Reverse engineering an amyloid aggregation pathway with dimensional analysis and scaling

Human islet amyloid polypeptide (hIAPP) is a cytotoxic protein that aggregates into oligomers and fibrils that kill pancreatic β-cells. Here we analyze hIAPP aggregation in vitro, measured via thioflavin-T fluorescence. We use mass-action kinetics and scaling analysis to reconstruct the aggregation pathway, and find that the initiation step requires four hIAPP monomers. After this step, monomers join the nucleus in pairs, until the first stable nucleus (of size approximately 20 monomers) is formed. This nucleus then elongates by successive addition of single monomers. We find that the best-fit of our data is achieved when we include a secondary fibril-dependent nucleation pathway in the reaction scheme. We predict how interventions that change rates of fibril elongation or nucleation rates affect the accumulation of potentially cytotoxic oligomer species. Our results demonstrate the power of scaling analysis in reverse engineering biochemical aggregation pathways.     

Applications of finite-element scaling analysis in primatology

The study of biological shape in three dimensions using landmark data can now be accomplished using several alternative methods. This report focuses on the use of finite-element scaling analysis in primate craniofacial morphology. The method is particularly useful in its ability to localize the differences between forms, thereby indicating those loci that differ most between specimens. Several examples of this feature are provided from primatological research. Particulars of the methods are also discussed in an attempt to provide the reader with cautionary knowledge for prudent application of the method in future research.     

Two dimensional NMR studies on the solution structure of d-CTCGAGCTCGAG

Two dimensional (2D) FT-NMR investigations have been carried out on the self-complementary dodecanucleotide d-CTCGAGCTCGAG, which has cleavage sites for the restriction enzyme Xho I (between C and T). The central TCG portion is also known to show a preference for DNAase activity. Complete resonance assignments have been obtained for the non-exchangeable sugar and base protons of the oligonucleotide. Information regarding sugar geometries, glycosidic torsion angles and other structural parameters has been obtained from the relative intensities of the cross peaks in the COSY and NOESY spectra. The results indicate that deoxyribose rings of C1 and C7 adopt a conformation different from the remaining sugars in the double helical oligonucleotide. The central TCG portion also exhibits variations in the backbone structure. The base stacking in the double helix shows interesting sequence dependent effects suggesting that the sequence effects are not localised to nearest neighbours but extended over longer stretches.     

A scaling analysis in the SIRI epidemiological model

For the spatial stochastic epidemic reinfection model SIRI, where susceptibles S can become infected I, then recover and remain only partial immune against reinfection R, we determine the phase transition lines using pair approximation for the moments derived from the master equation. We introduce a scaling argument that allows us to determine analytically an explicit formula for these phase transition lines and prove rigorously the heuristic results obtained previously.     

Perspectives on hair evolution based on some comparative studies on vertebrate cornification

Hair evolution contributed to the biological success of mammals. Hair origin from synapsid scales is speculative and requires extensive modifications of the morphogenetic process transforming lens-shaped dermis of scales into small dermal papillae in hair. Hair evolution from glands is hypothetical but is supported from studies on the signaling control of hair vs. glandular morphogenesis. Based on immunocytochemical and comparative studies, it is hypothesized that the onion-like organization of hair derived from glandular pegs which central part produced lipids and some keratin. In a following stage, involucrin, trichohyalin, and keratins were produced in the central cells of the gland and formed a solid medulla surrounded by keratinocytes of the inner root sheath. The origin of this protohair was possibly related to increased concentration of beta-catenin and other signaling molecules in epithelial cells following the evolution of a dermal papilla. The latter activated the keratogenic genes, already utilized in cells of the claws, in concentric layers of cells of the glandular peg. Lipidogenic genes were depressed. As new genes evolved in the genome of synapsids, new circular layers of keratinocytes containing specialized hard keratins and keratin-associated proteins were formed around medullary cells. The new keratinocytes probably originated the cortex separating medulla from the external cells that became the inner root sheath. The hypothesis indicates that in a following stage, the medulla was obliterated or replaced by cortical cells while the external part of the cortex formed a cuticular surface due to the different growth rate with inner root sheath cells.     

A scaling analysis in the SIRI epidemiological model

For the spatial stochastic epidemic reinfection model SIRI, where susceptibles S can become infected I, then recover and remain only partial immune against reinfection R, we determine the phase transition lines using pair approximation for the moments derived from the master equation. We introduce a scaling argument that allows us to determine analytically an explicit formula for these phase transition lines and prove rigorously the heuristic results obtained previously.     

A multi-dimensional scaling approach to shape analysis

We propose an alternative to Kendall's shape space for reflectionshapes of configurations in with k labelled vertices, where reflection shape consistsof all the geometric information that is invariant under compositionsof similarity and reflection transformations. The proposed approachembeds the space of such shapes into the space of (k – 1) x (k – 1) real symmetricpositive semidefinite matrices, which is the closure of an opensubset of a Euclidean space, and defines mean shape as the naturalprojection of Euclidean means in on to the embedded copy of the shape space. This approachhas strong connections with multi-dimensional scaling, and themean shape so defined gives good approximations to other commonlyused definitions of mean shape. We also use standard perturbationarguments for eigenvalues and eigenvectors to obtain a centrallimit theorem which then enables the application of standardstatistical techniques to shape analysis in two or more dimensions.     

Perspectives on the use of an endogenous gene target in studies of mutational specificity

Mutational spectra have become increasingly important tools in generating a molecular level understanding of mutagenesis in mammalian cells. The work in this field has primarily involved the use of shuttle vector systems although some work has also been reported using endogenous cellular genes as mutational targets. In this communication we discuss the relative utility of these two approaches. We specifically focus on UV light-induced mutagenesis since this agent has been studied in both types of system. We conclude that shuttle vector and endogenous gene studies of mutagenesis are highly complementary, each possessing unique advantages.     

A biomechanical analysis of mandibular scaling in old world monkeys

Scaling of mandibular dimensions in male Old World monkeys was investigated. Mandibular condyle length, width, and area were regressed separately against body mass and mandibular length for a total of 14 species of Cercopithecoids. Scaling of mandibular depth and width against both body mass and mandibular length were also investigated. When results of regression analysis using the two different independent variables (body mass and mandibular length) were compared, there were significant pattern differences in scaling of cercopithecines versus colobines. Compared to body mass, male cercopithecines had relatively large mandibles (length, width, and depth) and also relatively large condyles (length, width, and area). However, compared to mandibular length, cercopithecines had relatively transversely thin and shallow mandibles and relatively narrow condyles. It is shown that a “biomechanical” interpretation of mandibular scaling patterns against body mass in Old World monkeys demonstrates only that cercopithecines have prognathic faces, an already well-known and well-documented condition. When the biomechanical effects of prognathic faces are controlled for (by scaling against mandibular length), it is shown that cercopithecines possess special adaptations in condyle length while colobines possess special adaptations in condyle width and mandibular depth and width. These results clearly demonstrate the importance of selecting a relevant reference variable in scaling studies where biomechanical interpretations are attempted.     

Finite element scaling analysis of human craniofacial growth

The study of form change is central to traditional cephalometric research. Unfortunately, traditional cephalometric studies operate within systems of measurement that are based on registration and orientation. Measurements produced in registered systems are insufficient for the craniofacial biologist who is interested in locating morphological differences between forms. In this article we apply a registration-free method called finite element scaling analysis in a study of the form change occurring during growth of the normal human craniofacial complex. The method provides form change data that can be summarized at various morphological levels. Twenty normal male individuals are used to analyze the form change that occurs from age 4 to ages 5, 7, 8, 9, 10, 12, 13, and 15 years. The magnitude and direction of growth expressed as shape and size change specific to craniofacial landmarks are presented. Although exceptions occur, our analysis shows that localized size change is, on the average, greater than localized shape change. The relation between size and shape change during growth shows allometry (shape change increasing during growth along with size change) but at a lesser magnitude and slower rate. We conclude that although shape change occurs throughout ontogeny, the magnitude and rate of shape change in relation to size change diminishes as age increases. This analysis represents new insights into the understanding of human craniofacial growth at various levels of morphological integration.     

Craniofacial growth in apert syndrome as measured by finite-element scaling analysis

A new tool for the study of biological form change is applied in a comparison of craniofacial growth in normal children and those affected with Apert syndrome. Using finite-element scaling analysis, the magnitude of size change during postnatal growth in the Apert sample was determined to be generally less than normal, and the magnitude of shape change was generally greater than normal. No consistent, statistically significant, alteration from normal growth was defined in the Apert sample, however. There appears to be no consistent effect on general cell and tissue proliferation in Apert syndrome. Rather, specific subpopulations of cells and tissues may be affected differentially over time.     

A tree swaying in a turbulent wind: a scaling analysis

A tentative scaling theory is presented of a tree swaying in a turbulent wind. It is argued that the turbulence of the air within the crown is in the inertial regime. An eddy causes a dynamic bending response of the branches according to a time criterion. The resulting expression for the penetration depth of the wind yields an exponent which appears to be consistent with that pertaining to the morphology of the tree branches. An energy criterion shows that the dynamics of the branches is basically passive. The possibility of hydrodynamic screening by the leaves is discussed.     

Intrinsic time scaling in survival analysis: Application to biological populations

A method of dimensionless time-scaling based on extrinsic expectation of life at birth but intrinsic to a system generating a survival distribution is introduced. Such scaling allows the survival fraction function and its associated mortality function to serve as Green's functions for their generalized equivalents. i.e. a “population” function and a “death” function. The analytical mechanics of utilizing these concepts are formulated, applied to the classical Gompertz and Weibull survival models, and discussed with respect to biological relevance.     

An analysis of epipubic bone function in mammals using scaling theory

Linear dimensions of epipubic bones in 61 species of metatherians and monotremes scale to mass differently in groups with or without marsupia, presumably reflecting emphasis on different but non-mutually exclusive functions. Sexual dimorphism of epipubic form exists. However, the allometric relationships of the epipubic bones of taxa that possess marsupia do not conform to the hypothesis that epipubic bones support the marsupium nearly as well as those without a marsupium. This observation renders a new hypothesis relating litter mass to epipubic form in taxa without marsupia. It appears that support of the marsupium is not the primary function or, at least, not the most proximate determinate of epipubic form in taxa with marsupia. The scaling of epipubic bone dimensions is consistent with the hypothesis that predicts epipubic bones serve to assist in locomotion by acting with the hypaxial muscles of the trunk and pectineus to protract the pelvic limbs. Epipubic length is shown to scale to maintain a mechanical advantage between these opposing muscle groups that approximates the rate that inertia of the hind limbs increases with total mass and speed of locomotion. This hypothesis provides an explanation for a skeletal element scaling significantly above geometric similarity. This observation has important theoretical significance as it suggests that skeletal architecture may, within limits, scale independently of mass-related stress.