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Nature has evolved many mechanisms for achieving directed motion on the subcellular level. The burnt-bridges ratchet (BBR) is one mechanism used to achieve superdiffusive molecular motion over long distances through the successive cleavage of surface-bound energy-rich substrate sites. This mechanism has been associated with both nanoscale and microscale movement, with the latter accomplished through polyvalent interactions between a large hub (e.g. influenza virus) and substrate (e.g. cell surface receptors). Experimental successes in achieving superdiffusive motion by synthetic polyvalent BBRs have raised questions about the dynamics of their motility, including whether rolling or translation is better able to direct motion of microscale spherical hubs. Here we simulate the three-dimensional dynamics of a polyvalent sphere moving on and cleaving an elastic substrate. We find that substrate stiffness plays an important role in controlling both the motor's mode of motility and its directional persistence. As we tune lateral substrate stiffness from soft to stiff we find there exists an intermediate value that optimizes rolling behaviour. We also find that there is an optimal substrate stiffness for maximizing persistence length, while stiffness does not influence as strongly the superdiffusive dynamics of the particle. Lastly, we examine the effect of substrate density, and show that softer landscapes are better able to buffer against decreases in substrate occupancy, with the spherical motor maintaining superdiffusive motion more on softer landscapes than on stiff landscapes as occupancy drops. Our results highlight the importance of surface in controlling the motion of polyvalent BBRs.

The mean-squared displacement (MSD) is an averaged quantity widely used to assess anomalous diffusion. In many cases, such as molecular motors with finite processivity, dynamics of the system of interest produce trajectories of varying duration. Here we explore the effects of finite processivity on different measures of the MSD. We do so by investigating a deceptively simple dynamical system: a one-dimensional random walk (with equidistant jump lengths, symmetric move probabilities, and constant step duration) with an origin-directed detachment bias. By tuning the time dependence of the detachment bias, we find through analytical calculations and trajectory simulations that the system can exhibit a broad range of anomalous diffusion, extending beyond conventional diffusion to superdiffusion and even superballistic motion. We analytically determine that protocols with a time-increasing detachment lead to an ensemble-averaged velocity increasing in time, thereby providing the effective acceleration that is required to push the system above the ballistic threshold. MSD analysis of burnt-bridges ratchets similarly reveals superballistic behavior. Because superdiffusive MSDs are often used to infer biased, motor-like dynamics, these findings provide a cautionary tale for dynamical interpretation.

Two approaches to using optical floating zone (OFZ) technique for single crystal growth of the perovskite Pr1−xLaxAlO3 are discussed, along with the influence on the physical properties of the resulting single crystals due to oxidizing and reducing post anneals. In method one (M1) we used pre-reduced Pr2O3 powder starting material, while in the other method, M2, we employed an argon 5% hydrogen reducing environment during the floating zone single crystal growth. Magnetic susceptibility of the low temperature monoclinic phase of Pr0.2La0.8AlO3 is shown to be sensitive to the precise annealing protocol followed. For the post-growth reduced single crystal the magnetic susceptibility is flat across the R-3c to C2/m structural transition, whereas the oxidized and as-grown samples display a sharp upturn and downturn, respectively. We attribute the low temperature susceptibility differences to relative proportions of Pr3+ and Pr4+.

Many experiments and applications require the chemical coupling of target molecules to surfaces, during which the elimination of nonspecific interactions presents a difficult challenge. We report on a technologically accessible surface passivation and chemical conjugation method based on an NHS end-labeled F127 Pluronic block copolymer (F127-NHS). To quantify interactions between the F127-NHS surface and magnetic microspheres, we developed a simple assay: the microsphere adhesion by gravity, inversion, then counting, or "MAGIC" assay. To improve blocking of microspheres while maintaining the ability to chemically couple additional molecules, we implemented a pH-dependent two-step chemical modification process for amine microspheres. This process achieves an extremely high level of blocking nonspecific interactions (less than 2% nonspecific adhesion) for a variety of microsphere surface charges and chemical functionalities. We also demonstrate the ability to specifically tether magnetic microspheres to an F127-NHS surface, using single DNA molecules. Using the DNA microspheres, we establish the applicability of the surface for force spectroscopy (stable with an applied load >30 pN) via the massively parallel technique of centrifuge force microscopy. Finally, we demonstrate that the surface can be used in fluorescence studies with a fluorogenic peptide cleavage assay, with high levels of blocking achieved for both the fluorogenic peptide and trypsin. These results suggest applications including, but not limited to, single-molecule force spectroscopy and fluorescence, biosensors, medical implants, and anti-biofouling, which could make use of the F127-NHS surface.

The burnt-bridges ratchet (BBR) mechanism is a model for biased molecular motion whereby the construct destroys track binding sites as it progresses, and therefore acts as a diffusing forager, seeking new substrate sites. Using Monte Carlo simulations that implement the Gillespie algorithm, we investigate the kinetic characteristics of simple polyvalent BBRs as they move on tracks of increasing width. We find that as the track width is increased the BBRs remain nearly ballistic for considerable track widths proportional to the span (leg length) of the polyvalent walker, before transitioning to near-conventional diffusion on two-dimensional tracks. We find there exists a tradeoff in BBR track association time and superdiffusivity in the BBR design parameter space of span, polyvalency and track width. Furthermore, we develop an analytical model to describe the ensembleaverage motion on the track and find it is in good agreement with our Gillespie simulation results. This work offers insights into design criteria for de novo BBRs and their associated tracks, where experimentalists seek to optimize directionality and track association time., Includes SI, but not supporting movies