Mathematical modeling of dose-response curves using microarray gene expression data



A central question in toxicology is “How does it work?” meaning what are the molecular mechanisms of action that make the poison effective. An important tool to study mechanisms of action is the response of a living organism to a range of doses of toxicants. The dose response curve is the gold standard for measuring effects of drug treatment, but is rarely used in genome-wide transcriptional profiling due to obstacles of cost and analysis. Mathematical models of these dose-response curves have been around since the early 20th century. A common issue in the analysis of high-throughput gene expression toxicology data is how to select a subset of the genes for a more detailed study. We propose to combine a sigmoidal dose-response model (the Hill model) with a statistical mixture modeling approach to cluster genes with similar gene expression responses to toxicants. The student is expected to have affinity with statistical modeling and programming (Matlab or R).

The aim of this study is to filter out subsets of genes that exert dose-dependent gene expression in response to Cadmium (Cd) and Phenanthrene (Phe). Furthermore, we can assess the influence of Cadmium on Phenantrene toxicity and vice versa, due to the availability of microarray data from a full factorial binary mixture experiment.


The toxicity of mixtures of environmental xenobiotic compounds on the transcriptional level is gaining attention in the last few years. However, these studies do often include a limited number of mixture ratio combinations. Foslomia candida was used to conduct a binary mixture experiment with Cd and Phe as shown in Figure 1. Four repicates of all exposure combinations (black dots) were assayed using the invertebrate Soil Quality (iSQ) chip, capturing over 5000 unique gene probes.

The candidate will develop sigmoidal dos-response model to retrieve genes that respond dose dependend on Cd without any interference of Phe. The second group of genes that respond dose dependend to Phe without any interference of Cd will be selected as well.

A final group of genes can be defined as responsive to both toxicants. However, it is currently unclear how we can classify such genes in distinct response groups. Perhaps, clustering tools need to be applied or multivariate statistics. All statistical modeling and programming can be performed in Matlab or R.

Roelofs-Setup mixtox-4

Figure 1:  The radial design of exposure. The 1:4, 1:2 1:1 and 2:1, and 4:1 represent the ratios of the nominal concentration series of phenantrene and cadnmium respectively.

Supervision and information

Dr. Ir. Dick Roelofs (Room H147, W&N building, Vrije Universiteit)
Phone: +31 (0)20 – 59 87078


Dr. Tjeerd Dijkstra, Machine learning group, Radboud University Leiden.