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Modeling of coupled momentum, heat and solute transport during DNA hybridization in a microchannel in the presence of electro-osmotic effects and axial pressure gradients

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Abstract

An integrated thermofluidic analysis of DNA hybridization, in the presence of combined electrokinetically and/or pressure-driven microchannel flows, is presented in this work. A comprehensive model is developed that combines bulk and surface transport of momentum, heat and solute with the pertinent hybridization kinetics, in a detailed manner. Results confirm that electrokinetic accumulation of DNA occurs within a few seconds or minutes, as compared to passive hybridization that could sometimes take several hours. Further, it is observed that by increasing the accumulation time, significantly higher concentration of DNA can be achieved at the capture probes. However, this eventually tends to attain a saturation state, due to a lesser probability of successful hybridization on account of a prior accumulation of target DNA molecules on the capture probe strands. While favorable pressure gradients augment DNA hybridization rates that are otherwise established by the electro-osmotic transport, adverse pressure gradients of comparable magnitude may turn out to be much less consequential in retarding the same. Such effects can be of potential significance in the designing of a microfluidic arrangement to achieve the fastest rate of DNA hybridization.

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Authors and Affiliations

  1. Department of Mechanical Engineering, Indian Institute of Technology, Kharagpur, 721302, West Bengal, India

    Siddhartha Das & Suman Chakraborty

  2. Department of Biotechnology and Biochemical Engineering, Indian Institute of Technology, Kharagpur, 721302, West Bengal, India

    Tamal Das

Authors
  1. Siddhartha Das
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  2. Tamal Das
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  3. Suman Chakraborty
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Corresponding author

Correspondence to Suman Chakraborty.

Appendices

Appendix

Relationship between c 2,s and c 3,m

Corresponding to a particular position on the microchannel wall, Eq. 18 can be written in the form:

$$ \frac{{dc_{{2},{s}}}}{{{d}t}} = P -Qc_{{2},{s}} $$
(32)

where P=AB + DE, Q= A +C +D +F. The coefficients A, B, C, D, E and F are as:

$$A = k_{3}^{1} c_{3,m}, B=E=c_{\rm 2,s,max}, C=k_{3}^{-1}, D=k_{2}^{1} c_{\rm 2,ns}, F=k_{2}^{-1}.$$

Integrating Eq. 32, one obtains

$$ \int\limits_{0}^{c_{_{{2},{s}}}}{\frac{{dc_{{2},{s}}}}{{P - Qc_{{2},{s}}}}} = \int\limits_{0}^t {{d}t} $$
(33)

On integration, it follows that

$$c_{{2},{s}} = \frac{P}{Q}{(1} - e^{- Qt})$$
(34)

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Das, S., Das, T. & Chakraborty, S. Modeling of coupled momentum, heat and solute transport during DNA hybridization in a microchannel in the presence of electro-osmotic effects and axial pressure gradients. Microfluid Nanofluid 2, 37–49 (2006). https://doi.org/10.1007/s10404-005-0052-9

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  • DOI: https://doi.org/10.1007/s10404-005-0052-9

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