Modeling and simulation for toxicity assessment.

The effect of various toxicants on growth/death and morphology of human cells is investigated using the xCELLigence Real-Time Cell Analysis High Troughput in vitro assay. The cell index is measured as a proxy for the number of cells, and for each test substance in each cell line, time-dependent concentration response curves (TCRCs) are generated. In this paper we propose a mathematical model to study the effect of toxicants with various initial concentrations on the cell index. This model is based on the logistic equation and linear kinetics. We consider a three dimensional system of differential equations with variables corresponding to the cell index, the intracellular concentration of toxicant, and the extracellular concentration of toxicant. To efficiently estimate the model's parameters, we design an Expectation Maximization algorithm. The model is validated by showing that it accurately represents the information provided by the TCRCs recorded after the experiments. Using stability analysis and numerical simulations, we determine the lowest concentration of toxin that can kill the cells. This information can be used to better design experimental studies for cytotoxicity profiling assessment.

Machine learning algorithms for mode-of-action classification in toxicity assessment.

BACKGROUND: Real Time Cell Analysis (RTCA) technology is used to monitor cellular changes continuously over the entire exposure period. Combining with different testing concentrations, the profiles have potential in probing the mode of action (MOA) of the testing substances. RESULTS: In this paper, we present machine learning approaches for MOA assessment. Computational tools based on artificial neural network (ANN) and support vector machine (SVM) are developed to analyze the time-concentration response curves (TCRCs) of human cell lines responding to tested chemicals. The techniques are capable of learning data from given TCRCs with known MOA information and then making MOA classification for the unknown toxicity. A novel data processing step based on wavelet transform is introduced to extract important features from the original TCRC data. From the dose response curves, time interval leading to higher classification success rate can be selected as input to enhance the performance of the machine learning algorithm. This is particularly helpful when handling cases with limited and imbalanced data. The validation of the proposed method is demonstrated by the supervised learning algorithm applied to the exposure data of HepG2 cell line to 63 chemicals with 11 concentrations in each test case. Classification success rate in the range of 85 to 95 % are obtained using SVM for MOA classification with two clusters to cases up to four clusters. CONCLUSIONS: Wavelet transform is capable of capturing important features of TCRCs for MOA classification. The proposed SVM scheme incorporated with wavelet transform has a great potential for large scale MOA classification and high-through output chemical screening.

Novel stability results for traveling wavefronts in an age-structured reaction-diffusion equation.

For a time-delayed reaction-diffusion equation of age-structured single species population, the linear and nonlinear stability of the traveling wavefronts were proved by Gourley [4] and Li-Mei-Wong [8] respectively. The stability results, however, assume the delay-time is sufficiently small. We now prove that the wavefronts remain stable even when the delay-time is arbitrarily large. This essentially improves the previous stability results obtained in [4, 8]. Finally, we point out that this novel stability can be applied to the age-structured reaction-diffusion equation with a more general maturation rate.

Nonlinear stability of traveling wavefronts in an age-structured reaction-diffusion population model.

The paper is devoted to the study of a time-delayed reaction- diffusion equation of age-structured single species population. Linear stability for this model was first presented by Gourley [4], when the time delay is small. Here, we extend the previous result to the nonlinear stability by using the technical weighted-energy method, when the initial perturbation around the wavefront decays to zero exponentially as x--> -infinity, but the initial perturbation can be arbitrarily large on other locations. The exponential convergent rate (in time) of the solution is obtained. Numerical simulations are carried out to confirm the theoretical results, and the traveling wavefronts with a large delay term in the model are reported.