Sample distribution in peak mode isotachophoresis

Abstract

We present an analytical study of peak mode isotachophoresis (ITP), and provide closed form solutions for sample distribution and electric field, as well as for leading-, trailing-, and counter-ion concentration profiles. Importantly, the solution we present is valid not only for the case of fully ionized species, but also for systems of weak electrolytes which better represent real buffer systems and for multivalent analytes such as proteins and DNA. The model reveals two major scales which govern the electric field and buffer distributions, and an additional length scale governing analyte distribution. Using well-controlled experiments, and numerical simulations, we verify and validate the model and highlight its key merits as well as its limitations. We demonstrate the use of the model for determining the peak concentration of focused sample based on known buffer and analyte properties, and show it differs significantly from commonly used approximations based on the interface width alone. We further apply our model for studying reactions between multiple species having different effective mobilities yet co-focused at a single ITP interface. We find a closed form expression for an effective-on rate which depends on reactants distributions, and derive the conditions for optimizing such reactions. Interestingly, the model reveals that maximum reaction rate is not necessarily obtained when the concentration profiles of the reacting species perfectly overlap. In addition to the exact solutions, we derive throughout several closed form engineering approximations which are based on elementary functions and are simple to implement, yet maintain the interplay between the important scales. Both the exact and approximate solutions provide insight into sample focusing and can be used to design and optimize ITP-based assays.

Isotachophoresis-Based Surface Immunoassay

“…Here, we neglect any dispersion because the focused plug motion is characterized by small Pećlet numbers and the effective diffusivity can be approximated by the molecular one. 27,29 As shown by Karsenty et al, 24 the concentration at the ITP interface does not change significantly during the short reaction time, and thus, the concentration profile (eq 1) can be assumed to be constant in time. Substituting eq 1 into eq 3 and integrating over the transition time of the sample over the interface (τ PO ), the expression for the fraction of bound sites is obtained:…”

“…Far from the reaction site, at a distance x itp (t) from the channel entrance and for negligible dispersive effects, the analyte concentration can be approximated as a Gaussian, 24,27…”

Isotachophoresis applied to biomolecular reactions

“…In particular, ITP peaks wherein sample ions had mobilities near those of the TE or LE exhibited significant tailing into these respective zones and an associated asymmetry. Rubin et al 58 presented a study focused on sample distribution within ITP zones, and the effect of these species specific distributions on reaction rates. They presented closed-form solutions for peak shapes and production rates for the case of ITP dynamics dominated by pure diffusion (e.g., no advective dispersion) and electromigration.…”

Recent progress in analytical capillary isotachophoresis

“…Rubin et al. published a detailed mathematical model describing the ITP boundary including a stacked minor analyte migrating in the so‐called peak mode. This model extends the so far available theory especially by including acid‐base equilibria and multivalent ions.…”

“…The analytes were (A) ATTO647N, (B, C) Dylight647. Reprinted with permission from . Copyright [2014], AIP Publishing LLC .…”