Combined use of NMR relaxation measurements and hydrodynamic calculations to study protein association. Evidence for tetramers of low molecular weight protein tyrosine phosphatase in solution

We describe a novel method for determining weak association constants of oligomeric protein complexes formed transiently under equilibrium conditions. This type of equilibrium process is recognized as being biologically important, but generally hard to study. Heteronuclear spin relaxation rates measured at multiple protein concentrations are analyzed using relaxation rates predicted from hydrodynamic calculations, yielding equilibrium constants and structural characterization of the protein complexes. The method was used to study the oligomerization equilibrium of bovine low molecular weight protein tyrosine phosphatase. X-ray structures of monomeric and dimeric forms of the protein have been reported previously. Using longitudinal and transverse (15)N relaxation rates measured at four different protein concentrations, we detected the monomer, dimer, and a previously unknown tetramer and measured the dissociation constants of the equilibria involving these species. A comparison of experimental and predicted relaxation rates for individual backbone amide (15)N spins enabled delineation of the tetramerization interface. The results suggest a novel concept for substrate modulation of enzymatic activity based on a "supramolecular proenzyme". The fast and reversible switching of the "supramolecular proenzyme" would have obvious advantages for the regulation of enzymes involved in cell signaling pathways.     

Internal rotation in squaramide and related compounds. A theoretical ab initio study

The structural and energetic changes associated with C–N bond rotation in a squaric acid derivative as well as in formamide, 3-aminoacrolein and vinylamine have been studied theoretically using ab initio molecular orbital methods. Geometry optimizations at the MP2(full)/6-31+G* level confirmed an increase in the C–N bond length and a smaller decrease in the C=O length on going from the equilibrium geometry to the twisted transition state. Other geometrical changes are also discussed. Energies calculated at the QCISD(T)/6-311+G** level, including zero-point-energy correction, show barrier heights decreasing in the order formamide, squaric acid derivative, 3-aminoacrolein and vinylamine. The origin of the barriers were examined using the atoms-in-molecules approach of Bader and the natural bond orbital population analysis. The calculations agree with Pauling's resonance model, and the main contributing factor of the barrier is assigned to the loss of conjugation on rotating the C–N bond. Finally, molecular interaction potential calculations were used to study the changes in the nucleophilicity of N and O (carbonyl) atoms upon C–N rotation, and to obtain a picture of the abilities of the molecules to act in nonbonded interactions, in particular hydrogen bonds. The molecular interaction potential results confirm the suitability of squaramide units for acting as binding units in host–guest chemistry. Received: 13 March 2002 / Accepted: 23 June 2002 / Published online: 21 August 2002     

Comparison between the geometric and electronic structures and reactivities of [FeNO]7 and [FeO2]8 complexes: a density functional theory study

In a previous study, we analyzed the electronic structure of S = 3/2 [FeNO](7) model complexes [Brown et al. J. Am. Chem. Soc. 1995, 117, 715-732]. The combined spectroscopic data and SCF-X alpha-SW electronic structure calculations are best described in terms of Fe(III) (S = 5/2) antiferromagnetically coupled to NO(-) (S = 1). Many nitrosyl derivatives of non-heme iron enzymes have spectroscopic properties similar to those of these model complexes. These NO derivatives can serve as stable analogues of highly labile oxygen intermediates. It is thus essential to establish a reliable density functional theory (DFT) methodology for the geometry and energetics of [FeNO](7) complexes, based on detailed experimental data. This methodology can then be extended to the study of [FeO(2)](8) complexes, followed by investigations into the reaction mechanisms of non-heme iron enzymes. Here, we have used the model complex Fe(Me(3)TACN)(NO)(N(3))(2) as an experimental marker and determined that a pure density functional BP86 with 10% hybrid character and a mixed triple-zeta/double-zeta basis set lead to agreement between experimental and computational data. This methodology is then applied to optimize the hypothetical Fe(Me(3)TACN)(O(2))(N(3))(2) complex, where the NO moiety is replaced by O(2). The main geometric differences are an elongated Fe[bond]O(2) and a steeper Fe[bond]O[bond]O angle in the [FeO(2)](8) complex. The electronic structure of [FeO(2)](8) corresponds to Fe(III) (S = 5/2) antiferromagnetically coupled to O(2)(-) (S = 1/2), and, consistent with the extended bond length, the [FeO(2)](8) unit has only one Fe(III)-O(2)(-) bonding interaction, while the [FeNO](7) unit has both sigma and pi type Fe(III)-NO(-) bonds. This is in agreement with experiment as NO forms a more stable Fe(III)-NO(-) adduct relative to O(2)(-). Although NO is, in fact, harder to reduce, the resultant NO(-) species forms a more stable bond to Fe(III) relative to O(2)(-) due to the different bonding interactions.     

Hankel operators on exponential Bergman spaces

We completely describe the boundedness and compactness of Hankel operators with general symbols acting on Bergman spaces with exponential type weights.     

Continuous minimax optimization using modal intervals

Many real life problems can be stated as a continuous minimax optimization problem. Well-known applications to engineering, finance, optics and other fields demonstrate the importance of having reliable methods to tackle continuous minimax problems. In this paper a new approach to the solution of continuous minimax problems over reals is introduced, using tools based on modal intervals. Continuous minimax problems, and global optimization as a particular case, are stated as the computation of semantic extensions of continuous functions, one of the key concepts of modal intervals. Modal intervals techniques allow to compute, in a guaranteed way, such semantic extensions by means of an efficient algorithm. Several examples illustrate the behavior of the algorithms in unconstrained and constrained minimax problems.     

Synthesis of novel, simplified, C-7 substituted eleutheside analogues with potent microtubule-stabilizing activity

The synthesis of a number of novel, simplified, C-7 substituted eleutheside analogues with potent tubulin-assembling and microtubule-stabilizing properties is described, using ring closing metathesis as the key-step for obtaining the 6-10 fused bicyclic ring system. The RCM precursors were synthesized starting from aldehyde 3 [prepared in six steps on a multigram scale from R-(−)-carvone in 30% overall yield] via multiple stereoselective Hafner-Duthaler allyltitanations and/or Brown allylborations. ‘Second generation’ RCM-catalyst 15 gave the desired ring closed ten-membered carbocycles as single Z stereoisomers in good yields. The RCM stereochemical course (100% Z) is likely to reflect thermodynamic control. Molecular mechanics and semi-empirical calculations also show that the Z stereoisomers of these ten-membered carbocycles are consistently more stable than the E. The crucial role of the homoallylic and allylic substituents and of their protecting groups for the efficiency of the RCM reactions is discussed. In particular, we have found that p-methoxyphenyl (PMP) protected allylic alcohols, the products of a stereoselective oxyallylation, are compatible with the RCM reaction and give better yields than the corresponding free allylic alcohols. One of the simplified analogues of the natural product (44, lacking inter alia the C-4/C-7 ether bridge) retains potent microtubule-stabilizing activity. However, the cytotoxicity tests did not parallel the potent tubulin-assembling and microtubule-stabilizing properties: limited cytotoxicity was observed against three common tumor cell lines (human ovarian carcinoma, human colon carcinoma and human leukemia cell lines, IC₅₀ in the μM range), approximately two orders of magnitude less than paclitaxel (IC₅₀ in the nM range). The mechanism of cell cycle arrest induced by compound 44 is similar to that obtained with paclitaxel.