Dissection of complex molecular recognition interfaces

The synthesis of a family of zinc porphyrins and pyridine ligands equipped with peripheral H-bonding functionality has provided access to a wide range of closely related supramolecular complexes featuring between zero and four intramolecular H-bonds. An automated UV/vis titration system was used to characterize 120 different complexes, and these data were used to construct a large of number of different chemical double mutant cycles to quantify the intramolecular H-bonding interactions. The results probe the quantitative structure-activity relationship that governs cooperativity in the assembly of complex molecular recognition interfaces. Specifically, variations in the chemical structures of the complexes have allowed us to change the supramolecular architecture, conformational flexibility, geometric complementarity, the number and nature of the H-bond interactions, and the overall stability of the complex. The free energy contributions from individual H-bonds are additive, and there is remarkably little variation with architecture in the effective molarity for the formation of intramolecular interactions. Intramolecular H-bonds are not observed in complexes where they are geometrically impossible, but there are no cases where excellent geometric complementarity leads to very high affinities. Similarly, changes in conformational flexibility seem to have limited impact on the values of effective molarity (EM). The major variation that was found for all of the 48 intramolecular interactions that were examined using double mutant cycles is that the values of EM for intramolecular carboxylate ester-phenol H-bonds (200 mM) are an order of magnitude larger than those found for phosphonate diester-phenol H-bonds (30 mM). The corresponding intermolecular phosphonate diester-phenol H-bonds are 2 orders of magnitude more stable than carboxylate ester-phenol H-bonds, and the large differences in EM may be due to some kind of compensation effect, where the stronger H-bond is harder to make, because it imposes tighter constraints on the geometry of the complex.     

Relationship between conformational flexibility and chelate cooperativity

A family of four biscarbamates (AA) and four bisphenols (DD) were synthesized, and H-bonding interactions between all AA?DD combinations were characterized using (1)H NMR titrations in carbon tetrachloride. A chemical double mutant cycle analysis shows that there are no secondary electrostatic interactions or allosteric cooperativity in these systems, and the system therefore provides an ideal platform for investigating the relationship between chemical structure and chelate cooperativity. Effective molarities (EMs) were measured for 12 different systems, where the number of rotors in the chains connecting the two H-bond sites was varied from 5 to 20. The association constants vary by less than an order of magnitude for all 12 complexes, and the variation in EM is remarkably small (0.1-0.9 M). The results provide a relationship between EM and the number of rotors in the connecting chains (r): EM ≈ 10r(-3/2). The value of 10 M is the upper limit for the value of EM for a noncovalent intramolecular interaction. Introduction of rotors reduces the value of EM from this maximum in accord with a random walk analysis of the encounter probability of the chain ends (r(-3/2)). Noncovalent EMs never reach the very high values observed for covalent processes, which places limitations on the magnitudes of the effects that one is likely to achieve through the use of chelate cooperativity in supramolecular assembly and catalysis. On the other hand, the decrease in EM due to the introduction of conformational flexibility is less dramatic than one might expect based on the behavior of covalent systems, which limits the losses in binding affinity caused by poor preorganization of the interaction sites.     

Probing the limits of rate acceleration mediated by hydrogen bonds

[Structure: see text] A simple receptor and substrate are used to probe the relationship between transition-state charge and the level of rate acceleration that can be created by stabilizing the transition state through hydrogen bonding. Pericyclic reactions are accelerated less than 2-fold by the receptor, whereas a conjugate addition reaction is accelerated more than 30-fold. Therefore, substrate polarization by hydrogen bonding would only appear to be effective for reactions that generate significant charge at the transition state.     

Simple Zeros of the Riemann Zeta-Function

Assuming the Riemann Hypothesis, Montgomery showed by meansof his pair correlation method that at least two-thirds of thezeros of Riemann's zeta-function are simple. Later he and Taylorimproved this to 67.25 percent and, more recently, Cheer andGoldston increased the percentage to 67.2753. Here we proveby a new method that if the Riemann and Generalized LindelöofHypotheses hold, then at least 70.3704 percent of the zerosare simple and at least 84.5679 percent are distinct. Our methoduses mean value estimates for various functions defined by Dirichletseries sampled at the zeros of the Riemann zeta-function. 1991Mathematics Subject Classification: 11M26.     

Quantum Zeno and anti-Zeno paradoxes

Continuous observation of a time independent projection operator is known to prevent change of state (the quantum Zeno paradox). We discuss the recent result that generic continuous measurement of time dependent projection operators will in fact ensure change of state: an anti-Zeno paradox.     

粉粒体两相流的电容层析成象测量

粉粒体系统中的固相浓度分布的在线测量是十分困难的问题．电容层析成象技术是一种近年来发展起来的非侵入式快速浓度场测量技术．它不干扰流场，不受流动中颗粒浓度、加速度、不透明等因素的制约．本文讨论其测量原理、应用、近期进展、存在的主要问题及其解决的对策．     

ac Conductivity of mixed spinel NiAl0.7Cr0.7Fe0.6O4

ac Conductivity measurements are carried out across the metal to insulator transition in NiAl_0.7Cr_0.7Fe_0.6O₄. The low frequency data is analyzed using Summerfield scaling theory for hopping conductivity. The exponent of the scaling behavior has significantly different values in the conducting and insulating regimes. The hopping frequency and the zero frequency conductivity are found to increase with temperature, slowly in the metallic regime and rapidly in the insulating regime.