Development of the dendritic branching pattern of the Medial Giant Interneuron in the grasshopper embryo

The embryonic development of the grasshopper's Medial Giant Interneuron (MGI) was examined by injecting the cell with the fluorescent dye Lucifer Yellow at a series of stages in its growth. Particular attention was given to the way in which this neuron constructs its stereotyped dendritic branching pattern. The MGI's dendrites originate as secondary processes which sprout at characteristic points along the neurite after the primary growth cone has passed. These processes then arborize to form a miniature version of their adult branching pattern before the end of embryonic life. While growing, the dendritic branches are covered with a radiant profusion of filopodia; however, these filopodia are ephemeral structures and disappear once the cell matures. By contrast there is no significant reduction in either the number or the spatial extent of the actual dendrites at any embryonic stage. This implies that the stereotyped branching pattern of the mature MGI is primarily determined by a precise pattern of initial growth, and that secondary pruning of branches does not play an important role in shaping the final form of this cell. The coordinate ingrowth of the first cercal sensory axons was examined by cobalt filling the embryonic nerve, and the means by which these sensory axons make their initial contacts with the MGI's dendrites is herein discussed. The following paper considers the degree to which this sensory innervation regulates dendritic growth and branching.     

One Rule to Grow Them All: A General Theory of Neuronal Branching and Its Practical Application

Understanding the principles governing axonal and dendritic branching is essential for unravelling the functionality of single neurons and the way in which they connect. Nevertheless, no formalism has yet been described which can capture the general features of neuronal branching. Here we propose such a formalism, which is derived from the expression of dendritic arborizations as locally optimized graphs. Inspired by Ramón y Cajal''s laws of conservation of cytoplasm and conduction time in neural circuitry, we show that this graphical representation can be used to optimize these variables. This approach allows us to generate synthetic branching geometries which replicate morphological features of any tested neuron. The essential structure of a neuronal tree is thereby captured by the density profile of its spanning field and by a single parameter, a balancing factor weighing the costs for material and conduction time. This balancing factor determines a neuron''s electrotonic compartmentalization. Additions to this rule, when required in the construction process, can be directly attributed to developmental processes or a neuron''s computational role within its neural circuit. The simulations presented here are implemented in an open-source software package, the “TREES toolbox,” which provides a general set of tools for analyzing, manipulating, and generating dendritic structure, including a tool to create synthetic members of any particular cell group and an approach for a model-based supervised automatic morphological reconstruction from fluorescent image stacks. These approaches provide new insights into the constraints governing dendritic architectures. They also provide a novel framework for modelling and analyzing neuronal branching structures and for constructing realistic synthetic neural networks.     

Damping by branching: a bioinspiration from trees

Man-made slender structures are known to be sensitive to high levels of vibration due to their flexibility which often cause irreversible damage. In nature, trees repeatedly endure large amplitudes of motion, mostly caused by strong climatic events, yet with minor or no damage in most cases. A new damping mechanism inspired by the architecture of trees is identified here and characterized in the simplest tree-like structure, a Y-shaped branched structure. Through analytical and numerical analyses of a simple two-degree-of-freedom model, branching is shown to be the key ingredient in this protective mechanism that we call damping-by-branching. It originates in the geometrical nonlinearities so that it is specifically efficient to damp out large amplitudes of motion. A more realistic model, using flexible beam approximation, shows that the mechanism is robust. Finally, two bioinspired architectures are analyzed, showing significant levels of damping achieved via branching with typically 30% of the energy being dissipated in one oscillation. This concept of damping-by-branching is of simple practical use in the design of very slender and flexible structures subjected to extreme dynamical loadings.     

Modeling of biological tree structures

Biological tree-like structures, such as mammalian tracheobronchial airways, are complicated branching systems. One problem in modeling such systems is the reassignment of the number of segments at a given generation in the model being constructed. A hypothesis is proposed which has successfully been used in modeling mammalian lung airways. Research supported by the National Institute of Environmental Health Sciences through U.S. Department of Energy Contract Number EY-76-C-04-1013.     

Complex Collagen Fiber and Membrane Morphologies of the Whole Porcine Aortic Valve

Objectives

Replacement aortic valves endeavor to mimic native valve function at the organ, tissue, and in the case of bioprosthetic valves, the cellular levels. There is a wealth of information about valve macro and micro structure; however, there presently is limited information on the morphology of the whole valve fiber architecture. The objective of this study was to provide qualitative and quantitative analyses of whole valve and leaflet fiber bundle branching patterns using a novel imaging system.

Methods

We developed a custom automated microscope system with motor and imaging control. Whole leaflets (n = 25) were imaged at high resolution (e.g. 30,000×20,000 pixels) using elliptically polarized light to enhance contrast between structures without the need for staining or other methods. Key morphologies such as fiber bundle size and branching were measured for analyses.

Results

The left coronary leaflet displayed large asymmetry in fiber bundle organization relative to the right coronary and non-coronary leaflets. We observed and analyzed three main patterns of fiber branching; tree-like, fan-like, and pinnate structures. High resolution images and quantitative metrics are presented such as fiber bundle sizes, positions, and branching morphological parameters.

Significance

To our knowledge there are currently no high resolution images of whole fresh leaflets available in the literature. The images of fiber/membrane structures and analyses presented here could be highly valuable for improving the design and development of more advanced bioprosthetic and/or bio-mimetic synthetic valve replacements.     

Extracellular matrix and cytoskeletal dynamics during branching morphogenesis

Branching morphogenesis is a fundamental developmental process which results in amplification of epithelial surface area for exchanging molecules in organs including the lung, kidney, mammary gland and salivary gland. These complex tree-like structures are built by iterative rounds of simple routines of epithelial morphogenesis, including bud formation, extension, and bifurcation, that require constant remodeling of the extracellular matrix (ECM) and the cytoskeleton. In this review, we highlight the current understanding of the role of the ECM and cytoskeletal dynamics in branching morphogenesis across these different organs. The cellular and molecular mechanisms shared during this morphogenetic process provide insight into the development of other branching organs.     

Extracellular matrix and cytoskeletal dynamics during branching morphogenesis

Branching morphogenesis is a fundamental developmental process which results in amplification of epithelial surface area for exchanging molecules in organs including the lung, kidney, mammary gland and salivary gland. These complex tree-like structures are built by iterative rounds of simple routines of epithelial morphogenesis, including bud formation, extension, and bifurcation, that require constant remodeling of the extracellular matrix (ECM) and the cytoskeleton. In this review, we highlight the current understanding of the role of the ECM and cytoskeletal dynamics in branching morphogenesis across these different organs. The cellular and molecular mechanisms shared during this morphogenetic process provide insight into the development of other branching organs.     

Predation and the evolution of gregariousness. II. An economic model for predator-prey interaction

An earlier paper presented models which allow the relative advantages of different prey dispersions to be assessed for two cases: when the prey's main defence is concealment, and when prey may evade the predator (Treisman 1975). With these as a basis, an economic model for predator-prey interaction is developed which takes explicit account of the conflicts between the need to maintain watch for a predator and the prey's other needs. The model embodies arguments based on statistical decision theory which allow factors such as the degree of predation threat, the watchfulness of the prey and the number of watchers to be related to the expected value of the prey's performance. The model provides a basis for predicting the optimal number of watchers or optimal group size under various conditions. The advantages of different group configurations are compared, and it is shown that animals which aggregate (and maintain a high sensory decision criterion) will have an advantage over solitary animals under certain conditions.     

Segmentation of 3D tubular objects with adaptive front propagation and minimal tree extraction for 3D medical imaging

We present a new fast approach for segmentation of thin branching structures, like vascular trees, based on Fast-Marching (FM) and Level Set (LS) methods. FM allows segmentation of tubular structures by inflating a “long balloon” from a user given single point. However, when the tubular shape is rather long, the front propagation may blow up through the boundary of the desired shape close to the starting point. Our contribution is focused on a method to propagate only the useful part of the front while freezing the rest of it. We demonstrate its ability to segment quickly and accurately tubular and tree-like structures. We also develop a useful stopping criterion for the causal front propagation. We finally derive an efficient algorithm for extracting an underlying 1D skeleton of the branching objects, with minimal path techniques. Each branch being represented by its centerline, we automatically detect the bifurcations, leading to the “Minimal Tree” representation. This so-called “Minimal Tree” is very useful for visualization and quantification of the pathologies in our anatomical data sets. We illustrate our algorithms by applying it to several arteries datasets.     

Afferent innervation shapes the dendritic branching pattern of the Medial Giant Interneuron in grasshopper embryos raised in culture

In the adult grasshopper the Medial Giant Interneuron (MGI) receives synaptic input from the peripheral sensory neurons of the cercus. We prevented this innervation in grasshopper embryos by cutting off one or both cerci at a stage when the first sensory axons are just beginning to reach the central nervous system (CNS), and the MGI has not yet formed its mature branching pattern. Following this operation the embryos were raised in vitro for 3–9 days, and the MGI injected with the fluorescent dye Lucifer Yellow to determine its morphology. The development of the deprived cells was then compared to that of the normal MGI (described in M. Shankland and C. S. Goodman, 1982, Develop. Biol., 92, 483–500) and of cultured, but unoperated, controls to ascertain whether these presynaptic axons influence the embryonic growth and branching of the MGI's dendrites. The results of these experiments show that dendrite formation is enhanced in regions of the neuropil containing sensory axon terminals and that the afferents exert their influence locally on restricted portions of the branching structure. The enhanced growth of innervated dendrites appears to occur at the expense of dendritic outgrowth elsewhere, suggesting that the growing dendrites may be competing for a limited supply of some cellular component necessary for continued growth. Thus, the MGI's final branching pattern is at least partially dictated by the spatial distribution of presynaptic axons within the embryonic nervous system.     

Observations of the Effect of Water on the Hyphal Apices of Fusarium oxysporum

When colonies of Fusarium oxysporum, growing on plates of mineral-sucroseagar, are flooded with the mineral-sucrose solution, withoutadded agar, or with solutions of any of the constituents ofthe mineral-sucrose mixture at a concentration of 0.076 M theleading hyphal apices at the agar surface continue to grow onunchecked. If, however, the colonies are flooded with solutionsof decreasing and increasing molarity from 0.076 M an increasingproportion of the leading hyphal apices at the agar surfacestop growing, and branch subterminally. In distilled water about50 per cent. of the apices branch and this branching is precededby swelling, whereas in 0.5 M sucrose more than 90 per cent.of the apices branch and the branching is not accompanied byswelling. In the distilled water those hyphae which do not branchswell a little and grow on from the apex within 40 seconds. When hyphal apices are flooded with distilled water for from10 to 40 seconds and then transferred to mineral-sucrose solutionmore than 90 per cent, of the hyphal apices branch, whereasflooding with distilled water for 60 seconds or longer givesthe same percentage of branched apices as does flooding withdistilled water alone. It is shown that swelling and branching of the hyphal apex arenot causally related but that branching always occurs followingarrestment of the hyphal apex for more than 60 seconds. It issuggested that the phenomena reported can be explained in termsof an irreversible change in the apical cap of the arrestedhypha such that continued extension can no longer take placein this region and fresh outlets for growth must then be foundsubterminally. Such a mechanism, however triggered, could accountfor a wide variety of morphogenetic forms in the fungi.     

Cytochemical analysis of the haplosporosomes and vesicle-like droplets of Haplosporidium lusitanicum (Haplosporida,Haplosporidiidae), parasite of Helcion pellucidus (Prosobranchia)

A cytochemical study of the spore of Haplosporidium lusitanicum, a haplosporidian parasite recently found in Helcion pellucidus, is described. Cytochemical analysis with Sudan Black B at the light microscope level revealed that the vesicle-like droplets (VLD) situated in the apical and basal zones of the endosporoplasm in close contact with the external membrane is strongly stained dark blue. These structures are partially digested with lipase. Both reactions suggest the presence of lipoid components. The dense bodies of the exosporoplasm seem to be analogous in chemical composition. On the other hand, these two distinct structures, when subjected to Thiéry's test for glycoproteins, gave positive results. We think that these materials are complex structures simultaneously containing lipids and glycoproteins. They may be involved in the formation of the complex membranous system (“spherule”) that develops during spore maturation in this species. The matrix of haplosporosomes submitted to Thiéry's test for glycoproteins was also positive. A comparative cytochemical analysis has revealed that the external membrane of the haplosporosomes is more glycoproteinaceous than the internal one, which is more lipoidal.     

Segmentation of 3D tubular objects with adaptive front propagation and minimal tree extraction for 3D medical imaging

We present a new fast approach for segmentation of thin branching structures, like vascular trees, based on Fast-Marching (FM) and Level Set (LS) methods. FM allows segmentation of tubular structures by inflating a "long balloon" from a user given single point. However, when the tubular shape is rather long, the front propagation may blow up through the boundary of the desired shape close to the starting point. Our contribution is focused on a method to propagate only the useful part of the front while freezing the rest of it. We demonstrate its ability to segment quickly and accurately tubular and tree-like structures. We also develop a useful stopping criterion for the causal front propagation. We finally derive an efficient algorithm for extracting an underlying 1D skeleton of the branching objects, with minimal path techniques. Each branch being represented by its centerline, we automatically detect the bifurcations, leading to the "Minimal Tree" representation. This so-called "Minimal Tree" is very useful for visualization and quantification of the pathologies in our anatomical data sets. We illustrate our algorithms by applying it to several arteries datasets.     

Synthesis of mathematical models of branching axons and dendrites

A synthesis was made of models of branching neuronal cable structures from a full set of standard basic models. The study aimed to produce an instrument of mathematical modelling making it possible to reflect true life morphological and electrophysiological characteristics of axons and dendrites, discarding some of the restrictions and simplifications characterizing existing models of the structures mentioned. Equivalent electrical circuits of branching axons and dendrites were set up with in-series and node connections of standard four-terminal networks corresponding to basic segments with active or passive membrane. Equations were obtained for electrical processes in branching neuronal neurites, generalized in the case of multiple binary branching with arbitrary symmetry and branching structure. A difference scheme common to the whole class of models contemplated was produced and the algorithm of a numerical solution to the difference equations thus obtained was elaborated. The instrument described makes it possible to synthesize diverse models of branching axons and dendrites, offering considerably greater opportunities for modelling the main electrophysiological processes developing in these structures of electrotonus, propagation of excitation, and interaction between these two factors.State University Commemorating Tricentenary of Russo-Ukrainian Union. Dnepropetrovsk. Translated from Neirofiziologiya, Vol. 20, No. 4, pp. 471–479, July–August, 1988.     

The Probability of Extinction of Infectious Salmon Anemia Virus in One and Two Patches

Single-type and multitype branching processes have been used to study the dynamics of a variety of stochastic birth–death type phenomena in biology and physics. Their use in epidemiology goes back to Whittle’s study of a susceptible–infected–recovered (SIR) model in the 1950s. In the case of an SIR model, the presence of only one infectious class allows for the use of single-type branching processes. Multitype branching processes allow for multiple infectious classes and have latterly been used to study metapopulation models of disease. In this article, we develop a continuous time Markov chain (CTMC) model of infectious salmon anemia virus in two patches, two CTMC models in one patch and companion multitype branching process (MTBP) models. The CTMC models are related to deterministic models which inform the choice of parameters. The probability of extinction is computed for the CTMC via numerical methods and approximated by the MTBP in the supercritical regime. The stochastic models are treated as toy models, and the parameter choices are made to highlight regions of the parameter space where CTMC and MTBP agree or disagree, without regard to biological significance. Partial extinction events are defined and their relevance discussed. A case is made for calculating the probability of such events, noting that MTBPs are not suitable for making these calculations.     

How does the reliability of a model affect children's choice to learn socially or individually?

The effect of model reliability on children's choices to learn socially versus individually is pertinent to theories addressing cultural evolution and theories of selective trust. Here the effect of a reliable versus unreliable model on children's preferences to learn socially or individually was examined, as well as their subsequent imitation on a puzzle box task. Experiment One (N = 156) found children were more likely to ask to learn socially when presented with a novel task, after witnessing an unreliable rather than a reliable model. Experiment Two (N = 40) found children select a new unknown model, over the previously unreliable model, suggesting a preference to learn socially was created, although not specifically from the unreliable model. Experiment Three (N = 48) replicated children's learning preference in Experiment One with a new task, and showed children's attention is drawn towards other sources of social information (another adult model) when viewing an unreliable model, and also found a reliable model caused more fidelity of imitation. Together these results suggest that model unreliability causes greater social learning requests and attention to other, even novel, models when they are available. These findings evidence human children's strong propensity to learn socially compared with non-human animals; and suggest there is a more complicated relationship between learning preference, model reliability and selective trust than has been captured in previous research.     

The Reovirus Mutant tsA279 L2 Gene Is Associated with Generation of a Spikeless Core Particle: Implications for Capsid Assembly

Previous studies which used intertypic reassortants of the wild-type reovirus serotype 1 Lang and the temperature-sensitive (ts) serotype 3 mutant clone tsA279 identified two ts lesions; one lesion, in the M2 gene segment, was associated with defective transmembrane transport of restrictively assembled virions (P. R. Hazelton and K. M. Coombs, Virology 207:46–58, 1995). In the present study we show that the second lesion, in the L2 gene segment, which encodes the λ2 protein, is associated with the accumulation of a core-like particle defective for the λ2 pentameric spike. Physicochemical, biochemical, and immunological studies showed that these structures were deficient for genomic double-stranded RNA, the core spike protein λ2, and the minor core protein μ2. Core particles with the λ2 spike structure accumulated after temperature shift-down from a restrictive to a permissive temperature in the presence of cycloheximide. These data suggest the spike-deficient, core-like particle is an assembly intermediate in reovirus morphogenesis. The existence of this naturally occurring primary core structure suggests that the core proteins λ1, λ3, and ς2 interact to initiate the process of virion capsid assembly through a dodecahedral mechanism. The next step in the proposed capsid assembly model would be the association of the minor core protein μ2, either preceding or collateral to the condensation of the λ2 pentameric spike at the apices of the primary core structure. The assembly pathway of the reovirus double capsid is further elaborated when these observations are combined with structures identified in other studies.     

Parametric Analysis of RNA Branching Configurations

Motivated by recent work in parametric sequence alignment, we study the parameter space for scoring RNA folds and construct an RNA polytope. A vertex of this polytope corresponds to RNA secondary structures with common branching. We use this polytope and its normal fan to study the effect of varying three parameters in the free energy model that are not determined experimentally. Our results indicate that variation of these specific parameters does not have a dramatic effect on the structures predicted by the free energy model. We additionally map a collection of known RNA secondary structures to the RNA polytope.     

On Chitty's theory for fluctuating populations: The importance of genetic polymorphism in the generation of regular density cycles

Chitty's theory is, in literature, interpreted in two different ways: Either that (i) regular density cycles are caused by intrinsic factors only; or that (ii) these regular cycles are caused by the interaction of intrinsic and extrinsic factors. The first interpretation of Chitty's theory is the common one, at least among theoreticians; based on a general model, this version of Chitty's theory is concluded implausible.