Insights from a new analytical electrophoresis apparatus

Control of microtubule trajectory within an electric field by altering surface charge density

One of challenges for using microtubules (MTs) driven by kinesin motors in microfluidic environments is to control their direction of movement. Although applying physical biases to rectify MTs is prevalent, it has not been established as a design methodology in conjunction with microfluidic devices. In the future, the methodology is expected to achieve functional motor-driven nanosystems. Here, we propose a method to guide kinesin-propelled MTs in multiple directions under an electric field by designing a charged surface of MT minus ends labeled with dsDNA via a streptavidin-biotin interaction. MTs labeled with 20-bp or 50-bp dsDNA molecules showed significantly different trajectories according to the DNA length, which were in good agreement with values predicted from electrophoretic mobilities measured for their minus ends. Since the effective charge of labeled DNA molecules was equal to that of freely dispersed DNA molecules in a buffer solution, MT trajectory could be estimated by selecting labeling molecules with known charges. Moreover, the estimated trajectory enables to define geometrical sizes of a microfluidic device. This rational molecular design and prediction methodology allows MTs to be guided in multiple directions, demonstrating the feasibility of using molecular sorters driven by motor proteins.

Modeling the sequence-dependent diffusion coefficients of short DNA molecules

A boundary element model for the computation of sequence-dependent hydrodynamic properties of short DNA molecules is introduced. The hydrated surface is modeled as a curved tube of uniform radius with ends capped by hemispheres, and the axis of the tube is a general space curve whose length and curvature are determined locally by the sequence using a rigid basepair model of double-helical DNA with parameters based on x-ray crystallography. Diffusion coefficients for families of random and periodic DNA sequences are computed and compared with theories for straight tubes and experimental data. Our results indicate that sequence-dependent curvature can have a measurable impact on both the translational and rotational diffusion coefficients, even for relatively short fragments of lengths less than about 150 basepairs, and that previous estimates of the hydrated radius of DNA are likely to be underestimates. Moreover, our results suggest a possible method for refining the rigid basepair model parameters for DNA in solution as well as the hydrated radius.

Nonequilibrium thermodynamics of membrane-confined electrophoresis

Membrane-confined electrophoresis (MCE) is an electrophoretic transport method in which macromolecules in solution are confined within a cuvette through which a current flows. Small ions that can permeate the membranes permit current flow. The method is the electrophoretic analog to analytical ultracentrifugation. Systems in the MCE instrument are described by nonequilibrium thermodynamics. This description forms the basis of a program, implemented using finite element methods, that can model transport processes in such systems over an extended time, from arbitrary starting conditions to steady state. Issues relevant to the analysis of systems in which macromolecular species are involved in mass-action associations are discussed. Particular attention is given to steady-state electrophoresis, from which measurements of reduced molecular charge are sought. The relationship of such measurements to valence is discussed.

Use of T4 lysozyme charge mutants to examine electrophoretic models

The electrophoretic mobility of a macro-ion is affected in a complex manner by a variety of forces that arise from the applied field. Coupling of the macro-ion and small-ion flows gives rise to non-conserved forces that are greater than those expected from ordinary hydrodynamic considerations. It is difficult to separate the steady-state hydrodynamic and electrodynamic contributions to the macro-ion mobility. Membrane-confined electrophoresis (MCE), a free solution technique, provides an experimental means by which to gain insight into these contributions. In this work we used MCE steady-state electrophoresis (SSE) of a series of T4 lysozyme charge mutants to investigate these effects and to examine the existing theoretical descriptions. These experiments isolate the effects of charge on electrophoretic mobility and permit a unique test of theories by Debye-Hückel-Henry, Booth and Allison. Our results show that for wild type (WT) T4, where divergence is expected to be greatest, the predicted results are within 15, 8 and 1%, respectively, of experimental SSE results. Parallel experiments using another free-solution technique, capillary electrophoresis, were in good agreement with MCE results. The theoretical predictions were within 20, 13 and 5% of CE mobilities for WT. Boundary element modeling by Allison and co-workers, using continuum hydrodynamics based on detailed structural information, provides predictions in excellent agreement with experimental results at ionic strengths of 0.11 M.

Conformation and ion-binding of oligonucleotides

The effective charge and the conformation of oligonucleotides may influence their pharmaceutical properties. Therefore, a method based on the convective diffusion process was used to measure both the diffusion coefficient and the effective charge number of four oligonucleotides with different chain lengths. Determinations were carried out at physiological ionic strength and at two temperatures, 20 and 40 degrees C. The results indicate that the longer oligonucleotides, i.e. number of nucleotides in the molecule from 15 to 30, are strongly ion-paired (75-80%) and the shorter oligonucleotide (seven nucleotides) is only ca. 50% ion-paired. The extent of ion-binding was not dependent on temperature. The conformation of the oligonucleotides appeared to be fairly compact in 0.15 M NaCl solution. The compact conformation and strong ion-pairing may influence the pharmacokinetics of oligonucleotides, possibly facilitating distribution into tissues.

Boundary element modeling of biomolecular transport

The boundary element (BE) methodology has emerged as a powerful tool in modeling a broad range of different transport phenomena of biomolecules in dilute solution. These include: sedimentation, diffusion (translational and rotational), intrinsic viscosity, and free solution electrophoresis. Modeling is carried out in the framework of the continuum primitive model where the biomolecule is modeled as an arbitrary array of solid platelets that contains fixed charges within. The surrounding fluid is modeled as a electrodynamic/hydrodynamic continuum which obeys the Poisson and low Reynolds number Navier-Stokes equations. Ion relaxation (the distortion of the ion atmosphere from equilibrium) can also be accounted for by solving the coupled ion transport equation (for each mobile ion species present), Poisson, and Navier-Stokes equations in tandem. Several examples are presented in this work. It is first applied to a detailed model of 20 bp DNA and it is concluded that it is not necessary to include a layer of bound water to reconcile experimental and model translational diffusion constants. With regards to diffusion, the BE approach is also applied to a 375-bp supercoiled DNA model (without ion relaxation), and also 20-60-bp DNA fragments with ion relaxation included in order to assess the magnitude of the electrolyte friction effect under a number of different salt/buffer conditions. Attention is then turned to modeling the electrophoretic mobility of three different cases. First of all, we consider a sphere with a central charge large enough in magnitude to insure that ion relaxation is significant. Excellent agreement with independent theory is obtained. Finally, it is applied to modeling short DNA fragments in KCl and Tris acetate salts. Quantitative agreement is achieved when the salt is KCl, but the calculated (absolute) mobility in Tris acetate is substantially higher than the experimental value. The interpretation of this is that there is an association between Tris(+) and DNA (perhaps hydrogen bonding) not accounted for in our modeling that is responsible for this discrepancy.

The length dependence of translational diffusion, free solution electrophoretic mobility, and electrophoretic tether force of rigid rod-like model duplex DNA

In this work, boundary element modeling is used to study the transport of highly charged rod-like model polyions of various length under a variety of different aqueous salt conditions. Transport properties considered include free solution electrophoretic mobility, translational diffusion, and the components of the "tether force" tensor. The model parameters are chosen to coincide with transport measurements of duplex DNA carried out under six different salt/temperature conditions. The focus of the analysis is on the length dependence of the free solution electrophoretic mobility. In a solution containing 0.04 M Tris-acetate buffer at 25 degrees C, calculated mobilities using straight rod models show a stronger dependence on fragment length than that observed experimentally. By carrying out model studies on curved rod models, it is concluded that the "leveling off" of mobility with fragment length is due, in part at least, to the finite curvature of DNA. Experimental mobilities of long duplex DNA in monovalent alkali salts are reasonably well explained once account is taken of long-range bending and the simplifying assumptions of the model studies.

Quantitative three-dimensional analysis and diffusion modeling of oligonucleotide concentrations after direct intraparenchymal brain infusion

We compared quantitative experimental results on the diffusion of 35S-labeled phosphorothioate oligonucleotide (PS-ODN) after intraparenchymal infusion in rat brain, with the distributions predicted by Fick's second law of diffusion. Fischer 344 rats underwent identical intracerebral infusions of 36S-PS-ODN. After 0, 5, 11, 23, and 47 h, groups of animals were sacrificed and sequential brain cryosections subjected to autoradiography. The resulting experimental data were compared to the predicted distributions, for estimation of the apparent free diffusion coefficient, D*. Volumes of distribution and total content of 36 S-PS-ODN in the parenchyma were also computed, to monitor loss of total material. The values for D* were within the expected range for the 21-mer PS-ODN used, but a progressive decrease in D* over time was noted. The model requires D* to remain constant and, thus, does not adequately explain the spread of 35S-PS-ODN following infusion. The progressive slowing of spread over time suggests that at later time points, 35S-PS-ODN may be fixed by tissue binding or cellular uptake in the brain. Loss of material via vascular and CSF clearance may also contribute to the lack of fit. Our results highlight issues to be addressed in the modeling and experimental design of the intraparenchymal infusion process.

Visualizing ion relaxation in the transport of short DNA fragments

Ion relaxation plays an important role in a wide range of phenomena involving the transport of charged biomolecules. Ion relaxation is responsible for reducing sedimentation and diffusion constants, reducing electrophoretic mobilities, increasing intrinsic viscosities, and, for biomolecules that lack a permanent electric dipole moment, provides a mechanism for orienting them in an external electric field. Recently, a numerical boundary element method was developed to solve the coupled Navier-Stokes, Poisson, and ion transport equations for a polyion modeled as a rigid body of arbitrary size, shape, and charge distribution. This method has subsequently been used to compute the electrophoretic mobilities and intrinsic viscosities of a number of model proteins and DNA fragments. The primary purpose of the present work is to examine the effect of ion relaxation on the ion density and fluid velocity fields around short DNA fragments (20 and 40 bp). Contour density as well as vector field diagrams of the various scalar and vector fields are presented and discussed at monovalent salt concentrations of 0.03 and 0.11 M. In addition, the net charge current fluxes in the vicinity of the DNA fragments at low and high salt concentrations are briefly examined and discussed.

An apparatus for membrane-confined analytical electrophoresis

A membrane-confined analytical electrophoresis apparatus for measuring the solution charge of macromolecules has been described previously (T. M. Laue et al., Anal. Biochem. 1989, 182, 377-382). Presented here is a design for this apparatus, which permits the on-line acquisition and display of absorbance data from up to 512 positions along an analysis chamber. Concentration distributions of macromolecules in solution can be monitored in the chamber to provide steady-state electrophoresis, electrophoretic mobility and diffusion measurements. Buffer chambers press semipermeable membranes against the open ends of a fused-silica cuvette to form the analysis chamber. This configuration permits both the flow of buffer and the establishment of an electric field across the cuvette, while retaining macromolecules in the field of view. Though a gel may be included in the analysis chamber, none is required for gradient stabilization. The volume of sample required for analysis is 8 microL, most of which is recoverable. Experimental conditions can be varied during study by simply changing the circulating buffer and/or the electric field. The analysis and buffer chambers are held in an aluminum housing that sits in an aluminum water jacket. The water jacket provides temperature control, shielding from external electrical noise and also serves as an optical mask. Plans for the cell assembly, optical system and the computer interface for data acquisition are provided. The assembly and operation of the apparatus and the analysis of data are described.

DNA--DNA interactions

The forces that govern DNA double helix organization are being finally systematically measured. The non-specific longer-range interactions--such as electrostatic interactions, hydration, and fluctuation forces--that treat DNA as a featureless rod are reasonably well recognized. Recently, specific interactions--such as those controlled by condensing agents or those consequent to helical structure-are beginning to be recognized, quantified and tested.