Mater. Res. Soc. Symp. Proc. Vol. 1061 2008 Materials Research Society 1061-MM09-25 Electrostatic Field Calculations for Electrophoresis Using Surfaces Perumal Ramasamy 1, Raafat M Elmaghrabi 2, and Gary Halada 3 1 Materials Science and Engineering, Stony Brook University, 317, Old Engineering Building, SUNY - Stony Brook University, Stony Brook, NY, 11794-2275 2 Dept of Physiology & Biophysics, Stony Brook University, T6-170 Health Sciences Center, Stony Brook, NY 11794-8661, Stony Brook, NY, 11794-8661 3 Materials Science and Engineering, Stony Brook University, 308 Engineering Building, Stony Brook, NY 11794-2275, Stony Brook, NY, 11794-2275 ABSTRACT The distribution of electric field in and near the surface of the electrophoretic cell determines the motion of proteins in the buffer and along the surface. This is a complicated problem, influenced by buffer ion concentration, electrode configuration, and surface and substrate conductivities. Steady state calculations approximating the experimental geometry were made for different arrangements of electrodes using MAFIA (Computer Simulation Technologies) program and ESTAT programs. Electric field distributions in both conducting surfaces like ITO (Indium Tin Oxide) (Kevley Technologies), gold and aluminum and non conducting surfaces were studied. In order to measure the EOF of the buffer neutrally charged fluorescent Poly-Styrene beads of 1 µm diameter were included in the buffer and imaged using confocal microscope. It was observed that the electric filed was highly modified by various factors like the conducting nature of the surface, position of the electrodes, salt concentration in the buffer and distance from the separation surface. INTRODUCTION Recent experiments in DNA flat-surface electrophoresis have yielded much success in terms of its use as a separation mechanism. Separation of polymers like DNA and proteins by surface electrophoresis can be faster than conventional gel electrophoresis. Also it is easier to retrieve the polymers by surface electrophoresis experiments unlike gel electrophoresis methods. In conventional gel electrophoresis the distribution of electric fields is uniform unlike in surface electrophoresis. The distribution of electric field in and near the surface of the electrophoretic cell determines the motion of polymer in the buffer and along the surface. This is a complicated problem, influenced by buffer ion concentration, electrode configuration, and surface and substrate conductivities. For this one has to understand the distribution of electric fields in an electrphoretic cells thoroughly before interpreting the results of an electrophoresis experiment (1-9). In this article, we try to study the effects of various factors upon the distribution of electric fields in a home made electrophoretic cell having different surfaces for separation. The charge distribution is governed by the Poisson Boltzmann equation (10) Where Ψ is the electroosmotic potential, ρ e is the charge density and ε is permittivity. (1)
In addition to the calculation of the electrical field distributions in the electrophoretic cell, the determination of electro osmotic flow (EOF) is essential. The electrophoretic mobility observed during electrophoresis is the difference between the electrophoretic mobility of the macromolecule and the electrophoretic mobility of the solvent due to EOF. EOF arises from the fact that the negatively charged surface (substrate surface for electrophoresis) attracts positively charged cations from the buffer, creating an electrical double layer next to the surface. When an electric field is applied to the solution in the capillary, the cations in the diffuse portion of the double layer migrate toward the cathode, carrying along buffer and solvent. The result is a net flow of solvent toward the cathode. The observed (net) mobility µ obs = µ macromolecule - µ EOF (2) Here µ macromolecule is the true electrophoretic mobility of the macromolecule and µ EOF is the mobility due to EOF and µ obs is the observed mobility. Here we investigate the variation in the electric field in the electrophoretic cell and EOF as a function of conductivity of the surface, conductivity of the buffer, position of the electrodes and ionic concentration of the buffer. EXPERIMENT Electrostatics field calculations programs The electric filed distribution in the electrophoretic cell has to be determined for the proper understanding of the electric field distribution in the cell. The electric field distribution was determined using ESTAT electrostatic field calculations software to calculate the two dimensional electric field distributions in the cell and MAFIA field calculations program to calculate the three dimensional electric field distributions in the cell. In a region of ideal dielectrics and space charge, the electrostatic potential ф is determined by the Poisson equation. The boundary conditions for electrostatic problems can be of Dirichlet or Neumann type. For Dirichlet conditions, the electrostatic potential V is specified on the boundary. For Neumann conditions, the surface charge is specified on the boundary. For a Drichlet boundary the electric field lines are normal to it. For a Neumann boundary the normal derivative of the poteintial is specified. The special Neumann condition implies that the electric field is parallel to the boundary. One of the advantages of the finite- element method is that all boundaries that are not fixed automatically satisfy the special Neumann condition, even if they are slanted or curved, The electrophoretic set up was varied as a function of the size of the cell, position of the electrodes, conductivity of the buffer, dimension of the metallic surface and conductivity of the metallic surface used for the separation of the proteins. The variation in the electric field distributions due to these modifications are as under. DISCUSSION Effect of position of electrodes upon electric field distributions: When the conductivity of the buffer was kept constant, and when the dimension of the conducting metallic surface is changed, electric filed distribution in the surface depended upon the dimension of the surface. It was observed that when the electrodes were placed close to the surface or touching the surface, the electric field in the cell was very uniform. As shown in the
figures below, both electrostatic calculations (Figure 1 a-c) and MAFIA field calculations (Figure 1 d-f) confirmed this. From these Figures 1a-1f; it is clear that the field distributions are not uniform when the length of the conducting surface is lesser than the distance between the electrodes and that the field distribution is uniform when the electrodes touch the conducting surface. Therefore, in order to have a uniform field distribution on the surface that is equal to the ratio of the voltage between the electrodes and the distance of their separation, the conducting surface should have its dimensions such that its length should be equal or close to that of the distance between the electrodes. Figure 1 a, d: Electric field distribution when electrodes do not touch the conducting surface. The field distribution is not uniform between the electrodes. Figure 1 b, e: Electric field distribution when electrodes touch the conducting surface from inside the buffer. The field distribution is uniform between the electrodes. Figure 1 c, f: Electric field distribution when Electrodes touch the surface from outside the buffer. The field distribution is uniform between the electrodes. Effect of conductivity of the surface When the conductivity of a surface placed in the cell was increased the electric field flow in the surface decreased. For a metallic surface it was observed that the field flows through the buffer space surrounding the surface. These results are shown in Fig 2a Fig 2d for surfaces with conductivity 5, 10,100 and 1500 times that of the buffer (0.01x TBE). The dimension of the surface was chosen as 4cm x 2 cm. The space between the electrodes was chosen as 10 cm. The
space available for the buffer was chosen as 10cm x 10 cm and the applied voltage was chosen as 30V. Figure 2 (a-d): Electrostatic potential when conductivity of surface is (a) 5x, (b) 10x, (c) 100x and (d) 1500 x conductivity of buffer. Dependence of EOF upon distance from separating surfaces: In order to measure the EOF of the buffer neutrally charged fluorescent Poly-Styrene (PS) beads of 1 µm diameter (Fluo spheres F-13083; red fluorescent (580 / 605nm); 1x10 10 beads/ml from Molecular probe) were included in the electrolytic buffer. ITO and silicon were chosen as the surface. It was observed that when the electrodes are placed upon an ITO surface during electrophoresis (Figure 3) the migration of the PS beads was uniform close to the surface and it varied linearly with the applied electric field (Figure 4). For ITO surface the migration of the beads was uniform till ITO cracked due to high voltage (~ 5V cm -1 ). It was also observed that the velocity of the beads was uniform for about 25 µm above the conducting surface. This was performed by moving the objective lens of the confocal microscope. Similar results were obtained for silicon. Figure 3: schematic representations for the measurement of EOF using PS beads. Figure 4: Trajectory of PS beads on ITO surface when electrodes placed touching the IRO surface. (a) Electric field = 1Vcm -1 ; time = 10 sec, (b) Electric field = 1.5 Vcm -1 ; time = 10 sec, and (c) Electric field = 2.0 Vcm -1 ; time = 10 sec. For all conditions, 0.001x TBE buffer was used as electrolyte.
For higher TBE concentrations, it was observed that the mobility of the beads was zero for gold surfaces while the mobility of the beads was same for up to a height of 25 microns for both Silicon and Glass substrates. Hence the conductivity of the surface influences the EOF greatly. Dependence of EOF upon conductivities of the surfaces When substrates of same dimensions were used it was observed that the EOF of the PS beads was dependent upon the conductivity of the surface. When two surfaces, silicon and gold, both of dimension 2cm x 0.75 cm were placed adjacent to each other with their sides touching one another in a cell having 0.1x TBE buffer, the polystyrene beads had only half the mobility on gold surface when compared with silicon (data not shown). This suggests that using surfaces with micro patterns of materials with different conductivities can lead to non uniform polymer migration that involves moving and slowing. This effect can possibly be used to separate polymers with different sizes. Effect of salt concentration in the electrolytic buffer upon EOF For electrodes touching the substrate surface, it was observed that when glass or silicon surfaces were used as the substrates the mobility of the PS beads decreased as the salt concentration in the TBE buffer increased. The PS beads were observed to migrate towards the negative electrode for lower buffer concentrations less than 5x TBE. When the buffer concentration was 5x TBE, it was observed that the PS beads did not move. When the buffer concentration was as high as 10x TBE it was observed that the PS beads migrated towards the positive electrode. The variation in the mobility for PS beads on glass surface as a function of salt concentration is shown in (Fig. 5). 5 0 Velocity (µm/s) -5-10 -15-20 0.01x TBE 0.1x TBE 1x TBE 6x TBE 10x TBE -25 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 Electric filed (V/cm) Figure 5. Variation of velocity of PS beads for different salt concentrations. Particles that travel towards the negative electrode are considered to have negative velocity.
The decrease in the EOF with increase in the salt concentrations in the buffer can be explained as follows. Glass and silicon have negative charges on their surface. When placed in a buffer, due to its surface charge, the glass surface will attract cations from the buffer. In a buffer with lower salt concentration, upon application of an electric field, the cations that were drawn to the surface of the glass will migrate towards the negative electrode. For higher salt concentrations in the buffer, the availability of anions that will cancel the adsorbed cations of the buffer will be more. Hence there might be some charge cancellations leading to a less net positive charge on the substrate surface. Hence the EOF will be lesser. When the salt concentration in the buffer increases further more (like for 10x TBE), charge reversal can take place on the surface of the substrate due to abundance of ions. This will therefore lead to a reversal in the direction of the PS beads and the beads will go to the positive electrode. Hence the EOF depends upon the salt concentration in the buffer. CONCLUSIONS Field calculations programs and EOF measurements shows that the electric field distribution in the electrophoretic cell depend upon various factors like the position of the electrodes, conductivity of the surface, distance from the conducting surface, dimensions of the conducting surface and concentration of salt in the electrolytic buffer. Hence unlike conventional gel electrophoresis, surface electrophoresis demands a thorough understanding of the electric field distributions in an electrophoretic cell to serve as a useful tool for separations. ACKNOWLEDGMENTS We would like to thank Prof. Ilan Ben - Zvi of Brook Haven National LAB for providing MAFIA software facility. REFERENCES (1) Anna-Maria Spehar, Sander Koster, Vincent Linder, Sakari Kulmala, Nico F. de Rooij, Elisabeth Verpoorte, Hans Sigrist and Wolfgang Thormann, Electrophoresis 3674-3678, 24 (2003). (2) Jacobson, S. C.; Hergenroder, R.; Koutny, L. B.; Ramsey, J. M. Anal. Chem. 2369-2373, 66 (1994). (3) D.A. Hoagland, E. Arvanitidou and C. Welch, Macromolecules 6180 6190, 32 (1999). (4) Griffiths, S. K.; Nilson, R. H. Anal. Chem.5522-5529, 71(1999). (5) Samulel K. Sia and George M. Whitesides, Electrophorsesis 3563 3576, 24 (2003). (6) Ermakov, S. V.; Jacobson, S. C.; Ramsey, J. M. Anal. Chem. 4494-4504, 70 (1998). (7) C. L. Rice and R. Whitehead, J. Phys. Chem, 1084 1091, 69 (1965). (8) EB Cummings, SK Griffiths and RH Nilson, PH Paul, Analytical Chemistry, 2526 2532 72 (2000). (9) N. A. Poison and M.A. Hayes, Analytical Chemistry, 4455-4459, 71(1999). (10) Probstein, R. F., Physiochemical Hydrodynamics, John Wiley & Sons Inc, NY, 1993.