Complex epithelial remodeling underlie the fusion event in early fetal development of the human penile urethra.

We recently described a two-step process of urethral plate canalization and urethral fold fusion to form the human penile urethra. Canalization ("opening zipper") opens the solid urethral plate into a groove, and fusion ("closing zipper") closes the urethral groove to form the penile urethra. We hypothesize that failure of canalization and/or fusion during human urethral formation can lead to hypospadias. Herein, we use scanning electron microscopy (SEM) and analysis of transverse serial sections to better characterize development of the human fetal penile urethra as contrasted to the development of the human fetal clitoris. Eighteen 7-13 week human fetal external genitalia specimens were analyzed by SEM, and fifteen additional human fetal specimens were sectioned for histologic analysis. SEM images demonstrate canalization of the urethral/vestibular plate in the developing male and female external genitalia, respectively, followed by proximal to distal fusion of the urethral folds in males only. The fusion process during penile development occurs sequentially in multiple layers and through the interlacing of epidermal "cords". Complex epithelial organization is also noted at the site of active canalization. The demarcation between the epidermis of the shaft and the glans becomes distinct during development, and the epithelial tag at the distal tip of the penile and clitoral glans regresses as development progresses. In summary, SEM analysis of human fetal specimens supports the two-zipper hypothesis of formation of the penile urethra. The opening zipper progresses from proximal to distal along the shaft of the penis and clitoris into the glans in identical fashion in both sexes. The closing zipper mechanism is active only in males and is not a single process but rather a series of layered fusion events, uniquely different from the simple fusion of two epithelial surfaces as occurs in formation of the palate and neural tube

Replica symmetry breaking in an adiabatic spin-glass model of adaptive evolution

We study evolutionary canalization using a spin-glass model with replica theory, where spins and their interactions are dynamic variables whose configurations correspond to phenotypes and genotypes, respectively. The spins are updated under temperature T_S, and the genotypes evolve under temperature T_J, according to the evolutionary fitness. It is found that adaptation occurs at T_S < T_S^{RS}, and a replica symmetric phase emerges at T_S^{RSB} < T_S < T_S^{RS}. The replica symmetric phase implies canalization, and replica symmetry breaking at lower temperatures indicates loss of robustness.Comment: 5pages, 2 figure

Comparison of imaging with sub-wavelength resolution in the canalization and resonant tunnelling regimes

We compare the properties of subwavelength imaging in the visible wavelength range for metal-dielectric multilayers operating in the canalization and the resonant tunnelling regimes. The analysis is based on the transfer matrix method and time domain simulations. We show that Point Spread Functions for the first two resonances in the canalization regime are approximately Gaussian in shape. Material losses suppress transmission for higher resonances, regularise the PSF but do not compromise the resolution. In the resonant tunnelling regime, the MTF may dramatically vary in their phase dependence. Resulting PSF may have a sub-wavelength thickness as well as may be broad with multiple maxima and a rapid phase modulation. We show that the width of PSF may be reduced by further propagation in free space, and we provide arguments to explain this surprising observation.Comment: 17 pages,12 figure

Pseudocanalization regime for magnetic dark-field hyperlens

Hyperbolic metamaterials (HMMs) are the cornerstone of the hyperlens, which brings the superresolution effect from the near-field to the far-field zone. For effective application of the hyperlens it should operate in so-called canalization regime, when the phase advancement of the propagating fields is maximally supressed, and thus field broadening is minimized. For conventional hyperlenses it is relatively straightforward to achieve canalization by tuning the anisotropic permittivity tensor. However, for a dark-field hyperlens designed to image weak scatterers by filtering out background radiation (dark-field regime) this approach is not viable, because design requirements for such filtering and elimination of phase advancement i.e. canalization, are mutually exclusive. Here we propose the use of magnetic ($\mu$-positive and negative) HMMs to achieve phase cancellation at the output equivalent to the performance of a HMM in the canalized regime. The proposed structure offers additional flexibility over simple HMMs in tuning light propagation. We show that in this ``pseudocanalizing'' configuration quality of an image is comparable to a conventional hyperlens, while the desired filtering of the incident illumination associated with the dark-field hyperlens is preserved

Symmetry in Critical Random Boolean Network Dynamics

Using Boolean networks as prototypical examples, the role of symmetry in the dynamics of heterogeneous complex systems is explored. We show that symmetry of the dynamics, especially in critical states, is a controlling feature that can be used both to greatly simplify analysis and to characterize different types of dynamics. Symmetry in Boolean networks is found by determining the frequency at which the various Boolean output functions occur. There are classes of functions that consist of Boolean functions that behave similarly. These classes are orbits of the controlling symmetry group. We find that the symmetry that controls the critical random Boolean networks is expressed through the frequency by which output functions are utilized by nodes that remain active on dynamical attractors. This symmetry preserves canalization, a form of network robustness. We compare it to a different symmetry known to control the dynamics of an evolutionary process that allows Boolean networks to organize into a critical state. Our results demonstrate the usefulness and power of using the symmetry of the behavior of the nodes to characterize complex network dynamics, and introduce a novel approach to the analysis of heterogeneous complex systems

Canalization and Symmetry in Boolean Models for Genetic Regulatory Networks

Canalization of genetic regulatory networks has been argued to be favored by evolutionary processes due to the stability that it can confer to phenotype expression. We explore whether a significant amount of canalization and partial canalization can arise in purely random networks in the absence of evolutionary pressures. We use a mapping of the Boolean functions in the Kauffman N-K model for genetic regulatory networks onto a k-dimensional Ising hypercube to show that the functions can be divided into different classes strictly due to geometrical constraints. The classes can be counted and their properties determined using results from group theory and isomer chemistry. We demonstrate that partially canalized functions completely dominate all possible Boolean functions, particularly for higher k. This indicates that partial canalization is extremely common, even in randomly chosen networks, and has implications for how much information can be obtained in experiments on native state genetic regulatory networks.Comment: 14 pages, 4 figures; version to appear in J. Phys.

The Influence of Canalization on the Robustness of Boolean Networks

Time- and state-discrete dynamical systems are frequently used to model molecular networks. This paper provides a collection of mathematical and computational tools for the study of robustness in Boolean network models. The focus is on networks governed by $k$-canalizing functions, a recently introduced class of Boolean functions that contains the well-studied class of nested canalizing functions. The activities and sensitivity of a function quantify the impact of input changes on the function output. This paper generalizes the latter concept to $c$-sensitivity and provides formulas for the activities and $c$-sensitivity of general $k$-canalizing functions as well as canalizing functions with more precisely defined structure. A popular measure for the robustness of a network, the Derrida value, can be expressed as a weighted sum of the $c$-sensitivities of the governing canalizing functions, and can also be calculated for a stochastic extension of Boolean networks. These findings provide a computationally efficient way to obtain Derrida values of Boolean networks, deterministic or stochastic, that does not involve simulation.Comment: 16 pages, 2 figures, 3 table