PPI 4/DNA MESOPHASE FORMATION

In a first set of SAXS experiments,²⁰⁹ a 10mg^.mL^-1 DNA solution is injected in the main channel with a mean velocity of uDNA = 100µm^.s^-1 and 20mg^.mL^-1 PPI 4 dendrimer solutions are added to the side channel with a mean velocity of uPPI4 = 4^.uDNA. The well defined, purely diffusive mixing of components reduces the likelihood of the creation of kinetically trapped phases. Experimental conditions are

7. DNA Compaction: Dendrimers of Intermediate Size

Figure 7-8: Radial averaging (a) and azimuthal integration along the peak q0 (b) for the same positions x along the microchannel revealing preferential orientation at χ = ±90°. Baseline intensities are annotated on the right-hand side (dotted lines).²⁰⁹

chosen to result in a final charge ratio N/P < 6 at the furthest measurable point of the device (x ≈ 3mm). A lateral scanning of the sample allows for spatially resolved small angle X-ray diffraction experiments along the microfluidic channels. The positional accuracy of absolute x and y coordinates in the microdevice is on the order of the beam size (20µm). CCD images are collected with exposure times of 30−120s per position.

Representative X-ray diffraction patterns of PPI 4 induced DNA condensation measured at different distances x from the confluence center are shown in Figure 7-7 (bottom). It is important to note that all images reveal oriented diffraction rings. Owing to a concurrent orientation during the assembly process in microflow, the characterization of biomolecular materials, which are difficult to crystallize and normally form liquid-crystalline structures, is significantly improved.^{57, 63, 64} This is a clear advantage of using flow to assemble dendrimer/DNA complexes. Qualitative differences (i.e. in the peak width and in the azimuthal orientation) between these images are readily seen.

7. DNA Compaction: Dendrimers of Intermediate Size

Figure 7-9: The real space distance d of the 2D square lattice (a) and the degree of preference ∆χ showing good agreement with the calculated strain rate

ε& (solid line) in dependence of the x position along the microchannel.

A quantitative evaluation of Raman data obtained from measuring the non-equilibrium DNA compaction under hydrodynamic focusing conditions shows the enormous benefit to our understanding of comparing experimental results to simulation data.

Accordingly, flow velocity and concentration profiles in the hydrodynamic focusing device are again modeled using parameters consistent to results presented in chapter 5.3 and 7.1.2.²¹⁰ The simulated velocity field is exemplarily shown in Figure 7-7 (top).

Small angle X-ray diffraction data plotted in terms of the reciprocal vector q and obtained via a radial integration of the raw image data are given in Figure 7-8a.⁶¹ Plots of X-ray data in the figures are offset for clarity. Baseline values of intensity for azimuthal integrations are included in the data plots in Figure 7-8b.

Starting at the confluence center of the microchannels (x = y = 0), a single peak at q0 = 2.0nm^-1 is identified (lowest curve in Figure 7-8a). Moving the observation position towards larger x, which corresponds to larger N/P ratios, the q0-peak is shifted towards smaller q values and a second peak q1 is concurrently acquired. The ratio q1 = 2^.q0 of the two peak positions is consistent with a columnar mesophase with in-plane square symmetry.

The lattice constant d of such a unit cell is related to the peak position q0 using the relation d = 2π/q0. An increase in the lattice spacing d is obtained at observation points

7. DNA Compaction: Dendrimers of Intermediate Size

Figure 7-10: Schematic representation of the microdomain orientation in the region of maximum strain.

further downstream. This can be understood by the incorporation of additional dendrimers within the PPI 4/DNA condensate. The increase in d (obtained experimentally) is shown in Figure 7-9a to overlay remarkably well with N/P values provided by finite element simulations (solid line in Figure 7-9a) as a function of the measurement position x in the device. These data are consistent with previously reported bulk X-ray diffraction measurements,⁵³ citing a 2D columnar lattice of PPI 4/DNA condensates for N/P values 2 ≤ N/P < 6. The precise diffusive mixing of components in flow uniquely allows visualizing an increase in d over the entire range of columnar mesophases explored here.

The mesoscale alignment of macromolecular assemblies is not easily achieved using standard sample preparation methods. However, an alignment in flow is comparatively straightforward using the setup reported here. At the confluence of the microchannels, the main stream is focused and fluid elements are accelerated. Owing to this extensional flow, DNA molecules as well as dendrimer/DNA assemblies experience an additional hydrodynamic stress, which leads to an orientation along the flow direction.

Scans of the intensity along the azimuthal angle χ on the ring of the q0-peak at different channel positions x are shown in Figure 7-8b. Moving from x = 0 along the reaction channel, all X-ray scans of dendrimer/DNA assemblies show a strong preferential orientation along the flow direction (χ ≈ ±90°) down to a position x = 3000µm.

According to the discussion in chapter 5.3.1, such a superimposed hydrodynamic stress, which can be experienced up to several 1000µm downwards the reaction channel, is expected for experimental situations characterized by a significantly higher viscosity of the main channel solution compared to side channel streams.

The extensional flow leads to a favored orientation of DNA macromolecules parallel to the applied stress (Figure 7-9b). The degree of orientation can be quantified as the full width at half maximum of the azimuthal peaks ∆χ. Figure 7-9b clearly shows a

7. DNA Compaction: Dendrimers of Intermediate Size

minimum value of ∆χ, corresponding to the highest extent of material orientation, at a position x = 300µm. Remarkably, this behavior is quantitatively predicted in the calculation of the strain rate ε_&=∂u ∂x (solid line in Figure 7-9b) that is calculated from the simulated velocity field given in Figure 7-7 (top). This indicates that the strain rate, which describes mechanical effects on the material under flow, can accurately describe the phenomena of supramolecular alignment within microdevices.

The extensive alignment of PPI 4/DNA assemblies in the region of high strain rate enables the visualization of further details regarding the 2D columnar lattice. At x = 300µm and 400µm, two additional local maxima at χ ≈ 0° and 180° can be found (red arrows in Figure 7-8b). This additional weak orientation perpendicular to the flow direction provides interesting insights into the response of a 2D phase of long chain DNA molecules to external stress. The majority of PPI 4/DNA microdomains are oriented parallel to the flow direction. In the region of maximum strain rate however, a concomitant orientation of some microdomains perpendicular to the flow direction occurs. This is most likely due to structural restrictions imposed by the long DNA strands and the square symmetry of the mesophase (schematically represented in Figure 7-10). The observed decrease in the intensity for x ≥ 1000µm is puzzling. Two phenomena are assumed to account for this decrease: firstly, a disintegration of formed complexes might have taken place owing to the strong increase in the dendrimer concentration, and, secondly, experimental inadequacies might have resulted in the fact that the X-ray beam did not fully hit the hydrodynamic focused DNA jet any more.