Biomedical subjects

B K Shoichet

Publications and source records attributed to B K Shoichet.

18 recordsLinked to original sources

PubMed2001

Docking molecules by families to increase the diversity of hits in database screens: computational strategy and experimental evaluation.

Molecular docking programs screen chemical databases for novel ligands that fit protein binding sites. When one compound fits the site well, close analogs typically do the same. Therefore, many of the compounds that are found in such screens resemble one another. This reduces the variety and novelty of the compounds suggested. In an attempt to increase the diversity of docking hit lists, the Available Chemicals Directory was grouped into families of related structures. All members of every family were docked and scored, but only the best scoring molecule of a high-ranking family was allowed in the hit list. The identity and scores of the other members of these families were recorded as annotations to the best family member, but they were not independently ranked. This family-based docking method was compared with molecule-by-molecule docking in screens against the structures of thymidylate synthase, dihydrofolate reductase (DHFR), and the cavity site of the mutant T4 lysozyme Leu99 --> Ala (L99A). In each case, the diversity of the hit list increased, and more families of known ligands were found. To investigate whether the newly identified hits were sensible, we tested representative examples experimentally for binding to L99A and DHFR. Of the six compounds tested against L99A, five bound to the internal cavity. Of the seven compounds tested against DHFR, six inhibited the enzyme with apparent K(i) values between 0.26 and 100 microM. The segregation of potential ligands into families of related molecules is a simple technique to increase the diversity of candidates suggested by database screens. The general approach should be applicable to most docking methods. Proteins 2001;42:279-293.

Algorithms↗

PubMed1999

Comparing the thermodynamic stabilities of a related thermophilic and mesophilic enzyme.

Several models have been proposed to explain the high temperatures required to denature enzymes from thermophilic organisms; some involve greater maximum thermodynamic stability for the thermophile, and others do not. To test these models, we reversibly melted two analogous protein domains in a two-state manner. E2cd is the isolated catalytic domain of cellulase E2 from the thermophile Thermomonospora fusca. CenAP30 is the analogous domain of the cellulase CenA from the mesophile Cellulomonas fimi. When reversibly denatured in a common buffer, the thermophilic enzyme E2cd had a temperature of melting (Tm) of 72.2 degrees C, a van't Hoff enthalpy of unfolding (DeltaHVH) of 190 kcal/mol, and an entropy of unfolding (DeltaSu) of 0.55 kcal/(mol*K); the mesophilic enzyme CenAP30 had a Tm of 56.4 degrees C, a DeltaHVH of 107 kcal/mol, and a DeltaSu of 0. 32 kcal/(mol*K). The higher DeltaHVH and DeltaSu values for E2cd suggest that its free energy of unfolding (DeltaGu) has a steeper dependence on temperature at the Tm than CenAP30. This result supports models that predict a greater maximum thermodynamic stability for thermophilic enzymes than for their mesophilic counterparts. This was further explored by urea denaturation. Under reducing conditions at 30 degrees C, E2cd had a concentration of melting (Cm) of 5.2 M and a DeltaGu of 11.2 kcal/mol; CenAP30 had a Cm of 2.6 M and a DeltaGu of 4.3 kcal/mol. Under nonreducing conditions, the Cm and DeltaGu of CenAP30 were increased to 4.5 M and 10.8 kcal/mol at 30 degrees C; the Cm for E2cd was increased to at least 7.4 M at 32 degrees C. We were unable to determine a DeltaGu value for E2cd under nonreducing conditions due to problems with reversibility. These data suggest that E2cd attains its greater thermal stability (DeltaTm = 15.8 degrees C) through a greater thermodynamic stability (DeltaDeltaGu = 6.9 kcal/mol) compared to its mesophilic analogue CenAP30.

Actinomycetales↗

PubMed1999

Structure-based design of inhibitors specific for bacterial thymidylate synthase.

Thymidylate synthase is an attractive target for antiproliferative drug design because of its key role in the synthesis of DNA. As such, the enzyme has been widely targeted for anticancer applications. In principle, TS should also be a good target for drugs used to fight infectious disease. In practice, TS is highly conserved across species, and it has proven to be difficult to develop inhibitors that are selective for microbial TS enzymes over the human enzyme. Using the structure of TS from Lactobacillus casei in complex with the nonsubstrate analogue phenolphthalein, inhibitors were designed to take advantage of features of the bacterial enzyme that differ from those of the human enzyme. Upon synthesis and testing, these inhibitors were found to be up to 40-fold selective for the bacterial enzyme over the human enzyme. The crystal structures of two of these inhibitors in complex with TS suggested the design of further compounds. Subsequent synthesis and testing showed that these second-round compounds inhibit the bacterial enzyme at sub-micromolar concentrations, while the human enzyme was not inhibited at detectable levels (selectivities of 100-1000-fold or greater). Although these inhibitors share chemical similarities, X-ray crystal structures reveal that the analogues bind to the enzyme in substantially different orientations. Site-directed mutagenesis experiments suggest that the individual inhibitors may adopt multiple configurations in their complexes with TS.

Amino Acid Substitution↗

PubMed1999

Ligand solvation in molecular docking.

Solvation plays an important role in ligand-protein association and has a strong impact on comparisons of binding energies for dissimilar molecules. When databases of such molecules are screened for complementarity to receptors of known structure, as often occurs in structure-based inhibitor discovery, failure to consider ligand solvation often leads to putative ligands that are too highly charged or too large. To correct for the different charge states and sizes of the ligands, we calculated electrostatic and non-polar solvation free energies for molecules in a widely used molecular database, the Available Chemicals Directory (ACD). A modified Born equation treatment was used to calculate the electrostatic component of ligand solvation. The non-polar component of ligand solvation was calculated based on the surface area of the ligand and parameters derived from the hydration energies of apolar ligands. These solvation energies were subtracted from the ligand-receptor interaction energies. We tested the usefulness of these corrections by screening the ACD for molecules that complemented three proteins of known structure, using a molecular docking program. Correcting for ligand solvation improved the rankings of known ligands and discriminated against molecules with inappropriate charge states and sizes.

Aniline Compounds↗

PubMed1999

Structure-based discovery and in-parallel optimization of novel competitive inhibitors of thymidylate synthase.

BACKGROUND: The substrate sites of enzymes are attractive targets for structure-based inhibitor design. Two difficulties hinder efforts to discover and elaborate new (nonsubstrate-like) inhibitors for these sites. First, novel inhibitors often bind at nonsubstrate sites. Second, a novel scaffold introduces chemistry that is frequently unfamiliar, making synthetic elaboration challenging. RESULTS: In an effort to discover and elaborate a novel scaffold for a substrate site, we combined structure-based screening with in-parallel synthetic elaboration. These techniques were used to find new inhibitors that bound to the folate site of Lactobacillus casei thymidylate synthase (LcTS), an enzyme that is a potential target for proliferative diseases, and is highly studied. The available chemicals directory was screened, using a molecular-docking computer program, for molecules that complemented the three-dimensional structure of this site. Five high-ranking compounds were selected for testing. Activity and docking studies led to a derivative of one of these, dansyltyrosine (Ki 65 microM). Using solid-phase in-parallel techniques 33 derivatives of this lead were synthesized and tested. These analogs are dissimilar to the substrate but bind competitively with it. The most active analog had a Ki of 1.3 microM. The tighter binding inhibitors were also the most specific for LcTS versus related enzymes. CONCLUSIONS: TS can recognize inhibitors that are dissimilar to, but that bind competitively with, the folate substrate. Combining structure-based discovery with in-parallel synthetic techniques allowed the rapid elaboration of this series of compounds. More automated versions of this approach can be envisaged.

Catalytic Domain↗

PubMed1999

The complexed structure and antimicrobial activity of a non-beta-lactam inhibitor of AmpC beta-lactamase.

Beta-lactamases are the major resistance mechanism to beta-lactam antibiotics and pose a growing threat to public health. Recently, bacteria have become resistant to beta-lactamase inhibitors, making this problem pressing. In an effort to overcome this resistance, non-beta-lactam inhibitors of beta-lactamases were investigated for complementarity to the structure of AmpC beta-lactamase from Escherichia coli. This led to the discovery of an inhibitor, benzo(b)thiophene-2-boronic acid (BZBTH2B), which inhibited AmpC with a Ki of 27 nM. This inhibitor is chemically dissimilar to beta-lactams, raising the question of what specific interactions are responsible for its activity. To answer this question, the X-ray crystallographic structure of BZBTH2B in complex with AmpC was determined to 2.25 A resolution. The structure reveals several unexpected interactions. The inhibitor appears to complement the conserved, R1-amide binding region of AmpC, despite lacking an amide group. Interactions between one of the boronic acid oxygen atoms, Tyr150, and an ordered water molecule suggest a mechanism for acid/base catalysis and a direction for hydrolytic attack in the enzyme catalyzed reaction. To investigate how a non-beta-lactam inhibitor would perform against resistant bacteria, BZBTH2B was tested in antimicrobial assays. BZBTH2B significantly potentiated the activity of a third-generation cephalosporin against AmpC-producing resistant bacteria. This inhibitor was unaffected by two common resistance mechanisms that often arise against beta-lactams in conjunction with beta-lactamases. Porin channel mutations did not decrease the efficacy of BZBTH2B against cells expressing AmpC. Also, this inhibitor did not induce expression of AmpC, a problem with many beta-lactams. The structure of the BZBTH2B/AmpC complex provides a starting point for the structure-based elaboration of this class of non-beta-lactam inhibitors.

Anti-Bacterial Agents↗

PubMed1999

Functional analyses of AmpC beta-lactamase through differential stability.

Despite decades of intense study, the complementarity of beta-lactams for beta-lactamases and penicillin binding proteins is poorly understood. For most of these enzymes, beta-lactam binding involves rapid formation of a covalent intermediate. This makes measuring the equilibrium between bound and free beta-lactam difficult, effectively precluding measurement of the interaction energy between the ligand and the enzyme. Here, we explore the energetic complementarity of beta-lactams for the beta-lactamase AmpC through reversible denaturation of adducts of the enzyme with beta-lactams. AmpC from Escherichia coli was reversibly denatured by temperature in a two-state manner with a temperature of melting (Tm) of 54.6 degrees C and a van't Hoff enthalpy of unfolding (deltaH(VH)) of 182 kcal/mol. Solvent denaturation gave a Gibbs free energy of unfolding in the absence of denaturant (deltaG(u)H2O) of 14.0 kcal/mol. Ligand binding perturbed the stability of the enzyme. The penicillin cloxacillin stabilized AmpC by 3.2 kcal/mol (deltaTm = +5.8 degrees C); the monobactam aztreonam stabilized the enzyme by 2.7 kcal/mol (deltaTm = +4.9 degrees C). Both acylating inhibitors complement the active site. Surprisingly, the oxacephem moxalactam and the carbapenem imipenem both destabilized AmpC, by 1.8 kcal/mol (deltaTm = -3.2 degrees C) and 0.7 kcal/mol (deltaTm = -1.2 degrees C), respectively. These beta-lactams, which share nonhydrogen substituents in the 6(7)alpha position of the beta-lactam ring, make unfavorable noncovalent interactions with the enzyme. Complexes of AmpC with transition state analog inhibitors were also reversibly denatured; both benzo(b)thiophene-2-boronic acid (BZBTH2B) and p-nitrophenyl phenylphosphonate (PNPP) stabilized AmpC. Finally, a catalytically inactive mutant of AmpC, Y150F, was reversibly denatured. It was 0.7 kcal/mol (deltaTm = -1.3 degrees C) less stable than wild-type (WT) by thermal denaturation. Both the cloxacillin and the moxalactam adducts with Y150F were significantly destabilized relative to their WT counterparts, suggesting that this residue plays a role in recognizing the acylated intermediate of the beta-lactamase reaction. Reversible denaturation allows for energetic analyses of the complementarity of AmpC for beta-lactams, through ligand binding, and for itself, through residue substitution. Reversible denaturation may be a useful way to study ligand complementarity to other beta-lactam binding proteins as well.

Amino Acid Substitution↗

PubMed1998

Three-dimensional structure of AmpC beta-lactamase from Escherichia coli bound to a transition-state analogue: possible implications for the oxyanion hypothesis and for inhibitor design.

The structures of AmpC beta-lactamase from Escherichia coli, alone and in complex with a transition-state analogue, have been determined by X-ray crystallography. The native enzyme was determined to 2.0 A resolution, and the structure with the transition-state analogue m-aminophenylboronic acid was determined to 2.3 A resolution. The structure of AmpC from E. coli resembles those previously determined for the class C enzymes from Enterobacter cloacae and Citrobacter freundii. The transition-state analogue, m-aminophenylboronic acid, makes several interactions with AmpC that were unexpected. Perhaps most surprisingly, the putative "oxyanion" of the boronic acid forms what appears to be a hydrogen bond with the backbone carbonyl oxygen of Ala318, suggesting that this atom is protonated. Although this interaction has not previously been discussed, a carbonyl oxygen contact with the putative oxyanion or ligand carbonyl oxygen appears in most complexes involving a beta-lactam recognizing enzyme. These observations may suggest that the high-energy intermediate for amide hydrolysis by beta-lactamases and related enzymes involves a hydroxyl and not an oxyanion, although the oxyanion form certainly cannot be discounted. The involvement of the main-chain carbonyl in ligand and transition-state recognition is a distinguishing feature between serine beta-lactamases and serine proteases, to which they are often compared. AmpC may use the interaction between the carbonyl of Ala318 and the carbonyl of the acylated enzyme to destabilize the ground-state intermediate, this destabilization energy might be relieved in the transition state by a hydroxyl hydrogen bond. The structure of the m-aminophenylboronic acid adduct also suggests several ways to improve the affinity of this class of inhibitor and points to the existence of several unusual binding-site-like features in the region of the AmpC catalytic site.

Anions↗

PubMed1998

Structure-based enhancement of boronic acid-based inhibitors of AmpC beta-lactamase.

The expression of beta-lactamases is the most common form of bacterial resistance to beta-lactam antibiotics. To combat these enzymes, agents that inhibit (e.g. clavulanic acid) or evade (e.g. aztreonam) beta-lactamases have been developed. Both the beta-lactamase inhibitors and the beta-lactamase-resistant antibiotics are themselves beta-lactams, and bacteria have responded to these compounds by expressing variant enzymes resistant to inhibition (e.g. IRT-3) or that inactivate the beta-lactamase-resistant antibiotic (e.g. TEM-10). Moreover, these compounds have increased the frequency of bacteria with intrinsically resistant beta-lactamases (e.g. AmpC). In an effort to identify non-beta-lactam-based beta-lactamase inhibitors, we used the crystallographic structure of the m-aminophenylboronic acid-Escherichia coli AmpC beta-lactamase complex to suggest modifications that might enhance the affinity of boronic acid-based inhibitors for class C beta-lactamases. Several types of compounds were modeled into the AmpC binding site, and a total of 37 boronic acids were ultimately tested for beta-lactamase inhibition. The most potent of these compounds, benzo[b]thiophene-2-boronic acid (36), has an affinity for E. coli AmpC of 27 nM. The wide range of functionality represented by these compounds allows for the steric and chemical "mapping" of the AmpC active site in the region of the catalytic Ser64 residue, which may be useful in subsequent inhibitor discovery efforts. Also, the new boronic acid-based inhibitors were found to potentiate the activity of beta-lactam antibiotics, such as amoxicillin and ceftazidime, against bacteria expressing class C beta-lactamases. This suggests that boronic acid-based compounds may serve as leads for the development of therapeutic agents for the treatment of beta-lactam-resistant infections.

Anti-Bacterial Agents↗

PubMed1998

Flexible ligand docking using conformational ensembles.

Molecular docking algorithms suggest possible structures for molecular complexes. They are used to model biological function and to discover potential ligands. A present challenge for docking algorithms is the treatment of molecular flexibility. Here, the rigid body program, DOCK, is modified to allow it to rapidly fit multiple conformations of ligands. Conformations of a given molecule are pre-calculated in the same frame of reference, so that each conformer shares a common rigid fragment with all other conformations. The ligand conformers are then docked together, as an ensemble, into a receptor binding site. This takes advantage of the redundancy present in differing conformers of the same molecule. The algorithm was tested using three organic ligand protein systems and two protein-protein systems. Both the bound and unbound conformations of the receptors were used. The ligand ensemble method found conformations that resembled those determined in X-ray crystal structures (RMS values typically less than 1.5 A). To test the method's usefulness for inhibitor discovery, multi-compound and multi-conformer databases were screened for compounds known to bind to dihydrofolate reductase and compounds known to bind to thymidylate synthase. In both cases, known inhibitors and substrates were identified in conformations resembling those observed experimentally. The ligand ensemble method was 100-fold faster than docking a single conformation at a time and was able to screen a database of over 34 million conformations from 117,000 molecules in one to four CPU days on a workstation.

Algorithms↗

PubMed1996

Predicting the structure of protein complexes: a step in the right direction.

In a blind test of protein-docking algorithms, six groups used different methods to predict the structure of a protein complex. All six predicted structures were close enough to the experimental complex to be useful; nevertheless, several important details of the experimental complex were missed or only partially predicted.

Algorithms↗

PubMed1996

Molecular docking programs successfully predict the binding of a beta-lactamase inhibitory protein to TEM-1 beta-lactamase.

Crystallization of the 1:1 molecular complex between the beta-lactamase TEM-1 and the beta-lactamase inhibitory protein BLIP has provided an opportunity to put a stringent test on current protein-docking algorithms. Prior to the successful determination of the structure of the complex, nine laboratory groups were given the refined atomic coordinates of each of the native molecules. Other than the fact that BLIP is an effective inhibitor of a number of beta-lactamase enzymes (KI for TEM-1 approximately 100 pM) no other biochemical or structural data were available to assist the practitioners in their molecular docking. In addition, it was not known whether the molecules underwent conformational changes upon association or whether the inhibition was competitive or non-competitive. All six of the groups that accepted the challenge correctly predicted the general mode of association of BLIP and TEM-1.

Amino Acid Sequence↗

PubMed1995

A relationship between protein stability and protein function.

Enzymes are thought to use their ordered structures to facilitate catalysis. A corollary of this theory suggests that enzyme residues involved in function are not optimized for stability. We tested this hypothesis by mutating functionally important residues in the active site of T4 lysozyme. Six mutations at two catalytic residues, Glu-11 and Asp-20, abolished or reduced enzymatic activity but increased thermal stability by 0.7-1.7 kcal.mol-1. Nine mutations at two substrate-binding residues, Ser-117 and Asn-132, increased stability by 1.2-2.0 kcal.mol-1, again at the cost of reduced activity. X-ray crystal structures show that the substituted residues complement regions of the protein surface that are used for substrate recognition in the native enzyme. In two of these structures the enzyme undergoes a general conformational change, similar to that seen in an enzyme-product complex. These results support a relationship between stability and function for T4 lysozyme. Other evidence suggests that the relationship is general.

Bacteriophage T4↗

PubMed1995

Enhancement of protein stability by the combination of point mutations in T4 lysozyme is additive.

A number of mutations have been shown previously to stabilize T4 lysozyme. By combining up to seven such mutations in the same protein, the melting temperature was incrementally increased by up to 8.3 degrees C at pH 5.4 (delta delta G = 3.6 kcal/mol). This shows that it is possible to engineer a protein of enhanced thermostability by combining a series of rationally designed point mutations. It is also shown that this stabilization is achieved with only minor, localized changes in the structure of the protein. This is consistent with the observation that the change in stability of each of the multiple mutants is, in each case, additive, i.e. equal to the sum of the stability changes associated with the constituent single mutants. One of the seven substitutions, Asn116-->Asp, changes a residue that participates in substrate binding; not surprisingly, it causes a significant loss in activity. Ignoring this mutation, there is a gradual reduction in activity as successively more mutations are combined.

Bacteriophage T4↗

PubMed1994

Partial restoration of activity to Lactobacillus casei thymidylate synthase following inactivation by domain deletion.

Thymidylate synthase (TS) from Lactobacillus casei has a 50 amino acid insert (residues 90-139) in the small domain that is found in only one other TS. A deletion mutant was constructed which lacked the entire insert, thereby reducing the small domain to the size found in Escherichia coli TS. This mutant did not catalyze the formation of dTMP. From the crystal structure of L. casei TS, we surmised that the loss of activity might have resulted from the exposure of residues of helices C and D, which were previously buried by the insert. To restore the local structure of helices C and D in the deletion mutants, we replaced several residues in this region by the corresponding residues found in E. coli TS. The mutant whose sequence most closely resembled that of E. coli TS carried six mutations and possessed partially restored TS activity. The mutant which had all those mutations except F87D did not catalyze any dTMP formation. The crucial role of F87D was proven in a deletion mutant which had only this change and showed greatly increased activity. All of the mutants catalyzed the debromination of BrdUMP in the absence of cofactor about as well as wild type TS. The kinetic parameters for dTMP formation of the active mutants show that the deletion has its major effect on kcat and binding of cofactor CH2H4folate, with less effect on binding of the substrate dUMP. Removal of residues 90-139 is believed to disorder helices C and D, which in turn decreases cofactor binding and catalysis.

Amino Acid Sequence↗

PubMed1993

Structure-based discovery of inhibitors of thymidylate synthase.

A molecular docking computer program (DOCK) was used to screen the Fine Chemical Directory, a database of commercially available compounds, for molecules that are complementary to thymidylate synthase (TS), a chemotherapeutic target. Besides retrieving the substrate and several known inhibitors, DOCK proposed putative inhibitors previously unknown to bind to the enzyme. Three of these compounds inhibited Lactobacillus casei TS at submillimolar concentrations. One of these inhibitors, sulisobenzone, crystallized with TS in two configurations that differed from the DOCK-favored geometry: a counterion was bound in the substrate site, which resulted in a 6 to 9 angstrom displacement of the inhibitor. The structure of the complexes suggested another binding region in the active site that could be exploited. This region was probed with molecules sterically similar to sulisobenzone, which led to the identification of a family of phenolphthalein analogs that inhibit TS in the 1 to 30 micromolar range. These inhibitors do not resemble the substrates of the enzyme. A crystal structure of phenolphthalein with TS shows that it binds in the target site in a configuration that resembles the one suggested by DOCK.

Amino Acid Sequence↗

PubMed1993

Matching chemistry and shape in molecular docking.

We have added a chemical filter to the ligand placement algorithm of the molecular docking program DOCK. DOCK places ligands in receptors using local shape features. Here we label these shape features by chemical type and insist on complementary matches. We find fewer physically unrealistic complexes without reducing the number of complexes resembling the known ligand-receptor configurations. Approximately 10-fold fewer complexes are calculated and the new algorithm is correspondingly 10-fold faster than the previous shape-only matching. We tested the new algorithm's ability to reproduce three known ligand-receptor complexes: methotrexate in dihydrofolate reductase, deoxyuridine monophosphate in thymidylate synthase and pancreatic trypsin inhibitor in trypsin. The program found configurations within 1 A of the crystallographic mode, with fewer non-native solutions compared with shape-only matching. We also tested the program's ability to retrieve known inhibitors of thymidylate synthase and dihydrofolate reductase by screening molecular databases against the enzyme structures. Both algorithms retrieved many known inhibitors preferentially to other compounds in the database. The chemical matching algorithm generally ranks known inhibitors better than does matching based on shape alone.

Algorithms↗

PubMed1991

Protein docking and complementarity.

Predicting the structures of protein-protein complexes is a difficult problem owing to the topographical and thermodynamic complexity of these structures. Past efforts in this area have focussed on fitting the interacting proteins together using rigid body searches, usually with the conformations of the proteins as they occur in crystal structure complexes. Here we present work which uses a rigid body docking method to generate the structures of three known protein complexes, using both the bound and unbound conformations of the interacting molecules. In all cases we can regenerate the geometry of the crystal complexes to high accuracy. We also are able to find geometries that do not resemble the crystal structure but nevertheless are surprisingly reasonable both mechanistically and by some simple physical criteria. In contrast to previous work in this area, we find that simple methods for evaluating the complementarity at the protein-protein interface cannot distinguish between the configurations that resemble the crystal structure complex and those that do not. Methods that could not distinguish between such similar and dissimilar configurations include surface area burial, solvation free energy, packing and mechanism-based filtering. Evaluations of the total interaction energy and the electrostatic interaction energy of the complexes were somewhat better. Of the techniques that we tried, energy minimization distinguished most clearly between the "true" and "false" positives, though even here the energy differences were surprisingly small. We found the lowest total interaction energy from amongst all of the putative complexes generated by docking was always within 5 A root-mean-square of the crystallographic structure. There were, however, several putative complexes that were very dissimilar to the crystallographic structure but had energies that were close to that of the low energy structure. The magnitude of the error in energy calculations has not been established in macromolecular systems, and thus the reliability of the small differences in energy remains to be determined. The ability of this docking method to regenerate the crystallographic configurations of the interacting proteins using their unbound conformations suggests that it will be a useful tool in predicting the structures of unsolved complexes.

Algorithms↗