Control of chaos in nonlinear systems with time-periodic coefficients.

In this study, some techniques for the control of chaotic nonlinear systems with periodic coefficients are presented. First, chaos is eliminated from a given range of the system parameters by driving the system to a desired periodic orbit or to a fixed point using a full-state feedback. One has to deal with the same mathematical problem in the event when an autonomous system exhibiting chaos is desired to be driven to a periodic orbit. This is achieved by employing either a linear or a nonlinear control technique. In the linear method, a linear full-state feedback controller is designed by symbolic computation. The nonlinear technique is based on the idea of feedback linearization. A set of coordinate transformation is introduced, which leads to an equivalent linear system that can be controlled by known methods. Our second idea is to delay the onset of chaos beyond a given parameter range by a purely nonlinear control strategy that employs local bifurcation analysis of time-periodic systems. In this method, nonlinear properties of post-bifurcation dynamics, such as stability or rate of growth of a limit set, are modified by a nonlinear state feedback control. The control strategies are illustrated through examples. All methods are general in the sense that they can be applied to systems with no restrictions on the size of the periodic terms.

Structures, mechanism, regulation and evolution of class III nucleotidyl cyclases.

Cyclic 3',5'-guanylyl and adenylyl nucleotides function as second messengers in eukaryotic signal transduction pathways and as sensory transducers in prokaryotes. The nucleotidyl cyclases (NCs) that catalyze the synthesis of these molecules comprise several evolutionarily distinct groups, of which class III is the largest. The domain structures of prokaryotic and eukaryotic class III NCs are diverse, including a variety of regulatory and transmembrane modules. Yet all members of this family contain one or two catalytic domains, characterized by an evolutionarily ancient topological motif (betaalphaalphabetabetaalphabeta) that is preserved in several other enzymes that catalyze the nucleophilic attack of a 3'-hydroxyl upon a 5' nucleotide phosphate. Two dyad-related catalytic domains compose one catalytic unit, with the catalytic sites formed at the domain interface. The catalytic domains of mononucleotidyl cyclases (MNCs) and diguanylate cyclases (DGCs) are called cyclase homology domains (CHDs) and GGDEF domains, respectively. Prokaryotic NCs usually contain only one catalytic domain and are catalytically active as intermolecular homodimers. The different modes of dimerization in class III NCs probably evolved concurrently with their mode of binding substrate. The catalytic mechanism of GGDEF domain homodimers is not completely understood, but they are expected to have a single active site with each subunit contributing equivalent determinants to bind one GTP molecule or half a c-diGMP molecule. CHD dimers have two potential dyad-related active sites, with both CHDs contributing determinants to each site. Homodimeric class III MNCs have two equivalent catalytic sites, although such enzymes may show half-of-sites reactivity. Eukaryotic class III MNCs often contain two divergent CHDs, with only one catalytically competent site. All CHDs appear to use a common catalytic mechanism, which requires the participation of two magnesium or manganese ions for binding polyphosphate groups and nucleophile activation. In contrast, mechanisms for purine recognition and specificity are more diverse. Class III NCs are subject to regulation by small molecule effectors, endogenous domains, or exogenous protein partners. Many of these regulators act by altering the interface of the catalytic domains and therefore the integrity of the catalytic site(s). This review focuses on both conserved and divergent mechanisms of class III NC function and regulation.

The PRT protein family.

Members of the homologous PRT family are catalytic and regulatory proteins involved in nucleotide synthesis and salvage. New crystal structures have revealed key elements of PRT protein function, as well as glimpses of how the fold has evolved to perform both catalytic and regulatory functions.

Catalytic antibody route to the naturally occurring epothilones: total synthesis of epothilones A-F.

Naturally occurring epothilones have been synthesized starting from enantiomerically pure aldol compounds 9-11, which were obtained by antibody catalysis. Aldolase antibody 38C2 catalyzed the resolution of (+/-)-9 by enantioselective retro-aldol reaction to afford 9 in 90% ee at 50 % conversion. Compounds 10 and 11 were obtained in more than 99% ee at 50% conversion by resolution of their racemic mixtures using newly developed aldolase antibodies 84G3, 85H6 or 93F3. Compounds 9, 10 and 11 were resolved in multigram quantities and then converted to the epothilones by metathesis processes, which were catalyzed by Grubbs' catalysts.

Synthesis of epothilone analogues by antibody-catalyzed resolution of thiazole aldol synthons on a multigram scale. Biological consequences of C-13 alkylation of epothilones.

Three monoclonal aldolase antibodies (84G3, 85H6, and 93F3), generated against a beta-diketone hapten (II) by the reactive immunization technique, catalyzed highly enantioselective retro-aldol reactions of the racemic thiazole aldols 13-20. Antibody 84G3 (0.0004-0.005 mol%) was used to resolve (+/-)-13-(+/-)-18 to afford compounds 13-18 in multigram quantities. Multiple 13-alkyl analogues of epothilone (7-12) and their trans isomers ((E)-7-(E)-12) were synthesized starting from thiazole aldols 13-18. Construction of the trisubstituted olefin moiety in compounds 7-12 and (E)-7-(E)-12 was catalyzed by Grubbs' catalyst (X). Initial biological testing with compounds 7-10 and their trans isomers showed that compounds 9, 10, and (E)-10 have appreciable tubulin polymerization and antiproliferative activities that approached those of epothilone C. The most active compound, (E)-9, even displayed potencies comparable to those observed for epothilones A and D. Interestingly, all trans analogues were more potent than their corresponding cis isomers. While introduction of an alkyl group at C-13 in the cis series led to an overall reduction in biological activity (compared to epothilone C), appropriate modification of the thiazole moiety (replacement of the 2-methyl substituent by a 2-methylthio group) was able to compensate for this loss. These results are encouraging in view of the expectation that epoxidations of these compounds should further increase their cellular activities. Thus, compounds 9, 10, and (E)-9 and (E)-10 represent highly promising candidates for further studies.

Total synthesis of asimicin and bullatacin.

The efficient total synthesis of asimicin, 1, and bullatacin, 2, has demonstrated the advantages of three different strategies for the synthesis of the tricyclic intermediates 6 and 7, which represent the key fragment of the bis-THF Annonaceous acetogenins. The naked carbon skeleton strategy is based on the production of all asymmetric centers by selective placement of the oxygen functions onto an unsaturated, nonfunctionalized carbon skeleton. Diversity in this approach arises from the relative timing of highly stereoselective reactions, such as the Sharpless asymmetric dihydroxylation (AD) reaction, the Kennedy oxidative cyclization (OC) with rhenium(VII) oxide, the Mitsunobu-type alcohol epimerization reaction, and the Williamson etherification reaction. The convergent strategy, which is based on the combinatorial coupling of two series of diastereomeric fragments, to produce intermediates such as 11 and 12, enjoys the advantages of both efficiency and versatility. The third approach, which is based on partially functionalized intermediates, such as 13, combines the advantages of both the linear and the convergent strategies-synthetic efficiency and diversity.

Treatment of true bifurcation stenosis by elective stent implantation in parent vessel and non-stent dilatation of side branch: immediate and follow-up results.

Data of 67 consecutive patients who underwent stent implantation in the parent vessel and non-stent dilatation of the side branch of a true bifurcation stenosis was retrospectively analysed. The mean age was 53.2 +/- 9.7 years, with majority (89.6%) being males. Forty-seven (70.1%) lesions involved the bifurcation of left anterior descending artery and its major diagonal branch. The parent vessel was treated using balloon angioplasty in 50 (74.6%), rotational atherectomy in 15 (22.4%) and directional coronary atherectomy in 2 (3.0%) patients. All the patients subsequently received an intracoronary stent in the parent vessel. Depending upon the treatment strategy for the side branch, the patients were divided into two groups: (1) Percutaneous transluminal coronary angioplasty group, which included 37 patients in whom the side branch was dilated by plain balloon angioplasty, and (2) Debulking group, in which 30 patients underwent debulking of the side branch using rotablation or directional coronary atherectomy. Overall, the procedure was successful in 64 (95.6%) patients. One (1.5%) patient developed non-Q wave myocardial infarction during the hospital stay. There were no Q-wave myocardial infarction, need for emergency coronary artery bypass surgery or death. Clinical follow-up of at least six months was available in all patients with a mean duration of 9.5 +/- 3.2 months. Recurrence of symptoms developed in 19 (28.4%) patients. Fourteen (20.9%) patients required target vessel revascularisation, of which 11 (29.7%) belonged to the percutaneous transluminal coronary angioplasty group and 3 (10.0%) to the debulking group, the difference being statistically significant (p = 0.045). The freedom from target vessel revascularisation was 93.1 and 89.4 percent at 6 and 12 months in the debulking group, compared to 78.4 and 68.9 percent at the same time in the percutaneous transluminal coronary angioplasty group. This study thus demonstrates that percutaneous intervention for true bifurcation stenosis with stent implantation in the parent vessel and non-stent dilatation in the side branch provides favourable immediate and follow-up results. Debulking in comparison to plain balloon angioplasty of the side branch results in further improvement in clinical outcome and need for target vessel revascularisation on follow-up.

High speed rotational atherectomy for diffuse in-stent restenosis: short- and mid-term follow-up results.

Between January 1997 to May 1998, 37 consecutive patients underwent high speed rotational atherectomy with adjunctive balloon angioplasty for the management of first-time diffuse variety of in-stent restenosis in the native coronary arteries. Their age ranged from 38 to 71 years (mean 54.3 +/- 9.7 years). All the patients underwent initial stent implantation at moderate to high pressure. Patients were either symptomatic or demonstrated significant ischaemia by non-invasive testing. The median time from the index procedure to in-stent restenosis was 20 weeks (range 9-40 weeks). Majority (78.1%) of lesions were in the territory of left anterior descending coronary artery. The mean lesion length was 24.3 +/- 8.3 mm (range 12-42 mm). Five lesions each (12.2%) were total occlusion and ostial in location. High speed rotational atherectomy was performed using stepped burr technique in majority (90.2%) with the largest burr corresponding to approximately 70 percent of the reference vessel diameter. The initial burr size ranged from 1.5-2.0 mm, final burr was 1.75-2.25 mm and the average number of burrs used per target vessel was 2.2 +/- 0.3 (range 1-3). Adjunctive balloon angioplasty was performed in all (100%) cases using a semi-compliant oversized balloon (balloon-to-artery ratio 1.1:1) inflated at a pressure of 6.5 +/- 2.1 atmospheres (range 4-10). The procedure was successful in all cases without any major complications (death, Q-MI, CABG or repeat PTCA). Over a median follow-up of 10 months, 27 (73%) patients were asymptomatic. Recurrence of clinical events occurred in 10 (27%) patients at median interval of 16 weeks after rotational atherectomy. Angina was controlled on drug therapy in six (16.2%) and target vessel revascularisation was required in three (8.1%) cases. By the Kaplan-Meier estimate, an event-free survival (absence of death, Q-MI, recurrence of angina, target vessel revascularisation) was 97.3, 94.6, 75.7 and 72.6 percent at 1, 3, 6 and 12 months, respectively. Thus, rotational atherectomy using a stepped burr approach for adequate debulking, followed by adjunctive balloon angioplasty is safe with excellent in-hospital results for the treatment of diffuse in-stent restenosis. Although recurrence of symptoms develops in approximately one-fourth of patients on follow-up, it is much less than reported with balloon angioplasty in this subgroup of patients.

Sets of aldolase antibodies with antipodal reactivities. Formal synthesis of epothilone E by large-scale antibody-catalyzed resolution of thiazole aldol.

[formula: see text] Three monoclonal aldolase antibodies, generated against a beta-diketone hapten by reactive immunization, catalyzed rapid and highly enantioselective retro-aldol reactions of ent-8a-k, providing optically pure 8a-k by kinetic resolution. Compounds (+/-)-8a, (+/-)-8g, and (+/-)-8k have been resolved in multigram quantities using 0.003, 0.005, and 0.0004 mol% antibody catalysts, respectively. Resolved compounds 8a-k are useful synthons for the construction of epothilones A-E (2-6) and their analogues. Here, a formal synthesis of epothilone E, 6 has been achieved starting from compound 8g.

The antibody catalysis route to the total synthesis of epothilones.

An efficient monoclonal aldolase antibody that proceeds by an enamine mechanism was generated by reactive immunization. Here, this catalyst has been used in the total synthesis of epothilones A (1) and C (3). The starting materials for the synthesis of these molecules have been obtained by using antibody-catalyzed aldol and retro-aldol reactions. These precursors were then converted to epothilones A (1) and C (3) to complete the total synthesis.

Elective stent implantation after optimal debulking for complex coronary lesions: acute and mid-term results.

Between January 1995 to December 1997, 45 patients with complex lesions in coronary arteries were treated by using the strategy of initial debulking with an atherectomy device followed by elective stenting. Their age ranged from 35-73 years (mean +/- SD:53.9 +/- 9.1) and 93.3 percent were males. The lesion morphology was type B1 in 14 (31.1%), B2 in 16 (35.6%) and type C in 13 (28.9%) patients. The choice of atherectomy device, based primarily on the morphology of lesion, was rotational atherectomy in 23 (51.1%) and directional coronary atherectomy in 22 (48.9%) patients. While majority (73.9%) of the lesions treated by rotablation were long, diffuse and calcified, directional atherectomy was preferred for highly eccentric stenoses in large-sized arteries. All patients underwent elective stent implantation after optimal lesion debulking using a mean burr size of 1.74 +/- 0.2mm for rotablation and a 7Fr. atherocath in majority (90.9%) of patients treated by directional coronary atherectomy. Angiographic success was achieved in all, while clinical success was 97.8 percent. One patient died of acute-on-chronic renal failure during hospitalisation. There were no other major in-hospital adverse cardiac events. At a median follow-up of 13 months (range 1-36 months), recurrence of angina developed in 10 (22.7%), out in which target lesion revascularisation was required in 5 (11.4%) and elective coronary artery bypass graft surgery in one (2.2%) patient. The event-free survival as calculated by the Kaplan-Meier method was 85.8 percent at six, 77.2 at 12 71.7 percent at 18 months of follow-up. In conclusion, optimal debulking before stent implantation provides a larger lumen, and thus eliminates sub-acute stent thrombosis in complex coronary lesions. This strategy also resulted in a high incidence of event-free survival and a low frequency of target lesion revascularisation on mid-term follow-up.

Immediate and follow-up clinical outcome after multivessel coronary stenting.

Seventy-two out of 656 patients treated by coronary stenting between January 1995 to May 1997 underwent elective multivessel stenting as a strategy for nonsurgical revascularization in patients with two-vessel (n = 37) and three-vessel (n = 35) disease. Their age ranged from 35 to 77 years (mean: 53.6 +/- 9.2) and the majority (77.8%) were males. The patients were included if the target vessel was more than 2.7 mm in diameter and subserved a moderate to large area of viable myocardium, provided the target lesion was considered approachable by stent. In all, 160 stents were deployed in 146 vessels with a mean of 2.2 stents per patient. The procedure was performed on all the target lesions in one stage in 51(70.8%) and two stages in 21(29.2%) patients. Two-vessel stenting was done in all except 2 patients who received stents in all the three major arteries. Successful deployment of the stent was achieved at the target site in all patients without any major in-hospital complications including subacute stent thrombosis, myocardial infarction (MI), emergency bypass graft surgery (CABG) or death. Clinical follow-up was available in 66(91.6%) patients at a mean of 7.8 +/- 5.5 months. The actuarial survival rates were 98.6, 96.7 and 94.6 percent, respectively at one, 3 and 6 to 12 months after the procedure with an event-free survival (absence of death, MI, recurrence of angina or any revascularization) of 98.5 percent at one, 93 percent at 3, 83.2 percent at 6 and 68.4 percent at 12 months. Only 15(22.7%) patients developed any event and target lesion revascularization was required in 8(12%) patients. In conclusion, multivessel stenting in patients with two- and three-vessel coronary disease is feasible, safe and effective in preventing major in-hospital complications as well as reducing the recurrence of clinical events and need for revascularization on follow-up.

Asymmetric organic synthesis with catalytic antibodies.

The science of catalytic antibodies has undergone a rapid maturation process within its first nine years of existence. From initial 'proof of concept' and demonstration of fundamental, enzyme-like characteristics, antibodies have been shown to catalyze a remarkably broad scope of organic transformations, including difficult and unfavorable chemical reactions. Yet, the ultimate testing ground for new concepts in organic chemistry has always been the synthesis of natural products. Here we focus on several issues related to the applicability of antibody catalysis in organic synthesis. We show that (a) in the hydrophobic environment of the antibody active site, short-lived intermediates can be formed and reacted in a controlled way, thus allowing antibodies to catalyze reactions that are normally incompatible with aqueous media, (b) the intrinsic order of reactivity (chemoselectivity) in a series of structurally related enol ethers and ketals can be inverted from 1:10 in the uncatalyzed hydrolysis reaction to 1000:1 under antibody catalysis, and (c) an efficient total synthesis of alpha-multistriatin, an important, biologically active natural product can be achieved via antibody catalysis.

Using antibodies to perturb the coordination sphere of a transition metal complex.

Metal ions in the active sites of many metalloenzymes exhibit distinctive spectral and chemical features which are different from those of small inorganic complexes. These features are the result of the unusual geometric and electronic constraints that are imposed on the metal ion within the protein environment. Much effort has been invested to try to mimic this feature of metalloenzymes in synthetic systems, but this remains a formidable task. Here we show that one of the key lessons learned from the science of catalytic antibodies--that binding energy can be converted into chemical energy--can be exploited to 'fine-tune' the physicochemical properties of a metal complex. We show that an antibody's binding site can reversibly perturb the coordination geometry of a metal ion, and can stabilize a high-energy coordinated species. Specifically, antibodies designed to bind the organosilicon compound 1 also bind the geometrically similar Cu(I) complex 2. However, the antibody binds a slightly compressed form of 2, which is closer in size to 1. This distortion is manifested by a spectral shift--an 'immunochromic' effect.

Antibody-catalyzed reversal of chemoselectivity.

A monoclonal antibody, 14D9, which has been elicited against a cationic hapten, N-alkyl-N-methyl-3-glutarylamidomethyl piperidinium, in which alkyl = [4-(2-hydroxyethylamido)carbonyl]phenylmethyl, is capable of inverting the intrinsic order of reactivity in a series of structurally related enol ethers and ketals towards hydrolysis. The order of reactivity of compounds 2 (1-methoxy-2-alkylcyclopent-1-ene), 3 (1-methoxy-5-alkylcylopent-1-ene), and 4 (1,1-dimethoxy-2-alkylcyclopentane) has changed from 0.09:0.17:1 in the uncatalyzed reaction to 1100:25:1 under antibody catalysis. Also, the order of reactivity of the three chemically similar ketals, 6a (1-alkyl-2,2-dimethoxypropane), 6b (1-alkyl-1-methyl-2,2-dimethoxypropane), and 4, has changed from 0.23:0.38:1 in the uncatalyzed hydrolysis to 100:9:1 within the antibody active site. As all compounds bind the antibody with very similar affinities, these effects cannot be simply attributed to selective binding by the antibody. In fact, ketal 4, which shows no measurable catalysis, acts as a competitive inhibitor of 14D9-catalyzed hydrolysis of 6a. Both the solution and the antibody-catalyzed hydrolysis of the ketal substrates are shown to be specific acid catalyzed, involving the unimolecular cleavage of the protonated substrate or antibody-substrate complex in the rate-determining step. Reactivity effects from the acid catalyst itself on ketal hydrolysis (reagent-controlled reactivity) are ruled out under this mechanistic scheme.

Physalindicanols, New Biogenetic Precursors of C28-Steroidal Lactones from Physalis minima var. indica.

The structures of two isomeric C (28)-sterols isolated from PHYSALIS MINIMA Linn. var. INDICA were elucidated as ergosta-5,25-dien-3beta,24zeta,-diol and ergosta-5,24(28)-dien-3beta,25-diol on the basis of detailed spectral analysis. The isolated sterols are regarded as precursors in the elaboration of complex C (28)-steroidal lactones, native in this plant and related species.