Competitive hybridization models.

Microarray technology, in its simplest form, allows one to gather abundance data for target DNA molecules, associated with genomes or gene-expressions, and relies on hybridizing the target to many short probe oligonucleotides arrayed on a surface. While for such multiplexed reactions conditions are optimized to make the most of each individual probe-target interaction, subsequent analysis of these experiments is based on the implicit assumption that a given experiment yields the same result regardless of whether it was conducted in isolation or in parallel with many others. It has been discussed in the literature that this assumption is frequently false, and its validity depends on the types of probes and their interactions with each other. We present a detailed physical model of hybridization as a means of understanding probe interactions in a multiplexed reaction. Ultimately, the model can be derived from a system of ordinary differential equations (ODE's) describing kinetic mass action with conservation-of-mass equations completing the system. We examine pairwise probe interactions in detail and present a model of "competition" between the probes for the target--especially, when the target is effectively in short supply. These effects are shown to be predictable from the affinity constants for each of the four probe sequences involved, namely, the match and mismatch sequences for both probes. These affinity constants are calculated from the thermodynamic parameters such as the free energy of hybridization, which are in turn computed according to the nearest neighbor (NN) model for each probe and target sequence. Simulations based on the competitive hybridization model explain the observed variability in the signal of a given probe when measured in parallel with different groupings of other probes or individually. The results of the simulations can be used for experiment design and pooling strategies, based on which probes have been shown to have a strong effect on each other's signal in the in silico experiment. These results are aimed at better design of multiplexed reactions on arrays used in genotyping (e.g., HLA typing, SNP, or CNV detection, etc.) and mutation analysis (e.g., cystic fibrosis, cancer, autism, etc.).

A sense of life: computational and experimental investigations with models of biochemical and evolutionary processes.

We collaborate in a research program aimed at creating a rigorous framework, experimental infrastructure, and computational environment for understanding, experimenting with, manipulating, and modifying a diverse set of fundamental biological processes at multiple scales and spatio-temporal modes. The novelty of our research is based on an approach that (i) requires coevolution of experimental science and theoretical techniques and (ii) exploits a certain universality in biology guided by a parsimonious model of evolutionary mechanisms operating at the genomic level and manifesting at the proteomic, transcriptomic, phylogenic, and other higher levels. Our current program in "systems biology" endeavors to marry large-scale biological experiments with the tools to ponder and reason about large, complex, and subtle natural systems. To achieve this ambitious goal, ideas and concepts are combined from many different fields: biological experimentation, applied mathematical modeling, computational reasoning schemes, and large-scale numerical and symbolic simulations. From a biological viewpoint, the basic issues are many: (i) understanding common and shared structural motifs among biological processes; (ii) modeling biological noise due to interactions among a small number of key molecules or loss of synchrony; (iii) explaining the robustness of these systems in spite of such noise; and (iv) cataloging multistatic behavior and adaptation exhibited by many biological processes.

Shrinkage-based similarity metric for cluster analysis of microarray data.

The current standard correlation coefficient used in the analysis of microarray data was introduced by M. B. Eisen, P. T. Spellman, P. O. Brown, and D. Botstein [(1998) Proc. Natl. Acad. Sci. USA 95, 14863-14868]. Its formulation is rather arbitrary. We give a mathematically rigorous correlation coefficient of two data vectors based on James-Stein shrinkage estimators. We use the assumptions described by Eisen et al., also using the fact that the data can be treated as transformed into normal distributions. While Eisen et al. use zero as an estimator for the expression vector mean mu, we start with the assumption that for each gene, mu is itself a zero-mean normal random variable [with a priori distribution N(0,tau 2)], and use Bayesian analysis to obtain a posteriori distribution of mu in terms of the data. The shrunk estimator for mu differs from the mean of the data vectors and ultimately leads to a statistically robust estimator for correlation coefficients. To evaluate the effectiveness of shrinkage, we conducted in silico experiments and also compared similarity metrics on a biological example by using the data set from Eisen et al. For the latter, we classified genes involved in the regulation of yeast cell-cycle functions by computing clusters based on various definitions of correlation coefficients and contrasting them against clusters based on the activators known in the literature. The estimated false positives and false negatives from this study indicate that using the shrinkage metric improves the accuracy of the analysis.