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Theory

The currently used microarray technology, where signal intensity after stringent washing is a measure for the number of hybridized targets is already in a mature state. There is still an ongoing discussion on quality improvements of microarray experiments. In general the measured intensity is

I = ISp(c) + IBg

where ISp(c) is the specific signal due to hybridization of the complementary probe-target duplex and IBg is the background due to nonspecific effects. ISp depends on the concentration c of the complementary strand in solution (target). For hybridization to surface immobilized  nucleic acids there are several factors influencing the unspecific term IBg e.g. cross hybridization, optical effects, microarray surface composition and intra- and interarray process variations. The discrimination of specific and nonspecific hybridization of similar targets is still a challenge in microarray probe design and data analysis. Further the development of advanced model based algorithms for background determination is still a matter of research.

Microarray based real-time data acquisition during hybridization and melting tries to overcome these problems by recording the change of specific intensity signal ISp during the hybridization and denaturation relative to the unspecific signal IBg. Thus it gives the possibility to monitor melting of nucleic acid duplexes within the environment of the application. This way the fact that hybridization kinetics can provide information for the discrimination between specific and unspecific hybridization and for quantification of targets can be exploited. The multiple measurements of intensity changes opens the door for advanced signal processing and noise reduction techniques, model-based fitting can solve the inherent weakness of single sampling measurement.

Here we report on the development of a physical model based nonlinear regression algorithm for real-time microarray data analysis and the implementation within a Matlab programmed GUI. Based on the experimental data of 40 experiments we used equations of physico-chemical systems with similar behavior as fit function for the nonlinear regression putting the focus on high-density microarray applications.

 

 

Kinetic

Currently it is not possible to give a numerical description of the complex hydrodynamic transport processes. Thus nonlinear regression to physico-chemical model systems was used.

The intensity of kinetic measurements in microarray experiments is not necessarily monotonically increasing. In case of competitive hybridization a target with a high reaction rate but lower binding energy is replaced during hybridization process with targets of a higher binding energy

The kinetic parameters are being calculated as follow

I(X) =  a * kh e -kh (X - x0) - e -kc (X - x0)
kc - kh

For competitive hybridization the two constants kh and kc give the reaction rates of the two consecutive steps of hybridization and competitive displacement.

In case of non competitive hybridization kc = 0 the formula is still valid.

 

 

Melting

The fitting of the melting curves was based on a convolution of linear functions for the description of the temperature behavior of the dye and an exponential distribution function.

I(T)  = ka (kCy - x) - (kHT * T) + kconst
e kb (x - ktm) +1

with the intensity I(T) and the fitting parameters ktm, ka, kb, kCy, kHT and kconst.
ka is related to the amount of hybridized target.
kb is related to the slope of the melting curve at melting temperature (Tm).
The larger kb the steeper is the melting transition. In general, kb is larger for longer oligos.
kCy considers the linear temperature behavior of the dye.
The term -kHT * T + kconst is a first order correction considering the remaining fluorescent intensity at temperatures above the melting of the nucleic acids due to unspecific binding of fluorophores to the probe spots.
The whole nonlinear behavior of the system is described by the exponential function with the two parameters ktm and kb.
The parameter ktm gives the melting temperature.