Topological determination of early morphogenesis in Metazoa

This paper presents a topological interpretation of some developmental events through the use of well-known concepts and theorems of combinatorial geometry. The organization of early embryo using a simulation of cleavage considering only blastomere contacts is examined. Each blastomere is modeled as a topological cell and whole embryo—as cell packing. The egg cleavage results in a pattern of cellular contacts on the surface of each blastomere and whole embryo, a discrete morphogenetic field. We find topological distinctions between different types of early egg cleavage and suggest a topological classification of cleavage. Blastulation and gastrulation may be related to an inevitable emergence of discrete curvature that directs development in three-dimensional space. The relationship between local and global orders in metazoan development, i.e., between local morphogenetic processes and integral developmental patterns, is established. Thus, this methodology reveals a topological imperative: a certain set of topological rules that constrains and directs biological morphogenesis.     

Topological Patterns in Metazoan Evolution and Development

Topological patterns in the development and evolution of metazoa, from sponges to chordates, are considered by means of previously elaborated methodology, with the genus of the surface used as a topological invariant. By this means metazoan morphogenesis may be represented as topological modification(s) of the epithelial surfaces of an animal body. The animal body surface is an interface between an organism and its environment, and topological transformations of the body surface during metazoan development and evolution results in better distribution of flows to and from the external medium, regarded as the source of nutrients and oxygen and the sink of excreta, so ensuring greater metabolic intensity. In sponges and some Cnidaria, the increase of this genus up to high values and the shaping of topologically complicated fractal-like systems are evident. In most Bilateria, a stable topological pattern with a through digestive tube is formed, and the subsequent topological complications of other systems can also appear. The present paper provides a topological interpretation of some developmental events through the use of well-known mathematical concepts and theorems; the relationship between local and global orders in metazoan development, i.e., between local morphogenetic processes and integral developmental patterns, is established. Thus, this methodology reveals a “topological imperative”: A certain set of topological rules that constrains and directs biological morphogenesis.     

Considerations on the role of surface tension and epidermal growth factor in the mechanism of integumental pattern formation

The formation of the posterior parietal hair whorl during normal human development is proposed as a morphogenetic problem in which the effects of surface tension and the appearance of singularities figure prominently. Surface tension is considered in the sense of "Langer's lines" which define local contours of tension in the skin of the organism. According to this view, an analysis of the organism's skin tension field is fundamental to problems of integumental pattern formation. A computational analysis of the skin tension field is proposed, potentially using methods from finite element theory applied to molecular and cellular mechanisms within the skin which resist deformation. To this end, surface tension is provisionally defined as the differential adsorption (adhesion) of molecular and supramolecular binding elements within the skin. In practical applications, it is suggested that epidermal growth factor (EGF) and similar molecules have the physicochemical features and the biological effects required to experimentally probe surface tension phenomena at supramolecular levels. In this regard, the concept of topological discontinuities is introduced as a potential theoretical bridge across levels of organization. Specific examples of these discontinuities are given and discussed in terms of the development of singularities in control surfaces. It is hoped that these considerations will be useful in the mechanistic analysis of hair whorl formation during human embryo-genesis and in other problems of integumental pattern formation and nonequilibrium surface behavior.     

Wnt signaling underlies evolution and development of the butterfly wing pattern symmetry systems

Most butterfly wing patterns are proposed to be derived from a set of conserved pattern elements known as symmetry systems. Symmetry systems are so-named because they are often associated with parallel color stripes mirrored around linear organizing centers that run between the anterior and posterior wing margins. Even though the symmetry systems are the most prominent and diverse wing pattern elements, their study has been confounded by a lack of knowledge regarding the molecular basis of their development, as well as the difficulty of drawing pattern homologies across species with highly derived wing patterns. Here we present the first molecular characterization of symmetry system development by showing that WntA expression is consistently associated with the major basal, discal, central, and external symmetry system patterns of nymphalid butterflies. Pharmacological manipulations of signaling gradients using heparin and dextran sulfate showed that pattern organizing centers correspond precisely with WntA, wingless, Wnt6, and Wnt10 expression patterns, thus suggesting a role for Wnt signaling in color pattern induction. Importantly, this model is supported by recent genetic and population genomic work identifying WntA as the causative locus underlying wing pattern variation within several butterfly species. By comparing the expression of WntA between nymphalid butterflies representing a range of prototypical symmetry systems, slightly deviated symmetry systems, and highly derived wing patterns, we were able to infer symmetry system homologies in several challenging cases. Our work illustrates how highly divergent morphologies can be derived from modifications to a common ground plan across both micro- and macro-evolutionary time scales.     

Finite element,occlusal, microwear and microstructural analyses indicate that conodont microstructure is adapted to dental function

Conodonts constitute the earliest evidence of skeletal biomineralization in the vertebrate evolutionary lineage, manifest as a feeding apparatus of tooth‐like elements comprised of enamel‐ and dentine‐like tissues that evolved in parallel with these canonical tissues in other total‐group gnathostomes. As such, this remarkable example of evolutionary parallelism affords a natural experiment in which to explore the constraints on vertebrate skeletal evolution. Using finite element analysis, informed by occlusal and microwear analyses, we tested the hypothesis that coincidence of complex dental function and microstructural differentiation in the enamel‐like tissues of conodonts and other vertebrates is a consequence of functional adaptation. Our results show topological co‐variation in the patterns of stress distribution and crystallite orientation. In regions of high stress, such as the apex of the basal cavity and inner parts of the platform, the crown tissue comprises interwoven prisms, discontinuities between which would have acted to decussate cracks, preventing propagation. These results inform a general occlusal model for platform conodont elements and demonstrate that the complex microstructure of conodont crown tissue is an adaptation to the dental functions that the elements performed.     

Genetic constraints on wing pattern variation in Lycaeides butterflies: A case study on mapping complex,multifaceted traits in structured populations

Patterns of phenotypic variation within and among species can be shaped and constrained by trait genetic architecture. This is particularly true for complex traits, such as butterfly wing patterns, that consist of multiple elements. Understanding the genetics of complex trait variation across species boundaries is difficult, as it necessitates mapping in structured populations and can involve many loci with small or variable phenotypic effects. Here, we investigate the genetic architecture of complex wing pattern variation in Lycaeides butterflies as a case study of mapping multivariate traits in wild populations that include multiple nominal species or groups. We identify conserved modules of integrated wing pattern elements within populations and species. We show that trait covariances within modules have a genetic basis and thus represent genetic constraints that can channel evolution. Consistent with this, we find evidence that evolutionary changes in wing patterns among populations and species occur in the directions of genetic covariances within these groups. Thus, we show that genetic constraints affect patterns of biological diversity (wing pattern) in Lycaeides, and we provide an analytical template for similar work in other systems.     

Subbarrel Patterns in Somatosensory Cortical Barrels Can Emerge from Local Dynamic Instabilities

Complex spatial patterning, common in the brain as well as in other biological systems, can emerge as a result of dynamic interactions that occur locally within developing structures. In the rodent somatosensory cortex, groups of neurons called “barrels” correspond to individual whiskers on the contralateral face. Barrels themselves often contain subbarrels organized into one of a few characteristic patterns. Here we demonstrate that similar patterns can be simulated by means of local growth-promoting and growth-retarding interactions within the circular domains of single barrels. The model correctly predicts that larger barrels contain more spatially complex subbarrel patterns, suggesting that the development of barrels and of the patterns within them may be understood in terms of some relatively simple dynamic processes. We also simulate the full nonlinear equations to demonstrate the predictive value of our linear analysis. Finally, we show that the pattern formation is robust with respect to the geometry of the barrel by simulating patterns on a realistically shaped barrel domain. This work shows how simple pattern forming mechanisms can explain neural wiring both qualitatively and quantitatively even in complex and irregular domains.     

Morphology-induced collective behaviors: dynamic pattern formation in water-floating elements

Complex systems involving many interacting elements often organize into patterns. Two types of pattern formation can be distinguished, static and dynamic. Static pattern formation means that the resulting structure constitutes a thermodynamic equilibrium whose pattern formation can be understood in terms of the minimization of free energy, while dynamic pattern formation indicates that the system is permanently dissipating energy and not in equilibrium. In this paper, we report experimental results showing that the morphology of elements plays a significant role in dynamic pattern formation. We prepared three different shapes of elements (circles, squares, and triangles) floating in a water-filled container, in which each of the shapes has two types: active elements that were capable of self-agitation with vibration motors, and passive elements that were mere floating tiles. The system was purely decentralized: that is, elements interacted locally, and subsequently elicited global patterns in a process called self-organized segregation. We showed that, according to the morphology of the selected elements, a different type of segregation occurs. Also, we quantitatively characterized both the local interaction regime and the resulting global behavior for each type of segregation by means of information theoretic quantities, and showed the difference for each case in detail, while offering speculation on the mechanism causing this phenomenon.     

String analysis and energy minimization in the partition of DNA sequences

Two approaches to the understanding of biological sequences are confronted. While the recognition of particular signals in sequences relies on complex physical interactions, the problem is often analysed in terms of the presence or absence of literal motifs (strings) in the sequence. We present here a test-case for evaluating the potential of this approach. We classify DNA sequences as positive or negative depending on whether they contain a single melted domain in the middle of the sequence, which is a global physical property. Two sets of positive "biological" sequences were generated by a computer simulation of evolutionary divergence along the branches of a phylogenetic tree, under the constraint that each intermediate sequence be positive. These two sets and a set of random positive sequences were subjected to pattern analysis. The observed local patterns were used to construct expert systems to discriminate positive from negative sequences. The experts achieved 79% to 90% success on random positive sequences and up to 99% on the biological sets, while making less than 2% errors on negative sequences. Thus, the global constraints imposed on sequences by a physical process may generate local patterns that are sufficient to predict, with a reasonable probability, the behaviour of the sequences. However, rather large sets of biological sequences are required to generate patterns free of illegitimate constraints. Furthermore, depending upon the initial sequence, the sets of sequences generated on a phylogenetic tree may be amenable or refractory to string analysis, while obeying identical physical constraints. Our study clarifies the relationship between experts' errors on positive and negative sequences, and the contributions of legitimate and illegitimate patterns to these errors. The test-case appears suitable both for further investigations of problems in the theory of sequence evolution and for further testing of pattern analysis techniques.     

The Use of Discontinuities and Functional Groups to Assess Relative Resilience in Complex Systems

It is evident when the resilience of a system has been exceeded and the system qualitatively changed. However, it is not clear how to measure resilience in a system prior to the demonstration that the capacity for resilient response has been exceeded. We argue that self-organizing human and natural systems are structured by a relatively small set of processes operating across scales in time and space. These structuring processes should generate a discontinuous distribution of structures and frequencies, where discontinuities mark the transition from one scale to another. Resilience is not driven by the identity of elements of a system, but rather by the functions those elements provide, and their distribution within and across scales. A self-organizing system that is resilient should maintain patterns of function within and across scales despite the turnover of specific elements (for example, species, cities). However, the loss of functions, or a decrease in functional representation at certain scales will decrease system resilience. It follows that some distributions of function should be more resilient than others. We propose that the determination of discontinuities, and the quantification of function both within and across scales, produce relative measures of resilience in ecological and other systems. We describe a set of methods to assess the relative resilience of a system based upon the determination of discontinuities and the quantification of the distribution of functions in relation to those discontinuities.     

Color pattern analysis of nymphalid butterfly wings: revision of the nymphalid groundplan

To better understand the developmental mechanisms of color pattern variation in butterfly wings, it is important to construct an accurate representation of pattern elements, known as the "nymphalid groundplan". However, some aspects of the current groundplan remain elusive. Here, I examined wing-wide elemental patterns of various nymphalid butterflies and confirmed that wing-wide color patterns are composed of the border, central, and basal symmetry systems. The central and basal symmetry systems can express circular patterns resembling eyespots, indicating that these systems have developmental mechanisms similar to those of the border symmetry system. The wing root band commonly occurs as a distinct symmetry system independent from the basal symmetry system. In addition, the marginal and submarginal bands are likely generated as a single system, referred to as the "marginal band system". Background spaces between two symmetry systems are sometimes light in coloration and can produce white bands, contributing significantly to color pattern diversity. When an element is enlarged with a pale central area, a visually similar (yet developmentally distinct) white band is produced. Based on the symmetric relationships of elements, I propose that both the central and border symmetry systems are comprised of "core elements" (the discal spot and the border ocelli, respectively) and a pair of "paracore elements" (the distal and proximal bands and the parafocal elements, respectively). Both core and paracore elements can be doubled, or outlined. Developmentally, this system configuration is consistent with the induction model, but not with the concentration gradient model for positional information.     

Thermolysin and mitochondrial processing peptidase: how far structure-functional convergence goes

The structure-functional convergence between two Zn-dependent proteases, namely thermolysin and mitochondrial processing peptidase (MPP), is described. These two families of nonhomologous enzymes show not only functional convergence of several active site residues as in chymotrypsin and subtilisin, but also structural convergence of overall molecular architectures including the beta-sheet arrangement and packing of the surrounding alpha-helices. The major functionally important structural elements are present in both enzymes with different topological connections and often in reverse main-chain orientation, but display similar packing. The structural comparison helps to rationalize sequence "inversion" of the HEXXH thermolysin consensus present as HXXEH in MPP. The described structural convergence may be due to a limited number of alternatives to build a Zn-protease that utilizes hydrogen bonding between a substrate main chain and the enzyme beta-sheet for substrate binding.     

Comparative analysis of topological organization in Metazoa

Topological patterns in Metazoa, using previously elaborated methodology with employment of the genus of the surface (p) as topological invariant are considered. The term "density of the genus of the surface" is introduced. In sponges and in a lesser degree among Cnidaria and, Ctenophoria an increase of genus p up to indefinite high values and the shaping of topologically complicated quasifractal systems (irrigation system in sponges and gastro-vascular system in Radiata) are evident. In most Bilateria a stable topological pattern with open digestive tube is formed and subsequent topological complications of other systems may occur. Complicated topological patterns increasing the genus of the surface are evolved on the base of quasifractal systems: gut pockets in turbellaria, tracheal system in arthropods, bronchial system in birds, gills in bivalve mollusks, etc. Peculiarities of ordered and disordered topological patterns as well as topological origin of the increase of the genus of the surface are considered.     

Quantitative genetics of butterfly wing color patterns

Developmental processes exert their influence on the evolution of complex morphologies through the genetic correlations they engender between traits. Butterfly wing color patterns provide a model system to examine this connection between development and evolution. In butterflies, the nymphalid groundplan is a framework used to decompose complex wing patterns into their component pattern elements. The first goal of this work has been to determine whether the components of the nymphalid groundplan are the products of independent developmental processes. To test this hypothesis, the genetic correlation matrices for two species of butterflies, Precis coenia and Precis evarete, were estimated for 27 wing pattern characters. The second purpose was to test the hypothesis that the differentiation of serial homologs lowers their genetic correlations. The “eyespots” found serially repeated across the fore- and hindwing and on the dorsal and ventral wing surfaces provided an opportunity to test this hypothesis. The genetic correlation matrices of both species were very similar. The pattern of genetic correlation measured between the different types of pattern elements and between the homologous repeats of a pattern element supported the first hypothesis of developmental independence among the elements of the groundplan. The correlation pattern among the differentiated serial homologs was similarly found to support the second hypothesis: pairs of eyespots that had differentiated had lower genetic correlations than pairs that were similar in morphology. The implications of this study are twofold: First, the apparent developmental independence among the distinct elements of wing pattern has facilitated the vast diversification in morphology found in butterflies. Second, the lower genetic correlations betweendifferentiated homologs demonstrates that developmental constraints can in fact be broken. The extent to which genetic correlations readily change, however, remains unknown. © 1994 Wiley-Liss, Inc.     

GIANT: A Cytoscape Plugin for Modular Networks

Network analysis provides deep insight into real complex systems. Revealing the link between topological and functional role of network elements can be crucial to understand the mechanisms underlying the system. Here we propose a Cytoscape plugin (GIANT) to perform network clustering and characterize nodes at the light of a modified Guimerà-Amaral cartography. This approach results into a vivid picture of the a topological/functional relationship at both local and global level. The plugin has been already approved and uploaded on the Cytoscape APP store.     

Fast similarity search for protein 3D structures using topological pattern matching based on spatial relations

Similarity search for protein 3D structures become complex and computationally expensive due to the fact that the size of protein structure databases continues to grow tremendously. Recently, fast structural similarity search systems have been required to put them into practical use in protein structure classification whilst existing comparison systems do not provide comparison results on time. Our approach uses multi-step processing that composes of a preprocessing step to represent geometry of protein structures with spatial objects, a filter step to generate a small candidate set using approximate topological string matching, and a refinement step to compute a structural alignment. This paper describes the preprocessing and filtering for fast similarity search using the discovery of topological patterns of secondary structure elements based on spatial relations. Our system is fully implemented by using Oracle 8i spatial. We have previously shown that our approach has the advantage of speed of performance compared with other approach such as DALI. This work shows that the discovery of topological relations of secondary structure elements in protein structures by using spatial relations of spatial databases is practical for fast structural similarity search for proteins.     

Assembly constraints drive co-evolution among ribosomal constituents

Ribosome biogenesis, a central and essential cellular process, occurs through sequential association and mutual co-folding of protein–RNA constituents in a well-defined assembly pathway. Here, we construct a network of co-evolving nucleotide/amino acid residues within the ribosome and demonstrate that assembly constraints are strong predictors of co-evolutionary patterns. Predictors of co-evolution include a wide spectrum of structural reconstitution events, such as cooperativity phenomenon, protein-induced rRNA reconstitutions, molecular packing of different rRNA domains, protein–rRNA recognition, etc. A correlation between folding rate of small globular proteins and their topological features is known. We have introduced an analogous topological characteristic for co-evolutionary network of ribosome, which allows us to differentiate between rRNA regions subjected to rapid reconstitutions from those hindered by kinetic traps. Furthermore, co-evolutionary patterns provide a biological basis for deleterious mutation sites and further allow prediction of potential antibiotic targeting sites. Understanding assembly pathways of multicomponent macromolecules remains a key challenge in biophysics. Our study provides a ‘proof of concept’ that directly relates co-evolution to biophysical interactions during multicomponent assembly and suggests predictive power to identify candidates for critical functional interactions as well as for assembly-blocking antibiotic target sites.     

Landscape conservation genetics of <Emphasis Type="Italic">Dipteryx alata</Emphasis> (“baru” tree: Fabaceae) from Cerrado region of central Brazil

In this paper random amplified polymorphic DNA (RAPD) was used to evaluate the degree of among-population differentiation and associated spatial patterns of genetic divergence for Dipteryx alata Vogel populations from Cerrado region of central Brazil, furnishing support for future programs of conservation of this species. We analyzed patterns of genetic and spatial population structure using 45 RAPD loci scored for 309 trees, sampled from five different regions with two populations each. Genetic structure analysis suggested that panmixia null hypothesis can be rejected, with significant among-population components of 15%. Hierarchical partition by Analysis of Molecular Variance (AMOVA) shows that 5% of genetic variation is within regions, whereas 10% of variation is among regions, and these results were confirmed by a Bayesian analyses on HICKORY. The Mantel correlogram revealed that this divergence is spatially structured, so that local populations situated at short geographic distances could not be considered independent units for conservation and management. However, genetic discontinuities among populations were found in the northwest and southeast parts of the study area, corresponding to regions of recent socio-economic expansion and high population density, respectively. Taking both geographic distances and genetic discontinuities into account it is possible to establish a group of population to be conserved, covering most of D. alata geographic distribution and congruent with previously established priority areas for conservation in the Cerrado region.     

小鼠对不同拓扑性质图形的识别

视觉感知的一系列研究都支持大范围拓扑感知的理论．拓扑性质作为整体性质,是视觉感知的基础．视觉对图形拓扑特征差异的感知要优先于对局部特征差异的感知．采用Y迷宫研究了小鼠对不同拓扑性质图形的识别．训练小鼠学习识别圆环和实心矩形这一对拓扑性质不同的图形,之后用拓扑特征相同或不同的其他图形测试小鼠,这些图形包括空心矩形、实心圆、缺口的圆环、缺口的空心矩形．实验结果表明,学会识别圆环(奖励)和实心矩形(无奖励)的小鼠无法区分实心圆和实心矩形以及圆环和空心矩形,但是能够分别从缺口圆环、缺口的空心矩形、实心圆与空心矩形组成的图形对中识别出空心矩形．因此证实了小鼠的视觉系统能够感知拓扑特征的差异并且具有对拓扑性质的概括能力．结果为拓扑知觉对视觉系统来说是基本的这一假设提供了证据．