Abstract Methods are presented to determine the effec- tive macroion diffusion coefficient in the presence or ab- sence of an electric field, using a unique analytical elec- trophoresis apparatus in which both electrophoretic mobil- ity and steady-state electrophoresis may be studied. Ap- proximate analytic solutions to the differential equations and boundary conditions describing diffusion are derived. These solutions are shown to be good approximations to numerial simulations of the differential equations, and pro- vide a good phenomenological description of experimen- tal data for the oligonucleotide p(dA) 20 ·p(dT) 20 in 100 mM KCl, 20 mM Tris-HCl, pH 8.0 buffer. Diffusion and elec- trophoresis measurements are made on a single sample without changing the buffer or the macroion concentration, thus the data are directly comparable. Key words Analytical electrophoresis · Diffusion · Macromolecules · Simulations Introduction Charge is a fundamental property of macromolecules that is inextricably linked to their structure, solubility, stabil- ity and interactions. The most direct means of discerning a macroion’s effective charge in solution is by its response to an applied electric field. However, a macroion’s behav- ior is complicated by its connection with the behavior of the surrounding mobile ionic atmosphere (Henry 1931; Onsager 1932; Booth 1950; Overbeek and Wiersema 1967). A unique analytical electrophoresis apparatus (AEA) developed in our laboratory permits both the meas- urement of macroion electrophoretic mobilities and the de- termination of steady-state electrophoresis concentration distributions (Laue et al. 1989; Ridgeway et al. 1994; Laue et al. 1996). Interpretation of this electrophoretic data re- quires knowledge of the frictional and diffusion coeffi- cients of the macroion. In this paper we present methods for the determination of macroion diffusion coefficients both in the presence and absence of an electric field using the AEA. Diffusion and electrophoresis measurements may be made on a single sample without changing the ar- rangement of the apparatus. Experimental Instrument. A detailed description of the AEA has been presented elsewhere (Ridgeway et al. 1994). Briefly, the instrument is an imaging spectrophotometer using a line- ar photodiode array to measure the light intensities from up to 512 positions along a fused-silica cuvette. The cuvette’s cross-section is 2 × 2 mm, and its top and bottom are open. Cuvettes with distances of 2 mm and 4 mm between the openings are available. The open ends of the cuvette are sealed by semi-permeable membranes, which permits the establishment of an electric field along the cuvette’s length while retaining macroions in the field of view. Materials. All buffers and salts were reagent grade and were used without additional purification. Equimolar mix- tures of single stranded p(dA) 20 , Pharmacia #27-7984-01, and p(dT) 20 , Pharmacia #27-7841-01, were heated to 65 °C in 200 mM KCl, 20 mM Tris-HCl, pH 8.0 buffer, then cooled to form double stranded p(dA) 20 ·p(dT) 20 . Melting and circular dichroism studies were used to verify that p(dA) 20 ·p(dT) 20 was in a stable duplex form under the conditions of electrophoresis, and capillary zonal electro- phoresis was used to test for sample homogeneity (not shown). Concentrations were estimated from the A 260 measured in the apparatus. Eur Biophys J (1997) 25: 481–487 © Springer-Verlag 1997 Accepted: 4 October 1996 Harvey K. Shepard · Timothy J. Wilson Thomas P. Moody · John O. Wooll · Thomas M. Laue Determination of macroion diffusion coefficients using an analytical electrophoresis apparatus ARTICLE T. J. Wilson · T. P. Moody · J. O. Wooll · T. M. Laue () Department of Biochemistry and Molecular Biology, Rudman Hall, University of New Hampshire, Durham, NH 03824-3544, USA H. K. Shepard Department of Physics, University of New Hampshire, Durham, NH 03824-3544, USA (e-mail: shepard@curie.unh.edu)