High-frequency affine mechanics and nonaffine relaxation in a model cytoskeleton

The cytoskeleton is a network of crosslinked, semiflexible filaments, and it has been suggested that it has properties of a glassy state. Here we employ optical-trap-based microrheology to apply forces to a model cytoskeleton and measure the high-bandwidth response at an anterior point. Simulating the highly nonlinear and anisotropic stress-strain propagation assuming affinity, we found that theoretical predictions for the quasistatic response of semiflexible polymers are only realized at high frequencies inaccessible to conventional rheometers. We give a theoretical basis for determining the frequency when both affinity and quasistaticity are valid, and we discuss with experimental evidence that the relaxations at lower frequencies can be characterized by the experimentally obtained nonaffinity parameter

Aberrant behaviours of reaction diffusion self-organisation models on growing domains in the presence of gene expression time delays

Turing’s pattern formation mechanism exhibits sensitivity to the details of the initial conditions suggesting that, in isolation, it cannot robustly generate pattern within noisy biological environments. Nonetheless, secondary aspects of developmental self-organisation, such as a growing domain, have been shown to ameliorate this aberrant model behaviour. Furthermore, while in-situ hybridisation reveals the presence of gene expression in developmental processes, the influence of such dynamics on Turing’s model has received limited attention. Here, we novelly focus on the Gierer–Meinhardt reaction diffusion system considering delays due the time taken for gene expression, while incorporating a number of different domain growth profiles to further explore the influence and interplay of domain growth and gene expression on Turing’s mechanism. We find extensive pathological model behaviour, exhibiting one or more of the following: temporal oscillations with no spatial structure, a failure of the Turing instability and an extreme sensitivity to the initial conditions, the growth profile and the duration of gene expression. This deviant behaviour is even more severe than observed in previous studies of Schnakenberg kinetics on exponentially growing domains in the presence of gene expression (Gaffney and Monk in Bull. Math. Biol. 68:99–130, 2006). Our results emphasise that gene expression dynamics induce unrealistic behaviour in Turing’s model for multiple choices of kinetics and thus such aberrant modelling predictions are likely to be generic. They also highlight that domain growth can no longer ameliorate the excessive sensitivity of Turing’s mechanism in the presence of gene expression time delays. The above, extensive, pathologies suggest that, in the presence of gene expression, Turing’s mechanism would generally require a novel and extensive secondary mechanism to control reaction diffusion patterning

Turing patterns on networks

Turing patterns formed by activator-inhibitor systems on networks are considered. The linear stability analysis shows that the Turing instability generally occurs when the inhibitor diffuses sufficiently faster than the activator. Numerical simulations, using a prey-predator model on a scale-free random network, demonstrate that the final, asymptotically reached Turing patterns can be largely different from the critical modes at the onset of instability, and multistability and hysteresis are typically observed. An approximate mean-field theory of nonlinear Turing patterns on the networks is constructed.Comment: 4 pages, 4 figure

Polyamine sensitivity of gap junctions is required for skin pattern formation in zebrafish

Gap junctions allow the direct and bidirectional transfer of small molecules between cells. Polyamine sensitivity, which has been observed for a certain gap junction in vitro, confers rectification property to gap junction. Here we report that the polyamine sensitivity of gap junctions in vivo is crucial for skin pattern formation in zebrafish. Transgenic experiments have revealed that several connexin genes were able to rescue the spot phenotype of mutant zebrafish. Mutational analyses of the N-terminal region of connexins revealed that the ExxxE motif, a hypothetical polyamine-binding site, was important for connexin's role in pattern formation. Ectopic expression of spermidine/spermine N1-acetyltransferase (SSAT), a polyamine metabolic enzyme, also caused stripe pattern changes, which further indicates that the polyamine sensitivity of gap junctions is crucial. This is the first report to show that polyamine sensitivity has a physiologically relevant function and is related to skin pattern formation in animals

Basonuclin-2 Requirements for Zebrafish Adult Pigment Pattern Development and Female Fertility

Relatively little is known about the generation of adult form. One complex adult trait that is particularly amenable to genetic and experimental analysis is the zebrafish pigment pattern, which undergoes extensive remodeling during post-embryonic development to form adult stripes. These stripes result from the arrangement of three classes of neural crest-derived pigment cells, or chromatophores: melanophores, xanthophores, and iridophores. Here, we analyze the zebrafish bonaparte mutant, which has a normal early pigment pattern but exhibits a severe disruption to the adult stripe pattern. We show that the bonaparte mutant phenotype arises from mutations in basonuclin-2 (bnc2), encoding a highly conserved, nuclear-localized zinc finger protein of unknown function. We show that bnc2 acts non-autonomously to the melanophore lineage and is expressed by hypodermal cells adjacent to chromatophores during adult pigment pattern formation. In bonaparte (bnc2) mutants, all three types of chromatophores differentiate but then are lost by extrusion through the skin. We further show that while bnc2 promotes the development of two genetically distinct populations of melanophores in the body stripes, chromatophores of the fins and scales remain unaffected in bonaparte mutants, though a requirement of fin chromatophores for bnc2 is revealed in the absence of kit and colony stimulating factor-1 receptor activity. Finally, we find that bonaparte (bnc2) mutants exhibit dysmorphic ovaries correlating with infertility and bnc2 is expressed in somatic ovarian cells, whereas the related gene, bnc1, is expressed within oocytes; and we find that both bnc2 and bnc1 are expressed abundantly within the central nervous system. These findings identify bnc2 as an important mediator of adult pigment pattern formation and identify bonaparte mutants as an animal model for dissecting bnc2 functions

Mechanisms and in vivo functions of contact inhibition of locomotion

Contact inhibition of locomotion (CIL) is a process whereby a cell ceases motility or changes its trajectory upon collision with another cell. CIL was initially characterized more than half a century ago and became a widely studied model system to understand how cells migrate and dynamically interact. Although CIL fell from interest for several decades, the scientific community has recently rediscovered this process. We are now beginning to understand the precise steps of this complex behaviour and to elucidate its regulatory components, including receptors, polarity proteins and cytoskeletal elements. Furthermore, this process is no longer just in vitro phenomenology; we now know from several different in vivo models that CIL is essential for embryogenesis and in governing behaviours such as cell dispersion, boundary formation and collective cell migration. In addition, changes in CIL responses have been associated with other physiological processes, such as cancer cell dissemination during metastasis

A developmental model for branching morphogenesis of lake cress compound leaf

Lake cress, Rorippa aquatica (Brassicaceae), is a semi-aquatic plant that exhibits a variety of leaf shapes, from simple leaves to highly branched compound leaves, depending on the environment. Leaf shape can vary within a single plant, suggesting that the variation can be explained by a simple model. In order to simulate the branched structure in the compound leaves of R. aquatica, we implemented reaction-diffusion (RD) patterning onto a theoretical framework that had been developed for serration distribution in the leaves of Arabidopsis thaliana, with the modification of the one-dimensional reaction-diffusion domain being deformed with the spatial periodicity of the RD pattern while expanding. This simple method using an iterative pattern could create regular and nested branching patterns. Subsequently, we verified the plausibility of our theoretical model by comparing it with the experimentally observed branching patterns. The results suggested that our model successfully predicted both the qualitative and quantitative aspects of the timing and positioning of branching in growing R. aquatica leaves

Interactions between zebrafish pigment cells responsible for the generation of Turing patterns

The reaction–diffusion system is one of the most studied nonlinear mechanisms that generate spatially periodic structures autonomous. On the basis of many mathematical studies using computer simulations, it is assumed that animal skin patterns are the most typical examples of the Turing pattern (stationary periodic pattern produced by the reaction–diffusion system). However, the mechanism underlying pattern formation remains unknown because the molecular or cellular basis of the phenomenon has yet to be identified. In this study, we identified the interaction network between the pigment cells of zebrafish, and showed that this interaction network possesses the properties necessary to form the Turing pattern. When the pigment cells in a restricted region were killed with laser treatment, new pigment cells developed to regenerate the striped pattern. We also found that the development and survival of the cells were influenced by the positioning of the surrounding cells. When melanophores and xanthophores were located at adjacent positions, these cells excluded one another. However, melanophores required a mass of xanthophores distributed in a more distant region for both differentiation and survival. Interestingly, the local effect of these cells is opposite to that of their effects long range. This relationship satisfies the necessary conditions required for stable pattern formation in the reaction–diffusion model. Simulation calculations for the deduced network generated wild-type pigment patterns as well as other mutant patterns. Our findings here allow further investigation of Turing pattern formation within the context of cell biology