Self-diffusion of rod-like viruses in the nematic phase

– We measure the self-diffusion of colloidal rod-like virus fd in an isotropic and nematic phase. A low-volume fraction of viruses are labelled with a fluorescent dye and dissolved in a background of unlabelled rods. The trajectories of individual rods are visualized using fluorescence microscopy from which the diffusion constant is extracted. The diffusion parallel (D‖) and perpendicular (D⊥) to the nematic director is measured. The ratio (D‖/D⊥) increases monotonically with increasing virus concentration. Crossing the isotropic-nematic phase boundary results in increase of D‖ and decrease of D⊥ when compared to the diffusion in the isotropic phase (Diso). Introduction. – Suspensions of semi-flexible polymers exhibit a variety of dynamical phenomena, of great importance to both physics and biology, that are still only partially understood. Advances over the past decade include direct visual evidence for a reptationlike diffusion of polymers in a highly entangled isotropic solution and shape anisotropy of an isolated polymer [1–4]. If the concentration of the polymers is increased, a suspension undergoes a first-order phase transition to a nematic phase, which has long-range orientational order but no long-range positional order. As a result of the broken orientational symmetry, it is expected that the diffusion of polymers in the nematic liquid crystals will be drastically different from that in concentrated isotropic solutions. While the static phase behavior of semiflexible nematic polymers is well understood in terms of the Onsager theory and its extensions by Khoklov and Semenov [5, 6], the dynamics of semi-flexible polymers in the nematic phase is much less explored [7]. In this paper, we determine the concentration dependence of the anisotropic diffusion of semi-flexible viruses in a nematic phase and compare it to the diffusion in the isotropic phase. Experimentally, the only data on the translational diffusion of colloidal rods in the nematic phase was taken in a mixture of labelled and unlabelled polydysperse boehmite rods using fluorescence recovery after photobleaching (FRAP) [8]. Theoretically, molecular-dynamics simulations were performed on hard spherocylinder and ellipsoidal systems from which the anisotropic diffusion data was extracted [9–11]. The unisotropic diffusion has also been studied in low-molecular-weight thermotropic liquid crystals using NMR spectroscopy or inelastic scattering of neutrons [12]. c © EDP Sciences Article published by EDP Sciences and available at http://www.edpsciences.org/epl or http://dx.doi.org/10.1209/epl/i2005-10127-x M. P. Lettinga et al.: Self-diffusion of rod-like viruses etc. 693 Real-space microscopy is a powerful method that can reveal dynamics of colloidal and polymeric liquid systems that are inaccessible to other traditional techniques [3,7]. We use digital microscopy to directly visualize the dynamics of fluorescently labelled fd in a nematic background of unlabelled fd. The advantage of this method is an easy interpretation of data and no need to obtain macroscopically aligned monodomains in magnetic fields. The advantages of using fd are its large contour length which can be easily visualized with optical microscope and its phase behavior which can be quantitatively described with the Onsager theory extended to account for electrostatic repulsive interactions and semi-flexibility [13,14]. Viruses such as fd and TMV have been used earlier to study the rod dynamics in the isotropic phase [15]. Experimental methods. – The physical characteristics of the bacteriophage fd are its length L = 880 nm, diameter D = 6.6 nm, persistence length of 2200 nm and a surface charge of 10 e−/nm at pH 8.2 [16]. Bacteriophage fd suspension forms isotropic, cholesteric and smectic phases with increasing concentration [16–18]. The free energy difference between the cholesteric and nematic phase is very small and locally the cholesteric phase is identical to nematic. We expect that at short time scales the diffusion of the rods for these two cases would be the same. Hereafter, we refer to the liquid crystalline phase at intermediate concentration as a nematic instead of a cholesteric. The fd virus was prepared according to a standard biological protocol using XL1-Blue strain of E. coli as the host bacteria [19]. The yields are approximately 50mg of fd per liter of infected bacteria and the virus is typically grown in 6 liter batches. Subsequently, the virus is purified by repetitive centrifugation (108000 g for 5 hours) and re-dispersed in a 20mM phosphate buffer at pH = 7.5. First-order isotropic-nematic (I-N) phase transition for fd under these conditions takes place at a rod concentration of 15.5mg/ml. Fluorescently labelled fd viruses were prepared by mixing 1mg of fd with 1mg of succinimidyl ester Alexa-488 (Molecular Probes) for 1 hour. The dye reacts with free amine groups on the virus surface to form irreversible covalent bonds. The reaction is carried out in small volume (100μl, 100mM phosphate buffer, pH = 8.0) to ensure a high degree of labelling. Excess dye was removed by repeated centrifugation steps. Absorbance spectroscopy indicates that there are approximately 300 dye molecules per each fd virus. Viruses labelled with fluorescein isothiocynante, a dye very similar to Alexa 488, exhibit the phase behavior identical to that of unlabelled virus. Since liquid crystalline phase behavior is a sensitive test of interaction potential, it is reasonable to assume that the interaction potential between labelled viruses is very similar to that between unlabelled viruses. The samples were prepared by mixing one unit of anti-oxygen solution (2mg/ml glucose oxidase, 0.35mg/ml catalase, 30mg/ml glucose and 5% β-mercaptoethanol), one unit of a dilute dispersion of Alexa 488 labelled viruses and eight units of the concentrated fd virus suspension at the desired concentration. Under these conditions the fluorescently labelled viruses are relatively photostable and it is possible to continuously observe rods for 3-5 minutes without significant photobleaching. The ratio of labelled to unlabelled particles is roughly kept at 1 : 30000. The samples were prepared by placing 4μl of solution between a No 1.5 cover slip and coverslide. The thickness of the samples is about 10μm. Thin samples are important to reduce the signal of out-of-focus particles. Samples are equilibrated for half an hour, allowing flows to subside and liquid crystalline defects to anneal. We have analyzed data at various distances from the wall and have not been able to observe a significant influence of wall on the diffusion of viruses. For imaging we used an inverted Nikon TE-2000 microscope equipped with 100× 1.4 NA PlanApo oil immersion objective, a 100W mercury lamp and a fluorescence cube for Alexa 488 fluorescent dye. The images where taken with a cooled CCD Camera (CoolSnap HQ, 694 EUROPHYSICS LETTERS