A Theoretical Model of Pattern Formation in Coral Reefs

We present a mathematical model of the growth of coral subject to unidirectional ocean currents using concepts of porous-media flow and nonlinear dynamics in chemical systems. Linear stability analysis of the system of equations predicts that the growth of solid (coral) structures will be aligned perpendicular to flow, propagating against flow direction. Length scales of spacing between structures are selected based on chemical reaction and flow rates. In the fully nonlinear system, autocatalysis in the chemical reaction accelerates growth. Numerical analysis reveals that the nonlinear growth creates sharp fronts of high solid fraction that, as predicted by the linear stability, advance against the predominating flow direction. The findings of regularly spaced growth areas oriented perpendicular to flow are qualitatively supported on both a colonial and a regional reef scale. Received 1 October 2001; accepted 22 May 2002.     

Pattern Formation in a Model for Mountain Pine Beetle Dispersal: Linking Model Predictions to Data

Pattern formation occurs in a wide range of biological systems. This pattern formation can occur in mathematical models because of diffusion-driven instability or due to the interaction between reaction, diffusion, and chemotaxis. In this paper, we investigate the spatial pattern formation of attack clusters in a system for Mountain Pine Beetle. The pattern formation (aggregation) of the Mountain Pine Beetle in order to attack susceptible trees is crucial for their survival and reproduction. We use a reaction-diffusion equation with chemotaxis to model the interaction between Mountain Pine Beetle, Mountain Pine Beetle pheromones, and susceptible trees. Mathematical analysis is utilized to discover the spacing in-between beetle attacks on the susceptible landscape. The model predictions are verified by analysing aerial detection survey data of Mountain Pine Beetle Attack from the Sawtooth National Recreation Area. We find that the distance between Mountain Pine Beetle attack clusters predicted by our model closely corresponds to the observed attack data in the Sawtooth National Recreation Area. These results clarify the spatial mechanisms controlling the transition from incipient to epidemic populations and may lead to control measures which protect forests from Mountain Pine Beetle outbreak.     

Pattern Formation in a Nonlinear Membrane Model for Epithelial Morphogenesis

A theoretical model is presented for pattern formation in an epithelium. The epithelial model consists of a thin, incompressible, viscoelastic membrane on an elastic foundation (substrate), with the component cells assumed to have active contractile properties similar to those of smooth muscle. The analysis includes the effects of large strains and material nonlinearity, and the governing equations were solved using finite differences. Deformation patterns form when the cells activate while lying on the descending limb of their total (active + passive) stress-stretch curve. Various one-dimensional and two-dimensional simulations illustrate the effects of spatial and temporal variations in passive stiffness, as well as the effects of foundation stiffness and stretch activation. The model can be used to examine the mechanical aspects of pattern formation in morphogenetic processes such as angiogenesis and myocardial trabeculation.     

A Mathematical Model of Pattern Formation by Swimming Microorganisms*

Bioconvection in suspensions of Tetrahymena pyriformis and Crypthecodinium cohnii is described and 2 new patterns, the toroid and the cat's-eye, which appear in shallow suspensions of C. cohnii, are reported. Except in very dense cultures, bioconvection does not arise unless the depth of the suspensions or the mean concentration exceed certain critical values, other things being equal. A mathematical model describing the hydrodynamics of suspension of negatively geotactic microorganisms is described which predicts the existence of critical depths and concentrations. The equations presented admit solutions describing the “polka-dot” patterns seen at low organism concentration in suspensions slightly deeper than the critical value. The discussion here is limited to the case of fairly dilute suspensions, but the basic approach can be applied also to richer cultures.     

Genetics on the Fly: A Primer on the Drosophila Model System

Fruit flies of the genus Drosophila have been an attractive and effective genetic model organism since Thomas Hunt Morgan and colleagues made seminal discoveries with them a century ago. Work with Drosophila has enabled dramatic advances in cell and developmental biology, neurobiology and behavior, molecular biology, evolutionary and population genetics, and other fields. With more tissue types and observable behaviors than in other short-generation model organisms, and with vast genome data available for many species within the genus, the fly’s tractable complexity will continue to enable exciting opportunities to explore mechanisms of complex developmental programs, behaviors, and broader evolutionary questions. This primer describes the organism’s natural history, the features of sequenced genomes within the genus, the wide range of available genetic tools and online resources, the types of biological questions Drosophila can help address, and historical milestones.     

The Morphostatic Limit for a Model of Skeletal Pattern Formation in the Vertebrate Limb

A recently proposed mathematical model of a “core” set of cellular and molecular interactions present in the developing vertebrate limb was shown to exhibit pattern-forming instabilities and limb skeleton-like patterns under certain restrictive conditions, suggesting that it may authentically represent the underlying embryonic process (Hentschel et al., Proc. R. Soc. B 271, 1713–1722, 2004). The model, an eight-equation system of partial differential equations, incorporates the behavior of mesenchymal cells as “reactors,” both participating in the generation of morphogen patterns and changing their state and position in response to them. The full system, which has smooth solutions that exist globally in time, is nonetheless highly complex and difficult to handle analytically or numerically. According to a recent classification of developmental mechanisms (Salazar-Ciudad et al., Development 130, 2027–2037, 2003), the limb model of Hentschel et al. is “morphodynamic,” since differentiation of new cell types occurs simultaneously with cell rearrangement. This contrasts with “morphostatic” mechanisms, in which cell identity becomes established independently of cell rearrangement. Under the hypothesis that development of some vertebrate limbs employs the core mechanism in a morphostatic fashion, we derive in an analytically rigorous fashion a pair of equations representing the spatiotemporal evolution of the morphogen fields under the assumption that cell differentiation relaxes faster than the evolution of the overall cell density (i.e., the morphostatic limit of the full system). This simple reaction–diffusion system is unique in having been derived analytically from a substantially more complex system involving multiple morphogens, extracellular matrix deposition, haptotaxis, and cell translocation. We identify regions in the parameter space of the reduced system where Turing-type pattern formation is possible, which we refer to as its “Turing space.” Obtained values of the parameters are used in numerical simulations of the reduced system, using a new Galerkin finite element method, in tissue domains with nonstandard geometry. The reduced system exhibits patterns of spots and stripes like those seen in developing limbs, indicating its potential utility in hybrid continuum-discrete stochastic modeling of limb development. Lastly, we discuss the possible role in limb evolution of selection for increasingly morphostatic developmental mechanisms.     

A Mechanochemical Model for Embryonic Pattern Formation: Coupling Tissue Mechanics and Morphogen Expression

Motivated by recent experimental findings, we propose a novel mechanism of embryonic pattern formation based on coupling of tissue curvature with diffusive signaling by a chemical factor. We derive a new mathematical model using energy minimization approach and show that the model generates a variety of morphogen and curvature patterns agreeing with experimentally observed structures. The mechanism proposed transcends the classical Turing concept which requires interactions between two morphogens with a significantly different diffusivity. Our studies show how biomechanical forces may replace the elusive long-range inhibitor and lead to formation of stable spatially heterogeneous structures without existence of chemical prepatterns. We propose new experimental approaches to decisively test our central hypothesis that tissue curvature and morphogen expression are coupled in a positive feedback loop.     

Advances in Pattern Formation: Signaling and Transcription

Key Words: Wingless, Pair-Rule, FGF, Regeneration, Extracellular Matrix The 49th annual Drosophila research conference was held in the sunny confines of San Diego. As usual, large numbers of Drosophila scientists working in fields as different as immunology and evolution descended on the venue. The meeting showed that the fly community is still vibrant and diverse even with the funding crunch at the NIH and the renewed rumors that Drosophila may have outlived its usefulness. This short review will focus on one session of platform presentations detailing the recent advances in the field of pattern formation. This session offered a variety of topics reviewing the formation of pattern in various tissues through diverse mechanisms. I will focus on early embryonic patterning through pair-rule genes, specificity of FGF signaling, and tissue regeneration.     

植被格局的分形模型：植被格局的分形特征

 目前植被格局研究存在一些问题,分形模型是解决这些问题的有力工具。选择从分枝到景观的各个等级层次上若干有代表性的研究实例进行介绍,给出了尺度、自相似性和分形维数在植被格局研究中的应用方法,说明了分形模型描述植被格局的实用性和优越性。在此基础上提出植被格局的分形机制,认为植被格局是具有自组织特征的分形体。最后对植被格局的分形模型进行了评价,提出研究中需要注意的若干问题以及未来的发展方向。     

A Theoretical Model of Jigsaw-Puzzle Pattern Formation by Plant Leaf Epidermal Cells

Plant leaf epidermal cells exhibit a jigsaw puzzle–like pattern that is generated by interdigitation of the cell wall during leaf development. The contribution of two ROP GTPases, ROP2 and ROP6, to the cytoskeletal dynamics that regulate epidermal cell wall interdigitation has already been examined; however, how interactions between these molecules result in pattern formation remains to be elucidated. Here, we propose a simple interface equation model that incorporates both the cell wall remodeling activity of ROP GTPases and the diffusible signaling molecules by which they are regulated. This model successfully reproduces pattern formation observed in vivo, and explains the counterintuitive experimental results of decreased cellulose production and increased thickness. Our model also reproduces the dynamics of three-way cell wall junctions. Therefore, this model provides a possible mechanism for cell wall interdigitation formation in vivo.     

A Model for the Genetics of Handedness

Experimental data and theoretical work on the inheritance of handedness and cerebral dominance are reviewed. A two-gene, four-allele model, one locus pertaining to left or right hemispheric dominance and the other to contralateral or ipsilateral hand control relative to the dominant hemisphere, is constructed. It is in excellent agreement with all quantitative information regarding this problem. Refinements designed to explain relevant qualitative facts are proposed and discussed.     

Predicting the Distribution of Spiral Waves from Cell Properties in a Developmental-Path Model of Dictyostelium Pattern Formation

The slime mold Dictyostelium discoideum is one of the model systems of biological pattern formation. One of the most successful answers to the challenge of establishing a spiral wave pattern in a colony of homogeneously distributed D. discoideum cells has been the suggestion of a developmental path the cells follow (Lauzeral and coworkers). This is a well-defined change in properties each cell undergoes on a longer time scale than the typical dynamics of the cell. Here we show that this concept leads to an inhomogeneous and systematic spatial distribution of spiral waves, which can be predicted from the distribution of cells on the developmental path. We propose specific experiments for checking whether such systematics are also found in data and thus, indirectly, provide evidence of a developmental path.     

ConA对鲤鱼粘液细胞的影响

研究ＣｏｎＡ对鲤鱼粘液细胞的刺激作用,结果表明,腹腔注射ＣｏｎＡ能够使鲤鱼粘膜上皮、口腔粘膜上皮和皮肤的粘膜细胞数量明显增多,且在上皮的深层也出现部分粘膜细胞,但其形态、大小无明显变化。     

Population Genetics of the Eastern Hellbender (Cryptobranchus alleganiensis alleganiensis) across Multiple Spatial Scales

Conservation genetics is a powerful tool to assess the population structure of species and provides a framework for informing management of freshwater ecosystems. As lotic habitats become fragmented, the need to assess gene flow for species of conservation management becomes a priority. The eastern hellbender (Cryptobranchus alleganiensis alleganiensis) is a large, fully aquatic paedamorphic salamander. Many populations are experiencing declines throughout their geographic range, yet the genetic ramifications of these declines are currently unknown. To this end, we examined levels of genetic variation and genetic structure at both range-wide and drainage (hierarchical) scales. We collected 1,203 individuals from 77 rivers throughout nine states from June 2007 to August 2011. Levels of genetic diversity were relatively high among all sampling locations. We detected significant genetic structure across populations (F_st values ranged from 0.001 between rivers within a single watershed to 0.218 between states). We identified two genetically differentiated groups at the range-wide scale: 1) the Ohio River drainage and 2) the Tennessee River drainage. An analysis of molecular variance (AMOVA) based on landscape-scale sampling of basins within the Tennessee River drainage revealed the majority of genetic variation (∼94–98%) occurs within rivers. Eastern hellbenders show a strong pattern of isolation by stream distance (IBSD) at the drainage level. Understanding levels of genetic variation and differentiation at multiple spatial and biological scales will enable natural resource managers to make more informed decisions and plan effective conservation strategies for cryptic, lotic species.     

Structure of Flower in Arabidopsis thaliana: Spatial Pattern Formation

Morphological analysis of flowers was carried out in Arabidopsis thaliana wild type plants and agamous and apetala2 mutants. No direct substitution of organs takes place in the mutants, since the number and position of organs in them do not correspond to the structure of wild type flower. In order to explain these data, a notion of spatial pattern formation in the meristem was introduced, which preceded the processes of appearance of organ primordia and formation of organs. Zones of acropetal and basipetal spatial pattern formation in the flower of wild type plants were postulated. It was shown that the acropetal spatial pattern formation alone took place in agamous mutants and basipetal spatial pattern formation alone, in apetala2 mutants. Different variants of flower structure are interpreted as a result of changes in the volume of meristem (space) and order of spatial pattern formation (time).     

中国医院住院患者体验和满意监测量表的开发研究：量表的初步形成

目的 开发适合中国医院应用的住院患者体验与满意监测量表。方法 通过检索国内外的相关文献,收集国外成熟的满意度量表,结合国内现有的量表,通过专家组对条目进行筛选并修正。结果 研制出的CHPESM量表包含可及入院、一般住院服务、治疗服务、意见管理、环境与后勤以及出院指导6个维度28个核心条目,均采用Likert 5级评分法。结论 CHPESM量表具有较好的内容效度。