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.

The early embryo of Drosophila melanogaster provides a powerful model system to study the role of genes in pattern formation. The gap gene network constitutes the first zygotic regulatory tier in the hierarchy of the segmentation genes involved in specifying the position of body segments. Here, we use an integrative, systems-level approach to investigate the regulatory effect of the terminal gap gene huckebein (hkb) on gap gene expression. We present quantitative expression data for the Hkb protein, which enable us to include hkb in gap gene circuit models. Gap gene circuits are mathematical models of gene networks used as computational tools to extract regulatory information from spatial expression data. This is achieved by fitting the model to gap gene expression patterns, in order to obtain estimates for regulatory parameters which predict a specific network topology. We show how considering variability in the data combined with analysis of parameter determinability significantly improves the biological relevance and consistency of the approach. Our models are in agreement with earlier results, which they extend in two important respects: First, we show that Hkb is involved in the regulation of the posterior hunchback (hb) domain, but does not have any other essential function. Specifically, Hkb is required for the anterior shift in the posterior border of this domain, which is now reproduced correctly in our models. Second, gap gene circuits presented here are able to reproduce mutants of terminal gap genes, while previously published models were unable to reproduce any null mutants correctly. As a consequence, our models now capture the expression dynamics of all posterior gap genes and some variational properties of the system correctly. This is an important step towards a better, quantitative understanding of the developmental and evolutionary dynamics of the gap gene network.

Abstract. A second-order, L-stable Rosenbrock method from the field of stiff ordinary differential equations is studied for application to atmospheric dispersion problems describing photochemistry, advective, and turbulent diffusive transport. Partial differential equation problems of this type occur in the field of air pollution modeling. The focal point of the paper is to examine the Rosenbrock method for reliable and efficient use as an atmospheric chemical kinetics box-model solver within Strang-type operator splitting. In addition, two W-method versions of the Rosenbrock method are discussed. These versions use an inexact J1tcobian matrix and are meant to provide alternatives for Strang-splitting. Another alternative for Strang-splitting is a technique based on so-called source-splitting. This technique is briefly discussed.

To identify components of the mitochondrial protein import pathway in yeast, we have adopted a positive selection procedure for isolating mutants disturbed in protein import. We have cloned and sequenced a gene, termed MPI1, that can rescue the genetic defect of one group of these mutants. MPI1 encodes a hydrophilic 48.8 kDa protein that is essential for cell viability. Mpi1p is a low abundance and constitutively expressed mitochondrial protein. Mpi1p is synthesized with a characteristic mitochondrial targeting sequence at its amino‐terminus, which is most probably proteolytically removed during import. It is a membrane protein, oriented with its carboxy‐terminus facing the intermembrane space. In cells depleted of Mpi1p activity, import of the precursor proteins that we tested thus far, is arrested. We speculate that the Mpi1 protein is a component of a proteinaceous import channel for translocation of precursor proteins across the mitochondrial inner membrane.

In the numerical simulation of atmospheric transport-chemistry processes, a major task is the integration of the stiff systems of ordinary differential equations describing the chemical transformations. It is therefore of interest to systematically search for stiff solvers which can be identified as close to optimal for atmospheric applications. In this paper we continue our investigation from Sandu et al. (1996, CWI Report NM-R9603 and Report in Comput. Math., No. 85) and compare eight solvers on a set of seven box-models used in present day models. The focus is on Rosenbrock solvers. These tum out to be very well suited for our application when they are provided with highly efficient sparse matrix techniques to economize on the linear algebra. Two of the Rosenbrock solvers tested are from the literature, viz. RODAS and ROs4, and two are new and specially developed for air quality applications, viz. RODAS3 and ROS3. (f) 1997 Elsevier Science Ltd.

Background: Mathematical modeling of real-life processes often requires the estimation of unknown parameters. Once the parameters are found by means of optimization, it is important to assess the quality of the parameter estimates, especially if parameter values are used to draw biological conclusions from the model.

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.

The essential yeast gene MPI1 encodes a mitochondrial membrane protein that is possibly involved in protein import into the organelle (A. C. Maarse, J. Blom, L. A. Grivell, and M. Meijer, EMBO J. 11:3619-3628, 1992). For this report, we determined the submitochondrial location of the MPI1 gene product and investigated whether it plays a direct role in the translocation of preproteins. By fractionation of mitochondria, the mature protein of 44 kDa was localized to the mitochondrial inner membrane and therefore termed MIM44. Import of the precursor of MIM44 required a membrane potential across the inner membrane and involved proteolytic processing of the precursor. A preprotein in transit across the mitochondrial membranes was cross-linked to MIM44, whereas preproteins arrested on the mitochondrial surface or fully imported proteins were not cross-linked. When preproteins were arrested at two distinct stages of translocation across the inner membrane, only preproteins at an early stage of translocation could be cross-linked to MIM44. Moreover, solubilized MIM44 was found to interact with in vitro-synthesized preproteins. We conclude that MIM44 is a component of the mitochondrial inner membrane import machinery and interacts with preproteins in an early step of translocation.Only six essential genes encoding mitochondrial proteins are known in Saccharomyces cerevisiae. The products of four of these genes are located in the mitochondrial matrix: the two heat shock proteins hsp70 (6, 17) and hsp60 (5,22,35), and the two components of the mitochondrial processing peptidase (16,30,48,49). ISP42, also termed MOM38, is located in the outer membrane and forms an essential part of the mitochondrial receptor complex that is responsible for the specific recognition and translocation of preproteins (2,18,20,41,43). All of the components mentioned were found to play a crucial role in the import pathways of cytosolically synthesized preproteins.The sixth essential mitochondrial protein, encoded by MPH, has also been implicated to be involved in import of preproteins (19). The gene MPh was identified by its ability to rescue the genetic defect of a mutant impaired in mitochondrial protein import. The gene product was localized to the mitochondrial membranes by using a modified protein carrying an epitope tag. It was proposed that the protein was synthesized with an amino-terminal presequence and thus located in the inner membrane (19). The identification and characterization of the inner membrane transport machinery is currently a major goal in the analysis of mitochondrial protein import. A demonstration that the MPI1 gene product is located in the inner membrane and directly participates in the import of preproteins would be an important first step toward this goal.Here we show that the MPh gene product indeed represents a genuine component of the mitochondrial inner membrane import machinery (MIM) (27). The protein was local-* Corresponding author.ized to the inner membrane and termed MIM44. By a cross-link approach with dis...