Correct wiring is crucial for the proper functioning of the nervous system. Molecular gradients provide critical signals to guide growth cones, which are the motile tips of developing axons, to their targets. However, in vitro, growth cones trace highly stochastic trajectories, and exactly how molecular gradients bias their movement is unclear. Here, we introduce a mathematical model based on persistence, bias, and noise to describe this behaviour, constrained directly by measurements of the detailed statistics of growth cone movements in both attractive and repulsive gradients in a microfluidic device. This model provides a mathematical explanation for why average axon turning angles in gradients in vitro saturate very rapidly with time at relatively small values. This work introduces the most accurate predictive model of growth cone trajectories to date, and deepens our understanding of axon guidance events both in vitro and in vivo.

/pdf/a-mathematical-model-explains-saturating-axon-guidance-2zdaj36yyn.pdf

A mathematical model explains saturating axon guidance responses to molecular gradients

TADDOLs, which contain two adjacent diarylhydroxymethyl groups in a trans relationship on a 1,3-dioxolane ring, can be prepared from acetals or ketals of tartrate esters by reaction of the latter with aromatic Grignard reagents. They are extraordinarily versatile chiral auxiliaries. Here, a historical review of the subject is followed by discussion of the preparation of TADDOLs and analogous systems, including TADDOLs with N-, P-, O-, and S-heteroatom ligands appropriate for metals. Crystal structure analysis reveals that the heteroatoms on the diarylmethyl groups are almost always in close proximity to each other, joined together by H-bonds, and predisposed to form chelate complexes in which the metallic centers reside in propeller-like chiral environments. Applications of TADDOL derivatives in enantioselective synthesis extend from utilization as stoichiometric chiral reagents or in Lewis acid mediated reactions, to roles in catalytic hydrogenation and stereoregular metathesis polymerization. Derivatives and complexes based on the following metals have so far been investigated: Li, B, Mg, Al, Si, Cu, Zn, Ce, Ti, Zr, Mo, Rh, Ir, Pd, Pt. The number of stereoselective reactions already accomplished with TADDOLs is correspondingly large. It is also easy to prepare TADDOL derivatives that are readily polymerizable and graftable, and to transform them into immobilized solid-phase catalysts. The result is catalysts, simply or dendritically immobilized in polystyrene or on silica gel and characterized by unexpected stability even after multiple use in titanium TADDOLate mediated reactions. TADDOLs show further unusual characteristics that make them useful for applications in material science and supramolecular chemistry: they are the most effective doping agents known for phase transformations of achiral (nematic) into chiral (cholesteric) liquid crystals. The TADDOL OH group that is not involved in intramolecular H-bonding shows a strong tendency to associate intermolecularly with H-bond acceptors. In the process of crystallization this leads, enantioselectively, to the formation of inclusion compounds that lend themselves to the separation of racemic mixtures not otherwise suited to the classical method of crystallization through diastereomeric salts. The high melting points of TADDOLs even make possible the resolution of racemates by distillation! Host-guest compounds formed between TADDOLs and achiral partners can serve as platforms for enantioselective photoreactions. It seems safe to predict that many more applications will be discovered for the TADDOLs and their derivatives. Supporting information for this article is available on the WWW under http://www.angewandte.com or from the author.

/pdf/taddols-their-derivatives-and-taddol-analogues-versatile-3khxc7t5en.pdf

TADDOLs, Their Derivatives, and TADDOL Analogues: Versatile Chiral Auxiliaries

Cyclohexadienone ketals and quinols: four building blocks potentially useful for enantioselective synthesis.

Stereocontrol in the synthesis of acyclic systems: applications to natural product synthesis

The chemistry of transition metals with three-membered ring heterocycles.

Regio- and stereoselective .gamma. substitution of allylic alcohols with alkyllithium compounds by using N,N-methylphenylaminotributylphosphonium iodide. Anti stereochemistry of SN2' reaction

The carbonylation of oxiranes catalyzed by rhodium complex afforded β-lactones. Various factors which control the above reaction are presented.

The reaction of small ring compound with carbon monoxide the carbonylation of oxirane

Novel substituent effects in 1H and 13C NMR spectra of 4-and 4'-substituted N-benzylideneanilines

Diphenylmethyleneimino radicals, Ph2C=N·, generated from photolysis of benzophenoxime benzoates undergo aromatic substitution on benzene as well as dimerization into azine. On the other hand, phenylmethyleneimino radicals, PhCH=N·, generated from photolysis of benzaldoxime benzoate are oxidized to benzonitrile in preference to dimerization.

Photolysis of Aromatic Oxime Esters. Finding of Aromatic Substitution by Diphenylmethyleneimino Radicals

The 9,10-dicyanoanthracene (DCA)-sensitized photo-oxygenation of the electron-rich stilbene oxides (1) gives the ozonides (2) almost quantitatively. The fluorescence of DCA is quenched by (1) at a diffusion-controlled rate and the above reaction is quenched by polymethoxybenzenes which indicates that an electron transfer mechanism is involved. The quantum yield for ozonide formation varies from 0.5 for trans-2-(4-methoxyphenyl)-3-phenyloxirane (1d) to 2.4 for trans-2,3-bis(4-methoxyphenyl)-2,3-diethyloxirane (1h), suggesting a duplex reaction mechanism such as photo-oxygenation by superoxide and a Barton mechanism after the initial electron transfer from the epoxides (1) to the excited singlet state of DCA.

Hiroyuki Ohta

Papers

Regio- and stereoselective .gamma. substitution of allylic alcohols with alkyllithium compounds by using N,N-methylphenylaminotributylphosphonium iodide. Anti stereochemistry of SN2' reaction

The reaction of small ring compound with carbon monoxide the carbonylation of oxirane

Novel substituent effects in 1H and 13C NMR spectra of 4-and 4'-substituted N-benzylideneanilines

Photolysis of Aromatic Oxime Esters. Finding of Aromatic Substitution by Diphenylmethyleneimino Radicals

Photoinduced electron transfer reaction. Part 3. 9,10-Dicyanoanthracene-sensitized photo-oxidation of electron-rich stilbene oxides