Bioorthogonal Cycloadditions: Computational Analysis with the Distortion/Interaction Model and Predictions of Reactivities

Abstract

Bioorthogonal chemistry has had a major impact on the study of biological processes in vivo. Biomolecules of interest can be tracked by using probes and reporters that do not react with cellular components and do not interfere with metabolic processes in living cells. Much time and effort has been devoted to the screening of potential bioorthogonal reagents experimentally. This Account describes how our groups have performed computational screening of reactivity and mutual orthogonality. Our collaborations with experimentalists have led to the development of new and useful reactions. Dozens of bioorthogonal cycloadditions have been reported in the literature in the past few years, but as interest in tracking multiple targets arises, our computational screening has gained importance for the discovery of new mutually orthogonal bioorthogonal cycloaddition pairs. The reactivities of strained alkenes and alkynes with common 1,3-dipoles such as azides, along with mesoionic sydnones and other novel 1,3-dipoles, have been explored. Studies of "inverse-electron-demand" dienes such as triazines and tetrazines that have been used in bioorthogonal Diels-Alder cycloadditions are described. The color graphics we have developed give a snapshot of whether reactions are fast enough for cellular applications (green), adequately reactive for labeling (yellow), or only useful for synthesis or do not occur at all (red). The colors of each box give an instant view of rates, while bar graphs provide an analysis of the factors that control reactivity. This analysis uses the distortion/interaction or activation strain model of cycloaddition reactivity developed independently by our group and that of F. Matthias Bickelhaupt in The Netherlands. The model analyzes activation barriers in terms of the energy required to distort the reactants to the transition state geometry. This energy, called the distortion energy or activation strain, constitutes the major component of the activation energy. The strong bonding interaction between the termini of the two reactants, which we call the interaction energy, overcomes the distortion energy and leads to the new bonds in the products. This Account describes how we have analyzed and predicted bioorthogonal cycloaddition reactivity using the distortion/interaction model and how our experimental collaborators have employed these insights to create new bioorthogonal cycloadditions. The graphics we use document and predict which combinations of cycloadditions will be useful in bioorthogonal chemistry and which pairs of reactions are mutually orthogonal. For example, the fast reaction of 5-phenyl-1,2,4-triazine and a thiacycloheptyne will not interfere with the other fast reaction of 3,6-diphenyl-1,2,4,5-tetrazine and a cyclopropene. No cross reactions will occur, as these are very slow reactions.

Figure 1

Representative bioorthogonal cycloaddition. The probe and reporter contain functional groups that undergo a cycloaddition to form a new ring, represented by the circle in the product.

Figure 2

Range of rate constants for various examples of bioorthogonal reactions. The first is the Staudinger ligation, one of the first bioorthogonal reactions developed by the Bertozzi group, and the other three reactions are later-developed bioorthogonal cycloadditions.

Figure 3

Examples of bioorthogonal cycloadditions that are also mutually orthogonal. R¹-N₃ = Alexa Fluor 647 azide; R² = (CH₂)₅NH₂; R³ = PEG4-CO₂H.

Figure 4

D/I model. Black arrow, activation energy; red arrow, interaction energy; blue and green arrows, distortion energies of the diene and dienophile, respectively.

Figure 5

Experimentally measured second-order rate constants for six bioorthogonal cycloadditions.^,

Figure 6

Computed activation free energies ( $\mathrm{\Delta }{G}_{\text{compt}}^{‡}$) correlate well with experimentally observed values ( $\mathrm{\Delta }{G}_{\text{expt}}^{‡}$).

Figure 7

(a) Cyclooctynes and dibenzo analogues (Oct, MOFO, DIFO, DIBO, DIBAC, BARAC) and their rate constants (in M⁻¹ s⁻¹) for reactions with benzyl azide. (b) Cycloaddition reactions of BARAC analogues 1–11 with benzyl azide.

Figure 8

D/I analysis of reactions of methyl azide with BARAC analogues 1 and 8–10.

Figure 9

D/I analyses of reactions of methyl azide and dimethyltetrazine with trans-cyclooctene, cyclooctyne, and dibenzocyclooctyne. Calculated energies are shown in kcal/mol.

Figure 10

Computationally designed mutually orthogonal cycloadditions.

Figure 11

Orthogonal reactions of 1,3-disubstituted cyclopropenes with tetrazines and 3,3-disubstituted cyclopropenes with nitrile imines.

Figure 12

D/I analysis of reactions of nitrile imine and tetrazine with 1,3- and 3,3-dimethylcyclopropene. Calculated energies are shown in kcal/mol.

Figure 13

Tetrazine ligation with 1-methyl-3-substituted cyclopropenes: (left) computed rate constants (k_compt); (right) experimentally measured rate constants (k_expt). The substrates used in the calculations were simplified versions of those used in the experiments.

Figure 14

D/I analysis of the reactions of 1,2,4-triazine and 1,2,4,5-tetrazine with ethylene and the LUMO+1 energies of 1,2,4-triazine and 1,2,4,5-tetrazine.

Figure 15

D/I analysis of factors controlling mutually orthogonal cycloadditions involving triazines and tetrazines.

Figure 16

Computational screening of cycloadditions of N-phenylsydnone (3 + 2) with dipolarophile candidates.

Figure 17

Mutual orthogonal cycloadditions of sydnone and tetrazine.

Figure 18

Reactivity matrix of cycloaddition reactions among known bioorthogonal compounds. Each box is color-coded according to the calculated second-order rate constant. Mutual orthogonal cycloaddition pairs are shown on the corners of the dashed boxes: green circles represent rapid reactions, while red circles stand for slow/unlikely reactions.