Elongational Flow Birefringence Investigation of Dynamics of DNA Molecules

up to 103–104 s−1. Miniaturized versions have been developed for microflow experiments [17, 19]. Figure 3.3 shows a scheme for another elongational flow field generator, the four-roller mill (FRM) [8, 52]. Flow lines in the four-roller mill near the surface of rollers are parabolic curves, while the roller surface is circle. This difference of the curvatures leads to the separation of the flow from the roller surface [53]. Strain rate generally achieved in an FRM is a few 102 s−1 at the most. Response of polymers to the elongational flow field generated by these methods has been observed by a flow-generated birefringence measurement, fluorescent microscopic image analysis [38, 47], light scattering [27, 29], and flow-generated stress measurements. Figure 3.4 shows an FRM apparatus equipped with a flow birefringence measuring system.


A314557_1_En_3_Fig1_HTML.gif


Fig. 3.1
(a) Opposed jets and flow lines of the resulting flow field. A small circle in the center of the field represents the stagnation point. From the stagnation point to both exit nozzles, there is a one-dimensional elongational flow field along the exit symmetry axis. Both the distance between nozzles and the orifice dimension are usually in the order of 1 mm. Arrows indicate flow directions. (b) Total flow circuit used with opposed jets. The opposed jet (OJ) apparatus is immersed in a reservoir R1. By evacuating a reservoir R2 with a rotary pump (RP), polymer solution in R1 is sucked into nozzles of opposed jets causing flow along the symmetry axis


A314557_1_En_3_Fig2_HTML.gif


Fig. 3.2
(a) Cross slots and flow lines of generated flow field. At the center of the cross slots, there is a stagnation point. Arrows indicate flow directions. (b) A total flow circuit used with cross slots. Solution in the reservoir R1 is drawn into the cross slots (CS) when the reservoir R2 is evacuated by a rotary pump (RP). Arrows indicate flow directions


A314557_1_En_3_Fig3_HTML.gif


Fig. 3.3
(a) A four-roller mill and generated flow field. Top view along rollers. By rotating rollers at angular velocity ω(s−1) to the indicated directions, a planar elongational flow field parallel to the rollers is generated in the space among the rollers. Arrows indicate flow directions. A small circle in the center of the field represents the stagnation point. Arrows indicate flow directions. (b) Four rollers of the same size are set parallel to one another. The rollers are immersed in polymer solution


A314557_1_En_3_Fig4_HTML.gif


Fig. 3.4
A setup of the four-roller mill in an optical polarization measuring system. Optical signal is detected by a photodiode




3.3 Response of Polymers to an Elongational Flow Field


Flexible polymers are extended in an elongational flow field to their stretched length. Using the dumbbell model [39], stretching of polymers in an elongational flow field is well described. The force exerting on a flexible random coil polymer molecule is


$$ \Delta F(l)=\frac{1}{2}\kern0.2em \zeta \dot{\varepsilon}l-{F}_{\mathrm{cont}}(l) $$

(3.1)
where l is polymer molecular size, ζ is friction coefficient, $$ \dot{\varepsilon} $$ is elongational strain rate, and F cont is the entropic contraction force of the polymer molecule. The first term is the drag force by the flow field. On increasing $$ \dot{\varepsilon} $$ , the sign of ΔF changes from − to + on passing through the point ΔF = 0. The strain rate $$ {\dot{\varepsilon}}_{\mathrm{c}} $$ at ΔF = 0 is termed the critical strain rate for the coil–stretch transition. In a flow birefringence experiment, for $$ \dot{\varepsilon}<{\dot{\varepsilon}}_c $$ , no birefringence is observed. As described above, the coil–stretch transition is considered to be a runaway process. When the drag force exceeds the entropic contraction force, the polymer chains are deformed along the flow direction. Once the polymer chain starts to become deformed, the drag force increases proportionally to the deformed length along the flow direction. Thus, for a strain rate slightly larger than $$ {\dot{\varepsilon}}_{\mathrm{c}} $$ , birefringence starts to appear. Figure 3.5 shows a schema of empirically obtainable birefringence intensity, Δn, resulting from the coil–stretch transition. From the strain rate dependence of Δn, for $$ \dot{\varepsilon}<{\dot{\varepsilon}}_{\mathrm{c}} $$ , after the coil–stretch transition occurs, localized birefringence appears in the pure elongational flow field. Figure 3.6 shows the localized birefringence in the central region of FRM, where the strain rate is larger than the critical value.

A314557_1_En_3_Fig5_HTML.gif


Fig. 3.5
Schematic of elongational flow-induced birefringence intensity of flexible polymers in the sample solution as a function of strain rate $$ \dot{\varepsilon} $$ . $$ {\dot{\varepsilon}}_{\mathrm{c}} $$ is a critical strain rate for the coil–stretch transition


A314557_1_En_3_Fig6_HTML.jpg


Fig. 3.6
Flow-induced birefringence pattern in a flexible polymer solution (high-molecular-weight polyethylene oxide (PEO) in low-molecular-weight PEO aqueous solution). Arrows indicate flow directions, and a circle represents optical microscopic field (From Sasaki et al. [43]. With permission from Elsevier)

The critical strain rate $$ {\dot{\varepsilon}}_{\mathrm{c}} $$ relates to the longest relaxation time τ L of the molecule through the inverse relation


$$ {\dot{\varepsilon}}_{\mathrm{c}}{\tau}_L\sim C, $$

(3.2)
where C is a numerical constant of the order of unity [9, 20, 31, 38].

When the polymer molecules in a solution are rigid rodlike, α-helical polypeptides, for example, such molecules respond to the flow field by rotating to orient in a definite direction [25]. The solution shows almost homogeneous birefringence throughout the irradiating field, where the orientation direction of each rodlike molecule is considered to be almost identical. Figure 3.7 shows the non-localized birefringence response of a solution containing rigid rodlike molecules as solute. By observing color information of the birefringence, Odell et al. determined that the orientation direction of rodlike molecules was parallel to the outlet flow direction [34]. In this case, birefringence starts to increase from $$ \dot{\varepsilon}\ge 0 $$ and there is no critical strain rate for the appearance of birefringence. Figure 3.8 shows the birefringence intensity, Δn, plotted against strain rate $$ \dot{\varepsilon} $$ . The shape of the curve is described by the strain rate dependence of the orientational order parameter S,

A314557_1_En_3_Fig7_HTML.jpg


Fig. 3.7
Flow-induced birefringence pattern of a rigid rodlike polymer solution (poly(γ-methyl d-glutamate) in chloroform). White circles indicate four rollers. Arrows show flow directions (From Sasaki et al. [43]. With permission from Elsevier)


A314557_1_En_3_Fig8_HTML.gif


Fig. 3.8
Schematic drawing of elongational flow-induced birefringence intensity of rigid rodlike molecules in the sample solution as a function of strain rate $$ \dot{\varepsilon} $$



$$ S=\frac{2}{3}\left[\frac{1}{4}-\frac{3}{2\xi }+{\left(\frac{9}{16}-\frac{3}{4\xi }+\frac{9}{4{\xi}^2}\right)}^{\frac{1}{2}}\right] $$

(3.3)
where $$ \xi =\dot{\varepsilon}/{D}_{\mathrm{r}} $$ and D r is the rotational diffusion coefficient [11]. The D r value for a rodlike molecule can be determined from its birefringence data [34]. One method to determine the rotational diffusion coefficient of rigid rodlike molecules is to observe the decay of Δn after a sudden cessation of flow. The birefringence decay of a molecule having rotational diffusion coefficient D r is described by [3],


$$ \Delta n=\Delta {n}_0 \exp \left(-6\kern0.1em {D}_{\mathrm{r}}t\right). $$

(3.4)
The decay results from disorientation processes affecting the molecule after flow ceases.


3.4 The DNA Molecule as a Model System of Polymer Dynamics


There had been a debate whether a polymeric molecule in an elongational flow field is actually extended. Elongational flow birefringence experiments indicate that flexible polymer molecules are almost fully extended by the flow field in the regime above the critical strain rate [6, 35, 41]. On the other hand, light scattering studies on the elongating flexible polymers suggest that the elongation should not be so remarkable [7, 27, 29]. Using fluorescent microscopy and DNA molecules from a bacteriophage, Chu et al. showed that the DNA elongated to almost its stretched-out state, using an elongational flow field beyond the critical strain rate [38, 47]. This method of single-molecules visualization looks at each molecule in the solution, while flow birefringence measurements are macroscopic, and the result is averaged over all molecular in the solution. Correspondence between these two methods has been investigated, and the coil–stretch transition was observed to be sharper with single-molecular visualization than with birefringence. This discrepancy likely originates from the selection of molecules in a steady extension in the single-molecular observation, while birefringence averages over molecules in a broad range of extension states.

DNA molecules are often used as a model system for visualizing flexible polymer dynamics because each of them after staining is easily visualized separately by fluorescent microscopy. Before and after the elongational flow experiments, molecular weight was confirmed to be unchanged for the DNA molecules examined in the studies below.


3.5 Elongation of DNA Molecules in the Flow Field


As a model system, DNA was used to demonstrate that a flexible polymer chain could be stretched almost to its limit by an elongational flow. Figure 3.9 shows elongational flow-induced birefringence plotted against elongational strain rate for λ-phage DNA 0.2 M NaCl aqueous solutions of three different DNA concentrations [41]. The elongational flow field was generated by an FRM. Though at small values, there is a critical strain rate $$ {\dot{\varepsilon}}_{\mathrm{c}} $$ seen in each profile. After a small non-birefringent range of $$ \dot{\varepsilon} $$ , Δn increased rapidly at first and then gradually. The observed birefringence pattern in the irradiated region of the FRM was broadly localized around the elongational flow field, the broadness originated from the semiflexible nature of DNA chains. Before and after the experiments that covered a range up to $$ {\dot{\varepsilon}}_{\sim }160\kern0.35em {\mathrm{s}}^{-1} $$ , no evidence for DNA molecular scission by the elongational flow field was observed; this was also confirmed by an agarose gel electrophoresis assessment. Figure 3.10 shows a set of birefringence profiles along the inlet line containing the stagnation point in the FRM at indicated strain rates. The pattern and these profiles document the molecular elongation and underlying flow field evolution from quiescent state; (1) an almost non-localized birefringence appears first, (2) a sharp localized birefringence line then appears, and (3) the localized line thickens. The second process in the profile evolution corresponds to the rapid increasing process of Δn in the $$ \varDelta n\ \mathrm{v}\mathrm{s}.\ \dot{\varepsilon} $$ plot (Fig. 3.9). Odell and Taylor [33] regarded the criticality at $$ {\dot{\varepsilon}}_c $$ as the manifestation of the coil–stretch transition of DNA coils, where the chain hydrodynamic analogy changes from non-free draining to free draining. Figure 3.11 shows the decay in Δn after sudden cessation of the flow at $$ \dot{\varepsilon}=24\kern0.6em {\mathrm{s}}^{-1} $$ for 10 mg/ml of DNA solution. For all solutions measured, there were two distinct processes: an initial rapid relaxation (stage 1) and a slow relaxation (stage 2). This measurement was performed using a photodiode, and the observed birefringence was integrated over the entire microscopic field inside the FRM. Figure 3.12 shows the time evolution of the similar profile as Fig. 3.10 after the sudden cessation of the flow at $$ \dot{\varepsilon}=24\kern0.6em {\mathrm{s}}^{-1} $$ . It is clear that the birefringence at the off-symmetrical plane or foot region in the profile decreases faster than that near the stagnation point. Figure 3.13 shows Δn decay at indicated points in the inside area of FRM after the sudden cessation of the flow at $$ \dot{\varepsilon}=24\kern0.6em {\mathrm{s}}^{-1} $$ . Δn is plotted against the frame number of the video still, which is proportional to time after stopping the mill.

A314557_1_En_3_Fig9_HTML.gif


Fig. 3.9
Elongational flow-induced birefringence intensity, Δn, plotted against strain rate, $$ \dot{\varepsilon} $$ , for (○) 10 μg/ml, (●) 7 μg/ml, and (△) 5 μg/ml of λ-phage DNA solutions (From Sasaki et al. [41]. With permission from John Wiley & Sons, Inc.)


A314557_1_En_3_Fig10_HTML.gif


Fig. 3.10
Birefringence profile along the inlet symmetry axis including the stagnation point in an FRM for 10 μg/ml of λ-phage DNA solution at eight stages from $$ \dot{\varepsilon}=2\ \mathrm{t}\mathrm{o}\ 24\kern0.5em {\mathrm{s}}^{-1}\kern-0.3em : $$ at (a) $$ \dot{\varepsilon}=2\kern0.5em {\mathrm{s}}^{-1} $$ , (b) 3 s−1, (c) 4 s−1, (d) 5 s−1, (e) 7 s−1, (f) 10 s−1, (g) 16 s−1, (h) 24 s−1. s indicates the stagnation point (From Sasaki et al. [41]. With permission from John Wiley & Sons, Inc.]


A314557_1_En_3_Fig11_HTML.gif


Fig. 3.11
A typical decay curve of flow-induced birefringence intensity, Δn, after sudden cessation of flow at strain rate $$ \dot{\varepsilon}=24\kern0.5em {\mathrm{s}}^{-1} $$ , for 10 μg/ml of DNA solution (From Sasaki et al. [41]. With permission from John Wiley & Sons, Inc.)


A314557_1_En_3_Fig12_HTML.gif


Fig. 3.12
Change in the birefringence profile along the inlet symmetry axis for 10 μg/ml DNA solution at (a) t = 0.2 s, (b) 0.3 s, (c) 0.5 s, (d) 0.8 s, and (e) 1 s, after sudden cessation of flow (From Sasaki et al. [41]. With permission from John Wiley & Sons, Inc.)


A314557_1_En_3_Fig13_HTML.gif


Fig. 3.13
Logarithm of Δn plotted against time (in video frame units) on the inlet symmetry plane at (○) the stagnation point, (●) 0.5 mm, (△) 1.0 mm, (▲) 1.5 mm, (□) 2.0 mm, and (■) 205 mm from the stagnation point for 10 μg/ml DNA solution (From Sasaki et al. [41]. With permission from John Wiley & Sons, Inc.)

In this stopped flow experiment for semiflexible DNA molecules, the Δn relaxation is considered to contain both a disorientation process of deformed molecules oriented by the flow and the recovery process from a deformed internal conformation. Because both the stage 1 and the stage 2 relaxations are described by simple exponential decay, each of them is regarded as a single mechanism. The relaxation time for stage 1 was 0.52 s and for stage 2, 6.7 s. According to a direct imaging studies, the relaxation time for the extended λ-phage DNA to contract has been reported to be 3 s [37] for molecules of 12.8 μm long. From these facts, the main contribution to stage 2 was concluded to be the contraction process of extended DNA molecules and for stage 1, the disorientation process of deformed DNA molecules.

As the classification of stages was made by observing the Δn decay after flow stopped, processes in Fig. 3.13 should be categorized as stage 1. Figure 3.14 shows the birefringence relaxation time τ at each point in the FRM, estimated from Fig. 3.13. All relaxation times plotted are in stage 1. From Eq. (3.4), the orientation relaxation time is related to the rotational diffusion coefficient,

A314557_1_En_3_Fig14_HTML.gif


Fig. 3.14
Relative relaxation time, τ r, plotted against distance from the stagnation point, R s. The relaxation time at each point was normalized by the value at the stagnation point (From Sasaki et al. [41]. With permission from John Wiley & Sons, Inc.)



$$ {\tau}^{-1} = 6{D}_{\mathrm{r}}. $$

(3.5)

At the same time, D r is a function of an aspect ratio ( $$ p=b/a\le 1 $$ ) when the molecules are assumed to be a prolate spheroid with longer radius a and shorter radius b,


$$ {D}_{\mathrm{r}}=\frac{3kT}{16\pi a{b}^2{\eta}_{\mathrm{s}}}\left[\frac{p^2}{1-{p}^4}\right]\left\{\left[\frac{2-{p}^2}{2\sqrt{1-{p}^2}}\right] \ln \left(\frac{1+{\left[1-{p}^2\right]}^{\frac{1}{2}}}{1-{\left[1-{p}^2\right]}^{\frac{1}{2}}}\right)-1\right\} $$

(3.6)
where k is the Boltzmann constant, T is the absolute temperature, and η s is the viscosity of the solvent [11]. In order to compare the shape of molecules just entering the inner region of the FRM to those around the stagnation point, the ratio of D r values at each point is used. The diffusion coefficient at the entrance was defined as D e and that at the stagnation point was D s. The ratio of D e against D s was defined as α,


$$ \alpha =\frac{D_{\mathrm{e}}}{D_{\mathrm{s}}}=\frac{a_{\mathrm{s}}^3{p}_{\mathrm{s}}^2}{a_{\mathrm{e}}^3{p}_{\mathrm{e}}^2}\frac{f\left({p}_{\mathrm{e}}\right)}{f\left({p}_{\mathrm{s}}\right)} $$

(3.7)
where


$$ f(p)=\left[\frac{p^2}{1-{p}^4}\right]\left\{\left[\frac{2-{p}^2}{2\sqrt{1-{p}^2}}\right] \ln \left(\frac{1+{\left[1-{p}^2\right]}^{\frac{1}{2}}}{1-{\left[1-{p}^2\right]}^{\frac{1}{2}}}\right)-1\right\}. $$

(3.8)

For the DNA random coil, assuming incompressible deformation


$$ \frac{4\pi {a}_{\mathrm{s}}^3{p}_{\mathrm{s}}^2}{3}=\frac{4\pi {a}_{\mathrm{e}}^3{p}_{\mathrm{e}}^2}{3}, $$

(3.9)
hence,


$$ \alpha =\frac{f\left({p}_s\right)}{f\left({p}_e\right)}. $$

(3.10)
From Fig. 3.14, α was found to be 20. A DNA molecule just entering the mill space must have an aspect ratio slightly smaller than 1 because weak flow-induced birefringence was observed. If we assume p e ~ 0.95, p s would be around 0.08; p s/p e ~ 1/12. Menasveta and Hoagland reported that the polystyrene (PS) molecule with M w = 2 × 107 Da shows a coil–stretch transition in an elongational flow field in toluene, where R g in the stretched state was ~650 nm and that in the coil state was ~350 nm [29]. The stretched state was observed in an opposed jet apparatus at $$ {\dot{\varepsilon}}_{\sim }2\times {10}^4\kern0.5em {\mathrm{s}}^{-1} $$ . This difference in R g between both states of PS molecules corresponds to a p s/p e value of 1/6. This value is significantly different from our DNA value observed by the stopped flow experiments at $$ \dot{\varepsilon}=24\kern0.5em {\mathrm{s}}^{-1} $$ . The difference is attributed to the semiflexible nature of DNA molecules, in contrast to the ideal flexible, non-free draining nature of PS in toluene. DNA molecules at $$ \dot{\varepsilon}=24{\mathrm{s}}^{-1} $$ are regarded as being stretched to their extension limit.


3.6 Helix–Coil Transition of DNA Molecules


Though double-stranded DNA molecules can be a model system for flexible or semiflexible polymer chains, at the same time, they show a helix–coil transition at a certain condition. In this section, I will discuss the helix–coil transition of DNA molecules observed by elongational flow birefringence studies. In Fig. 3.15, a schema for detecting the helix–coil transition of α-helical peptide molecules by an elongational flow birefringence method is shown [22]. Peptides are regarded as rigid rods in their helix conformation and flexible in their coil conformation. The difference in conformations is expected to be detectable by the difference in Δn. Because a double-stranded DNA molecule is semiflexible, the dynamics of its helix–coil transition are thought to be hydrodynamically different from those of an α-helical polypeptide chain. A heat-induced helix–coil transition in DNA has been studied: Figure 3.16 shows $$ \Delta n\ \mathrm{v}\mathrm{s}.\ \dot{\varepsilon} $$ plot for T4-phage DNA at different temperatures from 25 to 65 °C. Up to 53 °C, flow-induced birefringence Δn was observed, while at 55 and 65 °C, Δn was not detected [42]. In each curve, there was a critical strain rate, $$ {\dot{\varepsilon}}_{\mathrm{c}} $$ . The birefringence pattern was localized at the elongational flow field containing the stagnation point. These observations suggest an occurrence of the coil–stretch transition of DNA molecules, induced by an elongational flow field. Figure 3.17 shows the plateau value of Δn for each isothermal birefringence profile, plotted against temperature. With increasing temperature, Δn decreases gradually up to 40 °C and rapidly over 50 °C. Above 55 °C, no birefringence was detected. Figure 3.18 shows the temperature dependence of the critical strain rate, $$ {\dot{\varepsilon}}_{\mathrm{c}} $$ , for the coil–stretch transition. Over 50 °C, $$ {\dot{\varepsilon}}_{\mathrm{c}} $$ increases rapidly with temperature. Both the decrease in Δn and the increase in $$ {\dot{\varepsilon}}_{\mathrm{c}} $$ are considered to include the effect of the decrease in solvent viscosity and the conformational transition of DNA molecules. Figure 3.19 is the Arrhenius plot for $$ {\dot{\varepsilon}}_{\mathrm{c}} $$ . From 25 to 40 °C, the plot is linear but becomes nonlinear over 50 °C. It is expected that in the linear section the activation energy for the coil–stretch transition does not change, indicating that the hydrodynamic shape of a DNA chain remains unchanged in this temperature range. Figure 3.20 shows UV absorption at 260 nm as a function of temperature for the same DNA solution as that used for the elongational flow experiments. From these results, the conformational change in a DNA solution expected over 50 °C is regarded as a change from a double-stranded coil to an untwined one. In a partly untwined DNA molecule, an untwined part and a double-stranded part coexist along the chain. The untwined part is not birefringent, causing the remarkable reduction in Δn in temperatures over 50 °C (Fig. 3.17). At the same time, the untwined part is more flexible than a double-stranded chain. The increased flexibility produces a larger entropic contraction force in the DNA chain. Thus, the rapid increase in $$ {\dot{\varepsilon}}_{\mathrm{c}} $$ is also explained by untwining (Fig. 3.18). Figure 3.21 shows the similar Δn-temperature plot as Fig. 3.17 but with Δn values (filled circle) remeasured for those samples after cooling for 30 min at room temperature. The latter values for 50 and 53 °C recover the room-temperature values, although at these temperatures the chain shows untwining. The Δn value at 55 °C is 0, but after cooling, the value reaches about half of the room-temperature Δn. Over 60 °C, even after cooling, flow birefringence was not observed. At both 55 and 60 °C and at higher temperatures, DNA molecules are considered almost completely untwined. The partial recovery in Δn at 55 °C could be due to incorrect and/or incomplete repairing of base pairs among untwined DNA chains. Another explanation for this could be scission of DNA molecules at the untwined region, as well as untwining by the flow field, explaining the absence of flow birefringence for 60 °C and higher temperature solutions. Table 3.1 lists molecular weight values of DNA molecules after isothermal flow birefringence measurements at the temperatures indicated. The value at 25 °C is the molecular weight of intact T4-phage DNA. At 55 °C, the molecular weight of DNA is reduced to 1/2 of the intact value, and at 65 °C, it is only 1/20. These values confirm the validity of the scission mechanism of DNA molecules at these temperatures in an elongational flow field. In a previous section, I stated that DNA molecules did not reduced in molecular weight after elongational flow experiments. Observed results here seem to be a contradiction to this.
Tags:
Mar 22, 2018 | Posted by in BIOCHEMISTRY | Comments Off on Elongational Flow Birefringence Investigation of Dynamics of DNA Molecules

Full access? Get Clinical Tree
Get Clinical Tree app for offline access