(74a) On Diffusion Coefficients, Relaxation Times of Oligonucleotides

DNA microarrays have been applied to gene expression, genotyping and sequencing. The hybridization step between probe and target molecules may take several hours.  The understanding of the hybridization kinetics is important. Some investigators have found the hybridization overall reaction rate to be reaction rate limited in the 90s and some other investigators in the early 00s have found the overall hybridization reaction rate to be diffusion limited (Pascault and Zhou, 2008). They go further to improve the overall hybridization reaction rate by providing convective mass transfer to decrease the diffusion limitations. They obtain these recommendations after performing computer simulations  by finite element numerical solutions using Comsol Multiphysics software package. The length of the DNA target molecules range between 50 – 350 bp. The probe molecules are shorter than the target molecules and have about 10-60 bp of Adenine, Cytosine, Guanine and Thymine. The surface concentration of probe molecules range between 1.2 x 10 ^-10 – 4 x 10¹³ probes/cm² or 1 attomoles/m² to 0.1 micromoles/m².  The diffusion coefficient values for the base pairs decreased with the length of the oligonucleotide.  The variation of diffusivity values as a function of the length of the oligonucleotide from different investigators is shown in Figure 1.0.  With a R² value of 0.9956 the following curve could be seen from the trendline except for the data point from Ferrari and Bloomfied given in Pascault et. Al. [2008].  Their value is also given as a red rectangle in Figure 4.3. The diffusion coefficient can be written as follows;

                     D_{pl = al^0.639}

The relaxation time for oligonucleotides can be written as;

                       τ_r =b(l^1.639)/RT

Where l is the lengt of the oligonucleotide in terms of number of base pairs, and D_pt is the binary diffusivity of the probe molecules in target molecules. A₁ was found to be 6 x 10^-10 m²/s from the regression tool in MS Excel 2010 for Windows using a HP Compaq Elite 8300 desktop computer with i7 intel processor. R the universal molar gas constant, T the absolute temperature.  Target molecules of 1 – 1000 pM were considered. The channel height of the microfluidic elements range was 50 – 100s µm. Target microarray spot size considered was 200 µm. The two dimensional microfluidic chamber had a height of 100 µm.

Figure 1.0  Diffusion Coefficient of Oligonucleotide as a Function of Size