| Quantification of mRNA concentration levels is critical for elucidation of the molecular mechanism responsible for different physiological or developmental states. In this thesis, mathematical models are developed for four methods currently used to detect and quantify mRNA levels. The aim is to derive an expression for the efficiency of the experimental method and explore modifications that improve process performance.; A mathematical expression for the probability that a particular mRNA species is identified as being differentially expressed by the Suppression Subtractive Hybridization method is derived as a function of mRNA concentration, hybridization times and relative amounts of the two samples. It was used to demonstrate that the hybridization conditions currently used result in a high number of false positives. The effect of changes in reaction conditions on the process efficiency was investigated. The presence of partially homologous sequences changes the composition of the false positives obtained, and strategies for spiking the driver are suggested to decrease specific false positives.; Representational Difference Analysis is another subtractive hybridization method for the enrichment of differentially expressed sequences. A mathematical model for the process is presented and the critical steps affecting process efficiency are identified.; Models for various strategies for cDNA library construction are presented and their ability to normalize a given mRNA population is evaluated. Recommendations for changing process parameters in order to improve normalization efficiency have been presented.; DNA hybridization on a microarray is modeled as a diffusion-reaction process and finite element analysis is used to numerically solve the set of model equations. It is observed that for cDNA microarray hybridizations, diffusion mediates the rate of duplex formation. The effect of the nature of the immobilized and free strands, hybridization time, and total concentrations used is simulated. A novel strategy that has the potential of improving assay sensitivity is presented and analyzed using the developed models.; The models and solution strategies developed here provide a framework for a realistic simulation of these and other biological and chemical systems and processes. |
