Modeling of dielectrophoretic transport of myoglobin molecules in microchannels

Abstract

Myoglobin is one of the premature identifying cardiac markers, whose concentration increases from 90 pgml or less to over 250 ngml in the blood serum of human beings after minor heart attack. Separation, detection, and quantification of myoglobin play a vital role in revealing the cardiac arrest in advance, which is the challenging part of ongoing research. In the present work, one of the electrokinetic approaches, i.e., dielectrophoresis (DEP), is chosen to separate the myoglobin. A mathematical model is developed for simulating dielectrophoretic behavior of a myoglobin molecule in a microchannel to provide a theoretical basis for the above application. This model is based on the introduction of a dielectrophoretic force and a dielectric myoglobin model. A dielectric myoglobin model is developed by approximating the shape of the myoglobin molecule as sphere, oblate, and prolate spheroids. A generalized theoretical expression for the dielectrophoretic force acting on respective shapes of the molecule is derived. The microchannel considered for analysis has an array of parallel rectangular electrodes at the bottom surface. The potential and electric field distributions are calculated using Green's theorem method and finite element method. These results also compared to the Fourier series method, closed form solutions by Morgan et al. [J. Phys. D: Appl. Phys. 34, 1553 (2001)] and Chang et al. [J. Phys. D: Appl. Phys. 36, 3073 (2003)]. It is observed that both Green's theorem based analytical solution and finite element based numerical solution for proposed model are closely matched for electric field and square electric field gradients. The crossover frequency is obtained as 40 MHz for given properties of myoglobin and for all approximated shapes of myoglobin molecule. The effect of conductivity of medium and myoglobin on the crossover frequency is also demonstrated. Further, the effect of hydration layer on the crossover frequency of myoglobin molecules is also presented. Both positive and negative DEP effects on myoglobin molecules are obtained by switching the frequency of applied electric field. The effect of different shapes of myoglobin on DEP force is studied and no significant effect on DEP force is observed. Finally, repulsion of myoglobin molecules from the electrode plane at 1 KHz frequency and 10 V applied voltage is observed. These results provide the ability of applying DEP force for manipulating nanosized biomolecules such as myoglobin.

Figure 1

Approximated shapes of myoglobin molecule: (a) Sphere; (b) oblate spheroid; and (c) prolate spheroid.

Figure 2

Schematic view of DEP microfluidic device considered for manipulating the myoglobin molecules. Enlarged view shows the 2D computational domain considered for simulating the behavior of myoglobin molecules under DEP effects.

Figure 3

Comparison of nondimensional electric field along the length of channel near the electrodes for different solution methods.

Figure 4

Comparison of nondimensional square electric field gradient along the length of channel near the electrodes for different solution methods.

Figure 5

Comparison of nondimensional square electric field gradient along the height of channel at edge of the electrode, midpoint of the electrode, and midpoint of gap between the electrodes for different solution methods.

Figure 6

Comparison of nondimensional square electric field gradient along the length of channel near the electrodes for different nondimensional applied voltages.

Figure 7

Comparison of real part of the CM factor with respect to frequency of the applied electric field for different shapes of the myoglobin molecule.

Figure 8

Comparison of crossover frequency with respect to change in conductivity of medium for different shapes of the myoglobin molecule.

Figure 9

Comparison of real part of the CM factor with respect to frequency of the applied electric field for different shapes of myoglobin with the hydration layer.

Figure 10

Comparison of DEP force on different shapes of the myoglobin molecule along the length of channel near the electrodes at 50 MHz frequency and 10 V applied voltage.

Figure 11

Comparison of DEP force on different shapes of the myoglobin molecule along the length of channel near the electrodes at 1 KHz frequency and 10 V applied voltage.

Figure 12

Variation of mass concentration of the myoglobin molecules inside the microchannel under DEP effects at 1 KHz and 10 V applied voltage.

Figure 13

Variation of mass concentration of the myoglobin molecules along the height of channel under DEP effects at 1 KHz and 10 V applied voltage.