Target-induced amplification in a dynamic library of macrocycles. A quantitative study

Abstract

The perturbation caused by a silver template on the composition of a DCL of cyclophane formaldehyde acetals was investigated as a function of monomer concentration ranging from dilute solutions to values approaching the critical monomer concentration. The target-induced amplification of the dimeric macrocycle was quantitatively analyzed in terms of effective molarity of the macrocycle in the absence and presence of the target.

---

Introduction

A dynamic combinatorial library (DCL) is a complex chemical network generated by combination of suitable building blocks under reversible conditions.¹ A major motivation for intense studies in the field has been the prospect of amplification of one or more components of the equilibrated mixtures via specific interaction with an external target (template), taking advantage of the “proof reading and editing” capability which results from repeatedly occurring bond dissociation–recombination processes.² Given the complexity of the multiple equilibria established in a DCL in the absence and presence of a target, theoretical treatments have been based on numerical simulations of model systems.³ These numerical simulations have highlighted, inter alia, the crucial importance of target concentration, and have shown that a good correlation between binding affinity and amplification factor cannot be taken for granted in all cases.⁴

In our own work in the field of DCLs of macrocyclic compounds,⁵ we have made extensive use of the Jacobson–Stockmayer theory,⁶ conveniently adapted to real systems⁷ (see ESI†) and extended to complex systems composed of two or more building blocks.⁸ In this study, we explore the influence of monomer concentration on the amplification brought about by the addition of (CF₃SO₂)₂NAg to a DCL of cyclophanes obtained from a single building block.

Background

The acid-catalyzed transacetalation of formaldehyde acetals of 1,4-benzenedimethanol is a suitable reaction for the generation of well-behaved, long-lived DCLs of cyclophanes (Scheme 1), occurring viaS_N2-type ring-fusion/ring-fission reactions.⁹ In the low concentration domain, the overall process may be viewed as a ring-opening cyclooligomerization of the hypothetical monomer C₁1, whose five atom COCOC chain is too short to span a p-phenylene moiety. In practice, we found the composition of the equilibrated mixtures to be exactly the same, no matter what oligomer, or mixture of oligomers, was used as feedstock, on condition that the total monomer concentration, c_mon, was the same. The concentration profiles of the lowest oligomers (Fig. 1) show the saturation behavior predicted by theory,^6,7a according to which the concentration of each cyclic species increases on increasing c_mon, until a critical value, , is obtained. Above such value the concentration of each cyclic species remains constant and coincides with the thermodynamic effective molarity EM_i of the given cyclic oligomer. It has already been pointed out^7a that within the usual approximation of reactivity of end groups independent of chain length, the EM_i is both conceptually and operationally identical to the macrocyclization equilibrium constant K_i of the original Jacobson–Stockmayer theory.⁶ It is useful to recall eqn (1)–(3). The concentration-dependent populations of the various cyclic oligomers, eqn (1), are ruled by the quantity x, operationally defined in eqn (2).¹⁰ The values of x are confined in the range 0 ≤ x < 1. It was shown^7a that x coincides with the fraction of reacted end groups in the acyclic part of the polymer and, consequently, it is a measure of the extent of reaction in the equilibrated system.

[C_ii] = xⁱEM_i (1)

x = [C₁1]/EM₁ (2)

The quantity x increases on increasing c_mon and becomes very close to 1 at the critical monomer concentration , but the mathematical relationship between x and c_mon cannot be derived from theory. Data points in Fig. 1 were fitted to empirical equations.¹¹ It is important to stress that is the maximum amount of monomer that can be converted into cyclic species. In a pictorial representation, a DCL of macrocycles may be viewed as a system consisting of an infinite number of communicating vessels of capacity iEM_i.^8,12 All of the monomers added to the system at concentration below the critical value are collected in the vessels in a cyclic form. When the critical concentration is reached all the vessels fill up, and any further addition of monomers overflows in the form of open chain polymeric material. In previous studies^5a we found that (CF₃SO₂)₂NAg forms a strong 1 : 1 complex with the dimeric cyclophane C₂2 in chloroform solution. Complexation is fast on the ¹H NMR time-scale, and induces downfield shifts of the ArH and OCH₂O signals, whereas the ArCH₂O signal is shifted upfield. No sign of complexation is shown by the next higher homologues from C₃3 to C₅5, but there are broad indications of complexation phenomena involving high molecular weight materials. The X-ray crystal structure of the 1 : 1 complex of C₂2 with (CF₃SO₂)₂NAg shows that Ag⁺ is coordinated to two opposite oxygens of the COCOC chains, and establishes two sets of η³Ag⁺–C bonds with carbon atoms of opposite aromatic rings.^5b

Scheme 1

Fig. 1 Equilibrium concentrations of cyclic oligomers obtained from the acid catalyzed transacetalation of C₂2vs. total monomer concentration c_mon in CDCl₃ at 25 °C. EM₂ = 0.30 mM; EM₃ = 0.90 mM; EM₄ = 0.59 mM (data from ref. 5a).

Results and discussion

Now we report on the results of a set of target induced equilibration experiments (CDCl₃, 25 °C), as a function of c_mon. All runs were carried out in NMR tubes in the presence of excess solid (CF₃SO₂)₂NAg¹³ and a catalytic amount of CF₃SO₃H. In all cases pure cyclic trimer C₃3 was used as feedstock. The results of ¹H NMR monitoring of the composition of the equilibrated mixtures are summarized in Fig. 2.

Fig. 2 ¹H NMR spectra (aliphatic portions, CDCl₃, 25 °C) of equilibrated solutions of cyclic oligomers C_ii obtained from the transacetalation of C₃3 in the presence of solid (CF₃SO₂)₂NAg. For each run the total monomer concentration (c_mon) is reported on the left and the equilibrium total concentration of C₂2 is reported on the right. Signals related to C₂2 and C₃3 are marked with arrows.

A plot of [C₂2]_tot = [C₂2] + [C₂2·AgX] vs. c_mon (Fig. 3) shows a saturation behavior in the high monomer concentration domain, analogous to that observed in Fig. 1, but the limiting value of 39 mM is 130 times higher than the value of 0.30 mM measured in the absence of silver salt. Thus, the silver template dramatically increases the plateau concentration of C₂2 and, consequently, the c_mon value for the plateau region to be reached.

Fig. 3 Total concentration of C₂2 as a function of total monomer concentration c_mon in the presence of the silver template. Data points are experimental and the curve is a plot of the empirical equation in ref. 11, with EM^app₂ = 39 mM and a = 0.012 mM⁻¹. The curve fits the data with a rms deviation of 0.32 mM.

A quantitative analysis of the influence of the silver template on the composition of the DCL is simplified a great deal by the presence of undissolved silver salt in the equilibrated mixtures, which ensures an equal concentration of uncomplexed silver salt in all runs and, consequently, a constant ratio between free and complexed C₂2. Derivation of eqn (4) is straightforward. Here [AgX] is the saturation concentration of (CF₃SO₂)₂NAg, and K_AgX is defined in eqn (5). Combination of eqn (4) with eqn (1) leads to eqn (6).

[C₂2]_tot = [C₂2](1 + K_AgX[AgX]) (4)

[C₂2·AgX] = x²EM₂K_AgX[AgX] (6)

The value approached by [C₂2·AgX] as x → 1 is the quantity EM₂K_AgX[AgX], which may reasonably be called the effective molarity of the silver complexed dimeric cycle (EM^AgX₂), eqn (7). By the same token, the limiting value approached by [C₂2]_tot as x → 1 is defined here as the apparent effective molarity (EM^app₂) of C₂2 in the presence of the silver template, eqn (8). In the present case, EM₂ is negligibly small in comparison with EM^AgX₂ and, consequently, EM^app₂ ≈ EM^AgX₂. Using as above the pictorial representation of a DCL as a system of communicating vessels of capacity iEM_i, the effect of the silver template can be visualized as one which enlarges the vessel corresponding to C₂2 from a small capacity (2EM₂ = 0.60 mM) to a much greater one (2EM^AgX₂ = 78 mM).

EM^AgX₂ = EM₂K_AgX[AgX] (7)

EM^app₂ = EM₂ + EM^AgX₂ (8)

The population of metal-free species in equilibrium with metal-complexed species is not identical to that obtained in the absence of metal at the same monomer concentration, because the higher the value of , the smaller the quantity x. As a consequence, in the presence of the metal template a population of metal-free species identical to the limiting population occurring in the absence of metal is reestablished only when the monomer concentration approaches the new critical value. Tiny peaks corresponding to the benzylic protons of uncomplexed trimer C₃3 become increasingly visible in the ¹H NMR traces in Fig. 2 as c_mon increases. Although they are too small to allow precise integration, their sizes are compatible with the equilibrium concentrations plotted in Fig. 1.

A major problem with the concentration profiles in Fig. 1 and 3 is that they do not allow the to be precisely determined, because the concentrations of cyclic species approach their limiting values asymptotically. Nevertheless, comparison of Fig. 1 with Fig. 3 shows that the silver template increases from 80–100 mM to no less than 400 mM. The difference between in the presence and absence of silver salt amounts to no less than 300 mM, corresponding to 3/4 of the monomeric units supplied. Only a fraction of this material, namely, 2 × 39 = 78 mM is accounted for by the formation of the silver-complexed dimer. Much more than 1/2 of the material supplied has been presumably transformed into silver-complexed high molecular weight species, but this has no influence on the amplification of C₂2. This is another favorable consequence of the presence of undissolved silver salt in all runs which, acting as an inexhaustible source of material, allows each member of the DCL to bind to as much silver as it can, independent of the presence of other competitors.

A quantitative measure of the amplification caused by the presence of a target is given by the amplification factor, which is defined as the ratio of the equilibrium concentration of a member of the DCL in the presence and absence of the target.¹⁴Fig. 4a shows that the amplification factor caused by the silver template on the concentration of C₂2 is strongly dependent on c_mon. The amplification factor increases on increasing c_mon, and reaches a plateau value equal to the ratio EM^app₂/EM₂ = 130, which is a measure of the thermodynamic template effect of a saturated solution of (CF₃SO₂)₂NAg on the formation of C₂2 in chloroform at 25 °C. While the amplification factor increases on increasing c_mon, yields of C₂2 both in the presence and absence of silver salt (Fig. 4b) markedly decrease as c_mon increases,¹⁵ showing that reaction conditions favoring the largest amplification are not optimal for synthetic purposes. If a high yield of C₂2 is the criterion of choice, a very low monomer concentration is required. Here the amplification factor is far from its maximum value, but the low percent yields of C₂2 rise to 70–80% in the presence of the silver salt. However, for gram-scale preparations of C₂2 it is more convenient to work at monomer concentrations approaching saturation. Under these conditions yields of C₂2 are much lower, but a simple chromatographic treatment can separate C₂2 from its higher oligomers, which can be recycled via re-equilibration in the presence of silver salt.^5a

Fig. 4 (a) Amplification factor of C₂2 in the presence of (CF₃SO₂)₂NAg (saturated solution) as a function of monomer concentration c_mon. (b) Yield of C₂2 in the absence (□) and presence (○) of the silver template vs. total monomer concentration. Data points are experimental and the curves are calculated on the basis of empirical equations (see ref. 15).

Conclusion

To sum up, we have reported for the first time the saturation profile related to the concentration of the complex formed by a member of a DCL of macrocycles with the target. We have also shown that the amplification of the cyclic dimer C₂2 induced by the addition of (CF₃SO₂)₂NAg to a DCL of cyclophane formaldehyde acetals can be quantitatively analyzed in terms of the increase in the apparent effective molarity of C₂2 brought about by the target. The amplification factor increases on increasing c_mon, and reaches asymptotically a maximum value when c_mon approaches its critical value .

This work emphasizes the crucial role played by the total monomer concentration in the composition of a DCL, both in the absence and presence of the target, and shows that the amplification induced by the addition of the target to a DCL of macrocycles can hardly be analyzed in quantitative terms without resorting to the Jacobson–Stockmayer theory and to concepts derived therefrom, such as the EMs of the macrocycles involved, and the critical monomer concentration . Extension of our studies to DCLs composed of two or more building blocks is in progress.

Experimental section

Instruments, general methods and materials

¹H NMR spectra were registered with a 300 MHz spectrometer. Cyclic trimer C₃3 was available from previous investigation.^5a Stock solution of catalyst CF₃SO₃H was prepared in CD₃NO₂ because of the poor solubility of the former in CDCl₃. CDCl₃ used in the equilibration experiments was previously dried on activated molecular sieves (4 Å). The equilibrations were initiated by addition of 3–15 μL of CF₃SO₃H solution in CD₃NO₂ to 600 μL of C₃3 solutions in CDCl₃ so that the ratio between catalyst and total monomer concentrations was from 2.5 to 5% mol. To the resulting solutions, excess of commercial (CF₃SO₂)₂NAg was added until a solid was well-visible on the bottom of the NMR tube. All reaction mixtures were sonicated for 10 minutes and the presence of solid (CF₃SO₂)₂NAg was verified after sonication. The equilibrating mixtures were kept at 25 °C in the dark until the equilibrium was reached (no further variation of the ¹H NMR spectrum of each solution).

Acknowledgements

Progetti di Ricerca 2010, Università di Roma La Sapienza is acknowledged.

Notes and references

1. (a) P. T. Corbett, J. Leclaire, L. Vial, K. R. West, J.-L. Wietor, J. K. M. Sanders and S. Otto, Chem. Rev., 2006, 106, 3652–3711; (b) S. Ladame, Org. Biomol. Chem., 2008, 6, 219–226; (c) Dynamic Combinatorial Chemistry: in Drug Discovery, Bioorganic Chemistry and Material Science, ed. B. L. Miller, Wiley & Sons Inc., Hoboken (New Jersey), 2009; (d) Dynamic Combinatorial Chemistry, ed. J. N. H. Reek and S. Otto, Wiley-VCH Verlag GmbH & Co. KGaA Inc., Weinheim, 2010.
2. Recent selected papers on templated libraries: (a) M.-K. Chung, C. M. Hebling, J. W. Jorgenson, K. Severin, S. J. Lee and M. R. Gagné, J. Am. Chem. Soc., 2008, 130, 11819–11827; (b) J. W. Sadownik and D. Philp, Angew. Chem., Int. Ed., 2008, 47, 9965–9970; (c) K. Ziach and J. Jurczak, Org. Lett., 2008, 10, 5159–5162; (d) D. Berkovich-Berger and N. G. Lemcoff, Chem. Commun., 2008, 1686–1688; (e) S. M. Turega, C. Lorenz, J. W. Sadownik and D. Philp, Chem. Commun., 2008, 4076–4078; (f) A. L. Lindsey and M. L. Waters, J. Org. Chem., 2009, 74, 111–117; (g) H. Y. Au-Yeung, P. Pengo, G. D. Pantos, S. Otto and J. K. M. Sanders, Chem. Commun., 2009, 419–421; (h) P. Besenius, P. A. G. Cormack, R. F. Ludlow, S. Otto and D. C. Sherrington, Org. Biomol. Chem., 2010, 8, 2414–2418; (i) J. Leclaire, G. Husson, N. Devaux, V. Delorme, L. Charles, F. Ziarelli, P. Desbois, A. Chaumonnot, M. Jacquin and F. Fotiadu, J. Am. Chem. Soc., 2010, 132, 3582–3593; (j) S. Di Stefano, M. Mazzonna, E. Bodo, L. Mandolini and O. Lanzalunga, Org. Lett., 2011, 13, 142–145; (k) S. Beeren and J. K. M. Sanders, J. Am. Chem. Soc., 2011, 133, 3804–3807; (l) P. Lopez-Senin, I. Gomez-Pinto, A. Grandas and V. Marchan, Chem.–Eur. J., 2011, 17, 1946–1953.
3. (a) J. S. Moore and N. W. Zimmerman, Org. Lett., 2000, 2, 915–918; (b) K. Severin, Chem.–Eur. J., 2004, 10, 2565–2580; (c) P. T. Corbett, J. K. M. Sanders and S. Otto, Angew. Chem., Int. Ed., 2007, 46, 8858–8861; (d) R. A. R. Hunt, R. F. Ludlow and S. Otto, Org. Lett., 2009, 11, 5110–5113; (e) A. G. Orrillo and R. L. E. Furlan, J. Org. Chem., 2010, 75, 211–214.
4. (a) P. T. Corbett, S. Otto and J. K. M. Sanders, Org. Lett., 2004, 6, 1825–1827; (b) P. T. Corbett, S. Otto and J. K. M. Sanders, Chem.–Eur. J., 2004, 10, 3139–3143; (c) P. T. Corbett, J. K. M. Sanders and S. Otto, J. Am. Chem. Soc., 2005, 127, 9390–9392; (d) R. F. Ludlow and S. Otto, J. Am. Chem. Soc., 2010, 132, 5984–5986.
5. (a) R. Cacciapaglia, S. Di Stefano and L. Mandolini, J. Am. Chem. Soc., 2005, 127, 13666–13671; (b) R. Cacciapaglia, S. Di Stefano, L. Mandolini, P. Mencarelli and F. Ugozzoli, Eur. J. Org. Chem., 2008, 186–195; (c) R. Cacciapaglia, S. Di Stefano and L. Mandolini, J. Phys. Org. Chem., 2008, 21, 688–693.
6. (a) H. Jacobson and W. H. Stockmayer, J. Chem. Phys., 1950, 18, 1600–1606; (b) P. J. Flory and J. A. Semlyen, J. Am. Chem. Soc., 1996, 88, 3209–3212; (c) P. J. Flory, Statistical Mechanics of Chain Molecules, Wiley-Interscience, New York, 1969, Appendix D500.
7. (a) G. Ercolani, L. Mandolini, P. Mencarelli and S. Roelens, J. Am. Chem. Soc., 1993, 115, 3901–3908; (b) Z.-R. Chen, J. P. Claverie, R. H. Grubbs and J. A. Kornfield, Macromolecules, 1995, 28, 2147–2154.
8. R. Cacciapaglia, S. Di Stefano, G. Ercolani and L. Mandolini, Macromolecules, 2009, 42, 4077–4083.
9. R. Cacciapaglia, S. Di Stefano and L. Mandolini, Chem.–Eur. J., 2006, 12, 8566–8570.
10. The total absence of C₁1 in the DCL of Scheme 1 is irrelevant to the argument, as x may be equally well defined using any other cyclic oligomer whose concentration profile is analytically accessible. For example, x = ([C₂2]/EM₂)^½.
11. Surprisingly enough, the simple exponential equation
    

    [C_ii] = EM_i [1 − exp(−ac_mon)]

    where EM_i and a are adjustable parameters, fits the data remarkably well. Optimized values of EM_i (mM) and a (mM⁻¹), and the rms deviation (mM) are reported below in the given order for the various cyclic oligomers. C₂2: 0.30; 0.12; 0.014. C₃3: 0.90; 0.067; 0.012. C₄4: 0.59; 0.062; 0.018.
12. S. Di Stefano, J. Phys. Org. Chem., 2010, 23, 797–805.
13. (CF₃SO₂)₂NAg is sparingly soluble in chloroform. Its solubility at room temperature is ca. 0.2 mM. Only those members of the DCL for which the binding affinity is high (K_AgX > 10³ M⁻¹) will form significant amounts of the complex.
14. The amplification factor was calculated as follows (see ref. 11 and caption to Fig. 3):
    

    amplification factor = 39[1 − exp(−0.012 c_mon)]/0.30[1 − exp(−0.12 c_mon)]

    .
15. Yields of C₂2 in the absence and presence of the silver template were calculated as follows in the given order:
    

    yield% = 100 × 2 × 0.30[1 − exp(−0.12 c_mon)]/c_mon

    
    

    yield% = 100 × 2 × 39[1 − exp(−0.012 c_mon)]/c_mon

    .

---

Footnote

† Electronic supplementary information (ESI) available: A synopsis of the revised Jacobson–Stockmayer theory. See DOI: 10.1039/c1nj20801b

---