Jaap A. Kaandorp

Systems biology: parameter estimation for biochemical models

Mathematical models of biological processes have various applications: to assist in understanding the functioning of a system, to simulate experiments before actually performing them, to study situations that cannot be dealt with experimentally, etc. Some parameters in the model can be directly obtained from experiments or from the literature. Others have to be inferred by comparing model results to experiments. In this minireview, we discuss the identifiability of models, both intrinsic to the model and taking into account the available data. Furthermore, we give an overview of the most frequently used approaches to search the parameter space.

Spatial stochastic modelling of the phosphoenolpyruvate-dependent phosphotransferase (PTS) pathway in Escherichia coli

MOTIVATION Many biochemical networks involve reactions localized on the cell membrane. This can give rise to spatial gradients of the concentration of cytosolic species. Moreover, the number of membrane molecules can be small and stochastic effects can become relevant. Pathways usually consist of a complex interaction network and are characterized by a large set of parameters. The inclusion of spatial and stochastic effects is a major challenge in developing quantitative and dynamic models of pathways. RESULTS We have developed a particle-based spatial stochastic method (GMP) to simulate biochemical networks in space, including fluctuations from the diffusion of particles and reactions. Gradients emerging from membrane reactions can be resolved. As case studies for the GMP method we used a simple gene expression system and the phosphoenolpyruvate:glucose phosphotransferase system pathway. AVAILABILITY The source code for the GMP method is available at http://www.science.uva.nl/research/scs/CellMath/GMP.

Promoter sequence determines the relationship between expression level and noise.

A single transcription factor can activate or repress expression by three different mechanisms: one that increases cell-to-cell variability in target gene expression (noise) and two that decrease noise.

VLAM-G: A Grid-based virtual laboratory

The Grid-based Virtual Laboratory AMsterdam (VLAM-G), provides a science portal for distributed analysis in applied scientific research. It offers scientists remote experiment control, data management facilities and access to distributed resources by providing cross-institutional integration of information and resources in a familiar environment. The main goal is to provide a unique integration of existing standards and software packages. This paper describes the design and prototype implementation of the VLAM-G platform. In this testbed we applied several recent technologies such as the Globus toolkit, enhanced federated database systems, and visualization and simulation techniques. Several domain specific case studies are described in some detail. Information management will be discussed separately in a forthcoming paper.

Morphogenesis of the branching reef coral Madracis mirabilis

Understanding external deciding factors in growth and morphology of reef corals is essential to elucidate the role of corals in marine ecosystems, and to explain their susceptibility to pollution and global climate change. Here, we extend on a previously presented model for simulating the growth and form of a branching coral and we compare the simulated morphologies to three–dimensional (3D) images of the coral species Madracis mirabilis. Simulation experiments and isotope analyses of M. mirabilis skeletons indicate that external gradients of dissolved inorganic carbon (DIC) determine the morphogenesis of branching, phototrophic corals. In the simulations we use a first principle model of accretive growth based on local interactions between the polyps. The only species–specific information in the model is the average size of a polyp. From flow tank and simulation studies it is known that a relatively large stagnant and diffusion dominated region develops within a branching colony. We have used this information by assuming in our model that growth is entirely driven by a diffusion–limited process, where DIC supply represents the limiting factor. With such model constraints it is possible to generate morphologies that are virtually indistinguishable from the 3D images of the actual colonies.

The Skeletal Proteome of the Coral Acropora millepora: The Evolution of Calcification by Co-Option and Domain Shuffling

In corals, biocalcification is a major function that may be drastically affected by ocean acidification (OA). Scleractinian corals grow by building up aragonitic exoskeletons that provide support and protection for soft tissues. Although this process has been extensively studied, the molecular basis of biocalcification is poorly understood. Notably lacking is a comprehensive catalog of the skeleton-occluded proteins—the skeletal organic matrix proteins (SOMPs) that are thought to regulate the mineral deposition. Using a combination of proteomics and transcriptomics, we report the first survey of such proteins in the staghorn coral Acropora millepora. The organic matrix (OM) extracted from the coral skeleton was analyzed by mass spectrometry and bioinformatics, enabling the identification of 36 SOMPs. These results provide novel insights into the molecular basis of coral calcification and the macroevolution of metazoan calcifying systems, whereas establishing a platform for studying the impact of OA at molecular level. Besides secreted proteins, extracellular regions of transmembrane proteins are also present, suggesting a close control of aragonite deposition by the calicoblastic epithelium. In addition to the expected SOMPs (Asp/Glu-rich, galaxins), the skeletal repertoire included several proteins containing known extracellular matrix domains. From an evolutionary perspective, the number of coral-specific proteins is low, many SOMPs having counterparts in the noncalcifying cnidarians. Extending the comparison with the skeletal OM proteomes of other metazoans allowed the identification of a pool of functional domains shared between phyla. These data suggest that co-option and domain shuffling may be general mechanisms by which the trait of calcification has evolved.

Efficient parameter estimation for spatio-temporal models of pattern formation

MOTIVATION Diffusable and non-diffusable gene products play a major role in body plan formation. A quantitative understanding of the spatio-temporal patterns formed in body plan formation, by using simulation models is an important addition to experimental observation. The inverse modelling approach consists of describing the body plan formation by a rule-based model, and fitting the model parameters to real observed data. In body plan formation, the data are usually obtained from fluorescent immunohistochemistry or in situ hybridizations. Inferring model parameters by comparing such data to those from simulation is a major computational bottleneck. An important aspect in this process is the choice of method used for parameter estimation. When no information on parameters is available, parameter estimation is mostly done by means of heuristic algorithms. RESULTS We show that parameter estimation for pattern formation models can be efficiently performed using an evolution strategy (ES). As a case study we use a quantitative spatio-temporal model of the regulatory network for early development in Drosophila melanogaster. In order to estimate the parameters, the simulated results are compared to a time series of gene products involved in the network obtained with immunohistochemistry. We demonstrate that a (mu,lambda)-ES can be used to find good quality solutions in the parameter estimation. We also show that an ES with multiple populations is 5-140 times as fast as parallel simulated annealing for this case study, and that combining ES with a local search results in an efficient parameter estimation method.

Genetic, biological and structural hierarchies during sponge spicule formation: from soft sol–gels to solid 3D silica composite structures

Structural biomaterials are hierarchically organized and biofabricated. Although the structural complexity of most bioskeletons can be traced back from the millimeter-scale to the micrometer- or submicrometer-scale, the biological and/or genetic basis controlling the synthesis of these skeletons and their building blocks remained unknown. There is one distinguished example, the spicules of the siliceous sponges, for which the principle molecules and molecular-biological processes involved in their formation have been elucidated in the last few years. In this review, recent data on the different levels of molecular, biological and structural hierarchies controlling the synthesis of the picturesquely and intricately architectured spicules are summarized. The silicateins and their interacting/maturated proteins comprise the basic enzymatic/proteinous machinery that facilitates the polycondensation of silicate to biosilica. Two isoforms of silicatein, silicatein-α and silicatein-β, the enzyme that catalyzes the polymerization of orthosilicate to polymeric biosilica, have been identified. The remarkable feature of these enzymes is that, besides their enzymatic function, they act as structure-giving proteins that provide the platform for the organization of the silica spicules. Silicatein-α together with silicatein-β forms pentameric units that continue to grow in a linear pattern. The silicatein-interacting protein, silintaphin-1, stabilizes the initially formed silicatein fractals, while silintaphin-2 provides Ca2+ ions required for the appositional growth of the spicules. The biosilica formed during the enzymatically driven sol–gel process that is catalyzed by this multi-protein system is a soft, gel-like inorganic polymer. This soft biosilica undergoes a biologically controlled process of syneresis, resulting in a shrinkage of the silica network. During this reaction the biosilica is transformed into an elastic solid and gains the characteristic spicule morphology. A sizeable amount of protein, mostly silicatein, remains embedded in the biosilica material, thus forming a hybrid bioinorganic (“biosilica”) material. The process of syneresis involves the removal of water by cell-membrane-associated aquaporin channels and is guided by collagen bundles. Four cell types, sclerocytes, archaeocytes, chromocytes and lophocytes, participate in this structure-guiding process. In conclusion, this article attempts to overcome the frontiers in the understanding of the different levels of hierarchies, genetic, biological and structural, and to contribute towards the fabrication of new bioinspired functional materials.

Calcium homeostasis and signaling in yeast cells and cardiac myocytes

Calcium ions are the most ubiquitous and versatile signaling molecules in eukaryotic cells. Calcium homeostasis and signaling systems are crucial for both the normal growth of the budding yeast Saccharomyces cerevisiae and the intricate working of the mammalian heart. In this paper, we make a detailed comparison between the calcium homeostasis/signaling networks in yeast cells and those in mammalian cardiac myocytes. This comparison covers not only the components, structure and function of the networks but also includes existing knowledge on the measured and simulated network dynamics using mathematical models. Surprisingly, most of the factors known in the yeast calcium homeostasis/signaling network are conserved and operate similarly in mammalian cells, including cardiac myocytes. Moreover, the budding yeast S. cerevisiae is a simple organism that affords powerful genetic and genomic tools. Thus, exploring and understanding the calcium homeostasis/signaling system in yeast can provide a shortcut to help understand calcium homeostasis/signaling systems in mammalian cardiac myocytes. In turn, this knowledge can be used to help treat relevant human diseases such as pathological cardiac hypertrophy and heart failure.

Computational methods for diffusion-influenced biochemical reactions

MOTIVATION We compare stochastic computational methods accounting for space and discrete nature of reactants in biochemical systems. Implementations based on Brownian dynamics (BD) and the reaction-diffusion master equation are applied to a simplified gene expression model and to a signal transduction pathway in Escherichia coli. RESULTS In the regime where the number of molecules is small and reactions are diffusion-limited predicted fluctuations in the product number vary between the methods, while the average is the same. Computational approaches at the level of the reaction-diffusion master equation compute the same fluctuations as the reference result obtained from the particle-based method if the size of the sub-volumes is comparable to the diameter of reactants. Using numerical simulations of reversible binding of a pair of molecules we argue that the disagreement in predicted fluctuations is due to different modeling of inter-arrival times between reaction events. Simulations for a more complex biological study show that the different approaches lead to different results due to modeling issues. Finally, we present the physical assumptions behind the mesoscopic models for the reaction-diffusion systems. AVAILABILITY Input files for the simulations and the source code of GMP can be found under the following address: http://www.cwi.nl/projects/sic/bioinformatics2007/