systems chemistry: pattern formation in random dynamic combinatorial libraries

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  • Combinatorial ChemistryDOI: 10.1002/ange.200702460

    Systems Chemistry: Pattern Formation in Random DynamicCombinatorial Libraries**Peter T. Corbett, Jeremy K. M. Sanders, and Sijbren Otto*

    Complex systems have received much attention in mathe-matics, physics, and biology, but are underdeveloped inchemistry. The study of complex networks of interactingmolecules is however of fundamental importance in under-standing the organizational principles of biological systems,[1]

    and may well be the key to unraveling the origin of life.[1,2]

    One of the central challenges in complex-systems research isestablishing how the interactions between the components ina system give rise to emergent properties; that is, character-istics of the system that cannot be ascribed to any of itscomponents acting in isolation. Examples of such emergentbehavior in chemical systems include oscillating reactions andthe related formation of Turing patterns from a set ofinterconnected kinetically controlled reactions.[3] Otherimportant recent contributions to systems chemistry[4] includework on self-replicators[5] and self-sorting in multicomponentsystems,[6] chemical models for blood clotting,[7] and replicat-ing vesicles.[8]

    Dynamic combinatorial libraries (DCLs)[9] present anopportunity for exploring the behavior ofmixtures of interacting molecules that areunder thermodynamic control. Herein wereport a computational study of theglobal behavior of a DCL in response tomolecular-recognition events induced byexposing the complex equilibrium mix-ture to a template. We show how patternscan emerge in DCLs whose componentshave random affinities for the template.This unexpected behavior can be tracedback to a competition between librarymembers for specific building blocks, in which librarymembers that are not dependent on those building blockshave a competitive advantage.

    A DCL is an equilibrium mixture of molecules resultingfrom exchange between the building blocks from which thelibrary members are constructed. Molecular-recognitionevents that selectively stabilize particular library membersare likely to cause a shift in the library distribution towards

    these species. The relationship between the amplificationfactors[10] of the various library members and their affinitiesfor the template has received considerable attention.[11] Theemphasis of these studies has been on identifying conditionsunder which the amplification of library members is selectivefor the best binder, which ensures that these species arecorrectly identified in dynamic combinatorial selectionexperiments. More detailed studies which focus on theglobal behavior of DCLs as a goal in its own right have onlyrecently started to emerge. These include the use of dynamiccombinatorial libraries (DCLs) as sensors,[12] the explorationof different network topologies, based on self-sorting buildingblocks,[13] the interplay between complementary reversiblechemistries,[14] and strategies to simultaneously extract thevarious hostguest binding constants from library composi-tions.[15]

    We have recently shown how the amplification of thestrongly binding receptor 13 induced by template 3(Scheme 1) is reduced by binding of the same template to

    122, even though the latter is a weaker binder than 13.[11e]

    While it appears likely that such effects not only affect 13 , butpropagate through the entire DCL, it is not feasible to studythis experimentally owing to the low concentrations of mostof the other library members. Thus, we resorted to compu-tation for studying the global response of DCLs to competi-tion scenarios, such as that outlined above, using our recentlydeveloped software package (DCLSim) that allows theproduct distribution of a DCL to be simulated.[11c,d] Theinput consists of the equilibrium constants that describe theformation of all library members from the building blocks andthe free energies of binding of each of the members to thetemplate. No other chemical information, such as structure, isconsidered. We were particularly interested in the behavior ofDCLs in which the template binding energies are drawnrandomly from a log-normal distribution (mean log Ktemplate=2; standard deviation= 1).[11c] This situation is likely to reflectthat encountered in experimental systems, in which mostlibrary members would have a modest affinity for the

    Scheme 1. Combination of library members 1 and 2 with template 3 to form 122, 13, and othermembers.

    [*] Dr. P. T. Corbett, Prof. J. K. M. Sanders, Dr. S. OttoDepartment of Chemistry, University of CambridgeLensfield Road, Cambridge CB2 1EW (UK)Fax: (+44)1223-336017E-mail: so230@cam.ac.ukHomepage: http://www-otto.ch.cam.ac.uk

    [**] We are grateful for financial support from the Royal Society andEPSRC.

    Supporting information for this article is available on the WWWunder http://www.angewandte.org or from the author.

    Zuschriften

    9014 2007 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim Angew. Chem. 2007, 119, 9014 9017

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  • template, and only a few would bind particularly strongly (orparticularly weakly). Introduction of a template to such alibrary results in a change in the concentrations of mostlibrary members. A typical result of such a theoreticalexperiment is shown in Figure 1a, where the amplificationfactor[10] for each library member is plotted against the Gibbsenergy of binding to the template. The library was made fromseven building blocks AG (total concentration of 10 mm)which were allowed to combine into 322 different oligomericspecies ranging from dimers to tetramers. As intuitivelyexpected, introducing a template (1 mm) causes a net flow ofbuilding blocks from the weaker binders to the better binders(Figure 2a).

    Repeating the experiment in Figure 1a using a differentset of random binding affinities, but otherwise identicalconditions, can give drastically different results. Underparticular circumstances (see below) unexpected patterns

    emerge, where data points appear clustered in lines. Figure 1bshows an example of such behavior. Inspection of theindividual data points reveals that all the library memberson the top line are devoid of building blocks B and C. The linebelow consists exclusively of all the library members intowhich one copy of B or C has been incorporated. Each of thecompounds on the third line contains two units of B or two ofC or one of each. The fourth line features the compounds thatcontain three units of B and/or C, while the bottom line unitesthe tetramers built up exclusively from B and/or C. Thus, itappears that all compounds in this mixture that require B or Care penalized: with a given template binding energy, theirconcentration is increased less than that of their counterpartswhich do not have any of these two subunits in theirstructures. In the presence of the template, the incorporationof building block B or C requires more free energy than therecruitment of any of the other building blocks. The penaltyfor incorporating larger numbers of B or C building blocks iscorrespondingly larger and perfectly additive. This behaviorcan be traced to the influence of a single library member BC,which binds the template with a high (but not the highest)affinity. Repeating the simulation with weaker binding of BCto the template, but with all other equilibrium constantsunchanged, causes the pattern to disappear rapidly: areduction of BC binding affinity from 26 to 20 kJmol1causes the pattern to disappear completely (Figure 3).

    It is now well established that, in the presence of excesstemplate, library members that are made from a relativelysmall number of building blocks have a competitive advant-age over those that contain more building blocks.[11ac] It isimportant to realize that the library will maximize thetemplate binding energy of the entire system: Given thatthe amount of available building block is limited, producingmany copies of BC (DGtemplate=26.1 kJmol1) realizes morebinding energy than, for example, generating a smallernumber of the som