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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    &&&&&&&&&&&&&&&&&&&&&&&&&&&& Nutzen Sie die blauen Literaturverkn)pfungen &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&

  • 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 somewhat better binder B2C2 (DGtemplate=26.6 kJmol1; Figure 1b). This effect is similar to thatobserved experimentally in the competition between 122and 13 (see above), which bind template 3 with affinities of26.8 and 28.0 kJmol1, respectively.[11e]

    Figure 1. a) Typical correlation between the amplification factor[10] andthe affinity for the template for a 322-component DCL with randomlyassigned template binding constants. b) Emergence of a pattern in thesame library with different set of randomly assigned binding constants.Two members, BC and B2C2, are indicated, see text for details.

    Figure 2. Distribution of building blocks over different library membersgrouped in template binding affinity classes for the library in a) Fig-ure 1a and b) Figure 1b, in the absence (dark grey) and presence (lightgrey) of template. The contribution of the dimers in (b) is hatched.

    Figure 3. Correlation between amplification factor[10] and templatebinding affinity for the DCL of Figure 1b but with a reduced DG0 forBC of a) 24 kJmol1 and b) 20 kJmol1. See the SupportingInformation for the behavior across a wider range of DG0 values.

    AngewandteChemie

    9015Angew. Chem. 2007, 119, 9014 9017 2007 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim www.angewandte.de

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    &&&&&&&&&&&&&&&&&&&&&&&&&&&& Nutzen Sie die blauen Literaturverkn)pfungen &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&

  • There is a second factor which is of critical importance foremergence of the pattern in Figure 1b: the concentration ofBC in the mixture in the absence of template. At moderatebuilding-block concentrations, the formation of dimers suchas BC is favored over larger oligomers as it is entropically lessdemanding to make dimers than trimers or tetramers. Thissituation is evident from Figure 2b, which shows how thebuilding blocks are distributed over the different affinityclasses in the absence and presence of the template. Thehatched parts of the bars indicate the contributionof the various dimers, which between them accountfor 90% of the library material. The leftmost set ofbars captures the behavior of dimer BC, which, inthe presence of the template, accounts for 41% ofthe amount of B and C in the library. Repeating thesimulation with the original set of binding constantsbut starting from a tenfold-reduced concentrationof dimer BC (in the absence of the template)caused the pattern of Figure 1b to disappear(producing a graph very similar to Figure 3b).

    In general, for an individual library member toexert a dominant influence on the global behaviorof the mixture, four criteria need to be satisfied:1) the compound in question needs to have a highaffinity for the template, 2) the compound needs tobe among the smaller oligomers, 3) the compoundneeds to be abundant in the absence of thetemplate, and 4) not more than a modest excess oftemplate needs to be available (representativeexamples of the behavior of the library in Figure 1b atvarious template concentrations are provided in theSupporting Information). Patterns such as that in Figure 1bemerge when there is only one such high-affinity smalloligomer in the mixture. Given that the pattern is caused by alibrary member with an unexceptional affinity for thetemplate of 26.1 kJmol1, similar effects can in principleoccur in many of the experimental libraries, as thesefrequently feature library members with affinities of 25 to30 kJmol1.

    The results given above have important implications:information on the amount of the template in the mixture canbe transmitted to molecules that need not be able to directlyinteract with this template. This constitutes an indirect formof signaling, which relies on sharing of building blocks ratherthan on direct molecular interactions. This principle can beused to engineer dynamic mixtures that produce specificresponses to the presence of chemical entities. While we havedescribed how an individual library member can influence thebehavior of all other library members (potentially inducingpatterns), it is also possible to go in the other direction andconstruct equilibrium mixtures where the concentration of anindividual library member is controlled by the properties ofthe other species in the mixture. Two examples belowillustrate how such signaling systems may be constructed.

    Consider a small DCL made from equimolar amounts ofbuilding blocks AE, which can all combine with each otherand in which compound AB binds to effector molecule T1(Ka= 10

    6m1) while CD binds to another effector species T2(Ka= 10

    6m1). None of the other library members binds T1 or

    T2. The composition of this dynamic mixture will respond tothe presence of T1 by producing more AB and to the presenceof T2 by amplifying the amount of CD. Each of these eventswill indirectly result in an increase in the amount of reportermolecule EE because the alternative partners for buildingblock E are tied up in AB or CD. The largest increase in EEwill occur when both T1 and T2 are present (Figure 4a).Representative examples of the behavior of the system atother values of Ka are shown in the Supporting Information.

    More complex responses to the presence of T1 and T2 canalso be engineered. Consider, for example, another dynamicmixture based on equimolar amounts of building blocksWZ,in which T1 is recognised by WW and T2 by WXY. In thiscase, ZZ reports on the presence of the effector molecules in acomplex fashion: An increase in the amount of T2 will lead toan increase in the concentration of ZZ, but addition of T1 inthe presence of T2 will moderate the response. High levels ofT1 may cause a reduction of the amount of ZZ (Figure 4b) asT1 will recruit building block W from WXY that was formedunder the influence of T2. This then liberates X and Y thatcan pair up with Z, reducing the amount of ZZ.

    In conclusion, dynamic combinatorial libraries constitutea useful new entry point into the as-yet underdevelopeddiscipline of systems chemistry. Computer simulations repre-sent an efficient way of rapidly exploring the behavior and ofimproving the understanding of complex equilibrium systems.Starting from unexpected patterns that were observed inlibraries with randomly generated affinities between templateand library members, the rules that govern such behaviorwere uncovered. On the basis of these insights, new dynamicmixtures may be engineered that respond to the...

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