| Intrachain Reactions of Supercoiled DNA Simulated by Brownian Dynamics Biophysical Journal, Volume 81, Issue 4, 1 October 2001, Pages 1924-1929 Konstantin V. Klenin and Jörg Langowski Abstract We considered an irreversible biochemical intrachain reaction of supercoiled DNA as a random event that occurs, with certain probability, at the instant of collision between two reactive groups bound to distant DNA sites. Using the Brownian dynamics technique, we modeled this process for a supercoiled DNA molecule of 2.5kb length in dilute aqueous solution at an NaCl concentration of 0.1M. We calculated the mean reaction time as a function of the intrinsic second-order rate constant , the reaction radius and the contour separation of the reactive groups. At the diffusion-controlled limit ( → ∞), the kinetics of reaction are determined by the mean time of the first collision. The dependence of on is close to inversely proportional, implying that the main contribution to the productive collisions is made by bending of the superhelix axis. At sufficiently small , the mean reaction time can be satisfactory approximated by =+, where is the local concentration of one reactive group around the other, and is an adjustable parameter, which we called the apparent time of the first collision. The value of depends on very weakly and is approximately equal to the mean time of the first collision caused by mutual reptation of two DNA strands forming the superhelix. The quasi-one-dimensional reptation process provides the majority of productive collisions at small values. Abstract | Full Text | PDF (176 kb) |
| Diffusion of Macromolecules in Agarose Gels: Comparison of Linear and Globular Configurations Biophysical Journal, Volume 77, Issue 1, 1 July 1999, Pages 542-552 Alain Pluen, Paolo A. Netti, Rakesh K. Jain and David A. Berk Abstract The diffusion coefficients () of different types of macromolecules (proteins, dextrans, polymer beads, and DNA) were measured by fluorescence recovery after photobleaching (FRAP) both in solution and in 2% agarose gels to compare transport properties of these macromolecules. Diffusion measurements were conducted with concentrations low enough to avoid macromolecular interactions. For gel measurements, diffusion data were fitted according to different theories: polymer chains and spherical macromolecules were analyzed separately. As chain length increases, diffusion coefficients of DNA show a clear shift from a Rouse-like behavior ( ≅ ) to a reptational behavior ( ≅ ). The pore size, of a 2% agarose gel cast in a 0.1M PBS solution was estimated. Diffusion coefficients of the proteins and the polymer beads were analyzed with the Ogston model and the effective medium model permitting the estimation of an agarose gel fiber radius and hydraulic permeability of the gels. Not only did flexible macromolecules exhibit greater mobility in the gel than did comparable-size rigid spherical particles, they also proved to be a more useful probe of available space between fibers. Abstract | Full Text | PDF (165 kb) |
| Diffusion-Controlled Intrachain Reactions of Supercoiled DNA: Brownian Dynamics Simulations Biophysical Journal, Volume 80, Issue 1, 1 January 2001, Pages 69-74 Konstantin V. Klenin and Jörg Langowski Abstract The Brownian Dynamics technique was used to model a diffusion-controlled intramolecular reaction of supercoiled DNA (2500 basepairs) in 0.1M sodium chloride solution. The distance between the reactive groups along the DNA contour was 470 basepairs. The reaction radius was varied from 6 to 20nm. The results are presented in terms of the probability distribution () of the first collision time. The general form of the function () could be correctly predicted by a simple analytical model of one-dimensional diffusion of the superhelix ends along the DNA contour. The distribution () is essentially non-exponential: within a large initial time interval, it scales as () ∼ , which is typical for one-dimensional diffusion. However, the mean time of the first collision is inversely proportional to the reaction radius, as in three dimensions. A visual inspection of the simulated conformations showed that a considerable part of the collisions is caused by the bending of the superhelix axis in the regions of the end loops, where the axis is most flexible. This fact explains why the distribution () combines the features of one- and three-dimensional diffusion. The simulations were repeated for a DNA chain with a permanent bend of 100° in the middle position between the reactive groups along the DNA contour. The permanent bend changes dramatically the form of the distribution () and reduces the mean time of the first collision by approximately one order of magnitude. Abstract | Full Text | PDF (186 kb) |
Copyright © 2006 The Biophysical Society. All rights reserved.
Biophysical Journal, Volume 91, Issue 2, 639-644, 15 July 2006
doi:10.1529/biophysj.105.077404
Nucleic Acids
Hong Shen*, 1, Yueyue Hu† and W.M. Saltzman*,
, 
* Departments of Biomedical, Yale University, New Haven, Connecticut
† Chemical Engineering, Yale University, New Haven, Connecticut
Address reprint requests to W. M. Saltzman.Mucosal surfaces of the gastrointestinal, respiratory, and reproductive tracts have long been used as sites for delivering therapeutics, particularly low molecular weight drugs, but there is increasing evidence that mucosal sites may be appropriate and useful for delivery of vaccines for preventing infectious diseases, e.g., human papilloma virus (HPV)-associated diseases 1,2,3 and unwanted pregnancy 4,5. However, the mucus gel layer associated with mucosal surfaces may be a significant barrier to the delivery of macromolecules. Mucus can trap and slow the diffusion of macromolecules or particles by several mechanisms: 1, it has a densely packed fibrous structure (for example, the pore size of human cervical mucus is ∼100nm 6); 2, it can collaborate with secretory antibodies (e.g., sIgA), which can bind to macromolecules or particles 7,8,3, negatively charged glycosylated regions of mucin fibers can form low-affinity bonds with some molecules; and 4, hydrophobic surfaces in the mucus gel can trap some molecules.
The diffusion of macromolecules 6,9, leukocytes 10, and virus particles 11 through the mucus has been studied using epifluorescence microscope 6,9, direct visualization of movement of cells 10 or particles 12, diffusion chamber 13, and fluorescence recovery after photobleaching (FPR) 6,11. These studies indicate that most proteins, antibodies, and virus-sized particles can diffuse through human cervical mucus almost as rapidly as they diffuse through water, but there are exceptions: IgM, small aggregates of sIgA or HSV diffuse more slowly in mucus than in water. Diffusion appears to depend primarily on the molecular weight, although binding of certain macromolecules (such as sIgA and IgM) to mucin fibers can influence their rates of diffusion significantly 11.
DNA is another potential therapeutic macromolecule. Delivery of plasmid DNAs to mucosal surfaces has been promising as both therapeutic and prophylactic approaches to genetic diseases (e.g., cystic fibrosis 14) and infectious diseases (e.g., HIV 15). In this event, diffusion through mucus is the first physical barrier for DNA, which must be crossed to be available to underlying cells. Although DNA is often delivered to the mucosal surface in combination with agents designed to enhance transfection, diffusion of naked plasmid DNA may be important in some applications (see Shen et al. 5, for example).
Plasmid DNA is different in many aspects from other molecules and viruses. First, DNA is a large molecule (several million daltons), which may make it difficult for DNA to penetrate through the densely packed mucin fibers and reach the surface of epithelial cells. Second, a plasmid DNA can exist in different topological configurations such as linear or supercoiled. The supercoiled configuration of DNA shows higher gene expression in cells than a linear one does and, therefore, is most often used in gene therapy or DNA vaccines 16,17,18,19. The diffusion of a plasmid DNA through mucus may be affected by its topological configuration. Lastly, a plasmid DNA is usually complexed with a transfection reagent for improving gene transfer. Transfection reagents may change the size, charge, or topology of DNA, and thus affect DNA diffusion through mucus. No previous studies have evaluated the role of DNA size, topology and presence of transfection reagents in DNA diffusion through mucus. The goal of this study is to address these questions using FPR techniques and to use existing models to describe diffusion of DNA in bovine cervical mucus.
Plasmids (ϕX RFI (5.4kb), PUC 19 (2.7kb), PBR (4.4kb)) were purchased from New England Biolabs (Beverly, MA). PcDNA3/LDH-C4 (6kb) and gWiz/LacZ (8.3kb) were purchased from Aldevron (Fargo, ND). Oestrus bovine cervical mucus was obtained from Humagen Fertility Diagnostics (Charlottesville, VA). The mucus was used directly without further dilution. Two transfection reagents were used, Tfx-20 (Promega, Madison, MI) and Superfect (Qiagen, Valencia, CA).
All the purchased DNAs were in supercoiled form. Supercoiled DNAs were linearized using restriction enzymes. gWiz/LacZ was linearized by either Xho I or BmH I. ϕX RFI was linearized by Xho I. Other DNAs were linearized by EcoR I. All enzymes were purchased from New England Biolabs (Beverly, MA). Linearization reactions were carried under conditions as suggested by the manufacturer for each enzyme. The degree of linearization was determined by 1% agarose gel electrophoresis.
Both supercoiled and linearized DNAs were labeled using the Label IT Fluorescein Nucleic Acid labeling kit from Mirus Corporation (Madison, WI) following the procedure described by the manufacturer. The labeled DNAs were purified by ethanol precipitation and resuspended in DNase free TE buffer. Based on the manufacturer’s literature, DNAs remain intact after being labeled by Labeling IT reagents.
FPR was used to measure the diffusion of DNA or DNA/transfection reagent complex in mucus or PBS. All the measurements were carried out at room temperature (20°C). Solutions of 5μg of labeled DNA were prepared in 50μl of 10mM PBS or mucus, and then added to a spherical cavity microscope slide (5mm in diameter, 200μm in maximum depth). For studies in mucus, a very small amount of DNA solution was used to avoid diluting mucus samples. The well was sealed with a cover slip and equilibrated for 15min before measurement. FPR was carried out using a confocal laser scanning microscope (LSM 510 META, Zeiss, Thornwood, NY). The 488-nm line of a 30-mW argon ion laser was used for sample bleaching and fluorescence excitation. Emitted light was monitored at 520nm. Typical settings for bleaching and recovery imaging are 100% and 0.5% of maximum laser power, respectively. From the whole field, a circle (D=6.75μm) was selected for bleaching. The minimum bleach time was 0.5ms. For recovery, a time series of images of bleached region were recorded till the recovery approached 100%. The intensity of bleached region was recorded automatically. The diffusion coefficient is calculated by the equation: D=γR2/4 t1/2, where γ is a parameter depending on the degree of photobleaching, R is the radius of bleaching area, and t1/2 is the half-time for diffusive recovery of photobleaching-induced concentration fluctuation 20,21. Both γ and t1/2 can be estimated from the recovery curve.
We evaluated the size and topological structure of DNA molecules used in our measurements by agarose gel electrophoresis (Fig. 1). By comparison to supercoiled molecular weight markers, all the plasmids maintained supercoiled form with correct size (Figure 1left panel). Except for plasmid gWiz/LacZ, all the DNA preparations displayed a single band on electrophoresis. In contrast, plasmid gWiz/LacZ had two major bands: the larger band corresponded contaminating DNA of a slightly higher molecular weight. All the linearized DNAs were obtained by digesting the supercoiled DNAs with a single restriction endonuclease for which the plasmid had a single restriction site. All the linearized DNAs migrated as a single band with the anticipated size (Figure 1right panel) determined by 1-kb molecular weight ladder.
The diffusion of both supercoiled and linearized DNAs in PBS varied with DNA size, decreasing as the number of basepair increased (Fig. 2). The diffusion coefficients of linear DNAs in PBS were in agreement with previously published values obtained by various methods (Fig. 2), which validated our FPR method. Compared to linear DNAs of the same size, supercoiled DNAs diffused faster in PBS.
Linear gWiZ/LacZ diffused faster than any other linear DNAs. To test whether this behavior was due to a particular restriction enzyme, we digested supercoiled gWiZ/LacZ with different restriction enzymes. All the enzymes we used only produced a single band with anticipated size on the agarose gel (Figure 1right panel). The diffusion of all resulting linear gWiZ/LacZ DNAs was faster than expected. This unexpected behavior may be due to the sequence of gWiZ/LacZ DNA, which also affects diffusion of DNA 22,23. Because of its different behavior, we did not include linear gWiZ/LacZ in our analysis.
The diffusion coefficients for linear and supercoiled DNA molecules were determined in bovine mucus (Fig. 3). The diffusion coefficients of supercoiled DNAs in mucus were about the same as their linear form. The reduced diffusion coefficient, Dmucus/DPBS, was used to demonstrate the effect of mucus on diffusion of DNAs (Fig. 4). The hindrance of mucus to DNA diffusion was dependent on topology. The diffusion of linear DNA was not significantly retarded (Dmucus/DPBS∼1), but the diffusion of supercoiled DNA was significantly retarded (p<0.05), especially when DNA size was larger than 5kb.
where SD denotes standard deviation and D denotes mean of diffusion coefficients from Fig. 2 (DPBS) and Fig. 3 (Dmucus).Liposomes, such as Tfx 20, and dendrimers, such as Superfect, are commonly used transfection reagents. Both transfection reagents are positively charged, whereas DNA is highly negatively charged, so that mixture of DNA with either reagent leads to the formation of supramolecular complexes; with an increase in the ratio of Tfx 20 or Superfect to DNA, the charge of the complex shifts from more negative to more positive. DNA/Tfx 20 complexes were small and uniformly distributed in mucus (Figure 5a). With the increase of the ratio of Tfx 20 to DNA, DNA diffused faster in mucus (Fig. 6). Superfect formed large and nonuniform aggregates with DNA (Figure 5b), therefore, we were not able to use FPR to determine the diffusion coefficient of DNA/Superfect complex because the resulting recover curves was erratic and could not be fit by a single diffusion coefficient.
We investigated the diffusion of DNAs with various size and topology (linear or supercoiled configuration). Within the size range of DNA we examined, mucus did not retard the diffusion of linear DNAs, but significantly reduced the diffusion of supercoiled DNAs compared to diffusion in water (Fig. 4). This result demonstrates that mucus is a potential barrier to supercoiled DNAs, especially to larger DNAs (with over 5,000 basepairs). Two DNA delivery vectors (liposomes and dendrimers) were used for examining if delivery vectors would affect the diffusion of DNA in mucus. Liposomes (Tfx 20) increased the diffusion of supercoiled DNA (Fig. 6), whereas Superfect formed large aggregates with DNA which we expect to hinder DNA diffusion in mucus (Figure 5b).
Several mechanisms may hinder the diffusion of DNA molecules through a mucus gel. DNAs can either bind to mucin fibers or they can be trapped by the size of mesh spacing between the mucin fibers. Because of the geometric complexity of fibrous gels, it is difficult to predict the rate of diffusion of a macromolecule through a fibrous gel even in the absence of binding interactions. Several models have been proposed to describe the diffusion of macromolecules in gels or fibrous media (reviewed in Pluen et al. 24). These models are applicable for small spherical macromolecules, but not appropriate for flexible polymer chain molecules as DNAs.
Two models have been proposed for the diffusion of a polymer chain in gels based on the chain length relative to pore size. First, when the gyration radius, Rg, is smaller than half of the pore size and the polymer chain migrates in an ellipsoidal conformation, the diffusion of DNA in gel is described by the Zimm model 25:
![]() | (1) |
![]() | (2) |
When diffusion coefficients of DNAs in PBS are plotted as the function of the number of basepairs, N0, on a logarithmic scale, the slope represents the scaling exponent of D as a function of N0. Our results for linear DNA diffusion in PBS yield a scaling exponent of −0.63, which is in good agreement with Zimm’s prediction of −0.6 for a polymer chain diffusing in a good solvent, as well as other experimental observations for DNA diffusion (−0.611±0.016 27, −0.68 28, and −0.5 24). For supercoiled DNAs, D varied as a power of N0, giving a scaling factor of −0.68±0.01, which is also close to Zimm’s predictions for a good solvent. Therefore, the diffusion of both linear and supercoiled DNAs in PBS can be described reasonably well by the Zimm model (Eq. (1)). Using this model, we can estimate the radii of gyration of DNAs in PBS (Table 1). The radii of linear DNAs agree with the predictions by Smith et al. 27. The radius of supercoiled DNA was smaller than that of their linear form.
DNA diffusion in mucus can also be compared to the Zimm model (Eq. (1)); the diffusion coefficients of linear DNAs in mucus yield a scaling factor of −0.81 as a power of N0, and the diffusion coefficients of supercoiled DNAs in mucus yield a scaling factor of −1.3 (Fig. 3). The diffusion of DNAs in mucus revealed a steeper dependence on size of DNA (i.e., a more negative value of the scaling factor) than in PBS. Although no previous studies have reported DNA diffusion coefficients in mucus, Pluen et al. reported that the diffusion of small linear DNAs (N0<6000kb) in 2% agarose gel followed the Zimm model with a scaling exponent of −0.52 24. This difference from the scaling coefficient obtained in mucus suggests that diffusion of DNA in other gel systems (e.g., agarose gel, collagen) can be very different from mucus; similar observations have been made in the study of protein diffusion in various gels 6.
The diffusion of supercoiled DNA in mucus with a scaling factor of −1.3 is more consistent with that described by the reptational model, with the exception of the supercoiled PUC plasmid (see Fig. 3). PUC is 2.7kb—the smallest of the plasmids tested—and, as a result, more rigid than other larger plasmids. We did not thoroughly investigate the diffusion of small supercoiled DNAs (<2.7kb), but we suspect that smaller supercoiled DNAs may follow the Zimm model, as other studies suggested for diffusion of small size of linear DNAs in agarose gel 24. Though the theoretical prediction of the scaling factor for a purely reptation model is −2.0 26, other experimental observations and simulations suggest that the actual scaling factor can ranging from −1.0 to −2.0, depending on the type of polymer chains and gels used 29,30.
Assuming that the diffusion of supercoiled DNA in mucus obeys the reptational model, we can estimate the effective pore size of bovine cervical mucus using Eq. (2) (Table 2). The estimated pore size is 12.5±1.4μm, which is in agreement with confocal microscopic 31 and electron microscopic evidence (pore size ranges from 1 to 20μm) 32 for bovine cervical mucus. Previous theoretical calculations and electron microscopic evidence showed that interspacing of mucin fibers of human mucus is between 100 and ∼380nm 6, we expect that the diffusion of DNAs in human mucus could be different from what we observed in bovine cervical mucus.
| Table 2 Estimation of pore size of bovine mucus from the experimental diffusion coefficients of supercoiled DNA in mucus |
| Basepairs | No. of Kuhn segments, Nk | Pore size, a (μm) | |||
|---|---|---|---|---|---|
| PBR | 4361 | 148 | 11.8 | ||
| ϕ xRFi | 5386 | 183 | 11.8 | ||
| pcDNA3/LDH-C4 | 6000 | 204 | 11.8 | ||
| gWiZ/LacZ | 8278 | 281 | 14.6 | ||
| Note: to solve Eq. (2), the following parameters were used: the Kuhn friction coefficient δk=2.69×10−10Pa×m24, the Kuhn length=2p =100nm 35, the chain diameter d=2.4nm 24, and the temperature T=293K. |
Mucus hinders the diffusion of supercoiled DNAs in mucus, especially when the size of the DNA molecule is >5kb (Fig. 6). The liposomal reagent, e.g., Tfx 20, increased the diffusion of supercoiled DNA in mucus. One feature of Tfx 20 is its ability to condense DNA. The size and structure of the reagent/DNA complex depend on the procedure used for mixing the components, the technique used to observe them, as well as the liposome composition. The size of the complex ranges 50∼ 300nm 33. Previous studies suggest that there are mainly three types of structure formed on complexation: one where DNA is packed between a short-range lamellar structure composed of flat lipid bilayers; another where the DNA is encapsulated inside a lipid bilayer, forming cylindrical complexes that are closely packed on a hexagonal network; and finally the so-called “bean on a string” complexes, where DNA attaches to the outer surface of the positively charged liposomes 33. In all three of the structures, DNA is no longer a flexible chain, but a more rigid particle, which is not properly described by either the Zimm model or the reptation model.
Many empirical models have been developed to analyze diffusion of rigid particles in polymer gels. One model that fits a range of experimental data is the obstruction-scaling model 34, in which the ratio of diffusion in a gel to the diffusion in water is given by:
![]() | (3) |
In summary, the mucus gel diffusion barrier has been evaluated for delivery of DNA to the mucosal surface. Our data suggest, within the size range commonly used in gene therapy or DNA vaccines, that linear DNA can diffuse through mucus readily whereas supercoiled DNA is mildly hindered. Though transfection reagents can facilitate gene transfer into cells, they can either hinder or facilitate DNA diffusion through mucus. Therefore, it is crucial to carefully evaluate the effect of transfection reagents on DNA diffusion through mucus when choosing transfection reagents for delivering DNA to the mucosal surface.
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