Evolution and dynamics of branching colonial form in marine modular cnidarians: gorgonian octocorals

Multi-branched arborescent networks are common patterns for many sessile marine modular organisms but no clear understanding of their development is yet available. This paper reviews new findings in the theoretical and comparative biology of branching modular organisms (e.g. Octocorallia Cnidaria) and new hypotheses on the evolution of form are discussed. A particular characteristic of branching Caribbean gorgonian octocorals is a morphologic integration at two levels of colonial organization based on whether the traits are at the module or colony level. This revealed an emergent level of integration and modularity produced by the branching process itself and not entirely by the module replication. In essence, not just a few changes at the module level could generate changes in colony architecture, suggesting uncoupled developmental patterning for the polyp and branch level traits. Therefore, the evolution of colony form in octocorals seems to be related to the changes affecting the process of branching. Branching in these organisms is sub-apical, coming from mother branches, and the highly self-organized form is the product of a dynamic process maintaining a constant ratio between mother and daughter branches. Colony growth preserves shape but is a logistic growth-like event due to branch interference and/or allometry. The qualitative branching patterns in octocorals (e.g. sea feathers, fans, sausages, and candelabra) occurred multiple times when compared with recent molecular phylogenies, suggesting independence of common ancestry to achieve these forms. A number of species with different colony forms, particularly alternate species (e.g. sea candelabrum), shared the same value for an important branching parameter (the ratio of mother to total branches). According to the way gorgonians branch and achieve form, it is hypothesized that the diversity of alternate species sharing the same narrow variance in that critical parameter for growth might be the product of canalization (or a developmental constraint), where uniform change in growth rates and maximum colony size might explain colony differences among species. If the parameter preserving shape in the colonies is fixed but colonies differ in their growth rates and maximum sizes, heterochrony could be responsible for the evolution among some gorgonian corals with alternate branching.     

Colony growth responses of the Caribbean octocoral, Pseudopterogorgia elisabethae, to harvesting

Abstract. Colonies of the branching Caribbean gorgonian Pseudopterogorgia elisabethae were subjected to partial mortality at 2 sites in the Bahamas to study how colony growth responds to disturbances such as harvesting, grazing, and storm damage. Colonies were clipped so that either 4 branches or 10 branches remained. Growth rates of branches were then monitored over 1 year and compared with nearby unclipped colonies. No significant differences were found between branch extension rates among the 3 treatments. Extension rates of newly formed branches were significantly greater in all treatments than among branches present at the start of the experiment. Per capita branching rates were greater on the more severely clipped colonies and were smallest on control colonies. The absolute number of branches that became mother branches did not differ among treatments. Colonies clipped so that 4 and 10 branches remained had the same average number of mother branches per colony, and there was no significant difference between treatments in the average number of new branches formed on the colonies. Per capita branching rates were significantly different among treatments only because the relative proportion of branches that became mother branches was higher in colonies with four branches than in treatments with more initial branches. Total growth (cumulative growth on all branches) was not significantly different between the 2 clipped treatments. Many of the control colonies suffered extensive damage, which may have obscured the comparison of clipped and unclipped treatments; however, within the range of these clipping treatments, differing levels of partial mortality did not lead to different recovery rates. The lack of treatment effects is particularly relevant to assessing the effects of harvest techniques on the recovery and productivity of harvested, naturally occurring, colonies.     

Allometry of resource capture in colonial cnidarians and constraints on modular growth

1. Indeterminacy in growth of colonial organisms, such as corals, is commonly attributed to their modular construction which frees the colony from the allometric constraints that limit the size of single modules. However, as a colony grows, there may be a decrease in resource availability to interior modules because of active depletion and/or passive deflection by modules on the exterior. The effects of 'self-shading' on resource capture in modular animals are modelled using a simple allometric growth function.
2. The model assumes that resource capture by a module scales as an exponent ( γ ) of colony size (i.e. number of modules). Data taken from the literature indicate that model values of γ for light and prey capture range from – 0·80 to – 1·16 for branching and encrusting corals. Module-specific rates of resource use (i.e. metabolism) are less affected by colony size. Therefore, as a colony grows, net resource state eventually reaches zero, making further growth unsustainable or determinate.
3. The model also predicts an inverse relationship between module size and colony size such as that observed in Caribbean corals. This negative correlation results from the additive effects of module size and colony size on the degree of self-shading.
4. Resource capture is affected by growth form and flow regime, and the interaction between them can account for some of the morphological variation in corals and other colonial suspension feeders.     

Polyp oriented modelling of coral growth

The morphogenesis of colonial stony corals is the result of the collective behaviour of many coral polyps depositing coral skeleton on top of the old skeleton on which they live. Yet, models of coral growth often consider the polyps as a single continuous surface. In the present work, the polyps are modelled individually. Each polyp takes up resources, deposits skeleton, buds off new polyps and dies. In this polyp oriented model, spontaneous branching occurs. We argue that branching is caused by a so called “polyp fanning effect” by which polyps on a convex surface have a competitive advantage relative to polyps on a flat or concave surface. The fanning effect generates a more potent branching mechanism than the Laplacian growth mechanism that we have studied previously (J. Theor. Biol. 224 (2003) 153). We discuss the application of the polyp oriented model to the study of environmentally driven morphological plasticity in stony corals. In a few examples we show how the properties of the individual polyps influence the whole colony morphology. In our model, the spacing of polyps influences the thickness of coral branches and the overall compactness of the colony. Density variations in the coral skeleton may also be important for the whole colony morphology, which we address by studying two variants of the model. Finally, we discuss the importance of small scale resource translocation in the coral colony and its effects on the morphology of the colony.     

Collective colony growth is optimized by branching pattern formation in Pseudomonas aeruginosa

Branching pattern formation is common in many microbes. Extensive studies have focused on addressing how such patterns emerge from local cell–cell and cell–environment interactions. However, little is known about whether and to what extent these patterns play a physiological role. Here, we consider the colonization of bacteria as an optimization problem to find the colony patterns that maximize colony growth efficiency under different environmental conditions. We demonstrate that Pseudomonas aeruginosa colonies develop branching patterns with characteristics comparable to the prediction of modeling; for example, colonies form thin branches in a nutrient‐poor environment. Hence, the formation of branching patterns represents an optimal strategy for the growth of Pseudomonas aeruginosa colonies. The quantitative relationship between colony patterns and growth conditions enables us to develop a coarse‐grained model to predict diverse colony patterns under more complex conditions, which we validated experimentally. Our results offer new insights into branching pattern formation as a problem‐solving social behavior in microbes and enable fast and accurate predictions of complex spatial patterns in branching colonies.     

不同土壤雷竹盆栽苗地下茎分枝数量特征及其分布格局

为了探究竹子分株系统构建过程及其与人工经营的关系,本文对雷竹(Phyllostachys praecox C. D. Chu et C. S. Chao ‘Prevernalis’)不同年龄母竹、不同覆盖年限竹林进行土壤盆栽实验,比较了各处理竹苗地下茎分枝生长差异。结果显示：在盆栽竹苗分株系统构建过程中,地下茎以竹鞭分枝为主;2年生母竹盆栽苗地下茎分枝数量普遍高于1年生盆栽苗,且地下茎分枝表现出随竹林土壤覆盖年限增加而减少的趋势;盆栽苗地下茎分枝主要分布于第Ⅱ、Ⅲ、Ⅳ分枝的鞭中位置;1年生母竹盆栽苗地下茎分枝以第Ⅱ分枝级别的鞭中、鞭梢部位为多,而2年生母竹盆栽苗则以第Ⅲ分枝级别的鞭中、鞭梢部位为多;随土壤覆盖年限增加,地下茎分枝偏向分布于较为靠前的分枝级别。研究发现,母竹盆栽苗分株系统的构建主要采取了扩大地下分枝的策略,其2年生母竹与竹鞭中部着生侧芽的分枝生长对分株系统拓展贡献率较大;竹林土壤覆盖时间越久越不利于地下茎分枝。由于竹子分株系统具有时空拓展性,其地下茎分枝生长特征尚需持续观察。     

Complexity generated by iteration of hierarchical modules in bryozoa

Growth in colonial organisms by iteration of modules inherently provides for an increase in available morpho-ecospace relative to their solitary relatives. Therefore, the interpretation of the functional or evolutionary significance of complexity within groups that exhibit modular growth may need to be considered under criteria modified from those used to interpret complexity in solitary organisms. Primary modules, corresponding to individuals, are the fundamental building blocks of a colonial organism. Groups of primary modules commonly form a second-order modular unit, such as a branch, which may then be iterated to form a more complex colony. Aspects of overall colony form, along with their implications for ecology and evolution, are reflected in second-order modular (structural) units to a far greater degree than by primary modular units (zooids). A colony generated by modular growth can be classified by identifying its second-order modular (structural) unit and then by characterizing the nature and relationships of these iterated units within the colony. This approach to classifying modular growth habits provides a standardized terminology and allows for direct comparison of a suite of functionally analogous character states among taxa with specific parameters of their ecology.     

Determinate growth and modularity in a gorgonian octocoral

Growth rates of branches of colonies of the gorgonian Pseudopterogorgia elisabethae were monitored for 2 years on a reef at San Salvador Island, Bahamas. Images of 261 colonies were made at 6-month intervals and colony and branch growth analyzed. Branch growth rates differed between colonies and between the time intervals in which the measurements were made. Colonies developed a plumelike morphology through a pattern of branch origination and determinate growth in which branch growth rates were greatest at the time the branch originated and branches seldom grew beyond a length of 8 cm. A small number of branches had greater growth rates, did not stop growing, and were sites for the origination of subsequent "generations" of branches. The rate of branch origination decreased with each generation of branching, and branch growth rates were lower on larger colonies, leading to determinate colony growth. Although colonial invertebrates like P. elisabethae grow through the addition of polyps, branches behave as modules with determinate growth. Colony form and size is generated by the iterative addition of branches.     

Tree Branching: Leonardo da Vinci's Rule versus Biomechanical Models

This study examined Leonardo da Vinci''s rule (i.e., the sum of the cross-sectional area of all tree branches above a branching point at any height is equal to the cross-sectional area of the trunk or the branch immediately below the branching point) using simulations based on two biomechanical models: the uniform stress and elastic similarity models. Model calculations of the daughter/mother ratio (i.e., the ratio of the total cross-sectional area of the daughter branches to the cross-sectional area of the mother branch at the branching point) showed that both biomechanical models agreed with da Vinci''s rule when the branching angles of daughter branches and the weights of lateral daughter branches were small; however, the models deviated from da Vinci''s rule as the weights and/or the branching angles of lateral daughter branches increased. The calculated values of the two models were largely similar but differed in some ways. Field measurements of Fagus crenata and Abies homolepis also fit this trend, wherein models deviated from da Vinci''s rule with increasing relative weights of lateral daughter branches. However, this deviation was small for a branching pattern in nature, where empirical measurements were taken under realistic measurement conditions; thus, da Vinci''s rule did not critically contradict the biomechanical models in the case of real branching patterns, though the model calculations described the contradiction between da Vinci''s rule and the biomechanical models. The field data for Fagus crenata fit the uniform stress model best, indicating that stress uniformity is the key constraint of branch morphology in Fagus crenata rather than elastic similarity or da Vinci''s rule. On the other hand, mechanical constraints are not necessarily significant in the morphology of Abies homolepis branches, depending on the number of daughter branches. Rather, these branches were often in agreement with da Vinci''s rule.     

Contribution a l’etude de la forme des plantes: discussion d’un modele de ramification

The problem of the forms of plants and models of branching are discussed using experimental data on the mistletoe. The number of branches by division, the distribution of divisions with regard to the number of branches per division and to the level of division, the geometrical characters of branches according to the level of division and the host, the stability of model are studied. One gives an interpretation of the model of branching as a model of growth.      

Maintenance mechanisms of the pipe model relationship and Leonardo da Vinci’s rule in the branching architecture of <Emphasis Type="Italic">Acer rufinerve</Emphasis> trees

The pipe model relationship (constancy of branch cross-sectional area/leaf area) and Leonardo da Vinci’s rule (equality of total cross-sectional area of the daughter branches and cross-sectional area of their mother branch) are empirical rules of tree branching. Effects of branch manipulation on the pipe model relationships were examined using five Acer rufinerve trees. Half the branches in each tree were untreated (control branches, CBs), and, for the others (manipulated branches, MBs), either light intensity or leaf area (both relating to photosynthetic source activity), or shoot elongation (source + sink activities), was reduced, and responses of the pipe model relationships were followed for 2 years. The pipe model relationship in MBs changed by suppression of source activity, but not by simultaneous suppression of source + sink activities. The manipulations also affected CBs in the year of manipulation and both branches in the next year. The branch diameter growth was most affected by light, followed by shoot elongation and leaf area, in that order. Because of the decussate phyllotaxis of A. rufinerve, one branching node can potentially have one main and two lateral branches. Analysis of 295 branching nodes from 13 untreated trees revealed that the da Vinci’s rule held in branching nodes having one shed branch but not in the nodes without branch shedding, indicating the necessity of natural shedding of branches for da Vinci’s rule to hold. These analyses highlight the importance of the source–sink balance and branch shedding in maintenance of these empirical rules. This article was contributed at the invitation of the Editorial Committee.     

Heterogeneous and compensatory growth in Melithaea flabellifera (Octocorallia: Melithaeidae) in Japan

Melithaea flabellifera (Kükenthal, 1909) (Octocorallia, Gorgonacea), an endemic and predominant gorgonian in Japanese shallow waters, grows mostly in one plane and ramifies in a dichotomous way. The growth rates of all branches and of the colony were measured from photographs of tagged gorgonian corals for approximately 1 year from June 1995 to May 1996 on the western Pacific coast of Japan (34° 39′ N, 138° 56′ E). The most rapid growth occurred when the water temperature was less than 20 °C. Mean growth ranged from 2.9 to 11.4 mm year⁻¹. Linear growth of individual branches ranged between −30.4 and 24.8 mm year ^-1−1. Both seasonal and non-seasonal variations in growth rate were observed in each colony. When branches were lost, the adjacent branches grew faster, filling the open space in the fan. Heterogeneity in growth rate within a colony was partly caused by this compensatory growth. This indicates that the regular branching pattern of gorgonians is due to irregular and heterogeneous growth. The compensatory growth suggests that M. flabellifera is constrained by some potential optimal size or form.     

Growth velocities of branched actin networks

The growth of an actin network against an obstacle that stimulates branching locally is studied using several variants of a kinetic rate model based on the orientation-dependent number density of filaments. The model emphasizes the effects of branching and capping on the density of free filament ends. The variants differ in their treatment of side versus end branching and dimensionality, and assume that new branches are generated by existing branches (autocatalytic behavior) or independently of existing branches (nucleation behavior). In autocatalytic models, the network growth velocity is rigorously independent of the opposing force exerted by the obstacle, and the network density is proportional to the force. The dependence of the growth velocity on the branching and capping rates is evaluated by a numerical solution of the rate equations. In side-branching models, the growth velocity drops gradually to zero with decreasing branching rate, while in end-branching models the drop is abrupt. As the capping rate goes to zero, it is found that the behavior of the velocity is sensitive to the thickness of the branching region. Experiments are proposed for using these results to shed light on the nature of the branching process.     

Crown alterations induced by decline: a study of relationships between growth rate and crown morphology in beech (Fagus sylvatica L.)

One of the first symptoms expressed by declining trees is reduced growth in stem diameter and length increment. The possibility of a relationship between length increment and crown thinning in beech (Fagus sylvatica L.) was investigated by developing a computer model to simulate first order branching patterns of the apical 2 m of monopodially branching beech trees, 70–100 years old, for a range of length increment rates. The model was based on values for branching angle, main axis and branch length increment, number of branches produced per year and branch mortality rates for six healthy and declining trees. Shoot growth rates in the apical 2 m of the sample trees ranged from about 5 cm/year (decline class 3) to 43 cm/ year (healthy). Simulations of branching patterns in the apical 2 m of trees growing at different rates indicated that, when growth rate exceeded about 20 cm/year, total first order branch length and area explored were independent of growth rate. When growth rates fell below this value there was a reduction in total area explored and first order branch length due primarily to the formation of fewer branches. More acute branching angles contributed to a reduction in the area explored. Growth rate-related crown thinning could increase the risk of bark necrosis and secondary pathogen infection during dry and/or hot spells.     

Chimeric dihydrofolate reductases display properties of modularity and biophysical diversity

While reverse genetics and functional genomics have long affirmed the role of individual mutations in determining protein function, there have been fewer studies addressing how large‐scale changes in protein sequences, such as in entire modular segments, influence protein function and evolution. Given how recombination can reassort protein sequences, these types of changes may play an underappreciated role in how novel protein functions evolve in nature. Such studies could aid our understanding of whether certain organismal phenotypes related to protein function—such as growth in the presence or absence of an antibiotic—are robust with respect to the identity of certain modular segments. In this study, we combine molecular genetics with biochemical and biophysical methods to gain a better understanding of protein modularity in dihydrofolate reductase (DHFR), an enzyme target of antibiotics also widely used as a model for protein evolution. We replace an integral α‐helical segment of Escherichia coli DHFR with segments from a number of different organisms (many nonmicrobial) and examine how these chimeric enzymes affect organismal phenotypes (e.g., resistance to an antibiotic) as well as biophysical properties of the enzyme (e.g., thermostability). We find that organismal phenotypes and enzyme properties are highly sensitive to the identity of DHFR modules, and that this chimeric approach can create enzymes with diverse biophysical characteristics.     

Patterns of morphological integration in marine modular organisms: supra-module organization in branching octocoral colonies

Despite the relative simplicity of their modular growth, marine invertebrates such as arborescent gorgonian octocorals (Octocorallia: Cnidaria) generate complex colonial forms. Colony form in these taxa is a consequence of modular (polyp) replication, and if there is a tight integration among modular and supramodular traits (e.g. polyp aperture, inter-polyp spacing, branch thickness, internode and branch length), then changes at the module level may lead to changes in colony architecture. Alternatively, different groups of traits may evolve semi-independently (or conditionally independent). To examine the patterns of integration among morphological traits in Caribbean octocorals, we compared five morphological traits across 21 species, correcting for the effects of phylogenetic relationships among the taxa. Graphical modelling and phylogenetic independence contrasts among the five morphological characters indicate two groups of integrated traits based on whether they were polyp- or colony-level traits. Although all characters exhibited bivariate associations, multivariate analyses (partial correlation coefficients) showed the strongest integration among the colony-level characters (internode distance and branch length). It is a quantitative demonstration that branching characters within the octocorals studied are independent of characters of the polyps. Despite the universally recognized modularity of octocorals at the level of polyps, branching during colony development may represent an emergent level of integration and modularity.     

Ontogenetic changes in the capacity of the coral Pocillopora damicornis to originate branches

Most colonial corals vary intraspecifically in growth forms, and the diversity in branching morphology is especially striking. While the effects of environmental factors on growth forms have been studied, the genetic control of coral branching patterns has received little attention. The discovery of ontogenetic changes in the capacity to originate branching would set the stage for studies of how branch formation is genetically controlled. During experiments investigating contact reactions in the coral Pocillopora damicornis, we observed that young colonies derived from settled planulae and colonies regenerated from adult branch tips assumed different growth forms. Young colonies formed at least one branch from the central region of the colony, while colonies regenerated from adult branch tips (3-5 mm long) did not form branches during the 9-month observation period. This pattern was invariable, regardless of the types and outcomes of the contact experiments or the orientation of the branch tips. However, some fragments taken from 1- or 2-year-old colonies formed branches. This suggests that the rate of branch formation in P. damicornis colonies decreases with age. These findings will facilitate investigations of the mechanism of coral branch formation at the molecular level.     

TGF-beta superfamily members modulate growth, branching, shaping, and patterning of the ureteric bud

Protein-rich fractions inhibitory for isolated ureteric bud (UB) growth were separated from a conditioned medium secreted by cells derived from the metanephric mesenchyme (MM). Elution profiles and immunoblotting indicated the presence of members of the transforming growth factor-beta (TGF-beta) superfamily. Treatment of cultured whole embryonic kidney with BMP2, BMP4, activin, or TGF-beta1 leads to statistically significant differences in the overall size of the kidney, the number of UB branches, the length and angle of the branches, as well as in the thickness of the UB stalks. Thus, the pattern of the ureteric tree is altered. LIF, however, appeared to have only minimal effect on growth and development of the whole embryonic kidney in organ culture. The factors all directly inhibited, in a concentration-dependent fashion, the growth and branching of the isolated UB, albeit to different extents. Antagonists of some of these factors reduced their inhibitory effect. Detailed examination of TGF-beta1-treated UBs revealed only a slight increase in the amount of apoptosis in tips by TUNEL staining, but diminished proliferation throughout by Ki67 staining. These data suggest an important direct modulatory role for BMP2, BMP4, LIF, TGF-beta1, and activin (as well as their antagonists) on growth and branching of the UB, possibly in shaping the growing UB by playing a role in determining the number of branches, as well as where and how the branches occur. In support of this notion, UBs cultured in the presence of fibroblast growth factor 7 (FGF7), which induces the formation of globular structures with little distinction between the stalk and ampullae [Mech. Dev. 109 (2001) 123], and TGF-beta superfamily members lead to the formation of UBs with clear stalks and ampullae. This indicates that positive (i.e., growth and branch promoting) and negative (i.e., growth and branch inhibiting) modulators of UB morphogenesis can cooperate in the formation of slender arborized UB structures similar to those observed in the intact developing kidney or in whole embryonic kidney organ culture. Finally, purification data also indicate the presence of an as yet unidentified soluble non-heparin-binding activity modulating UB growth and branching. The data suggest how contributions of positive and negative growth factors can together (perhaps as local bipolar morphogenetic gradients existing within the mesenchyme) modulate the vectoral arborization pattern of the UB and shape branches as they develop, thereby regulating both nephron number and tubule/duct caliber. We suggest that TGF-beta-like molecules and other non-heparin-binding inhibitory factors can, in the appropriate matrix context, facilitate "braking" of the branching program as the UB shifts from a rapid branching stage (governed by a feed-forward mechanism) to a stage where branching slows down (negative feedback) and eventually stops.     

Do multi-branched colonial organisms exceed normal growth after partial mortality?

One of the advantages of modular colonial growth is the capability to recover after partial mortality. Tolerance to partial mortality is a known property of some resistant species of plants that respond to mortality with vigorous regrowth or overcompensation. It is not clear whether modular marine invertebrates such as octocorals overcompensate. This study provides evidence that following injury to colonies (by breaking apical dominance), new growth exceeds normal rates of branching, as observed in some plants, in a degree correlated to the original multi-branched network setting (e.g. the number of original branches connected to main stem), in colonies of the Caribbean gorgonian octocoral Pseudopterogorgia bipinnata. This can be explained by the network of communicating vessels and canals inside octocoral colonies, which provide the structure for effective allocation of resources to regenerating parts.     

Mechanistic basis of branch-site selection in filamentous bacteria

Many filamentous organisms, such as fungi, grow by tip-extension and by forming new branches behind the tips. A similar growth mode occurs in filamentous bacteria, including the genus Streptomyces, although here our mechanistic understanding has been very limited. The Streptomyces protein DivIVA is a critical determinant of hyphal growth and localizes in foci at hyphal tips and sites of future branch development. However, how such foci form was previously unknown. Here, we show experimentally that DivIVA focus-formation involves a novel mechanism in which new DivIVA foci break off from existing tip-foci, bypassing the need for initial nucleation or de novo branch-site selection. We develop a mathematical model for DivIVA-dependent growth and branching, involving DivIVA focus-formation by tip-focus splitting, focus growth, and the initiation of new branches at a critical focus size. We quantitatively fit our model to the experimentally-measured tip-to-branch and branch-to-branch length distributions. The model predicts a particular bimodal tip-to-branch distribution results from tip-focus splitting, a prediction we confirm experimentally. Our work provides mechanistic understanding of a novel mode of hyphal growth regulation that may be widely employed.