Simultaneous modeling of concentration-effect and time-course patterns in gene expression data from microarrays.

BACKGROUND: Time-course and concentration-effect experiments with multiple time-points and drug concentrations provide far more valuable information than experiments with just two design-points (treated vs. control), as commonly performed in most microarray studies. Analysis of the data from such complex experiments, however, remains a challenge. MATERIALS AND METHODS: Here we present a semi-automated method for fitting time profiles and concentration-effect patterns, simultaneously, to gene expression data. The submodels for time-course included exponential increase and decrease models with parameters, such as initial expression level, maximum effect, and rate-constant (or half-time). The submodel for concentration-effect was a 4-parameter Hill model. RESULTS: The method was applied to an Affymetrix HG-U95Av2 dataset consisting of 51 arrays. The specific study focused on the effects of two platinum drugs, cisplatin and oxaliplatin, on A2780 human ovarian carcinoma cells. Replicates were available at most time points and concentrations. Eighteen genes were selected, and after selection, time-course and concentration-effect were modeled simultaneously. CONCLUSION: Comparisons of model parameters helped to distinguish genes with different expression patterns between the two drug treatments. This overall paradigm can help in understanding the molecular mechanisms of the agents, and the timing of their actions.

Modeling the combination of amphotericin B, micafungin, and nikkomycin Z against Aspergillus fumigatus in vitro using a novel response surface paradigm.

Response surface methods for the study of multiple-agent interaction allow one to model all of the information present in full concentration-effect data sets and to visualize and quantify local regions of synergy, additivity, and antagonism. In randomized wells of 96-well plates, Aspergillus fumigatus was exposed to various combinations of amphotericin B, micafungin, and nikkomycin Z. The experimental design was comprised of 91 different fixed-ratio mixtures, all performed in quintuplicate. After 24 h of drug exposure, drug effect on fungal viability was assessed using the tetrazolium salt 2,3-bis {2-methoxy-4-nitro-5-[(sulfenylamino) carbonyl]-2H-tetrazolium-hydroxide} (XTT) assay. First, we modeled each fixed-ratio combination alone using the four-parameter Hill concentration-effect model. Then, we modeled each parameter, including the 50% inhibitory concentration (IC(50)) effect, versus the proportion of each agent using constrained polynomials. Finally, we modeled the three-agent response surface overall. The overall four-dimensional response surface was complex, but it can be explained in detail both analytically and graphically. The grand model that fit the best included complex polynomial equations for the slope parameter m and the combination index (equivalent to the IC(50) for a fixed-ratio concentration, but with concentrations normalized by the respective IC(50)s of the drugs alone). There was a large region of synergy, mostly at the nikkomycin Z/micafungin edge of the ternary plots for equal normalized proportions of each drug and extending into the center of the plots. Applying this response surface method to a huge data set for a three-antifungal-agent combination is novel. This new paradigm has the potential to significantly advance the field of combination antifungal pharmacology.