Characterization of a three-drug nonlinear mixture response model.

Our group recently developed a response-surface modeling paradigm (White et al: Curr Drug Metab 2, 399-409, 2003) and tested its application to both mixtures of anticancer agents and antifungals. This new model is a Hill-type equation, with the slope and potency parameters being functions of the normalized drug ratios, using polynomial expressions. Response surface methods allow one to model and interpret all of the information present in the full concentration-effect data set, to visualize local regions of synergy, additivity and antagonism, and even to quantify the degree of synergy or antagonism, both globally, and across local regions of the response surface. In the present article, we study the effect of changes in the different parameters of the polynomial expressions for two-drug and three-drug mixtures, on the geometrical shapes of several 2-dimensional representations of the 3-dimensional concentration-effect surface. A secondary goal of this report is to compare the mathematical characteristics of the rival White and (Minto et al: Anesthesiol 92, 1603-1616, 2000) modeling paradigms.

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.

Effect of amphotericin B and micafungin combination on survival, histopathology, and fungal burden in experimental aspergillosis in the p47phox-/- mouse model of chronic granulomatous disease.

Chronic granulomatous disease (CGD) is an inherited disorder of the NADPH oxidase characterized by recurrent life-threatening bacterial and fungal infections. We characterized the effects of single and combination antifungal therapy on survival, histopathology, and laboratory markers of fungal burden in experimental aspergillosis in the p47phox-/- knockout mouse model of CGD. CGD mice were highly susceptible to intratracheal Aspergillus fumigatus challenge, whereas wild-type mice were resistant. CGD mice were challenged intratracheally with a lethal inoculum (1.25 x 10(4) CFU/mouse) of A. fumigatus and received one of the following regimens daily from day 0 to 4 after challenge (n = 19 to 20 per treatment group): (i) vehicle, (ii) amphotericin B (intraperitoneal; 1 mg/kg of body weight), (iii) micafungin (intravenous; 10 mg/kg), or (iv) amphotericin B plus micafungin. The rank order of therapeutic efficacy based on prolonged survival, from highest to lowest, was as follows: amphotericin B plus micafungin, amphotericin B alone, micafungin alone, and the vehicle. Lung histology showed pyogranulomatous lesions and invasive hyphae, but without hyphal angioinvasion or coagulative necrosis. Treatment with micafungin alone or combined with amphotericin B produced swelling of invasive hyphae that was not present in mice treated with the vehicle or amphotericin B alone. Assessment of lung fungal burden by quantitative PCR showed no significant difference between treatment groups. Serum galactomannan levels were at background despite documentation of invasive aspergillosis by histology. Our findings showed the superior efficacy of the amphotericin B and micafungin combination compared to either agent alone after A. fumigatus challenge and also demonstrated unique features of CGD mice as a model for experimental aspergillosis.

A new nonlinear mixture response surface paradigm for the study of synergism: a three drug example.

A flexible approach to response surface modeling for the study of the joint action of three active anticancer agents is used to model a complex pattern of synergism, additivity and antagonism in an in vitro cell growth assay. The method for determining a useful nonlinear response surface model depends upon a series of steps using appropriate scaling of drug concentrations and effects, raw data modeling, and hierarchical parameter modeling. The method is applied to a very large in vitro study of the combined effect of Trimetrexate (TMQ), LY309887 (LY), and Tomudex (TDX) on inhibition of cancer cell growth. The base model employed for modeling dose-response effect is the four parameter Hill equation [1]. In the hierarchical aspect of the final model, the base Hill model is treated as a function of the total amount of the three drug mixture and the Hill parameters, background B, dose for 50% effect D50, and slope m, are understood as functions of the three drug fractions. The parameters are modeled using the canonical mixture polynomials from the mixture experiment methodologies introduced by Scheff [2]. We label the model generated a Nonlinear Mixture Amount model with control observations, or zero amounts, an "NLMAZ" model. This modeling paradigm provides for the first time an effective statistical approach to modeling complex patterns of local synergism, additivity, and antagonism in the same data set, the possibility of including additional experimental components beyond those in the mixture, and the capability of modeling three or more drugs.