The importance of intramolecular constraints in cyclic transition-state geometries is especially pronounced in nendo-tet cyclizations, where the usual backside approach of a nucleophile to the breaking bond is impossible for the rings containing less than eight atoms. Herein, we expand the limits of endo-tet cyclizations and show that donor−acceptor cyclopropanes can provide a seven-membered ring via a genuine 6-endo-tet process. Substrates containing a N-alkyl-N-arylcarbamoyl moiety as an acceptor group undergo Lewis acid-induced cyclization to form tetrahydrobenz[b]azepin-2-ones in high yields. The reaction proceeds with the inversion of the configuration at the electrophilic carbon. In this process, a formally six-membered transition state yields a seven-membered ring as the pre-existing cycle is merged into the forming ring. The stereochemistry of the products can be controlled by the reaction time and by the nature of Lewis acid, opening access to both diastereomers by tuning of the reaction conditions.
Despite an extensive literature on statistical methods and their proper application to biological data, incorrect analyses remain a critical and widely spread problem in research papers. Inherently hierarchical (nested, clustered) structure of biological measurements is often erroneously neglected, leading to pseudo-replication and false positive results. This, in turn, complicates the correct assessment of statistical power and impairs optimal planning of experiments. In order to attract more attention to this problem and to illustrate the importance of direct account for the nested structure of biological data, in this article we present a simple open-source simulator of two-level normally distributed stochastic data. By defining 'true' mean values and 'true' intraand inter-cluster variances of the simulated data, users of the simulator can test various scenarios, appreciate the importance of using correct multi-level analysis and the danger of neglecting the information about the data structure. Here we apply our nested data simulator to highlight some commonly arising mistakes with data analysis and propose a workflow, in which our simulator could be employed to correctly compare two nested groups of experimental data and to optimally plan new experiments in order to increase statistical power when necessary.
Microtubules are essential cytoskeletal polymers that exhibit stochastic switches between tubulin assembly and disassembly. Here, we examine possible mechanisms for these switches, called catastrophes and rescues. We formulate a four-state Monte Carlo model, explicitly considering two biochemical and two conformational states of tubulin, based on a recently conceived view of microtubule assembly with flared ends. The model predicts that high activation energy barriers for lateral tubulin interactions can cause lagging of curled protofilaments, leading to a ragged appearance of the growing tip. Changes in the extent of tip raggedness explain some important but poorly understood features of microtubule catastrophe: weak dependence on tubulin concentration and an increase in its probability over time, known as aging. The model predicts a vanishingly rare frequency of spontaneous rescue unless patches of guanosine triphosphate tubulin are artificially embedded into microtubule lattice. To test our model, we used in vitro reconstitution, designed to minimize artifacts induced by microtubule interaction with nearby surfaces. Microtubules were assembled from seeds overhanging from microfabricated pedestals and thus well separated from the coverslip. This geometry reduced the rescue frequency and the incorporation of tubulins into the microtubule shaft compared with the conventional assay, producing data consistent with the model. Moreover, the rescue positions of microtubules nucleated from coverslip-immobilized seeds displayed a nonexponential distribution, confirming that coverslips can affect microtubule dynamics. Overall, our study establishes a unified theory accounting for microtubule assembly with flared ends, a tip structure–dependent catastrophe frequency, and a microtubule rescue frequency dependent on lattice damage and repair.
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