A computational model to predict the Diels–Alder reactivity of aryl/alkyl-substituted tetrazines

Monatsh Chem https://doi.org/10.1007/s00706-017-2110-x ORIGINAL PAPER A computational model to predict the Diels–Alder reactivity of aryl/alkyl-substituted tetrazines Dennis Svatunek1 • Christoph Denk1 • Hannes Mikula1 Received: 18 October 2017 / Accepted: 20 November 2017  The Author(s) 2017. This article is an open access publication Abstract The tetrazine ligation is one of the fastest bioorthogonal ligations and plays a pivotal role in timecritical in vitro and in vivo applications. However, prediction of the reactivity of tetrazines in inverse electron demand Diels–Alder-initiated ligation reactions is not straight-forward. Commonly used tools such as frontier molecular orbital theory only give qualitative and often even wrong results. Applying density functional theory, we have been able to develop a simple computational method for the prediction of the reactivity of aryl/alkyl-substituted tetrazines in inverse electron demand Diels–Alder reactions. Graphical Abstract Keywords Cycloadditions  Computational chemistry  Click chemistry  Bioorthogonal chemistry Electronic supplementary material The online version of this article (https://doi.org/10.1007/s00706-017-2110-x) contains supplementary material, which is available to authorized users. & Hannes Mikula 1 Institute of Applied Synthetic Chemistry, TU Wien, Vienna, Austria Introduction Tetrazine ligations (TLs) are bioorthogonal inverse electron demand Diels–Alder (IEDDA) initiated cycloadditions proceeding with exceptional high second-order rates of up to 3,300,000 M-1 s-1 [1]. In TLs, an 1,2,4,5-tetrazine (Tz) reacts with an electron-rich dienophile in an IEDDA reaction followed by cycloreversion under the loss of nitrogen (Fig. 1). Strained alkenes such as norbornenes [2, 3], cyclopropenes [4, 5], and trans-cyclooctenes (TCOs) [1, 6–8] are commonly used dienophiles, with TCOs providing the highest reactivity. The rate-determining step is the Diels–Alder cycloaddition, while the cycloreversion has only a low energy barrier and is suspected to show strong non-statistical effects [9]. Due to the high reaction rates, these ligations can be used in time-critical applications such as rapid radiolabeling and pretargeted PET imaging [10–16] and provide high yields within short reaction times even at low concentrations as usually encountered in radiochemistry and in vivo. Therefore, kinetics is one of the most important characteristics of bioorthogonal reactions. However, prediction of reactivities using the chemist’s understanding of organic chemistry, especially of IEDDA reactions, might lead to wrong predictions [17] and only qualitative estimates. In addition, synthesis of tetrazines is often low yielding and involves handling or even requires the production of anhydrous hydrazine (not commercially available in Europe), which limits the feasibility of screening for high Diels–Alder reactivity. Hence, there is the need of reliable computational tools to predict the reactivity of various tetrazines in TLs. Herein, we introduce a computational model for the prediction of the reactivity of aryl/alkyl-substituted Tz in the cycloaddition with trans-cyclooctene (TCO), thus 123 D. Svatunek et al. Fig. 1 Mechanism of the bioorthogonal ligation of 1,2,4,5-tetrazine (Tz) and trans-cyclooctene (TCO) eliminating the need for expensive and even dangerous synthetic work, finally enabling in silico screening for tetrazines with desired reactivity. While 3,6-bisaryl- and 3-aryl-substituted Tz show the highest reactivity, aryl/alkyl-substituted Tz are commonly used due to higher stability [18, 19] and show favorable properties in Tz-triggered bioorthogonal elimination reactions [20, 21]. Results and discussion Recently, we have investigated the reactivity of several 3-aryl-6-(3-fluoropropyl)-1,2,4,5-tetrazines 1–8 as chemical probes for rapid radiolabeling and pretargeted PET Fig. 2 Investigated aryl/alkyl substituted 1,2,4,5-tetrazines in the IEDDA reaction with trans-cyclooctene (11) 123 imaging (Fig. 2). While the alkyl substituent is the same for all eight tetrazines the aryl component shows considerable variation including electron-rich and electron-poor aryl groups. In addition, Tz 9 and 10 were included to investigate the influence of the alkyl group and an orthosubstituted aryl residue, respectively. The second-order rate constants of Tz 1–10 in the reaction with trans-cyclooctene 11 at 25 C in anhydrous 1,4-dioxane were measured by stopped-flow spectrophotometry, which gave rates ranging from 1.00 M-1 s-1 for electron-rich trimethoxyphenyl-substituted Tz 3 to 14.6 M-1 s-1 for Tz 8 bearing an electron withdrawing 2-pyridyl substituent (Fig. 3). These experimental results were selected as a basis for the construction of a predictive computational tool. DFT was successfully used in the past by our group [16, 22] and others [7, 17, 23, 24] to predict or explain the reactivity of dienophiles and tetrazines in the tetrazine ligation. Therefore, the Minnesota density functional M06-2X in combination with the 6-311?G(d,p) basis set, was used as model chemistry. This density functional has been proven to produce accurate results for thermodynamics of cycloaddition reactions [25, 26]. Diels–Alder reactions can be described by HOMO/ LUMO interactions using the frontier molecular orbital (FMO) theory. In case of the IEDDA cycloaddition the main orbital interaction is between a low-lying unoccupied orbital of the dienophile, usually being the LUMO?1 for aryl/alkyl tetrazines (Fig. 4a) [17], and the HOMO of the electron-rich dienophile (in this case TCO, Fig. 4b). Fig. 3 Second-order rate constants of tetrazines 1–10 with transcyclooctene (11) in 1,4-dioxane at 25 C A computational model to predict the Diels–Alder reactivity of aryl/alkyl-substituted… Fig. 4 a HOMO, LUMO, and LUMO?1 of 3-methyl-6phenyl-Tz (9); b HOMO of TCO (11); c energy levels of selected orbitals for tetrazines 1–10 and TCO (11) a LUMO HOMO b LUMO+1 orbitalenergy / eV c HOMO 2.0 1.5 LUMO+1 1.0 LUMO 0.5 HOMO 0.0 -8 -10 -12 1 2 3 4 5 6 7 8 9 10 11 tetrazine According to the FMO theory, a smaller energy gap between the interacting orbitals facilitates the reaction. Thus, one might expect that a more electron withdrawing and thus LUMO?1-lowering substituent accelerates the reaction, while an electron-rich aryl substituent will decrease reactivity. HF/6-311?G(d,p)//M06-2X/6311?G(d,p)-calculated orbital energies are shown in Fig. 4c. Tz 4 and 7 bearing an electron-withdrawing trifluoromethyl or sulfone group, respectively, show the lowest LUMO and LUMO?1 energies. However, the tetrazine with the highest reactivity, Tz 8, has one of the highest LUMO and a rather high LUMO?1 energy within the series. As shown in Fig. 5, there is no significant correlation between the LUMO?1-energy levels and the rate constants (R2 = 0.07). This can be rationalized by the fact that FMO interactions are not the only major contributors to activation (...truncated)