Multiple, simultaneous, independent gradients for versatile multidimensional liquid chromatography. Part I: Theory

The general method for constructing coupled dual gradients in liquid chromatography (LC) is to begin by filling a reservoir A with a solution of one mobile phase (MP) component at concentration [c(1)(A)] and a second MP component at concentration [c(2)(A)], followed by filling a reservoir B with a solution containing MP component one at concentration [c(1)(B)] and the second MP component at concentration [c(2)(B)]. In another scenario the reservoirs A and B are filled with solutions of only one MP component at different concentrations [c(1)(A)] and [c(1)(B)] and the two solutions are titrated to a different pH value: pH (A) for the reservoir A and pH (B) for the reservoir B respectively. In either case, mixing of flows from the two reservoirs varies the concentrations of the two MP components (MP solutes) or the concentration of one MP component and pH along a particular compositional curve producing an eluent with two compositionally coupled gradients. This is a kind of a two dimensional LC utilizing dual simultaneous dependent gradients (DSDGs) wherein two parameters affecting the binding free energy of an analyte to a stationary phase (SP) are being altered simultaneously. Such a DSDG suffers from a significant limitation in that the gradient concentration of the two solutes or the concentration of one MP component and the pH cannot be varied independently. The only way to attain an optimal multigradient LC system, that promises a remarkable increase in chromatographic resolution of complex analyte mixtures, is to uncouple the multiple (dual) gradients, making each independent of the other(s). In this paper the theory of uncoupling of n such gradients, n ≥ 2 is developed. It is shown that for n solutes 2(n) reservoirs are required in concert with an LC eluent delivery system capable of freely apportioning the flows among the reservoirs according to equations we develop here. We go on to predict a substantial increase in chromatographic resolution when applying dual simultaneous independent gradients (DSIGs) of salt and pH to fractionate difficult to separate proteins. This prediction is naturally explained by the electrostatic interaction theory of protein binding to an ion exchanger. In subsequent experimental papers it will be shown that the algorithms presented here properly instruct a quad pump HPLC system to produce well controlled independent simultaneous gradients of pH and non-buffering solutes with attendant significant gain in chromatographic resolution of complex mixtures of protein isoforms.