Hierarchical Protofilament Intertwining Rules the Formation of Mixed-Curvature Amyloid Polymorphs.

Amyloid polymorphism is a hallmark of almost all amyloid species, yet the mechanisms underlying the formation of amyloid polymorphs and their complex architectures remain elusive. Commonly, two main mesoscopic topologies are found in amyloid polymorphs characterized by non-zero Gaussian and mean curvatures: twisted ribbons and helical fibrils, respectively. Here, a rich heterogeneity of configurations is demonstrated on insulin amyloid fibrils, where protofilament packing can occur, besides the common polymorphs, also in a combined mode forming mixed-curvature polymorphs. Through AFM statistical analysis, an extended array of heterogeneous architectures that are rationalized by mesoscopic theoretical arguments are identified. Notably, an unusual fibrillization pathway is also unraveled toward mixed-curvature polymorphs via the widespread recruitment and intertwining of protofilaments and protofibrils. The results present an original view of amyloid polymorphism and advance the fundamental understanding of the fibrillization mechanism from single protofilaments into mature amyloid fibrils.

Describing whisker morphology of the Carnivora.

One of the largest ecological transitions in carnivoran evolution was the shift from terrestrial to aquatic lifestyles, which has driven morphological diversity in skulls and other skeletal structures. In this paper, we investigate the association between those lifestyles and whisker morphology. However, comparing whisker morphology over a range of species is challenging since the number of whiskers and their positions on the mystacial pads vary between species. Also, each whisker will be at a different stage of growth and may have incurred damage due to wear and tear. Identifying a way to easily capture whisker morphology in a small number of whisker samples would be beneficial. Here, we describe individual and species variation in whisker morphology from two-dimensional scans in red fox, European otter and grey seal. A comparison of long, caudal whiskers shows inter-species differences most clearly. We go on to describe global whisker shape in 24 species of carnivorans, using linear approximations of curvature and taper, as well as traditional morphometric methods. We also qualitatively examine surface texture, or the presence of scales, using scanning electron micrographs. We show that gross whisker shape is highly conserved, with whisker curvature and taper obeying simple linear relationships with length. However, measures of whisker base radius, length, and maybe even curvature, can vary between species and substrate preferences. Specifically, the aquatic species in our sample have thicker, shorter whiskers that are smoother, with less scales present than those of terrestrial species. We suggest that these thicker whiskers may be stiffer and able to maintain their shape and position during underwater sensing, but being stiffer may also increase wear.

Morphological peculiarities of a harbour seal (Phoca vitulina) whisker revealed by normal skeletonisation.

Of all mammalian vibrissae, those of certain species of pinnipeds are exceptional. Researchers believe that their curious undulating form evolved for hydrodynamic detection. Our understanding of how these whiskers work depends on a geometrical model that captures the crucial pertinent features of the natural vibrissae including its tapering and curvature. It should also account for the form of the whisker when it flexes under external loading. We introduce and study a normal skeleton of a two-dimensional projection of a harbour seal whisker. The normal skeleton is a complete shape descriptor that involves reduction to the centreline equipped with a thickness function of the orthogonal cross-section. The contours of the whisker shape are extracted from a 2D greyscale scan. Our analysis reveals correspondence between the undulations of the width and oscillations of the centreline curvature as functions of arc length. We discuss two possible explanations for that remarkable feature: one based on consideration of growth and the other of plastic deformation. For the latter we employ a mechanical model to demonstrate appearance of curvature oscillations caused by extensive deflection of the undulating whisker due to external loading.

Ecomorphology reveals Euler spiral of mammalian whiskers.

Whiskers are present in many species of mammals. They are specialised vibrotactile sensors that sit within strongly innervated follicles. Whisker size and shape will affect the mechanical signals that reach the follicle, and hence the information that reaches the brain. However, whisker size and shape have not been quantified across mammals before. Using a novel method for describing whisker curvature, this study quantifies whisker size and shape across 19 mammalian species. We find that gross two-dimensional whisker shape is relatively conserved across mammals. Indeed, whiskers are all curved, tapered rods that can be summarised by Euler spiral models of curvature and linear models of taper, which has implications for whisker growth and function. We also observe that aquatic and semi-aquatic mammals have relatively thicker, stiffer, and more highly tapered whiskers than arboreal and terrestrial species. In addition, smaller mammals tend to have relatively long, slender, flexible whiskers compared to larger species. Therefore, we propose that whisker morphology varies between larger aquatic species, and smaller scansorial species. These two whisker morphotypes are likely to induce quite different mechanical signals in the follicle, which has implications for follicle anatomy as well as whisker function.

The Euler spiral of rat whiskers.

This paper reports on an analytical study of the intrinsic shapes of 523 whiskers from 15 rats. We show that the variety of whiskers on a rat's cheek, each of which has different lengths and shapes, can be described by a simple mathematical equation such that each whisker is represented as an interval on the Euler spiral. When all the representative curves of mystacial vibrissae for a single rat are assembled together, they span an interval extending from one coiled domain of the Euler spiral to the other. We additionally find that each whisker makes nearly the same angle of 47∘ with the normal to the spherical virtual surface formed by the tips of whiskers, which constitutes the rat's tactile sensory shroud or "search space." The implications of the linear curvature model for gaining insight into relationships between growth, form, and function are discussed.

Writhe formulas and antipodal points in plectonemic DNA configurations.

The linking and writhing numbers are key quantities when characterizing the structure of a piece of supercoiled DNA. Defined as double integrals over the shape of the double helix, these numbers are not always straightforward to compute, though a simplified formula was established in a theorem by Fuller [Proc. Natl. Acad. Sci. U.S.A. 75, 3557 (1978)]. We examine the range of applicability of this widely used simplified formula, and show that it cannot be employed for plectonemic DNA. We show that inapplicability is due to a hypothesis of Fuller theorem that is not met. The hypothesis seems to have been overlooked in many works.