Open source simulation tool for electrophoretic processes
M. Bercovici, S.K. Lele, and Juan G. Santiago
- New open-source simulation tool for electrophoretic preconcentration and separation processes such as capillary electrophoresis, isotachophoresis, and field amplified sample stacking.
- A new numerical approach combining a 6th order (non dissipative) compact scheme with an adaptive grid enables 75-fold reduction in computation time compared with equivalent uniform grid techniques.
- Accurate solutions of concentration shockwaves, free of numerical dissipation.
- Solves the one-dimensional transient advection-difusion equations for multiple multi-valent weak electrolytes, and includes models for acid-base reactions, pressure driven flow and Taylor-Aris dispersion.
- Available online at http://microfluidics.stanford.edu/spresso/
Movie 1. Simulation of isotachophoretic separation and focusing of five species using Spresso.
Figure 1. Schematic illustration of isotachophoresis process and physical mechanisms included in the current code. The code is a general solver for nonlinear electrophoresis of multiple, multivalent species. The code uses a high resolution adaptive grid scheme for reduced computational cost; this and a Taylor-Aris type dispersion model are unique to the code.
The need for fast and accurate electrophoresis simulation tools
Electrophoretic preconcentration and separation techniques are well established and widely used in a variety of fields, including chemistry, biochemistry, pharmacology and genetics). The interest in and utility of these techniques is evident from the large number of associated publications, now exceeding one paper per hour. In concert with experiments, computer simulations offer a strong research tool for elucidating fundamental processes ruling the dynamics of electrokinetic separation and preconcentration methods. Such tools also offer the potential of greatly reducing experimental time and achievement of assays with optimal resolution and sensitivity. Despite significant progress in computational techniques, there remain many electrokinetic flow problems outside the capabilities of existing codes. This is especially true of electrophoresis processes involving high electric fields and ion density gradients and their coupling with chemical reactions. Examples of challenging electrokinetic problems include the effects of electromigration dispersion on capillary zone electrophoresis injections; field amplified sample stacking (FASS) with strong concentration gradients; and isotachophoresis (ITP) assays with strong mobility differences and high current densities.
6th order compact adaptive scheme
Figure 2. Predicted concentration profiles showing the effect of spatial discretization and grid adaptation on the resolution of an ITP interface. N is the number of grid points used. Results obtained after 100 s on a 20 mm long domain, under a current density of 1800 A/m2. For clarity, we here zoom in on a 10 mm length which captures the area of interest. (a) Explicit centered second order scheme using an equally spaced grid. (b) Sixth-order compact scheme using an equally spaced grid. (c) sixth order compact scheme using the adaptive grid procedure results in a smooth interface, (d) even for one third the number of grid points.
Figure 3. Prediction showing the separation of aniline and pyridine in a 200 mm long channel using the HIRAG scheme with 400 grid points. At the top, are details of the analyte concentrations. High analyte concentrations (relative to background) result in nonlinear dynamics resulting in a sharp front and an electromigration dispersion tail. Grid density curves (thin black lines in main plots) indicate the ratio between the initial (uniform) grid spacing and the local grid spacing. The plot demonstrates how the adaptive grid recruits points from nearly constant (plateau) concentration regions and migrates these to regions of high gradients. A constant current of 5 uA was applied to the 50 um diameter channel, equivalent to a current density of 2547 A/m2.
Results and benchmarks
Figure 3. Speed ratio and grid size ratio associated with uniform and adaptive grid simulations of a single interface ITP experiment. LE is 100 mM hydrochloric acid, TE is 50 mM HEPES, and counter ion is 200 mM TRIS. The channel is a 20 mm long circular capillary with a 50 diameter. Simulation time varied depending on the current density such that the distance traveled by the interface was constant. The curves are truncated at the maximum current resolvable by the 300 node adaptive grid. The inset shows the actual grid size used for the uniform grid (circles), compared to the constant 300 grid point value used by our scheme (dashed line) to obtain the same resolution.
- Bercovici, M., Lele, S.K. & Santiago, J.G. Compact adaptive-grid scheme for high numerical resolution simulations of isotachophoresis. Journal of Chromatography A 1217, 588–599 (2010).
- Bercovici, M. Open source simulation tool for electrophoretic stacking, focusing, and separation. Journal of Chromatography A 1216, 1008-1018 (2009).
- Bahga, S.S., Bercovici, M. & Santiago, J.G. Ionic strength effects on electrophoretic focusing and separations. Electrophoresis 31, 910-919 (2010).