The intramolecular Buchner reaction of α-diazo-β-ketonitriles : development and application to the total synthesis of (+)-Salvileucalin B

Since its discovery in 1896, the Buchner reaction has fascinated chemists for more than a century. The highly reactive nature of the carbene intermediates allows for facile dearomatization of stable aromatic rings, and provides access to a diverse array of cyclopropane and seven-membered ring architectures. The power inherent in this transformation has been exploited in the context of a natural product total synthesis and methodology studies.

The total synthesis work details efforts employed in the enantioselective total synthesis of (+)-salvileucalin B. The fully-substituted cyclopropane within the core of the molecule arises from an unprecedented intramolecular Buchner reaction involving a highly functionalized arene and an α-diazo-β-ketonitrile. An unusual retro-Claisen rearrangement of a complex late-stage intermediate was discovered on route to the natural product.

The unique reactivity of α-diazo-β-ketonitriles toward arene cyclopropanation was then investigated in a broader methodological study. This specific di-substituted diazo moiety possesses hitherto unreported selectivity in intramolecular Buchner reactions. This technology was enables the preparation of highly functionalized norcaradienes and cyclopropanes, which themselves undergo various ring opening transformations to afford complex polycyclic structures.

Finally, an enantioselective variant of the intramolecular Buchner reaction is described. Various chiral copper and dirhodium catalysts afforded moderate stereoinduction in the cyclization event.

A unified strategy to ent-kauranoid natural products : total syntheses of (–)-maoecrystal Z, (–)-trichorabdal A, and (–)-longikaurin E

The diterpenoid constituents of the Isodon plants have attracted reasearchers interested in both their chemical structures and biological properties for more than a half-century. In recent years, the isolations of new members displaying previously unprecedented ring systems and highly selective biological properties have piqued interest from the synthetic community in this class of natural products.

Reported herein is the first total synthesis of such a recently isolated diterpenoid, (–)-maoecrystal Z. The principal transformations implemented in this synthesis include two highly diastereoselective radical cyclization reactions: a Sm^(II)-mediated reductive cascade cyclization, which forms two rings and establishes four new stereocenters in a single step, and a Ti^(III)-mediated reductive epoxide-acrylate coupling that yields a functionalized spirolactone product, which forms a core bicycle of maoecrystal Z.

The preparation of two additional ent-kauranoid natural products, (–)-trichorabdal A and (–)-longikaurin E, is also described from a derivative of this key spirolactone. These syntheses are additionally enabled by the palladium-mediated oxidative cyclization reaction of a silyl ketene acetal precursor that is used to install the bridgehead all-carbon quaternary stereocenter and bicyclo[3.2.1]octane present in each natural product. These studies have established a synthetic relationship among three architecturally distinct ent-kaurane diterpenoids and have forged a path for the preparation of interesting unnatural ent-kauranoid structural analogs for more thorough biological study.

Model studies of Ziegler-Natta olefin polymerization using group 3 and group 4 metallocenes

Evidence for the stereochemical isomerization of a variety of ansa metallocene compounds is presented. For the scandocene allyl derivatives described here, we have established that the process is promoted by a variety of salts in both ether and hydrocarbon solvents and is not accelerated by light. A plausible mechanism based on an earlier proposal by Marks, et al., is offered as an explanation of this process. It involves coordination of anions and/or donor solvents to the metal center with cation assistance to encourage metalcyclopentadienyl bond heterolysis, rotation about the Si-Cp bond of the detached cyclopentadienide and recoordination of the opposite face. Our observations in some cases of thermodynamic racemic:meso ratios under the reaction conditions commonly used for the synthesis of the metallocene chlorides suggests that the interchange is faster than metallation, such that the composition of the reaction mixture is determined by thermodynamic, not kinetic, control in these cases.

Two new ansa-scandocene alkenyl compounds react with olefins resulting in the formation of η³-allyl complexes. Kinetics and labeling experiments indicate a tuck-in intermediate on the reaction pathway; in this intermediate the metal is bound to the carbon adjacent to the silyllinker in the rear of the metallocene wedge. In contrast, reaction of permethylscandocene alkenyl compounds with olefins results, almost exclusively, in vinylic C-H bond activation. It is proposed that relieving transition state steric interactions between the cyclopentadienyl rings and the olefin by either linking the rings together or using a larger lanthanide metal may allow for olefin coordination, stabilizing the transition state for allylic σ-bond metathesis.

A selectively isotopically labeled propylene, CH₂CD(¹³CH₃), was synthesized and its polymerization was carried out at low concentration in toluene solution using isospecific metallocene catalysts. Analysis of the NMR spectra (¹³C, ¹H, and ²H) of the resultant polymers revealed that the production of stereoerrors through chain epimerization proceeds exclusively by the tertiaryalkyl mechanism. Additionally, enantiofacial inversion of the terminally unsaturated polymer chain occurs by a non-dissociative process. The implications of these results on the mechanism of olefin polymerization with these catalysts is discussed.

Some constructions, related to noncommutative tori; Fredholm modules and the Beilinson-Bloch regulator

A noncommutative 2-torus is one of the main toy models of noncommutative geometry, and a noncommutative n-torus is a straightforward generalization of it. In 1980, Pimsner and Voiculescu in [17] described a 6-term exact sequence, which allows for the computation of the K-theory of noncommutative tori. It follows that both even and odd K-groups of n-dimensional noncommutative tori are free abelian groups on 2^n-1 generators. In 1981, the Powers-Rieffel projector was described [19], which, together with the class of identity, generates the even K-theory of noncommutative 2-tori. In 1984, Elliott [10] computed trace and Chern character on these K-groups. According to Rieffel [20], the odd K-theory of a noncommutative n-torus coincides with the group of connected components of the elements of the algebra. In particular, generators of K-theory can be chosen to be invertible elements of the algebra. In Chapter 1, we derive an explicit formula for the First nontrivial generator of the odd K-theory of noncommutative tori. This gives the full set of generators for the odd K-theory of noncommutative 3-tori and 4-tori.

In Chapter 2, we apply the graded-commutative framework of differential geometry to the polynomial subalgebra of the noncommutative torus algebra. We use the framework of differential geometry described in [27], [14], [25], [26]. In order to apply this framework to noncommutative torus, the notion of the graded-commutative algebra has to be generalized: the "signs" should be allowed to take values in U(1), rather than just {-1,1}. Such generalization is well-known (see, e.g., [8] in the context of linear algebra). We reformulate relevant results of [27], [14], [25], [26] using this extended notion of sign. We show how this framework can be used to construct differential operators, differential forms, and jet spaces on noncommutative tori. Then, we compare the constructed differential forms to the ones, obtained from the spectral triple of the noncommutative torus. Sections 2.1-2.3 recall the basic notions from [27], [14], [25], [26], with the required change of the notion of "sign". In Section 2.4, we apply these notions to the polynomial subalgebra of the noncommutative torus algebra. This polynomial subalgebra is similar to a free graded-commutative algebra. We show that, when restricted to the polynomial subalgebra, Connes construction of differential forms gives the same answer as the one obtained from the graded-commutative differential geometry. One may try to extend these notions to the smooth noncommutative torus algebra, but this was not done in this work.

A reconstruction of the Beilinson-Bloch regulator (for curves) via Fredholm modules was given by Eugene Ha in [12]. However, the proof in [12] contains a critical gap; in Chapter 3, we close this gap. More specifically, we do this by obtaining some technical results, and by proving Property 4 of Section 3.7 (see Theorem 3.9.4), which implies that such reformulation is, indeed, possible. The main motivation for this reformulation is the longer-term goal of finding possible analogs of the second K-group (in the context of algebraic geometry and K-theory of rings) and of the regulators for noncommutative spaces. This work should be seen as a necessary preliminary step for that purpose.

For the convenience of the reader, we also give a short description of the results from [12], as well as some background material on central extensions and Connes-Karoubi character.

A dynamical systems analysis of vortex pinch-off

Vortex rings constitute the main structure in the wakes of a wide class of swimming and flying animals, as well as in cardiac flows and in the jets generated by some moss and fungi. However, there is a physical limit, determined by an energy maximization principle called the Kelvin-Benjamin principle, to the size that axisymmetric vortex rings can achieve. The existence of this limit is known to lead to the separation of a growing vortex ring from the shear layer feeding it, a process known as `vortex pinch-off', and characterized by the dimensionless vortex formation number. The goal of this thesis is to improve our understanding of vortex pinch-off as it relates to biological propulsion, and to provide future researchers with tools to assist in identifying and predicting pinch-off in biological flows.

To this end, we introduce a method for identifying pinch-off in starting jets using the Lagrangian coherent structures in the flow, and apply this criterion to an experimentally generated starting jet. Since most naturally occurring vortex rings are not circular, we extend the definition of the vortex formation number to include non-axisymmetric vortex rings, and find that the formation number for moderately non-axisymmetric vortices is similar to that of circular vortex rings. This suggests that naturally occurring vortex rings may be modeled as axisymmetric vortex rings. Therefore, we consider the perturbation response of the Norbury family of axisymmetric vortex rings. This family is chosen to model vortex rings of increasing thickness and circulation, and their response to prolate shape perturbations is simulated using contour dynamics. Finally, the response of more realistic models for vortex rings, constructed from experimental data using nested contours, to perturbations which resemble those encountered by forming vortices more closely, is simulated using contour dynamics. In both families of models, a change in response analogous to pinch-off is found as members of the family with progressively thicker cores are considered. We posit that this analogy may be exploited to understand and predict pinch-off in complex biological flows, where current methods are not applicable in practice, and criteria based on the properties of vortex rings alone are necessary.

Directed evolution of terpene synthases for non-natural substrates

Terpenes represent about half of known natural products, with terpene synthases catalyzing reactions to increase the complexity of substrates and generate cyclizations of the linear diphosphate substrates, therefore forming rings and stereocenters. With their diverse functionality, terpene synthases may be highly evolvable, with the ability to accept a wide range of non-natural compounds and with high product selectivity. Our hypothesis is that directed evolution of terpene synthases can be used to increase selectivity of the synthase on a specific substrate. In the first part of the work presented herein, three natural terpene synthases, Cop2, BcBOT2, and SSCG_02150, were tested for activity against the natural substrate and a non-natural substrate, called Surrogate 1, and the relative activities on both the natural and non-natural substrates were compared. In the second part of this work, a terpene synthase variant of BcBOT2 that has been evolved for thermostability, was used for directed evolution for increased activity and selectivity on the non-natural substrate referred to as Surrogate 2. Mutations for this evolution were introduced using random mutagenesis, with error prone polymerase chain reactions, and using site-specific saturation mutagenesis, in which an NNK library is designed with a specific active site amino acid targeted for mutation. The mutant enzymes were then screened and selected for enhancement of the desired functionality. Two neutral mutants, 19B7 W367F and 19B7 W118Q, were found to maintain activity on Surrogate 2, as measured by the screen.

Dynamics and scaling of self-excited passive vortex generators for underwater propulsion

A series of experiments was conducted on the use of a device to passively generate vortex rings, henceforth a passive vortex generator (PVG). The device is intended as a means of propulsion for underwater vehicles, as the use of vortex rings has been shown to decrease the fuel consumption of a vehicle by up to 40% Ruiz (2010).

The PVG was constructed out of a collapsible tube encased in a rigid, airtight box. By adjusting the pressure within the airtight box while fluid was flowing through the tube, it was possible to create a pulsed jet with vortex rings via self-excited oscillations of the collapsible tube.

A study of PVG integration into an existing autonomous underwater vehicle (AUV) system was conducted. A small AUV was used to retrofit a PVG with limited alterations to the original vehicle. The PVG-integrated AUV was used for self-propelled testing to measure the hydrodynamic (Froude) efficiency of the system. The results show that the PVG-integrated AUV had a 22% increase in the Froude efficiency using a pulsed jet over a steady jet. The maximum increase in the Froude efficiency was realized when the formation time of the pulsed jet, a nondimensional time to characterize vortex ring formation, was coincident with vortex ring pinch-off. This is consistent with previous studies that indicate that the maximization of efficiency for a pulsed jet vehicle is realized when the formation of vortex rings maximizes the vortex ring energy and size.

The other study was a parameter study of the physical dimensions of a PVG. This study was conducted to determine the effect of the tube diameter and length on the oscillation characteristics such as the frequency. By changing the tube diameter and length by factors of 3, the frequency of self-excited oscillations was found to scale as f~D_0^{-1/2} L_0^0, where D_0 is the tube diameter and L_0 the tube length. The mechanism of operation is suggested to rely on traveling waves between the tube throat and the end of the tube. A model based on this mechanism yields oscillation frequencies that are within the range observed by the experiment.

Studies directed toward the synthesis of palau'amine and axinellamines A-D

The use of spiro [2.4]hepta-4,6-diene-1-methanol 7 as a general precursor for the synthesis of highly functionalized cyclopentyl rings is described. Diene 7 was converted to its silyl protected 4-nitrile derivative 24 in 46% overall yield. The cyclopropyl ring of 24 reacted with soft carbanionic nucleophiles to give ring opened homo-conjugate addition products 25a-h in 76-97% yield without loss of optical purity. The addition products could be further manipulated by selective mono-hydrogenation to give 1,2 substituted cyclopentenes 26a-e in 85-96% yield.

Diene 7 was used as a starting material for studies directed toward the synthesis of the stereochemically dense chloro-cyclopentyl core of palau'amine 1. Two advanced intermediates 50 and 72 were synthesized. Attempts to effect intramolecular chlorine transfer with 50 were unsuccessful. Attempted intramolecular chlorine transfer with 72 led, instead, to an oxygenated species resulting from oxygen radical trapping.

The enantioselective synthesis of the stereochemically dense chloro-cyclopenty l core of axinellamines A-D 2-5 starting from 7 is also described. The core is synthesized in 4.6% yield over 24 steps. Nakamura's radical dehalogenative hydroxylation is applied for the first time to a cyclopropyl carbonyl iodide to give the ring-opened product in 86% yield. Bolm's meso-anhydride desymmetrization is used to introduce asymmetry in a norbornene intermediate. The final step is a diastereoselective intermolecular chlorination using Barton's methodology to achieve chlorine transfer in 76% yield.

Applications of nuclear magnetic resonance spectroscopy to the study of medium-sized rings. I. Conformational properties of cycloheptane. II. Conformational properties of cycloöctane

Conformational equilibrium in medium-sized rings has been investigated by the temperature variation of the fluorine-19 n.m.r. spectra of 1, 1-difluorocycloalkanes and various substituted derivatives of them. Inversion has been found to be fast on the n.m.r. time scale at -180˚ for 1, 1-difluorocycloheptane, but slow for 1, 1-difluoro-4, 4-dimethylcycloheptane at -150˚. At low temperature, the latter compound affords a single AB pattern with a chemical-shift difference of 841 cps. which has been interpreted in terms of the twist-chair conformation with the methyl groups on the axis position and the fluorine atoms in the 4-position. At room temperature, the n.m.r. spectrum of 1, 1-difluoro-4-t-butylcycloheptane affords an AB pattern with a chemical-shift difference of 185 cps. The presence of distinct trans and gauche couplings from the adjacent hydrogens has been interpreted to suggest the existence of a single predominant form, the twist chair with the fluorine atoms on the axis position.

Investigation of 1, 1-difluorocycloöctane and 1, 1, 4, 4-tetrafluorocycloöctane has led to the detection of two kinetic processes both having activation energies of 8-10 kcal./mole but quite different A values. In light of these results eleven different conformations of cycloöctane along with a detailed description of the ways in which they may be interconverted are discussed. An interpretation involving the twist-boat conformation rapidly equilibrating through the saddle and the parallel-boat forms at room temperature is compatible with the results.

Rings faithfully represented on their left socle

In 1964 A. W. Goldie [1] posed the problem of determining all rings with identity and minimal condition on left ideals which are faithfully represented on the right side of their left socle. Goldie showed that such a ring which is indecomposable and in which the left and right principal indecomposable ideals have, respectively, unique left and unique right composition series is a complete blocked triangular matrix ring over a skewfield. The general problem suggested above is very difficult. We obtain results under certain natural restrictions which are much weaker than the restrictive assumptions made by Goldie.

We characterize those rings in which the principal indecomposable left ideals each contain a unique minimal left ideal (Theorem (4.2)). It is sufficient to handle indecomposable rings (Lemma (1.4)). Such a ring is also a blocked triangular matrix ring. There exist r positive integers K₁,..., K_r such that the i,j^th block of a typical matrix is a K_i x K_j matrix with arbitrary entries in a subgroup D_ij of the additive group of a fixed skewfield D. Each D_ii is a sub-skewfield of D and D_ri = D for all i. Conversely, every matrix ring which has this form is indecomposable, faithfully represented on the right side of its left socle, and possesses the property that every principal indecomposable left ideal contains a unique minimal left ideal.

The principal indecomposable left ideals may have unique composition series even though the ring does not have minimal condition on right ideals. We characterize this situation by defining a partial ordering ρ on {i, 2,...,r} where we set iρj if D_ij ≠ 0. Every principal indecomposable left ideal has a unique composition series if and only if the diagram of ρ is an inverted tree and every D_ij is a one-dimensional left vector space over D_ii (Theorem (5.4)).

We show (Theorem (2.2)) that every ring A of the type we are studying is a unique subdirect sum of less complex rings A₁,...,A_s of the same type. Namely, each A_i has only one isomorphism class of minimal left ideals and the minimal left ideals of different A_i are non-isomorphic as left A-modules. We give (Theorem (2.1)) necessary and sufficient conditions for a ring which is a subdirect sum of rings A_i having these properties to be faithfully represented on the right side of its left socle. We show ((4.F), p. 42) that up to technical trivia the rings A_i are matrix rings of the form

[...]. Each Q_j comes from the faithful irreducible matrix representation of a certain skewfield over a fixed skewfield D. The bottom row is filled in by arbitrary elements of D.

In Part V we construct an interesting class of rings faithfully represented on their left socle from a given partial ordering on a finite set, given skewfields, and given additive groups. This class of rings contains the ones in which every principal indecomposable left ideal has a unique minimal left ideal. We identify the uniquely determined subdirect summands mentioned above in terms of the given partial ordering (Proposition (5.2)). We conjecture that this technique serves to construct all the rings which are a unique subdirect sum of rings each having the property that every principal-indecomposable left ideal contains a unique minimal left ideal.

The binding and catalytic properties of lysozyme

The binding and catalytic properties of hen's egg white lysozyme have been studied by a variety of techniques. These studies show that the enzyme has three contiguous binding subsites, A, B, and C. The application of nuclear magnetic resonance (NMR) spectroscopy to probe the binding environment of several saccharides to lysozyme has demonstrated that the reducing end sugar rings of chitotriose, chitobiose and the β-form of N-acetylglucosamine all bind in subsite C. The central sugar ring of chitotriose and the sugar ring at the nonreducing end of chitobiose were found to bind in subsite B, while the nonreducing end sugar residue of chitotriose occupied subsite A. The dynamics of the binding process has also been investigated by NMR. The formation rate constant of chitobiose--and chitotriose-enzyme complexes were found to be about 4 X 10^-6 M^-1 sec^-1 with small activation energies.

The stereochemical path of the lysozyme catalyzed hydrolysis of glycosidic bonds has been shown to proceed with at least 99.7% retention of configuration at C-1 of the sugar. The lysozyme catalyzed hydrolysis of glucosidic bonds has been shown to be largely carbonium ion in character by virtue of the α-deuterium kinetic isotope effect (k_H/k_D = 1.11) observed for the reaction. It is probable that the mechanism of action of the enzyme involves a carbonium ion intermediate which is stereospecifically quenched by solvent. However, acetamido group participation cannot be ruled out for natural substrates.

Structure theorems for noncommutative complete local rings

If R is a ring with identity, let N(R) denote the Jacobson radical of R. R is local if R/N(R) is an artinian simple ring and ∩N(R)ⁱ = 0. It is known that if R is complete in the N(R)-adic topology then R is equal to (B)_n, the full n by n matrix ring over B where E/N(E) is a division ring. The main results of the thesis deal with the structure of such rings B. In fact we have the following.

If B is a complete local algebra over F where B/N(B) is a finite dimensional normal extension of F and N(B) is finitely generated as a left ideal by k elements, then there exist automorphisms g_i,...,g_k of B/N(B) over F such that B is a homomorphic image of B/N[[x₁,…,x_k;g₁,…,g_k]] the power series ring over B/N(B) in noncommuting indeterminates x_i, where x_ib = g_i(b)x_i for all b ϵ B/N.

Another theorem generalizes this result to complete local rings which have suitable commutative subrings. As a corollary of this we have the following. Let B be a complete local ring with B/N(B) a finite field. If N(B) is finitely generated as a left ideal by k elements then there exist automorphisms g₁,…,g_k of a v-ring V such that B is a homomorphic image of V [[x₁,…,x_k;g₁,…,g_k]].

In both these results it is essential to know the structure of N(B) as a two sided module over a suitable subring of B.