A study of some aspects of the mechanical behaviour of cross-spring pivots and plate spring mechanisms with negative stiffness

Mechanical, Maritime and Materials Engineerin

Mathematical analysis of the real time array PCR (RTA PCR) process

Real time array PCR (RTA PCR) is a recently developed biochemical technique that measures amplification curves (like with quantitative real time Polymerase Chain Reaction (qRT PCR)) of a multitude of different templates in a sample. It combines two different methods in order to profit from the advantages of both, namely qRT PCR (real time quantitative detection) with microarrays (high multiplex capability). This enables the quantitative detection of many more target sequences than that can be done by qRT PCR. Thereby, the concentration of many different target molecules originally present in a sample can be measured. Labelled primers are used that are first elongated to form labelled amplicons in the bulk and these can hybridize to capture probes immobilized on the surface of the microarray. During each PCR cycle, there is a time window available during which the formed labelled amplicons can hybridize to the target sequences (capture probes) on the microarray surface. By detection of the fluorescence of the spots on the microarray, amplification curves comparable to qRT PCR are obtained, which can be used to deduce the information needed on the presence and the amount of targets initially present in the sample. We present a mathematical model that provides fundamental insights in the different steps of real time array PCR (RTA PCR). These findings can be used to optimize the different biochemical processes taking place. At the microarray surface specific molecules are captured and taken away from the solution, causing a concentration gradient that powers a material flow towards the microarray surface. Only labelled strands of the amplicons are captured by probes on the microarray surface and as a result locally the PCR process is not symmetric anymore. Moreover, in course of the process more and more single stranded DNA renatures, leaving relatively less strands and complexes available for hybridization. The main conclusion is that surface fluorescence scales with the bulk concentration of the targets involved. Our analysis shows that the Ct value is only slightly dependent on the initial enzyme load and the degradation of the capture probes. The Ct value, however, does depend strongly on the rate constants of the annealing/hybridization reactions in the bulk and on surface. Local asymmetry appears to be a minor effect. -------------------------------------------------------------------------------