Application of Chondroitin Sulfate Derivatives for Understanding Axonal Guidance in the Nervous System during Development

Neuronal axons and their growth cones recognize molecular guidance cues within the local environment, forming axonal pathways to produce precise neuronal networks during nervous system development. Chondroitin sulfates (CS), carbohydrate chains on chondroitin sulfate proteoglycans, exhibit great structural diversity and exert various influences on axons and growth cones as guidance cues or their modulators; however, the relationship between their structural diversity and function in axonal guidance is not well known. To uncover the roles of CS in axonal guidance, artificially modified hybrid molecules: CS derivatives of biotinylated CS and lipid-derivatized CS, were used.The experiments with biotinylated CS suggest that the growing axons act on their environment, modifying CS, and rendering it more favorable for their growth. The experiments with lipid-derivatized CS demonstrated that growth cones distinguish types of CS with different unit contents and are likely to discriminate the structural diversity of CS.The application of CS derivatives is useful in uncovering axon–environment interaction and structure–function relationship of CS directly

Page Curves for General Interacting Systems

We calculate in detail the Renyi entanglement entropies of cTPQ states as a function of subsystem volume, filling the details of our prior work [Nature Communications 9, 1635 (2018)], where the formulas were first presented. Working in a limit of large total volume, we find universal formulas for the Renyi entanglement entropies in a region where the subsystem volume is comparable to that of the total system. The formulas are applicable to the infinite temperature limit as well as general interacting systems. For example we find that the second Renyi entropy of cTPQ states in terms of subsystem volume is written universally up to two constants, $S_2(\ell)=-\ln K(\beta)+\ell\ln a(\beta)-\ln\left(1+a(\beta)^{-L+2\ell}\right)$, where $L$ is the total volume of the system and $a$ and $K$ are two undetermined constants. The uses of the formulas were already presented in our prior work and we mostly concentrate on the theoretical aspect of the formulas themselves. Aside from deriving the formulas for the Renyi Page curves, the expression for the von Neumann Page curve is also derived, which was not presented in our previous work.Comment: 29 pages, 3 figures; JHEP preparatio

Moderate repulsive effects of E-unit-containing chondroitin sulfate (CSE) on behavior of retinal growth cones

Chondroitin sulfate (CS), the carbohydrate chain of chondroitin sulfate proteoglycans, is involved in neuronal circuit formation during development. CS shows great structural diversity with combination of disaccharide units of different structure (A-, C-, D-, or Eunit).However, whether its structural diversity contributes to pathway formation remains unclear. We chemically coupled the reducing end of various types of CS to the amino group of phosphatidylethanolamine (lipid-derivatized CS, CS-PE) and established an in vitro time-lapse assay to observe the behaviors of growth cones of retinal ganglion cells from embryonic day 6 chick retina on exposure to beads coated with lipid-derivatized CS (CS-PE beads). Among CS-PEs with different content of the structural units, the beads coated with E-unit–containing CS-PE [E-unit: GlcAβ1-3GalNAc(4,6-O-disulfate)] (CSE-PE beads) significantly caused the growth cones to retract and to turn away from the beads, but the beads coated with CSA-, CSC- or CSDPE beads did not. Importantly, not all the growth cones retracted equally from the CSE-PE beads, but they showed continuum of the repulsive behaviors; some behaved moderately and others remarkably. The growth cones distinguished different samples of CS: CSE and the others. Moreover, the continuum of the repulsive behaviors suggests that CS might be involved with the fine regulation of growth cones\u27 behavior through its characteristic structure