RNA molecular weight measurements were carried out by gel electrophoresis under four different denaturing conditions including 99% formamide, 10 mM methyl mercury, 2.2 M formaldehyde, and 6 M urea at pH 3.8. Electrophoresis a t a series of gel concentrations and at least two different voltage gradients resulted in some RNA species exhibiting apparent molecular weights that vary with both gel concentration and voltage gradient. Three different deviations from the requirement for hydrodynamically equivalent conformations were observed: (1) deformation of the random coil structure of very large RNAs at moderately high gel concentrations and voltage gradients resulting, in extreme cases, in a molecular weight independent migration of RNA molecules; (2) incomplete denaturation of RNA molecules with very GC rich helical regions; and (3) varying charge/mass ratio due to G e l electrophoresis has become the major analytical procedure for characterizing charged macromolecules both because of the high resolution it provides and the relative simplicity of the technology it requires. The applicability of this procedure to molecular weight determination of nucleic acids and NaDodS04-protein complexes is based both on the fact that these macromolecules are polymers with a constant charge-mass ratio and hydrodynamically equivalent conformations, and on the linearity of the empirical log molecular weight-mobility relation used to determine molecular weights from mobilities. When these assumptions are fulfilled, molecular weights can be measured in a single experiment using standards of known molecular weight. Moreover, since RNA molecules do not have hydrodynamically equivalent conformations in aqueous solutions (Boedtker, 1968; Groot et al., 1970; MacLeod, 1975), several methods were developed in which R N A molecular weights could be determined by gel electrophoresis under denaturing conditions. Denaturing conditions first used included reaction with formaldehyde (Boedtker, 1971), 8 M urea at 60 'C (Rejinders et al., 1973) and 99% formamide at room temperature (Pinder et al., 1974), the latter being by far the most widely used. In addition to the denaturing gel systems first developed, three others have been reported more recently: 6 M urea at pH 3.5 run at 2 "C (Rosen et ai., 1975), 5 mM methyl mercury run at room temperature (Bailey and Davidson, 1976), and 99% formamide run at 45-55 'C (Spohr et al., 1976). This proliferation of denaturing gel systems arose because it was recognized that some of the denaturants first used were not able to denature very GC rich RNA and could not be used in the dilute agarose gels required t From the Department of Biochemistry and Molecular Biology, Harvard University, Cambridge, Massachusetts 02 138. Receiued March 30, 1977. H. Lehrach was the recipient of a postdoctoral fellowship from the Jane Coffin Childs Memorial Fund for Medical Research. John M. Wozney was awarded a Camille and Henry Dreyfus Foundation Summer Research Fellowship. This investigation was supported by National Institutes of Health Grant HD-01229. differential protonation at pH 3.8. Reliable molecular weight measurements of RNA molecules as large as 4.0 X lo6 containing G C rich helical regions could only be made on dilute (0.5-1.0%) agarose gels after reaction with either 2.2 M formaldehyde or 10 mM methyl mercury hydroxide. A theoretical justification for the use of the empirical log molecular weight-mobility relation is presented. It is also demonstrated that the gel electrophoretic behavior of a homologous series of random coils can be approximated by that of a series of spheres with radii proportional to the square root of radius of gyration of a random coil. Consequently, molecular weight determinations of denatured RNAs, especially those obtained by extrapolation, are more reliable if the square root of the molecular weight is plotted vs. log mobility. for molecular weight determinations of very large RNA molecules. We report here a comparison of the behavior of high molecular weight R N A molecules on four different denaturing gels: polyacrylamide in 99% formamide, agarose in 10 mM methyl mercury hydroxide, 2.2 M formaldehyde, and 6 M urea, pH 3.8. In addition, we offer a rationale for the use of the empirical log molecular weight-mobility relation and suggest an alternate method of obtaining RNA molecular weights from mobilities based on the finding that the migration of denatured RNA molecules depends on the square root of the radius of gyration, or the fourth root of the molecular weight. Materials and Methods RNA Samples. TMV and chicken ribosomal RNA were prepared as described previously (Boedtker, 1960; Boedtker et al., 1973). E. coli 23s and 16s rRNA was prepared by phenol-CHC13 extraction (Perry et al., 1972). followed by fractionation on linear 5-20% sucrose gradients. Mouse 28s rRNA was donated by Jesse F. Scott of the Harvard Medical School. Sindbis virus, a gift from Michelene McCarthy of the Department of Biochemistry and Molecular Biology, was extracted with phenol-CHC13 (Perry et al., 1972). Polyacrylamide Gel Electrophoresis in 99% Formamide. To achieve reproducible mobilities, pure reasonably dry deionized formamide is essential. 99% formamide (Eastman Chemical Co.) was deionized following the procedure of Pinder et al. (1 974) by stirring with 40 g /L mixed bed resin (Bio-Rad AG501-X8, 20-50 mesh). After about 5 h, the conductivity should decrease to about 70 pmho. We have found, however, that some batches of formamide are not deionized under these conditions even when more resin is used. Such formamide is unsuitable for gel electrophoresis because irreproducible polymerization of gels occurs. The deionized formamide was filtered through a sintered-glass filter and then distilled under B I O C H E M I S T R Y , V O L . 1 6 , N O . 2 1 , 1 9 7 7 4743 L E H R A C H E T A L electrophoresis buffer (E buffer): 0.05 M boric acid, 0.005 M NazB407.10H~0, 0.01 M sodium sulfate, and 0.001 M Na3EDTA, pH 8.2, without CH3HgOH. The suspension was heated for 5 min in an autoclave and diluted to the appropriate concentration with hot E buffer. CH3HgOH was added to the hot buffered agarose by syringe pipet and stirred rapidly at 60 “C. The gels were poured immediately using 2.5 mL per tube. Before samples were applied, the top of the gel was sliced off with a razor blade to provide a flat surface. RNA samples were prepared by dissolving the RNA in E buffer containing 5 or 10 mM methyl mercury hydroxide as indicated. One-half volume of a 1:l mixture of glycerol-HzO solution containing 0.004% bromophenol blue was added and the sample applied to the gel. Electrophoresis was carried out for various times as indicated at 2.5 or 3 mA per tube, at room temperature inside the closed hood. The latter was clearly designated as being hazardous both because of high voltage and CH3HgOH. All operations involving methyl mercury hydroxide were carried out in the hood, with the operator wearing gloves. The tops of the gels, leftover agarose, used gels, and any material contaminated with CH3HgOH (gloves, paper, disposable items) were placed in a disposable plastic bag and stored in the hood. CH3HgOH waste and contaminated items were disposed of every 3 months by the Department of Chemistry’s hazardous chemical disposal service, the Radiac Corp. The operator was monitored for CH3HgOH accumulation every 6 months by the Harvard Health Services. Agarose Gel Electrophoresis in 2.2 M Formaldehyde. RNA samples were heated in 2.2 M formaldehyde (prepared from 37% Mallinckrodt formaldehyde) in 50% formamide, 0.01 8 M NazHP04-0.002 M NaHzPO4, for 5 min at 60 “C. Agarose gels were prepared by heating a “3%” agarose-water suspension in the autoclave for 5 min and diluting wi th either 1 volume of 4.4 M formaldehyde in 0.036 M NazHP04-0.004 M NaH2P04 to make 1.5% gels or with 2 volumes of the latter plus 1 volume of water to make 0.75% gels. The gels were poured immediately using 2.5 mL per tube. Electrophoresis was carried out at 2 mA per tube at room temperature for the times indicated. The electrophoresis buffer was 2.2 M formaldehyde-0.018 M Na2HP04-0.002 M NaH2P04. Agarose Gel Electrophoresis in 6 M Urea at pH 3.8. Electrophoresis was performed following the procedure described by Rosen et al. ( I 975) with the following modifications. Three times agarose (usually 3 g/lOO mL of HzO) was heated in the autoclave and then diluted with 2 volumes of warm I .5X buffer to give the final concentration of agarose and 6.0 M urea, 0.025 M citric acid (pH 3.8), heated at 65 “ C for 20 s, and fast cooled. One-half volume of the glycerol dye was added as described above. Electrophoresis was carried out for 12 h at 0.38 mA per gel at 4 “C. Staining Gels with Ethidium Bromide. Agarose and polyacrylamide gels were stained overnight in 1 yg/mL ethidium bromide in 0.1 M ammonium acetate (Bailey and Davidson, 1976). After staining, the gels were photographed under short-wave U V light with a Polaroid M P 3 Land camera and high-speed type 57 film (Polaroid Corp.) using a yellow f i l ter.

RNA molecular weight determinations by gel electrophoresis under denaturing conditions, a critical reexamination.

Molecular Weight Determination of Protein-Dodecyl Sulfate Complexes by Gel Electrophoresis in a Discontinuous Buffer System

This thesis explores transport phenomena in nanochannels on a chip. Fundamental nanofluidic ionic studies form the basis for novel separation and preconcentration applications for proteomic purposes. The measurements were performed with 50-nm-high 1D nanochannels, which are easily accessible from both sides by two microchannels. Nanometer characteristic apertures were manufactured in the bonded structure of Pyrex-amorphous silicon – Pyrex, in which the thickness of the amorphous silicon layer serves as a spacer to define the height of the nanochannels. The geometry of the nanometer-sized apertures is well defined, which simplifies the modeling of the transport across them. Compared to biological pores, the present nanochannels in Pyrex offer increased stability. Fundamental characteristics of nanometer-sized apertures were obtained by impedance spectroscopy measurements of the nanochannel at different ionic strengths and pH values. A conductance plateau (on a log-log scale) was modeled and measured, establishing due to the dominance of the surface charge density in the nanochannels, which induces an excess of mobile counterions to maintain electroneutrality. The nanochannel conductance can be regulated at low ionic strengths by pH adjustment, and by an external voltage applied on the chip to change the zeta potential. This field-effect allows the regulation of ionic flow which can be exploited for the fabrication of nanofluidic devices. Fluorescence measurements confirm that 50-nm-high nanochannels show an exclusion of co-ions and an enrichment of counterions at low ionic strengths. This permselectivity is related to the increasing thickness of the electrical double layer (EDL) with decreasing salt concentrations, which results in an EDL overlap in an aperture if the height of the nanochannel and the thickness of the EDL are comparable in size. The diffusive transport of charged species and therefore the exclusion-enrichment effect was described with a simple model based on the Poisson-Boltzmann equation. The negatively charged Pyrex surface of the nanometer characteristic apertures can be inversed with chemical surface pretreatments, resulting in an exclusion of cations and an enrichment of anions. When a pressure gradient is applied across the nanochannels, charged molecules are electrostatically rejected at the entrance of the nanometer-sized apertures, which can be used for separation processes. Proteomic applications are presented such as the separation and preconcentration of proteins. The diffusion of Lectin proteins with different isoelectric points and very similar compositions were controlled by regulating the pH value of the buffer. When the proteins are neutral at their pI value, the diffusion coefficient is maximal because the biomolecules does not interact electrostatically with the charged surfaces of the nanochannel. This led to a fast separation of three Lectin proteins across the nanochannel. The pI values measured in this experiment are slightly shifted compared to the values obtained with isoelectric focusing because of reversible adsorption of proteins on the walls which affects the pH value in the nanochannel. An important application in the proteomic field is the preconcentration of biomolecules. By applying an electric field across the nanochannel, anionic and cationic analytes were preconcentrated on the cathodic side of the nanometer-sized aperture whereas on the anodic side depletion of ions was observed. This is due to concentration polarization, a complex of effects related to the formation of ionic concentration gradients in the electrolyte solution adjacent to an ion-selective interface. It was measured that the preconcentration factor increased with the net charge of the molecule, leading to a preconcentration factor of > 600 for rGFP proteins in 9 minutes. Such preconcentrations are important in micro total analysis systems to achieve increased detection signals of analytes contained in dilute solutions. Compared to cylindrical pores, our fabrication process allows the realization of nanochannels on a chip in which the exclusion-enrichment effect and a big flux across the nanometer-sized aperture can be achieved, showing the interest for possible micro total analysis system applications. The described exclusion-enrichment effect as well as concentration polarization play an important role in transport phenomena in nanofluidics. The appendix includes preliminary investigations in DNA molecule separation and fluorescence correlation spectroscopy measurements, which allows investigating the behavior of molecules in the nanochannel itself.

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Transport phenomena in nanofluidics

A theory of gel filtration and its exeperimental verification

Solute diffusion in hydrogels is important in many biotechnology fields. Solute behavior in hydrogels has been explained in terms of reduction in hydrogel free volume, enhanced hydrodynamic drag on the solute, increased path length due to obstruction, and a combination of hydrodynamic drag and obstruction effects. In this article the various mathematical models derived to explain and predict solute diffusion in hydrogels are reviewed and tested against literature data. These models can be divided into those applicable to hydrogels composed of flexible polymer chains (i.e., homogeneous hydrogels) and those composed of rigid polymer chains (i.e., heterogeneous hydrogels). For homogeneous hydrogels it was determined that a scaling hydrodynamic model provided the best explanation for solute diffusion, while for heterogeneous hydrogels obstruction models were more consistent with the experimental data. Both the scaling hydrodynamic model and the most appropriate obstruction model contain undefined parameters w...

A. G. Ogston

Papers

The spaces in a uniform random suspension of fibres