, this value is simply the rate or equilibrium constant of the unimolecular process divided by that of a bi-molecular comparator reaction (k_uni s⁻¹/k_bi M⁻¹•s⁻¹).^3,9,12 The resulting value (obtained in units of molarity) represents the theoretical reagent concentration at which the observed (pseudo-first-order) rate or equilibrium constant of the second-order process would match that of the unimolecular process. Effective molarities have been measured for a significant number of enzymatic processes, intramolecular organic reactions, and templated reactions involving small organic molecules.^3,5,6,8,9,12

The robust and predictable nature of DNA hybridization and duplex structure^13–15 can be used to juxtapose reactive groups and the resulting spatial confinement of reaction partners has the potential to increase the rates and equilibria of chemical processes.^16–21 Nucleic acid-controlled reactions have been exploited in the design of self-replicating systems,^21,22 template-directed ligation,^19,23–29 drug delivery vehicles,^30–33 tools for the detection of nucleic acid sequence,^19,34 and reagents for templated synthesis of small organic molecules.^35–37 Despite the widespread interest in nucleic acid-controlled reactions, there are few examples where effective molarities have been measured for such processes. Along these lines, Taylor and Dervan measured an effective molarity of 0.8 M for the alkylation of a guanine residue in duplex DNA by a bromoacetamide unit tethered via a six-atom linker to a triple helix-forming oligonucleotide bound in the major groove.³⁸ Coleman and Pires reported an effective molarity 3.1 M for alkylation of a guanine residue by a bromoacetamide unit connected by a five-atom linker to a 4-thiouridine residue on the opposing strand of a DNA duplex.³⁹ Beyond these two studies, there is little information addressing the important question: how large should we expect the kinetic and thermodynamic “payoffs” to be, when two reactive species are positioned within the structure of duplex DNA? Given that an assumption of increased effective molarity underlies the design of all nucleic acid-templated reactions it may be useful to gain additional quantitative information that speaks to this question.

In the work reported here, we measured the effective molarity afforded by duplex DNA to the reaction of 2′-deoxyadenosine with a 2-deoxyribose abasic (Ap) site 1. This reaction generates interstrand cross-links in 15–70% yields at 5′-ApT/5′-AA sequences in duplex DNA (Scheme 1) via reversible reaction of the N⁶-amino group of 2′-deoxyadenosine with the aldehyde residue of an Ap site (Scheme 1).^40–42 The rate and yield of dA-Ap cross-link formation in duplex DNA can be readily measured by denaturing polyacrylamide gel electrophoretic analysis,⁴¹ making this a good system for assessing effective molarities in a nucleic acid-controlled reaction.

Scheme 1.

Formation of the dA-Ap interstrand cross-link in duplex DNA.

We first set out to measure the rate and equilibrium constants associated with this cross-linking reaction in two different sequences of duplex DNA (duplexes A and B, Fig. 1). Cross-linking in these duplexes occurs at the locations indicated in Fig. 1.⁴¹ The Ap-containing, 5′-³²P-labeled duplexes A and B were generated as described previously^40–44 by the action of the enzyme uracil DNA glycosylase on the corresponding 2′-deoxyuridine-containing duplexes.^45–47 Subsequent time-dependent conversion of the resulting Ap-containing duplexes to cross-linked DNA was monitored by the appearance of a characteristic^17,40–44 slow-moving band on denaturing polyacrylamide gels (Figs. 1 and S1). This process can be described by a kinetic scheme where cross-link forms reversibly in competition with products derived from cleavage of the Ap site in the uncross-linked duplex (Scheme 2b). The differential equations describing the change in concentrations of various species with respect to time were solved by changing the kinetic parameters to give minimum residuals between calculated and measured concentrations at the specified time points. The cross-linking reaction was analyzed at both pH 5 and 7 (Figs. 1 and S1–S4). We obtained apparent rate constants of 1.6 ± 0.2 × 10⁻⁶ s⁻¹ and 3.5 ± 0.2 × 10⁻⁶ s⁻¹ and equilibrium constants of 0.57 ± 0.16 and 2.2 ± 0.4 for cross-link formation in duplexes A and B, respectively, in Hepes buffer (50 mM, pH 7, containing 100 mM NaCl) at 37 °C.

Figure 1.

Interstrand cross-link formation in duplexes A and B. Panel a. Sequences of the DNA duplexes used in this study. The duplexes were 5′-³²P-labeled on the top, Ap-containing strand. The location of sequence difference between A and B is shown in blue font. Panel b. Denaturing polyacrylamide gel electrophoretic analysis of cross-link formation in duplex A. The 5′-³²P-labeled abasic-site-containing DNA duplex was incubated in 10.3 mM Na₂HPO₄, 4.9 mM citric acid containing 100 mM NaCl (pH 5) at 37 °C. At various times aliquots were removed from the cross-linking reaction, frozen, and stored at −20 °C until gel electrophoretic analysis. Lane 1 is a marker consisting of the Ap oligomer treated with piperidine to induce strand cleavage; lanes 2–14 show the cross-linking reaction at times 0, 1, 2, 4, 6, 8, 20, 28, 48, 72, 72, 96, 120, 144 and 168 h. The ³²P-labeled oligodeoxynucleotides in the samples were resolved by electrophoresis on a 20% denaturing polyacrylamide gel and the radioactivity in each band quantitatively measured by phosphorimager analysis. Panel c. A plot of the percent yield of cross-linked DNA (top band in the gel) versus time.

Scheme 2.

Panel a. Strand cleavage at an absic site in DNA. Panel b. Kinetic model for formation cross-linked DNA, strand cleavage, and formation of a putative low molecular weight cross-link.

We speculate that the band migrating between the cross-linked duplex and the unmodified Ap DNA on the denaturing gel shown in Fig. 1 is a “low-molecular weight” (LMW) cross-link that arises from strand cleavage at the Ap site^48–50 to generate the 3′-4-hydroxy-2-pentenal-5-phosphate (3′-dRP) cleavage product, followed by reaction of the α,β-unsaturated aldehyde group with a nucleobase on the opposing strand (Scheme 2). Although this product remains to be characterized, the structure may be analogous to the low molecular weight cross-links derived from C4′-oxidized Ap sites described by Greenberg and co-workers.⁵¹ Most important in the context of this work, identical values were obtained for k₁ and K_eq (k₁/k₂) regardless of whether the kinetic model included strand cleavage and formation of the low molecular weight cross-link band (this is because processes leading to generation of the low molecular weight cross-link are relatively minor under the conditions of these experiments).

We next sought a bimolecular reaction whose rate and equilibrium constants could be compared with the DNA cross-linking data. For this purpose, we employed the reaction of 3,5-bis-O-methyl-2-deoxy-D-ribofuranose (5, Scheme 3)^52,53 with 2′-deoxyadenosine (dA). This reaction generates 6, a nucleosidic analog of the DNA cross-link 4. Reverse-phase HPLC analysis of the reaction between various concentrations of 5 (0.2–1 M) and 2′-deoxyadenosine (10 mM) in Hepes buffer (50 mM, pH 7, containing 100 mM NaCl) at 37 °C revealed time- and concentration-dependent growth of the diastereomeric nucleoside “cross-links” 6 (Fig. 2). Nonlinear least squares fitting of the data gave a formation rate constant of 1.4 ± 0.2 × 10⁻⁷ M⁻¹ s⁻¹ and an equilibrium constant of 0.51 ± 0.01 M⁻¹ for this reaction (Fig. 3). The method of initial rates^54,55 gave a similar result. It may be worth noting that, while equilibrium constants formally are unitless, it is common for chemists, biochemists, and chemical engineers to attach units as needed to express the effects that changes in reactant concentration exert on a system.⁵⁶ The formation of 6 was faster when carried out at pH 5 (Na₂HPO₄ (10.3 mM), citric acid (4.9 mM), containing NaCl (100 mM). For example, at a 1 M concentration of 5 the calculated second order rate constant for the reaction was 1.2 × 10⁻⁷ M⁻¹ s⁻¹at pH 7 and 3.8 × 10⁻⁶ M⁻¹ s⁻¹ at pH 5.

Scheme 3.

A nucleosidic analogue of the interstrand DNA cross-linking reaction.

Figure 2.

Formation of the nucleoside cross-link by reaction of 5 with 2′-deoxyadenosine. Panel a. HPLC analysis of the reaction between dA (10 mM) and compound 5 (800 mM) to generate 6 at 37 °C in HEPES (50 mM, pH 7) containing NaCl (100 mM). Panel b. Time course for the formation of 6 from the reaction of dA (10 mM) with 5 (0.2–1.0 M) in HEPES buffer (50 mM, pH 7) containing NaCl (100 mM) at 37 °C. The dashed lines represent calculated values resulting from least squares regression analysis.

Figure 3.

Graphical representation of the second-order rate constant, k_f, for the formation of 6 from dA and 5. The value k_ψ is the pseudo-first-order forward rate constant calculated from least squares regression, where k_ψ = k_f[5].⁵⁵ The slope = 1.1 × 10⁻⁷ M⁻¹ s⁻¹, R² = 0.996.

Characterization of the dA-Ap cross-linking reaction both “inside” and “outside” of duplex DNA allows us to calculate the kinetic and thermodynamic (equilibrium) effective molarities created by positioning of the 2′-deoxyadenosine and 2-deoxyribose reaction partners within the double helix (Table 1). In the best case (duplex B), the kinetic effective molarity of the duplex-driven reaction is 25 M, while the thermodynamic effective molarity is 4.3 M. In the context of duplex A, we calculate kinetic and thermodynamic effective molarities of 11 M and 1.1 M, respectively.

Table 1.

Rate constants, equilibrium constants, and effective molarities measured for the reaction of 2′-deoxyadenosine and the 2-deoxyribose unit in solution and in duplex DNA (EM = effective molarity).

Species	Keq	k1 (x107)	EMthermo (M)	EMkinetic (M)
Sequence A	0.57 ± 0.16	16 ± 2 s−1	1.1	11
Sequence B	2.2 ± 0.4	35 ± 2 s−1	4.3	25
dA + 5	0.51 ± 0.01 M−1	1.4 ± 0.2 M−1 s−1

In conclusion, our work provides a rare quantitative description of how spatial confinement within duplex DNA can increase reaction rates and equilibria. The effective molarities measured in this system are substantial, especially given that nucleic acid-controlled reactions usually are carried out at very low oligonucleotide concentrations where background bimolecular reaction rates are low.