Stereoselective total syntheses and reassignment of stereochemistry of the freshwater cyanobacterial hepatotoxins cylindrospermopsin and 7-epicylindrospermopsin

A stereoselective total synthesis of the structure 1 proposed for the freshwater cyanobacterial heptatotoxin cylindrospermopsin has been accomplished in approximately 30 operations starting from commercially available 4-methoxypyridine. Utilizing methodology developed by Comins, the tetrasubstituted piperidine A-ring unit of the hepatotoxin was efficiently constructed. The two remaining stereocenters in the natural product were then set by a stereospecific intramolecular N-sulfinylurea Diels-Alder cyclization/Grignard ring opening/allylic sulfoxide [2,3]-sigmatropic rearrangement sequence previously developed in these laboratories, leading to key intermediate 29. The stereochemical assignment of alcohol 29, which contains all six of the stereogenic centers of the natural product, was confirmed by an X-ray crystal structure determination of a derivative. Installation of the D-ring uracil moiety was effected by using our new methodology developed for this purpose, and construction of the C-ring guanidine completed the total synthesis of racemic structure 1. However, the (1)H NMR data for this compound do not match that of cylindrospermopsin, but instead agree with the data reported for 7-epicylindrospermopsin, a minor toxic metabolite that co-occurs with cylindrospermopsin. Therefore, we propose a revision of the stereochemical assignments of these natural products such that cylindrospermopsin is now represented as structure 2 and 7-epicylindrospermopsin is 1. This reassignment was further confirmed by Mitsunobu inversion of the C-7 alcohol 51 to epimer 52, and conversion of this compound to tetracyclic diol 57, which has previously been transformed to cylindrospermopsin (2).     

Interfacial pattern formation far from equilibrium

Over the past few years diffusion-controlled systems have been shown to share a common set of interfacial morphologies. The singular nature of the microscopic dynamics of surface tension and kinetic growth far from equilibrium are critical to morphology selection, with special importance attributed to the anisotropy of these effects. The morphologies which develop can be organized via a morphology diagram according to the driving force and the effective anisotropy. We focus on the properties of the dense-branching morphology (DBM) which appears for sufficiently weak effective anisotropy, and the nature of morphology transitions between the DBM and dendritic growth stabilized by either surface tension or kinetic effects. The DBM is studied in the Hele-Shaw cell, and its structure analyzed by linear stability analysis. A comparison is made between the power spectrum of the structure and the stability analysis. We then provide a detailed account of the morphology diagram and morphology transitions in an anisotropic Hele-Shaw cell. Theoretically the question of morphology transitions is addressed within the boundary-layer model by computing selected velocities as a function of the undercooling for different values of the surface tension and the kinetic term. We argue that the fastest growing morphology is selected whether it is the DBM, surface tension dendrites, or kinetic dendrites. A comparison is made with our experimental results in electrochemical deposition for the correspondence between growth velocities and morphology transitions.     

Kinetically locked-in colloidal transport in an array of optical tweezers

We describe measurements of colloidal transport through arrays of micrometer-scale potential wells created with holographic optical tweezers. Varying the orientation of the trap array relative to the external driving force results in a hierarchy of lock-in transitions analogous to symmetry-selecting processes in a wide variety of systems. Focusing on colloid as a model system provides the first opportunity to observe the microscopic mechanisms of kinetic lock-in transitions and reveals a new class of statistically locked-in states. This particular realization also has immediate applications for continuously fractionating particles, biological cells, and macromolecules.     

Structure of optical vortices

Helical modes of light can be focused into toroidal optical traps known as optical vortices, which are capable of localizing and applying torques to small volumes of matter. Measurements of optical vortices created with the dynamic holographic optical tweezer technique reveal an unsuspected dependence of their structure and angular momentum flux on their helicity. These measurements also provide evidence for a novel optical ratchet potential in practical optical vortices.     

Measuring a colloidal particle's interaction with a flat surface under nonequilibrium conditions

A new and general approach is proposed to analyze the dynamics of a colloidal particle interacting with a nearby wall. This analysis can be used to determine the acting forces even when the system is non-stationary. As an illustration, we use total internal reflection microscopy to investigate the forces acting on a polystyrene sulfate latex particle as it is receding from a charged glass surface. Received 10 October 2002 Published online: 16 April 2003 RID="a" ID="a"Present address: Department of Polymer Physics, BASF Aktiengesellschaft, 67056 Ludwigshafen, Germany RID="b" ID="b"Present address: Arryx. Inc., Chicago, IL 60601, USA     

Test-Based Variable Selection via Cross-Validation

Abstract

Test-based variable selection algorithms in regression often are based on sequential comparison of test statistics to cutoff values. A predetermined a level typically is used to determine the cutoffs based on an assumed probability distribution for the test statistic. For example, backward elimination or forward stepwise involve comparisons of test statistics to prespecified t or F cutoffs in Gaussian linear regression, while a likelihood ratio. Wald, or score statistic, is typically used with standard normal or chi square cutoffs in nonlinear settings. Although such algorithms enjoy widespread use, their statistical properties are not well understood, either theoretically or empirically. Two inherent problems with these methods are that (1) as in classical hypothesis testing, the value of α is arbitrary, while (2) unlike hypothesis testing, there is no simple analog of type I error rate corresponding to application of the entire algorithm to a data set. In this article we propose a new method, backward elimination via cross-validation (BECV), for test-based variable selection in regression. It is implemented by first finding the empirical p value α*, which minimizes a cross-validation estimate of squared prediction error, then selecting the model by running backward elimination on the entire data set using α* as the nominal p value for each test. We present results of an extensive computer simulation to evaluate BECV and compare its performance to standard backward elimination and forward stepwise selection.     

Influence of nonconservative optical forces on the dynamics of optically trapped colloidal spheres: the fountain of probability

We demonstrate both experimentally and theoretically that a colloidal sphere trapped in a static optical tweezer does not come to equilibrium, but rather reaches a steady state in which its probability flux traces out a toroidal vortex. This nonequilibrium behavior can be ascribed to a subtle bias of thermal fluctuations by nonconservative optical forces. The circulating sphere therefore acts as a Brownian motor. We briefly discuss ramifications of this effect for studies in which optical tweezers have been treated as potential energy wells.     

Colloidal electroconvection in a thin horizontal cell. III. Interfacial and transient patterns on electrodes

Previously we have reported a family of convective patterns formed by charge-stabilized aqueous colloidal suspensions under constant (dc) vertical electric fields [Y. Han and D. G. Grier, J. Chem. Phys. 122, 164701 (2005); and ibid. 125, 144707 (2006)]. These patterns form in the bulk when electrokinetic forces act in the opposite direction to gravity. Here, we report on cellular patterns that silica colloidal spheres form on a horizontal electrode when electrokinetic forces act in the same direction as gravity. We suggest that these cellular patterns form as a result of bulk electroconvection mediated by charge injection into the supporting aqueous electrolyte. This charge-injection mechanism also accounts for some aspects of electroconvective pattern formation in our earlier reports. Cellular patterns reorganize themselves into distinct transient patterns after the driving voltage is turned off. These transients cast new light on the complex interplay between the motions of charged colloidal spheres and the ionic relaxation of water undergoing electrolysis.