- Research article
- Open Access
Deconvolution of a multi-component interaction network using systems chemistry
© Ghosh et al; licensee BioMed Central Ltd. 2010
Received: 23 March 2010
Accepted: 18 August 2010
Published: 18 August 2010
We describe the stepwise construction of an 8-component self-sorted system (1 - 8) by the sequential addition of components. This process occurs via a large number of states (28 = 256) and even a larger number of pathways (8! = 40320). A pathway (5, 6, 7, 8, 4, 3, 2, then 1) that is self-sorted at every step along the way has been demonstrated experimentally. Another pathway (1, 8, 3, 5, 4, 7, 2, then 6) resembles a game of musical chairs and exhibits interesting shuttling of guest molecules among hosts. The majority of pathways - unlike the special ones described above - proceed through several non self-sorted states. We characterized the remainder of the 40320 pathways by simulation using Gepasi and describe the influence of concentration and binding constants on the fidelity of the self-sorting pathways.
Chemical events that transform a complex system from one well defined state into a different well defined state are of critical importance in both biotic and abiotic systems[1–3]. For example, inside the cellular environment, signal transduction proceeds through a sequence of steps that transforms the system from one state to a completely different state. In single cell and multi-cellular organisms these signal transduction pathways are typically guided by various protein-protein interactions that are in turn controlled by genetic regulatory networks. A recent study revealed that the transcription regulatory networks in yeast Saccharomyces cerevisiae involve 4549 physical interactions between 3278 yeast proteins where as genetic regulatory network is formed 1289 directed positive or negative direct transcriptional regulations within a set of 68 proteins[4, 5]. Such protein-protein interaction networks define pathways for the propagation of various signals such as phosphorylation and allosteric regulation of proteins. Another study on Escherichia coli was able to identify 1079 regulatory interactions out of which 741 interactions are involved in the network that regulate of amino acid biosynthesis, flagella biosynthesis, osmotic stress response, antibiotic resistance, and iron regulation. The complex network of interactions that characterizes biological systems results in remarkable emergent properties that ultimately give rise to life itself.
The success of systems biology[1, 7–11] in the reconstruction of complex functional systems based on a fundamental understanding of the behavior of a series of biological components has served as a stimulus for chemists to begin to develop systems chemistry with the goal of creating functional systems by combining the behaviors of well characterized chemical building blocks[12–14]. For example, the Ghadiri group has explored the behavior of complex systems comprising peptides, enzyme, and/or DNA toward the construction of systems that display self-replication, Boolean logic, and that even are subject to evolutionary pressures[15–20]. In another line of inquiry, the development of supramolecular aggregates (e.g. rotaxanes and related structures) that undergo well defined structural changes (e.g. shuttling) in response to suitable stimuli (e.g. electrochemistry, pH, photochemistry, chemical) has been shown to form the basis for molecular machines[21–23]. Although much work has been done to create individual functional components of future molecular machines, less work has been directed toward developing methods to integrate multiple components into a larger system and to allow efficient communication between different components as described above for Saccharomyces cerevisiae and Escherichia coli.
As first steps toward complex functional chemical systems, we have been developing multi-component systems that form a well-defined state consisting of a single set of supramolecular aggregates. We, and others[24–35], refer to such systems as self-sorting systems. For example, we selected 10 compounds from the literature well known to form supramolecular aggregates driven by H-bonding interactions and showed that this collection of aggregates forms even when all 10 components are mixed. Subsequent work by our group has shown that thermodynamic self-sorting processes can be designed to occur in water using cucurbit[n]uril (CB[n]) molecular containers as hosts and can even be engineered to create systems that slowly transform from kinetic self-sorted to thermodynamic self-sorted states[37, 38]. Most recently, we have begun to study the ability of such systems to respond to suitable chemical stimuli (guest addition) which resulted in artificial chaperones for folding of non-natural oligomers, pH controlled inter-aggregate molecular shuttles, metal-ion triggered folding and assembly of a heterochiral double helical structure, and as a method to control enzymatic catalytic processes[39–42].
Results and Discussion
This results and discussion section is organized as follows. First, we discuss the construction of an 8-component self-sorting system comprising hosts 1 - 4 and guests 5 - 8 in water. Next, we describe three experimental pathways that involve the stepwise construction of the 8-component self-sorted mixture. Subsequently, we discuss some of the theoretical considerations involved in the stepwise construction of an n-component mixture and use simulations to investigate the remainder of the 40320 pathways. Finally, we discuss the implications of these results toward the use of self-sorting processes as the basis for the creation of complex functional systems.
Selection of the Chemical Components Used in this Study
To design an 8-component social self-sorting mixture, we selected three members of the CB[n] family (6 - 8, CB - CB) because it is well-known that CB[n] compounds bind cationic guests with high affinity and selectivity in water. We choose β-cyclodextrin (β-CD) 5 as the fourth host in our study because it is commercially available and binds to a wide range of guests with low selectivity. After some experimentation we selected compounds 1 - 4 as our guests. Of critical importance in the selection of 1 - 4 were: 1) their host-guest complexes undergo slow exchange on the chemical shift time scale and 2) exhibit distinct changes in chemical shift upon complexation such that the composition of the mixture can be conveniently monitored by 1H NMR spectroscopy.
The System Comprising 1 - 8 Undergoes High Fidelity Self-Sorting
Stepwise Construction of the Eight-Component Self-Sorted Mixture
We were gratified that a mixture comprising 1 - 8 underwent high fidelity self-sorting process and decided to explore the stepwise construction of the final eight-component self-sorted state.
Computational Approach Towards a Global Understanding of the Stepwise Construction of a Four Component System
Given that the experimental systems described in this paper are at thermodynamic equilibrium, a detailed knowledge of all the initial concentrations and values of Ka is sufficient for the complete description of the system. These systems are, therefore, quite amenable to computational approaches. We use the program Gepasi[45–47] to simulate the steady state concentrations of a multi-component system by providing an interaction model, initial concentrations, and Ka values as inputs. In this section we present the simulation of a hypothetical 4-component system that sets the stage for the complete deconvolution of the 40320 pathways to the 8-component mixture (1 - 8) described above.
A plot of ΔG° versus number of components for each of the 24 (16) states of the system is shown in Figure 6d. Using a Matlab code [Additional file 1] we have colored self-sorted states with green dots and non-self-sorted states with red dots. Furthermore, pathways that connect two self-sorted states have been colored green; paths that connect a non-self-sorted state with a self-sorted state or two non-self-sorted states have been colored red. Of the 16 states of this system 14 are self-sorted and even more interesting is the fact that of the 24 pathways for the construction of the four-component mixture, 12 consist entirely of self-sorted states. We refer to them as self-sorted pathways. Several other features of this system deserve comment. First, although the stepwise formation of a multi-component complex mixture is a function of path, all paths must by definition lead to an identical final state under thermodynamic control. However, changing the sequence of addition of components leads to completely different sets of complexes along the way. Second, some pathways may be trivial. For example, addition of hosts (e.g. A) followed by their most tight binding guests (e.g. M) does not lead to interesting stimuli responsive changes in composition. Third, stimuli responsive movement of guest is common. For example, the state of the system comprising A and N gives complex AN after the second step despite the fact that BN is formed after step 4. The controlled movement of N from host A to host B - driven by the free energy inherent in the 1000-fold difference in equilibrium constant between KAM (109 M-1) and KBM (106 M-1) - signals the presence of guest M. These observations made in the simulation of this four-component system are conceptually related to the experimental observations made for the 8-component system comprising 1 - 8 described above.
Experimental Investigation of Other Pathways that Lead to the Eight Component Self-Sorted System
Computational Approach Towards Global Understanding of the Experimental System Comprising 1 - 8
Encouraged by the complete deconvolution of the interaction network involved in the stepwise formation of an eight-component self-sorted system, we decided to examine the behavior of various subsets of the pathways. There are four different kinds of transformations possible upon addition of a single component: a self-sorted state to another self-sorted state, a non self-sorted state to another non self-sorted state, a non self-sorted state to a self-sorted state, and a self-sorted state to a non self-sorted state (Figure 9c - f). Although the transformation from a self-sorted state to another self-sorted state is observed throughout the graph (Figure 9c), transformation from a non self-sorted state to another non self-sorted state is spatially segregated (Figure 9d) to the upper right hand corner. The formation of a highly organized self-sorted state from a disordered non self-sorted state upon addition of a compound is associated with a substantial decrease in overall free energy of the system as indicated by the fact that the slope of the lines in Figure 9e are larger than those those in Figure 9c, d, and 9f. In contrast, some transformations from a self-sorted state to a non self-sorted state are associated with a decrease in free energy while others are slightly uphill in energy due to statistical (e.g. entropic) considerations (Figure 9f). For example, a six component mixture 1, 2, 3, 5, 6, and 8 forms a self-sorted state consist of 1•6 (χ = 0.99), 2•5 (χ = 0.99), and 3•8 (χ = 0.99) (ΔG° = -28.9 kcal mol-1). Addition of 4 results in a non-self-sorted seven component mixture containing 1•6 (χ = 0.99), 2 (χ = 0.47), 3 (χ = 0.43), 2•5 (χ = 0.52), 3•5 (χ = 0.47), 3•8 (χ = 0.85) and 4•8 (χ = 0.91) (ΔG° = -31.1 kcal mol-1) and the transformation is associated with ΔΔG° = -2.2 kcal mol-1. The take home message is that maintaining self-sorted pathways usually requires the release of substantial amount of free energy at each step along the way (e.g. Figure 9c exhibits consistent stepwise decreases). Conversely, steps that do not result in a lowering of free energy of the system generally result in non-self-sorted states (e.g. many of the lines in Figure 9f are flat).
Effect of Number of Components on Self-Sorted States
Total Number of Self-Sorted and Non Self-Sorted States at Different Concentration.
Number of Components
Number of States
Conc. (1 M)
Conc. (1 mM)
Conc. (1 μM)
Non self-sorted states
Non self-sorted states
Non self-sorted states
Effect of Concentration of Components on Self-Sorted States and Pathways
Effect of concentration of components and sequence of addition on the number of self-sorted pathways.
Total Number of pathways
Conc. (1 M)
Conc. (1 mM)
Conc. (1 μM)
Non self-sorted pathways
Non self-sorted pathways
Non self-sorted pathways
Sequence HHHHGGGG a
Sequence GGGGHHHH a
Sequence GHGHGHGH a
Sequence HGHGHGHG a
Random sequence a
Non self-sorted paths
Non self-sorted paths
Non self-sorted paths
Non self-sorted paths
Non self-sorted paths
Effect of Sequence of Addition of Components on Pathways
The Effect of Equilibrium Constants
Assigned mean ± standard deviation values of Ka for the synthetic hosts used in the simulation and summary of binding constants for various interactions observed experimentally in biological systems as tabulated by Houk.
In summary, we showed that a mixture comprising 1 - 8 forms an eight-component self-sorting mixture consisting of 6•1, 5•2, 7•3, and 8•4. We investigated selected pathways by 1H NMR and the rest by simulations for the formation of the eight-component mixture. The formation of this eight-component self-sorted system can occur by way of 256 (28) states and 40320 (8!) pathways; the self-sorting nature of the final state has no bearing on whether the intermediate states are self-sorted or non-self-sorted. A particularly interesting pathway that resembles a game of musical chairs that is self-sorted at every step along the way was demonstrated experimentally. We performed simulations of the experimental system using the program Gepasi to gain further insight into the system (number of components, sequence of host/guest addition, concentration, and binding constant values). Of particular interest was the segregation of the self-sorted (non-self-sorted) pathways to the lower left (upper right) corner of plots of ΔG° versus number of components (Figure 9b) which we trace to the need for a steady decrease in the overall value of ΔG° to maintain self-sorted states. Finally, we used simulations of hypothetical eight-component systems based on input log Ka values (mean ± standard deviation) and observed that self-sorting is rather common (20%) but that self-sorted pathways are not. Given that the log Ka mean ± standard deviation values for CB[n] hosts are similar to those of biomolecular interactions bodes well for their use in complex functional systems in the future.
Several aspects of this study may be of interest beyond the system specific considerations described above. First, similar to the molecular networks operating inside living cells, our designed experimental system are based on an intricate web of molecular recognition events. The fact that both experiments and simulations show that self-sorting is a relatively common behavior (20%) suggests that the use of self-sorting systems - particularly ones with segregated network topologies - as the basis for the further development of non-natural functional complex systems is justified. One strategy that Nature uses to control the connectivity of its networks is compartmentalization. Compartmentalization serves to segregate incompatible chemical reactions and interactions and thereby greatly simplifies the overall network topology. The development of compartmentalized self-sorting systems represents a further step toward their integration with biological systems. Finally, we have begun to take steps toward using self-sorting systems to control enzymatic catalytic processes which will be very important for the development of feedback loops and adaptability that are so critical in biological systems. When such approaches can be extended to more complex biological media it may be possible to use self-sorting system to interface with and exert control over portions of the interaction network of the biological system. Second, we have shown how the addition of a new component can dramatically change the composition of the multi-component mixture which suggests that self-sorting systems will be useful in sensing applications. Lastly, this study highlights the power of combinations of simulation and experiment in systems chemistry. For example, we were able to use Gepasi simulation to fully explore 40320 pathways in a time comparable to that needed to investigate six pathways experimentally. These simulations highlighted that the successful generation of complex self-sorting systems relies on the availability of synthetic or biomolecular hosts that display both high affinity and high selectivity toward their guests.
The mixtures described in this paper were prepared as follows: 1) the calculated amounts of each component were weighed out separately and transferred to a 5 mL screw cap vial, 2) D2O (2 mL) was added, 3) the mixture was sonicated or vortexed for several minutes, 4) the pD was adjusted using conc. KOD or DCl solution, 5) the solution was stirred at room temperature overnight, 6) the solution was centrifuged, and 6) the solution was transferred to an NMR tube for analysis.
1H NMR spectra were measured on spectrometers operating at 400 or 500 MHz. Temperature was controlled to 298 ± 0.5 K with a temperature control module that had been calibrated using separation of resonances of methanol. All spectra were measured in D2O unless mentioned and referenced relative to external (CD3)3SiCD2CD2CO2D.
Simulations were performed using Gepasi 3.30 running on a Windows XP workstation. The Gepasi output files were processed using Microsoft Office Excel 2003 and MatLab running on a Windows XP workstation. The Gepasi model files and MatLab codes used in these simulations are deposited in the Supporting Information.
We thank the National Science Foundation (CHE-0615049 and CHE-0914745) for financial support.
- Bonneau R: Learning biological networks: from modules to dynamics. Nat Chem Biol 2008, 4: 658–664. 10.1038/nchembio.122View ArticleGoogle Scholar
- Hartwell LH, Hopfield JJ, Leibler S, Murray AW: From molecular to modular cell biology. Nature 1999, 402: C47-C52. 10.1038/35011540View ArticleGoogle Scholar
- Milo R, Shen-Orr S, Itzkovitz S, Kashtan N, Chklovskii D, Alon U: Network Motifs: Simple Building Blocks of Complex Networks. Science 2002, 298: 824–827. 10.1126/science.298.5594.824View ArticleGoogle Scholar
- Costanzo MC, Crawford ME, Hirschman JE, Kranz JE, Olsen P, Robertson LS, Skrzypek MS, Braun BR, Hopkins KL, Kondu P, et al.: YPD, PombePD and WORMPD: model organism volumes of the BioKnowledge Library, an integrated resource for protein information. Nucleic Acids Res 2001, 29: 75–79. 10.1093/nar/29.1.75View ArticleGoogle Scholar
- Ito T, Chiba T, Ozawa R, Yoshida M, Hattori M, Sakaki Y: A comprehensive two-hybrid analysis to explore the yeast protein interactome. Proc Natl Acad Sci USA 2001, 98: 4569–4574. 10.1073/pnas.061034498View ArticleGoogle Scholar
- Faith JJ, Hayete B, Thaden JT, Mogno I, Wierzbowski J, Cottarel G, Kasif S, Collins JJ, Gardner TS: Large-scale mapping and validation of Escherichia coli transcriptional regulation from a compendium of expression profiles. PLoS Biol 2007, 5: 54–66. 10.1371/journal.pbio.0050008View ArticleGoogle Scholar
- Aloy P, Russell RB: Structural systems biology: modelling protein interactions. Nat Rev Mol Cell Biol 2006, 7: 188–197. 10.1038/nrm1859View ArticleGoogle Scholar
- Butcher EC: Innovation: Can cell systems biology rescue drug discovery? Nat Rev Drug Discovery 2005, 4: 461–467. 10.1038/nrd1754View ArticleGoogle Scholar
- Kitano H: Systems biology: A brief overview. Science 2002, 295: 1662–1664. 10.1126/science.1069492View ArticleGoogle Scholar
- Oltvai ZN, Barabasi A-L: Perspectives: Systems biology: Life's complexity pyramid. Science 2002, 298: 763–764. 10.1126/science.1078563View ArticleGoogle Scholar
- Westerhoff HV, Palsson BO: The evolution of molecular biology into systems biology. Nat Biotechnol 2004, 22: 1249–1252. 10.1038/nbt1020View ArticleGoogle Scholar
- Ludlow RF, Otto S: Systems chemistry. Chem Soc Rev 2008, 37: 101–108. 10.1039/b611921mView ArticleGoogle Scholar
- Nitschke JR: Systems chemistry: Molecular networks come of age. Nature 2009, 462: 736–738. 10.1038/462736aView ArticleGoogle Scholar
- Wagner N, Ashkenasy G: Systems chemistry: logic gates, arithmetic units, and network motifs in small networks. Chem Eur J 2009, 15: 1765–1775. 10.1002/chem.200801850View ArticleGoogle Scholar
- Ashkenasy G, Ghadiri MR: Boolean Logic Functions of a Synthetic Peptide Network. J Am Chem Soc 2004, 126: 11140–11141. 10.1021/ja046745cView ArticleGoogle Scholar
- Ashkenasy G, Jagasia R, Yadav M, Ghadiri MR: Design of a directed molecular network. Proc Natl Acad Sci USA 2004, 101: 10872–10877. 10.1073/pnas.0402674101View ArticleGoogle Scholar
- Frezza BM, Cockroft SL, Ghadiri MR: Modular Multi-Level Circuits from Immobilized DNA-Based Logic Gates. J Am Chem Soc 2007, 129: 14875–14879. 10.1021/ja0710149View ArticleGoogle Scholar
- Gianneschi NC, Ghadiri MR: Design of molecular logic devices based on a programmable DNA-regulated semisynthetic enzyme. Angew Chem, Int Ed 2007, 46: 3955–3958. 10.1002/anie.200700047View ArticleGoogle Scholar
- Saghatelian A, Yokobayashi Y, Soltani K, Ghadiri MR: A chiroselective peptide replicator. Nature 2001, 409: 797–801. 10.1038/35057238View ArticleGoogle Scholar
- Ura Y, Beierle JM, Leman LJ, Orgel LE, Ghadiri MR: Self-Assembling Sequence-Adaptive Peptide Nucleic Acids. Science 2009, 325: 73–77. 10.1126/science.1174577View ArticleGoogle Scholar
- Balzani V, Credi A, Raymo FM, Stoddart JF: Artificial molecular machines. Angew Chem, Int Ed 2000, 39: 3348–3391.View ArticleGoogle Scholar
- Kay ER, Leigh DA, Zerbetto F: Synthetic molecular motors and mechanical machines. Angew Chem, Int Ed 2007, 46: 72–191. 10.1002/anie.200504313View ArticleGoogle Scholar
- Ko YH, Kim E, Hwang I, Kim K: Supramolecular assemblies built with host-stabilized charge-transfer interactions. Chem Commun 2007, 1305–1315. 10.1039/b615103eGoogle Scholar
- Kramer R, Lehn JM, Marquis-Rigault A: Self-recognition in helicate self-assembly: Spontaneous formation of helical metal complexes from mixtures of ligands and metal ions. Proc Natl Acad Sci USA 1993, 90: 5394–5398. 10.1073/pnas.90.12.5394View ArticleGoogle Scholar
- Nitschke JR: Construction, Substitution, and Sorting of Metallo-organic Structures via Subcomponent Self-Assembly. Acc Chem Res 2007, 40: 103–112. 10.1021/ar068185nView ArticleGoogle Scholar
- Rowan SJ, Hamilton DG, Brady PA, Sanders JKM: Automated Recognition, Sorting, and Covalent Self-Assembly by Predisposed Building Blocks in a Mixture. J Am Chem Soc 1997, 119: 2578–2579. 10.1021/ja963320kView ArticleGoogle Scholar
- Barboiu M, Dumitru F, Legrand Y-M, Petit E, van der Lee A: Self-sorting of equilibrating metallosupramolecular DCLs via constitutional crystallization. Chem Commun 2009, 2192–2194. 10.1039/b900155gGoogle Scholar
- Bilgicer B, Xing X, Kumar K: Programmed Self-Sorting of Coiled Coils with Leucine and Hexafluoroleucine Cores. J Am Chem Soc 2001, 123: 11815–11816. 10.1021/ja016767oView ArticleGoogle Scholar
- Braekers D, Peters C, Bogdan A, Rudzevich Y, Boehmer V, Desreux JF: Self-Sorting Dimerization of Tetraurea Calixarenes. J Org Chem 2008, 73: 701–706. 10.1021/jo702418zView ArticleGoogle Scholar
- Burd C, Weck M: Self-Sorting in Polymers. Macromolecules 2005, 38: 7225–7230. 10.1021/ma050755wView ArticleGoogle Scholar
- Jiang W, Winkler HDF, Schalley CA: Integrative Self-Sorting: Construction of a Cascade-Stoppered Heterorotaxane. J Am Chem Soc 2008, 130: 13852–13853. 10.1021/ja806009dView ArticleGoogle Scholar
- Kamada T, Aratani N, Ikeda T, Shibata N, Higuchi Y, Wakamiya A, Yamaguchi S, Kim KS, Yoon ZS, Kim D, Osuka A: High Fidelity Self-Sorting Assembling of meso-Cinchomeronimide Appended meso-meso Linked Zn(II) Diporphyrins. J Am Chem Soc 2006, 128: 7670–7678. 10.1021/ja0611137View ArticleGoogle Scholar
- Mahata K, Schmittel M: From 2-Fold Completive to Integrative Self-Sorting: A Five-Component Supramolecular Trapezoid. J Am Chem Soc 2009, 131: 16544–16554. 10.1021/ja907185kView ArticleGoogle Scholar
- Moffat JR, Smith DK: Controlled self-sorting in the assembly of 'multi-gelator' gels. Chem Commun 2009, 316–318. 10.1039/b818058jGoogle Scholar
- Taylor PN, Anderson HL: Cooperative Self-Assembly of Double-Strand Conjugated Porphyrin Ladders. J Am Chem Soc 1999, 121: 11538–11545. 10.1021/ja992821dView ArticleGoogle Scholar
- Wu A, Isaacs L: Self-Sorting: The Exception or the Rule? J Am Chem Soc 2003, 125: 4831–4835. 10.1021/ja028913bView ArticleGoogle Scholar
- Mukhopadhyay P, Wu A, Isaacs L: Social Self-Sorting in Aqueous Solution. J Org Chem 2004, 69: 6157–6164. 10.1021/jo049976aView ArticleGoogle Scholar
- Mukhopadhyay P, Zavalij PY, Isaacs L: High Fidelity Kinetic Self-Sorting in Multi-Component Systems Based on Guests with Multiple Binding Epitopes. J Am Chem Soc 2006, 128: 14093–14102. 10.1021/ja063390jView ArticleGoogle Scholar
- Chakrabarti S, Mukhopadhyay P, Lin S, Isaacs L: Reconfigurable Four-Component Molecular Switch Based on pH-Controlled Guest Swapping. Org Lett 2007, 9: 2349–2352. 10.1021/ol070730cView ArticleGoogle Scholar
- Ghosh S, Isaacs L: Biological Catalysis Regulated by Cucurbituril Molecular Containers. J Am Chem Soc 2010, 132: 4445–4454. 10.1021/ja910915kView ArticleGoogle Scholar
- Huang W-H, Zavalij PY, Isaacs L: Metal-Ion-Induced Folding and Dimerization of a Glycoluril Decamer in Water. Org Lett 2009, 11: 3918–3921. 10.1021/ol901539qView ArticleGoogle Scholar
- Liu S, Zavalij PY, Lam Y-F, Isaacs L: Refolding Foldamers: Triazene-Arylene Oligomers That Change Shape with Chemical Stimuli. J Am Chem Soc 2007, 129: 11232–11241. 10.1021/ja073320sView ArticleGoogle Scholar
- Isaacs L: Cucurbit[n]urils: from mechanism to structure and function. Chem Commun 2009, 619–629. 10.1039/b814897jGoogle Scholar
- Rekharsky MV, Inoue Y: Complexation Thermodynamics of Cyclodextrins. Chem Rev 1998, 98: 1875–1917. 10.1021/cr970015oView ArticleGoogle Scholar
- Mendes P: GEPASI: a software package for modeling the dynamics, steady states and control of biochemical and other systems. Comput Appl Biosci 1993, 9: 563–571.Google Scholar
- Mendes P: Biochemistry by numbers: simulation of biochemical pathways with Gepasi 3. Trends Biochem Sci 1997, 22: 361–363. 10.1016/S0968-0004(97)01103-1View ArticleGoogle Scholar
- Mendes P, Kell DB: Non-linear optimization of biochemical pathways: applications to metabolic engineering and parameter estimation. Bioinformatics 1998, 14: 869–883. 10.1093/bioinformatics/14.10.869View ArticleGoogle Scholar
- Mock WL, Shih NY: Structure and selectivity in host-guest complexes of cucurbituril. J Org Chem 1986, 51: 4440–4446. 10.1021/jo00373a018View ArticleGoogle Scholar
- Liu S, Ruspic C, Mukhopadhyay P, Chakrabarti S, Zavalij PY, Isaacs L: The Cucurbit[n]uril Family: Prime Components for Self-Sorting Systems. J Am Chem Soc 2005, 127: 15959–15967. 10.1021/ja055013xView ArticleGoogle Scholar
- Houk KN, Leach AG, Kim SP, Zhang X: Binding affinities of host-guest, protein-ligand, and protein-transition-state complexes. Angew Chem, Int Ed 2003, 42: 4872–4897. 10.1002/anie.200200565View ArticleGoogle Scholar
- Saur I, Scopelliti R, Severin K: Utilization of self-sorting processes to generate dynamic combinatorial libraries with new network topologies. Chem Eur J 2006, 12: 1058–1066. 10.1002/chem.200500621View ArticleGoogle Scholar
- Buryak A, Pozdnoukhov A, Severin K: Pattern-based sensing of nucleotides in aqueous solution with a multicomponent indicator displacement assay. Chem Commun 2007, 2366–2368. 10.1039/b705250bGoogle Scholar
- Day A, Arnold AP, Blanch RJ, Snushall B: Controlling Factors in the Synthesis of Cucurbituril and Its Homologues. J Org Chem 2001, 66: 8094–8100. 10.1021/jo015897cView ArticleGoogle Scholar
This article is published under license to BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.