Testing hypotheses on the calcification in scleractinian corals using a spatio-temporal model that shows a high degree of robustness.

Calcification in photosynthetic scleractinian corals is a complicated process that involves many different biological, chemical, and physical sub-processes that happen within and around the coral tissue. Identifying and quantifying the role of separate processes in vivo or in vitro is difficult or not possible. A computational model can facilitate this research by simulating the sub-processes independently. This study presents a spatio-temporal model of the calcification physiology, which is based on processes that are considered essential for calcification: respiration, photosynthesis, Ca2＋-ATPase, carbonic anhydrase. The model is used to test different hypotheses considering ion transport across the calicoblastic cells and Light Enhanced Calcification (LEC). It is also used to quantify the effect of ocean acidification (OA) on the Extracellular Calcifying Medium (ECM) and ATP-consumption of Ca2＋-ATPase. It was able to reproduce the experimental data of three separate studies and finds that paracellular transport plays a minor role compared to transcellular transport. In the model, LEC results from increased Ca2＋-ATPase activity in combination with increased metabolism. Implementing OA increases the concentration of CO2 throughout the entire tissue, thereby increasing the availability of CO3- in the ECM. As a result, the model finds that calcification becomes more energy-demanding and the calcification rate increases.

Branching archaeocyaths as ecosystem engineers during the Cambrian radiation.

The rapid origination and diversification of major animal body plans during the early Cambrian coincide with the rise of Earth's first animal-built framework reefs. Given the importance of scleractinian coral reefs as ecological facilitators in modern oceans, we investigate the impact of archaeocyathan (Class Archaeocyatha) reefs as engineered ecosystems during the Cambrian radiation. In this study, we present the first high-resolution, three-dimensional (3D) reconstructions of branching archaeocyathide (Order Archaeocyathida) individuals from three localities on the Laurentian paleocontinent. Because branched forms in sponges and corals display phenotypic plasticity that preserve the characteristics of the surrounding growth environment, we compare morphological measurements from our fossil specimens to those of modern corals to infer the surface conditions of Earth's first reefs. These data demonstrate that archaeocyaths could withstand and influence the flow of water, accommodate photosymbionts, and build topographically complex and stable structures much like corals today. We also recognize a stepwise increase in the roughness of reef environments in the lower Cambrian, which would have laid a foundation for more abundant and diverse coevolving fauna.

Epigenome-associated phenotypic acclimatization to ocean acidification in a reef-building coral.

There are increasing concerns that the current rate of climate change might outpace the ability of reef-building corals to adapt to future conditions. Work on model systems has shown that environmentally induced alterations in DNA methylation can lead to phenotypic acclimatization. While DNA methylation has been reported in corals and is thought to associate with phenotypic plasticity, potential mechanisms linked to changes in whole-genome methylation have yet to be elucidated. We show that DNA methylation significantly reduces spurious transcription in the coral Stylophora pistillata. Furthermore, we find that DNA methylation also reduces transcriptional noise by fine-tuning the expression of highly expressed genes. Analysis of DNA methylation patterns of corals subjected to long-term pH stress showed widespread changes in pathways regulating cell cycle and body size. Correspondingly, we found significant increases in cell and polyp sizes that resulted in more porous skeletons, supporting the hypothesis that linear extension rates are maintained under conditions of reduced calcification. These findings suggest an epigenetic component in phenotypic acclimatization that provides corals with an additional mechanism to cope with environmental change.

The effect of allometric scaling in coral thermal microenvironments.

A long-standing interest in marine science is in the degree to which environmental conditions of flow and irradiance, combined with optical, thermal and morphological characteristics of individual coral colonies, affects their sensitivity of thermal microenvironments and susceptibility to stress-induced bleaching within and/or among colonies. The physiological processes in Scleractinian corals tend to scale allometrically as a result of physical and geometric constraints on body size and shape. There is a direct relationship between scaling to thermal stress, thus, the relationship between allometric scaling and rates of heating and cooling in coral microenvironments is a subject of great interest. The primary aim of this study was to develop an approximation that predicts coral thermal microenvironments as a function of colony morphology (shape and size), light or irradiance, and flow velocity or regime. To do so, we provided intuitive interpretation of their energy budgets for both massive and branching colonies, and then quantified the heat-size exponent (b*) and allometric constant (m) using logarithmic linear regression. The data demonstrated a positive relationship between thermal rates and changes in irradiance, A/V ratio, and flow, with an interaction where turbulent regime had less influence on overall stress which may serve to ameliorate the effects of temperature rise compared to the laminar regime. These findings indicated that smaller corals have disproportionately higher stress, however they can reach thermal equilibrium quicker. Moreover, excellent agreements between the predicted and simulated microscale temperature values with no significant bias were observed for both the massive and branching colonies, indicating that the numerical approximation should be within the accuracy with which they could be measured. This study may assist in estimating the coral microscale temperature under known conditions of water flow and irradiance, in particular when examining the intra- and inter-colony variability found during periods of bleaching conditions.

A novel technique to combine and analyse spatial and temporal expression datasets: A case study with the sea anemone Nematostella vectensis to identify potential gene interactions.

Understanding genetic interactions during early development of a given organism, is the first step toward unveiling gene regulatory networks (GRNs) that govern a biological process of interest. Predicting such interactions from large expression datasets by performing targeted knock-down/knock-out approaches is a challenging task. We use the currently available expression datasets (in situ hybridization images & qPCR time series) for a basal anthozoan the sea anemone N. vectensis to construct continuous spatiotemporal gene expression patterns during its early development. Moreover, by combining cluster results from each dataset we develop a method that provides testable hypotheses about potential genetic interactions. We show that the analysis of spatial gene expression patterns reveals functional regions of the embryo during the gastrulation. The clustering results from qPCR time series unveils significant temporal events and highlights genes potentially involved in N. vectensis gastrulation. Furthermore, we introduce a method for merging the clustering results from spatial and temporal datasets by which we can group genes that are expressed in the same region and at the time. We demonstrate that the merged clusters can be used to identify GRN interactions involved in various processes and to predict possible activators or repressors of any gene in the dataset. Finally, we validate our methods and results by predicting the repressor effect of NvErg on NvBra in the central domain during the gastrulation that has recently been confirmed by functional analysis.

Quantitative morphological analysis of 2D images of complex-shaped branching biological growth forms: the example of branching thalli of liverworts.

BACKGROUND: Many organisms such as plants can be characterized as complex-shaped branching forms. The morphological quantification of the forms is a support for a number of areas such as the effects of environmental factors and species discrimination. To date, there is no software package suitable for our dataset representing the forms. We therefore formulate methods for extracting morphological measurements from images of the forms. RESULTS: As a case study we analyze two-dimensional images of samples from four groups belonging to three species of thalloid liverworts, genus Riccardia. The images are pre-processed and converted into binary images, then skeletonized to obtain a skeleton image, in which features such as junctions and terminals are detected. Morphological measurements known to characterize and discriminate the species in the samples such as junction thickness, branch thickness, terminal thickness, branch length, branch angle, and terminal spacing are then quantified. The measurements are used to distinguish among the four groups of Riccardia and also between the two groups of Riccardia amazonica collected in different locations, Africa and South America. Canonical discriminant analysis results show that those measurements are able to discriminate among the four groups. Additionally, it is able to discriminate R. amazonica collected in Africa from those collected in South America. CONCLUSIONS: This paper presents general automated methods implemented in our software for quantifying two-dimensional images of complex branching forms. The methods are used to compute a series of morphological measurements. We found significant results to distinguish Riccardia species by using the measurements. The methods are also applicable for analyzing other branching organisms. Our software is freely available under the GNU GPL.

Analysis of a spatial gene expression database for sea anemone Nematostella vectensis during early development.

BACKGROUND: The spatial distribution of many genes has been visualized during the embryonic development in the starlet sea anemone Nematostella vectensis in the last decade. In situ hybridization images are available in the Kahi Kai gene expression database, and a method has been developed to quantify spatial gene expression patterns of N. vectensis. In this paper, gene expression quantification is performed on a wide range of gene expression patterns from this database and descriptions of observed expression domains are stored in a separate database for further analysis. METHODS: Spatial gene expression from suitable in situ hybridization images has been quantified with the GenExp program. A correlation analysis has been performed on the resulting numerical gene expression profiles for each stage. Based on the correlated clusters of spatial gene expression and detailed descriptions of gene expression domains, various mechanisms for developmental gene expression are proposed. RESULTS: In the blastula and gastrula stages of development in N. vectensis, its continuous sheet of cells is partitioned into correlating gene expression domains. During progressing development, these regions likely correspond to different fates. A statistical analysis shows that genes generally remain expressed during the planula stages in those major regions that they occupy at the end of gastrulation. DISCUSSION: Observed shifts in gene expression domain boundaries suggest that elongation in the planula stage mainly occurs in the vegetal ring under the influence of the gene Rx. The secondary body axis in N. vectensis is proposed to be determined at the mid blastula transition. CONCLUSIONS: Early gene expression domains in N. vectensis appear to maintain a positional order along the primary body axis. Early determination in N. vectensis occurs in two stages: expression in broad circles and rings in the blastula is consolidated during gastrulation, and more complex expression patterns appear in the planula within these broad regions. Quantification and comparison of gene expression patterns across a database can generate hypotheses about collective cell movements before these movements are measured directly.

Gains and losses of coral skeletal porosity changes with ocean acidification acclimation.

Ocean acidification is predicted to impact ecosystems reliant on calcifying organisms, potentially reducing the socioeconomic benefits these habitats provide. Here we investigate the acclimation potential of stony corals living along a pH gradient caused by a Mediterranean CO2 vent that serves as a natural long-term experimental setting. We show that in response to reduced skeletal mineralization at lower pH, corals increase their skeletal macroporosity (features >10 µm) in order to maintain constant linear extension rate, an important criterion for reproductive output. At the nanoscale, the coral skeleton's structural features are not altered. However, higher skeletal porosity, and reduced bulk density and stiffness may contribute to reduce population density and increase damage susceptibility under low pH conditions. Based on these observations, the almost universally employed measure of coral biomineralization, the rate of linear extension, might not be a reliable metric for assessing coral health and resilience in a warming and acidifying ocean.

A computational approach towards a gene regulatory network for the developing Nematostella vectensis gut.

BACKGROUND: The starlet sea anemone Nematostella vectensis is a diploblastic cnidarian that expresses a set of conserved genes for gut formation during its early development. During the last decade, the spatial distribution of many of these genes has been visualized with RNA hybridization or protein immunolocalization techniques. However, due to N. vectensis' curved and changing morphology, quantification of these spatial data is problematic. A method is developed for two-dimensional gene expression quantification, which enables a numerical analysis and dynamic modeling of these spatial patterns. METHODS/RESULT: In this work, first standardized gene expression profiles are generated from publicly available N. vectensis embryo images that display mRNA and/or protein distributions. Then, genes expressed during gut formation are clustered based on their expression profiles, and further grouped based on temporal appearance of their gene products in embryonic development. Representative expression profiles are manually selected from these clusters, and used as input for a simulation-based optimization scheme. This scheme iteratively fits simulated profiles to the selected profiles, leading to an optimized estimation of the model parameters. Finally, a preliminary gene regulatory network is derived from the optimized model parameters. OUTLOOK: While the focus of this study is N. vectensis, the approach outlined here is suitable for inferring gene regulatory networks in the embryonic development of any animal, thus allowing to comparatively study gene regulation of gut formation in silico across various species.

Comparison between colony morphology and molecular phylogeny in the Caribbean scleractinian coral genus Madracis.

A major challenge in coral biology is to find the most adequate and phylogenetically informative characters that allow for distinction of closely related coral species. Therefore, data on corallite morphology and genetic data are often combined to increase phylogenetic resolution. In this study, we address the question to which degree genetic data and quantitative information on overall coral colony morphologies identify similar groupings within closely related morphospecies of the Caribbean coral genus Madracis. Such comparison of phylogenies based on colony morphology and genetic data will also provide insight into the degree to which genotype and phenotype overlap. We have measured morphological features of three closely related Caribbean coral species of the genus Madracis (M. formosa, M. decactis and M. carmabi). Morphological differences were then compared with phylogenies of the same species based on two nuclear DNA markers, i.e. ATPSα and SRP54. Our analysis showed that phylogenetic trees based on (macroscopical) morphological properties and phylogenetic trees based on DNA markers ATPSα and SRP54 are partially similar indicating that morphological characteristics at the colony level provide another axis, in addition to commonly used features such as corallite morphology and ecological information, to delineate genetically different coral species. We discuss this new method that allows systematic quantitative comparison between morphological characteristics of entire colonies and genetic data.

Regional decline in growth rates of massive Porites corals in Southeast Asia.

This study reports the first well-replicated analysis of continuous coral growth records from warmer water reefs (mean annual sea surface temperatures (SST) >28.5 °C) around the Thai-Malay Peninsula in Southeast Asia. Based on analyses of 70 colonies sampled from 15 reefs within six locations, region-wide declines in coral calcification rate (ca. 18.6%), linear extension rate (ca. 15.4%) and skeletal bulk density (ca. 3.9%) were observed over a 31-year period from 1980 to 2010. Decreases in calcification and linear extension rates were observed at five of the six locations and ranged from ca. 17.2-21.6% and ca. 11.4-19.6%, respectively, whereas decline in skeletal bulk density was a consequence of significant reductions at only two locations (ca. 6.9% and 10.7%). A significant link between region-wide growth rates and average annual SST was found, and Porites spp. demonstrated a high thermal threshold of ca. 29.4 °C before calcification rates declined. Responses at individual locations within the region were more variable with links between SST and calcification rates being significant at only four locations. Rates of sea temperature warming at locations in the Andaman Sea (Indian Ocean) (ca. 1.3 °C per decade) were almost twice those in the South China Sea (Pacific Ocean) (ca. 0.7 °C per decade), but this was not reflected in the magnitude of calcification declines at corresponding locations. Considering that massive Porites spp. are major reef builders around Southeast Asia, this region-wide growth decline is a cause for concern for future reef accretion rates and resilience. However, this study suggests that the future rates and patterns of change within the region are unlikely to be uniform or dependent solely on the rates of change in the thermal environment.

Promoter sequence determines the relationship between expression level and noise.

The ability of cells to accurately control gene expression levels in response to extracellular cues is limited by the inherently stochastic nature of transcriptional regulation. A change in transcription factor (TF) activity results in changes in the expression of its targets, but the way in which cell-to-cell variability in expression (noise) changes as a function of TF activity, and whether targets of the same TF behave similarly, is not known. Here, we measure expression and noise as a function of TF activity for 16 native targets of the transcription factor Zap1 that are regulated by it through diverse mechanisms. For most activated and repressed Zap1 targets, noise decreases as expression increases. Kinetic modeling suggests that this is due to two distinct Zap1-mediated mechanisms that both change the frequency of transcriptional bursts. Notably, we found that another mechanism of repression by Zap1, which is encoded in the promoter DNA, likely decreases the size of transcriptional bursts, producing a unique transcriptional state characterized by low expression and low noise. In addition, we find that further reduction in noise is achieved when a single TF both activates and represses a single target gene. Our results suggest a global principle whereby at low TF concentrations, the dominant source of differences in expression between promoters stems from differences in burst frequency, whereas at high TF concentrations differences in burst size dominate. Taken together, we show that the precise amount by which noise changes with expression is specific to the regulatory mechanism of transcription and translation that acts at each gene.

Modelling growth and form of the scleractinian coral Pocillopora verrucosa and the influence of hydrodynamics.

The growth of scleractinian corals is strongly influenced by the effect of water motion. Corals are known to have a high level of phenotypic variation and exhibit a diverse range of growth forms, which often contain a high level of geometric complexity. Due to their complex shape, simulation models represent an important option to complement experimental studies of growth and flow. In this work, we analyzed the impact of flow on coral's morphology by an accretive growth model coupled with advection-diffusion equations. We performed simulations under no-flow and uni-directional flow setup with the Reynolds number constant. The relevant importance of diffusion to advection was investigated by varying the diffusion coefficient, rather than the flow speed in Péclet number. The flow and transport equations were coupled and solved using COMSOL Multiphysics. We then compared the simulated morphologies with a series of Computed Tomography (CT) scans of scleractinian corals Pocillopora verrucosa exposed to various flow conditions in the in situ controlled flume setup. As a result, we found a similar trend associated with the increasing Péclet for both simulated forms and in situ corals; that is uni-directional current tends to facilitate asymmetrical growth response resulting in colonies with branches predominantly developed in the upstream direction. A closer look at the morphological traits yielded an interesting property about colony symmetry and plasticity induced by uni-directional flow. Both simulated and in situ corals exhibit a tendency where the degree of symmetry decreases and compactification increases in conjunction with the augmented Péclet thus indicates the significant importance of hydrodynamics.

Modeling biosilicification at subcellular scales.

Biosilicification occurs in many organisms. Sponges and diatoms are major examples of them. In this chapter, we introduce a modeling approach that describes several biological mechanisms controlling silicification. Modeling biosilicification is a typical multiscale problem where processes at very different temporal and spatial scales need to be coupled: processes at the molecular level, physiological processes at the subcellular and cellular level, etc. In biosilicification morphology plays a fundamental role, and a spatiotemporal model is required. In the case of sponges, a particle simulation based on diffusion-limited aggregation is presented here. This model can describe fractal properties of silica aggregates in first steps of deposition on an organic template. In the case of diatoms, a reaction-diffusion model is introduced which can describe the concentrations of chemical components and has the possibility to include polymerization chain of reactions.

Spatial gene expression quantification: a tool for analysis of in situ hybridizations in sea anemone Nematostella vectensis.

BACKGROUND: Spatial gene expression quantification is required for modeling gene regulation in developing organisms. The fruit fly Drosophila melanogaster is the model system most widely applied for spatial gene expression analysis due to its unique embryonic properties: the shape does not change significantly during its early cleavage cycles and most genes are differentially expressed along a straight axis. This system of development is quite exceptional in the animal kingdom.In the sea anemone Nematostella vectensis the embryo changes its shape during early development; there are cell divisions and cell movement, like in most other metazoans. Nematostella is an attractive case study for spatial gene expression since its transparent body wall makes it accessible to various imaging techniques. FINDINGS: Our new quantification method produces standardized gene expression profiles from raw or annotated Nematostella in situ hybridizations by measuring the expression intensity along its cell layer. The procedure is based on digital morphologies derived from high-resolution fluorescence pictures. Additionally, complete descriptions of nonsymmetric expression patterns have been constructed by transforming the gene expression images into a three-dimensional representation. CONCLUSIONS: We created a standard format for gene expression data, which enables quantitative analysis of in situ hybridizations from embryos with various shapes in different developmental stages. The obtained expression profiles are suitable as input for optimization of gene regulatory network models, and for correlation analysis of genes from dissimilar Nematostella morphologies. This approach is potentially applicable to many other metazoan model organisms and may also be suitable for processing data from three-dimensional imaging techniques.

Geometric theory predicts bifurcations in minimal wiring cost trees in biology are flat.

The complex three-dimensional shapes of tree-like structures in biology are constrained by optimization principles, but the actual costs being minimized can be difficult to discern. We show that despite quite variable morphologies and functions, bifurcations in the scleractinian coral Madracis and in many different mammalian neuron types tend to be planar. We prove that in fact bifurcations embedded in a spatial tree that minimizes wiring cost should lie on planes. This biologically motivated generalization of the classical mathematical theory of Euclidean Steiner trees is compatible with many different assumptions about the type of cost function. Since the geometric proof does not require any correlation between consecutive planes, we predict that, in an environment without directional biases, consecutive planes would be oriented independently of each other. We confirm this is true for many branching corals and neuron types. We conclude that planar bifurcations are characteristic of wiring cost optimization in any type of biological spatial tree structure.

Interaction of the retinoic acid signaling pathway with spicule formation in the marine sponge Suberites domuncula through activation of bone morphogenetic protein-1.

BACKGROUND: The formation of the spicules in siliceous sponges involves the formation of cylinder-like structures in the extraspicular space, composed of the enzyme silicatein and the calcium-dependent lectin. SCOPE OF REVIEW: Molecular cloning of the cDNAs (carotene dioxygenase, retinal dehydrogenase, and BMB-1 [bone morphogenic protein-1]) from the demosponge Suberites domuncula was performed. These tools were used to understand the retinoid metabolism in the animal by qRT-PCR, immunoblotting and TEM. MAJOR CONCLUSIONS: We demonstrate that silintaphin-2, a silicatein-interacting protein, is processed from a longer-sized 15-kDa precursor to a truncated, shorter-sized 13kDa calcium-binding protein via proteolytic cleavage at the dipeptide Ala↓Asp, mediated by BMP-1. The expression of this protease as well as the expression of two key enzymes of the carotinoid metabolism, the ß,ß-carotene-15,15'-dioxygenase and the retinal dehydrogenase/reductase, were found to be strongly up-regulated by retinoic acid. Hence retinoic acid turned out to be a key factor in skeletogenesis in the most ancient still existing metazoans, the sponges. GENERAL SIGNIFICANCE: It is shown that retinoic acid regulates the formation of the organic cylinder that surrounds the axis of the spicules and enables, as a scaffold, the radial apposition of new silica layers and hence the growth of the spicules.

A comparison between coral colonies of the genus Madracis and simulated forms.

In addition to experimental studies, computational models provide valuable information about colony development in scleractinian corals. Using our simulation model, we show how environmental factors such as nutrient distribution and light availability affect growth patterns of coral colonies. To compare the simulated coral growth forms with those of real coral colonies, we quantitatively compared our modelling results with coral colonies of the morphologically variable Caribbean coral genus Madracis. Madracis species encompass a relatively large morphological variation in colony morphology and hence represent a suitable genus to compare, for the first time, simulated and real coral growth forms in three dimensions using a quantitative approach. This quantitative analysis of three-dimensional growth forms is based on a number of morphometric parameters (such as branch thickness, branch spacing, etc.). Our results show that simulated coral morphologies share several morphological features with real coral colonies (M. mirabilis, M. decactis, M. formosa and M. carmabi). A significant correlation was found between branch thickness and branch spacing for both real and simulated growth forms. Our present model is able to partly capture the morphological variation in closely related and morphologically variable coral species of the genus Madracis.

Inferring Drosophila gap gene regulatory network: pattern analysis of simulated gene expression profiles and stability analysis.

BACKGROUND: Inference of gene regulatory networks (GRNs) requires accurate data, a method to simulate the expression patterns and an efficient optimization algorithm to estimate the unknown parameters. Using this approach it is possible to obtain alternative circuits without making any a priori assumptions about the interactions, which all simulate the observed patterns. It is important to analyze the properties of the circuits. FINDINGS: We have analyzed the simulated gene expression patterns of previously obtained circuits that describe gap gene dynamics during early Drosophila melanogaster embryogenesis. Using hierarchical clustering we show that amplitude variation and defects observed in the simulated gene expression patterns are linked to similar circuits, which can be grouped. Furthermore, analysis of the long-term dynamics revealed four main dynamical attractors comprising stable patterns and oscillatory patterns. In addition, we also performed a correlation analysis on the parameters showing an intricate correlation pattern. CONCLUSIONS: The analysis demonstrates that the obtained gap gene circuits are not unique showing variable long-term dynamics and highly correlating scattered parameters. Furthermore, although the model can simulate the pattern up to gastrulation and confirms several of the known regulatory interactions, it does not reproduce the transient expression of all gap genes as observed experimentally. We suggest that the shortcomings of the model may be caused by overfitting, incomplete model description and/or missing data.

Inferring Drosophila gap gene regulatory network: a parameter sensitivity and perturbation analysis.

BACKGROUND: Inverse modelling of gene regulatory networks (GRNs) capable of simulating continuous spatio-temporal biological processes requires accurate data and a good description of the system. If quantitative relations between genes cannot be extracted from direct measurements, an efficient method to estimate the unknown parameters is mandatory. A model that has been proposed to simulate spatio-temporal gene expression patterns is the connectionist model. This method describes the quantitative dynamics of a regulatory network in space. The model parameters are estimated by means of model-fitting algorithms. The gene interactions are identified without making any prior assumptions concerning the network connectivity. As a result, the inverse modelling might lead to multiple circuits showing the same quantitative behaviour and it is not possible to identify one optimal circuit. Consequently, it is important to address the quality of the circuits in terms of model robustness. RESULTS: Here we investigate the sensitivity and robustness of circuits obtained from reverse engineering a model capable of simulating measured gene expression patterns. As a case study we use the early gap gene segmentation mechanism in Drosophila melanogaster. We consider the limitations of the connectionist model used to describe GRN Inferred from spatio-temporal gene expression. We address the problem of circuit discrimination, where the selection criterion within the optimization technique is based of the least square minimization on the error between data and simulated results. CONCLUSION: Parameter sensitivity analysis allows one to discriminate between circuits having significant parameter and qualitative differences but exhibiting the same quantitative pattern. Furthermore, we show that using a stochastic model derived from a deterministic solution, one can introduce fluctuations within the model to analyze the circuits' robustness. Ultimately, we show that there is a close relation between circuit sensitivity and robustness to fluctuation, and that circuit robustness is rather modular than global. The current study shows that reverse engineering of GRNs should not only focus on estimating parameters by minimizing the difference between observation and simulation but also on other model properties. Our study suggests that multi-objective optimization based on robustness and sensitivity analysis has to be considered.