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We study edge fluctuations of a flat colloidal membrane comprised of a monolayer of aligned filamentous viruses. Experiments reveal that a peak in the spectrum of the in-plane edge fluctuations arises for sufficiently strong virus chirality. Accounting for internal liquid crystalline degrees of freedom by the length, curvature, and geodesic torsion of the edge, we calculate the spectrum of the edge fluctuations. The theory quantitatively describes the experimental data, demonstrating that chirality couples in-plane and out-of-plane edge fluctuations to produce the peak.

In the presence of a nonadsorbing polymer, monodisperse rod-like particles assemble into colloidal membranes, which are one-rod-length-thick liquid-like monolayers of aligned rods. Unlike 3D edgeless bilayer vesicles, colloidal monolayer membranes form open structures with an exposed edge, thus presenting an opportunity to study elasticity of fluid sheets. Membranes assembled from single-component chiral rods form flat disks with uniform edge twist. In comparison, membranes composed of a mixture of rods with opposite chiralities can have the edge twist of either handedness. In this limit, disk-shaped membranes become unstable, instead forming structures with scalloped edges, where two adjacent lobes with opposite handedness are separated by a cusp-shaped point defect. Such membranes adopt a 3D configuration, with cusp defects alternatively located above and below the membrane plane. In the achiral regime, the cusp defects have repulsive interactions, but away from this limit we measure effective long-ranged attractive binding. A phenomenological model shows that the increase in the edge energy of scalloped membranes is compensated by concomitant decrease in the deformation energy due to Gaussian curvature associated with scalloped edges, demonstrating that colloidal membranes have positive Gaussian modulus. A simple excluded volume argument predicts the sign and magnitude of the Gaussian curvature modulus that is in agreement with experimental measurements. Our results provide insight into how the interplay between membrane elasticity, geometrical frustration, and achiral symmetry breaking can be used to fold colloidal membranes into 3D shapes.

Purpose: Noncoplanar plans (NCPs) are commonly used for proton treatment of bilateral head and neck (HN) malignancies. NCP requires additional verification setup imaging between beams to correct residual errors of robotic couch motion, which increases imaging dose and total treatment time. This study compared the quality and robustness of NCPs with those of coplanar plans (CPs). Methods and Materials: Under an IRB‐approved study, CPs were created retrospectively for 10 bilateral HN patients previously treated with NCPs maintaining identical beam geometry of the original plan but excluding couch rotations. Plan robustness to the inter‐fractional variation (IV) of both plans was evaluated through the Dose Volume Histograms (DVH) of weekly quality assurance CT (QACT) sets (39 total). In addition, delivery efficiency for both plans was compared using total treatment time (TTT) and beam‐on time (BOT). Results: No significant differences in plan quality were observed in terms of clinical target volume (CTV) coverage (D95) or organ‐at‐risk (OAR) doses (p > 0.4 for all CTVs and OARs). No significant advantage of NCPs in the robustness to IV was found over CP, either. Changes in D95 of QA plans showed a linear correlation (slope = 1.006, R2 > 0.99) between NCP and CP for three CTV data points (CTV1, CTV2, and CTV3) in each QA plan (117 data points for 39 QA plans). NCPs showed significantly higher beam delivery time than CPs for TTT (539 ± 50 vs. 897 ± 142 s; p < 0.001); however, no significant differences were observed for BOT. Conclusion: NCPs are not more robust to IV than CPs when treating bilateral HN tumors with pencil‐beam scanning proton beams. CPs showed plan quality and robustness similar to NCPs while reduced treatment time (∼6 min). This suggests that CPs may be a more efficient planning technique for bilateral HN cancer proton therapy. [ABSTRACT FROM AUTHOR]

From determining the optical properties of simple molecular crystals to establishing the preferred handedness in highly complex vertebrates, molecular chirality profoundly influences the structural, mechanical and optical properties of both synthetic and biological matter on macroscopic length scales (1, 2). In soft materials such as amphiphilic lipids and liquid crystals, the competition between local chiral interactions and global constraints imposed by the geometry of the self-assembled structures leads to frustration and the assembly of unique materials (3-6). An example of particular interest is smectic liquid crystals, where the two-dimensional layered geometry cannot support twist and chirality is consequently expelled to the edges in a manner analogous to the expulsion of a magnetic field from superconductors (7-10). Here we demonstrate a consequence of this geometric frustration that leads to a new design principle for the assembly of chiral molecules. Using a model system of colloidal membranes (11), we show that molecular chirality can control the interfacial tension, an important property of multi-component mixtures. This suggests an analogy between chiral twist, which is expelled to the edges of two-dimensional membranes, and amphiphilic surfactants, which are expelled to oil-water interfaces (12). As with surfactants, chiral control of interfacial tension drives the formation of many polymorphic assemblages such as twisted ribbons with linear and circular topologies, starfish membranes, and double and triple helices. Tuning molecular chirality insitu allows dynamical control of line tension, which powers polymorphic transitions between various chiral structures. These findings outline a general strategy for the assembly of reconfigurable chiral materials that can easily be moved, stretched, attached to one another and transformed between multiple conformational states, thus allowing precise assembly and nanosculpting of highly dynamical and designable materials with complex topologies., In experiments on chiral self-assembly, we used a two-component mixture consisting of 880-nm-long rod-like fd viruses and the non-adsorbing polymer Dextran. In aqueous suspension, fd viruses alone have purely repulsive [...]

Purpose: A higher minimum monitor unit (minMU) for pencil-beam scanning proton beams in intensity-modulated proton therapy is preferred for more efficient delivery. However, plan quality may be compromised when the minMU is too large. This study aimed to identify the optimal minMU (OminMU) to improve plan delivery efficiency while maintaining high plan quality., Methods: We utilized clinical plans including six anatomic sites (brain, head and neck, breast, lung, abdomen, and prostate) from 23 patients previously treated with the Varian ProBeam system. The minMU of each plan was increased from the current clinical minMU of 1.1 to 3-24 MU depending on the daily prescribed dose (DPD). The dosimetric parameters of the plans were evaluated for consistency against a 1.1-minMU plan for target coverage as well as organs-at-risk dose sparing. DPD/minMU was defined as the ratio of DPD to minMU (cGy/MU) to find the OminMU by ensuring that dosimetric parameters did not differ by >1% compared to those of the 1.1-minMU plan., Results: All plans up to 5 minMU showed no significant dose differences compared to the 1.1-minMU plan. Plan qualities remained acceptable when DPD/minMU ≥35 cGy/MU. This suggests that the 35 cGy/MU criterion can be used as the OminMU, which implies that 5 MU is the OminMU for a conventional fraction dose of 180 cGy. Treatment times were decreased by an average of 32% (max 56%, min 7%) and by an average of 1.6 min when the minMU was increased from 1.1 to OminMU., Conclusion: A clinical guideline for OminMU has been established. The minMU can be increased by 1 MU for every 35 cGy of DPD without compromising plan quality for most cases analyzed in this study. Significant treatment time reduction of up to 56% was observed when the suggested OminMU is used., (© 2024 The Author(s). Journal of Applied Clinical Medical Physics published by Wiley Periodicals LLC on behalf of American Association of Physicists in Medicine.)