Multivalent Diffusive Transport

Enhanced diffusion through multivalency

The diffusion of macromolecules, nanoparticles, viruses, and bacteria is essential for targeting hosts or cellular destinations. While these entities can bind to receptors and ligands on host surfaces, the impact of multiple binding sites-referred to as multivalency-on diffusion along strands or surfaces is poorly understood. Through numerical simulations, we have discovered a significant acceleration in diffusion for particles with increasing valency, while maintaining the same overall affinity to the host surface. This acceleration arises from the redistribution of the binding affinity of the particle across multiple binding ligands. As a result, particles that are immobilized when monovalent can achieve near-unrestricted diffusion upon becoming multivalent. Additionally, we demonstrate that the diffusion of multivalent particles with a rigid ligand distribution can be modulated by patterned host receptors. These findings provide insights into the complex diffusion mechanisms of multivalent particles and biological entities, and offer new strategies for designing advanced nanoparticle systems with tailored diffusion properties, thereby enhancing their effectiveness in applications such as drug delivery and diagnostics.

Hopping and crawling DNA-coated colloids

Understanding the motion of particles with multivalent ligand-receptors is important for biomedical applications and material design. Yet, even among a single design, the prototypical DNA-coated colloids, seemingly similar micrometric particles hop or roll, depending on the study. We shed light on this problem by observing DNA-coated colloids diffusing near surfaces coated with complementary strands for a wide array of coating designs. We find colloids rapidly switch between 2 modes: They hop-with long and fast steps-and crawl-with short and slow steps. Both modes occur at all temperatures around the melting point and over various designs. The particles become increasingly subdiffusive as temperature decreases, in line with subsequent velocity steps becoming increasingly anticorrelated, corresponding to switchbacks in the trajectories. Overall, crawling (or hopping) phases are more predominant at low (or high) temperatures; crawling is also more efficient at low temperatures than hopping to cover large distances. We rationalize this behavior within a simple model: At lower temperatures, the number of bound strands increases, and detachment of all bonds is unlikely, hence, hopping is prevented and crawling favored. We thus reveal the mechanism behind a common design rule relying on increased strand density for long-range self-assembly: Dense strands on surfaces are required to enable crawling, possibly facilitating particle rearrangements.

Motility of an autonomous protein-based artificial motor that operates via a burnt-bridge principle

Inspired by biology, great progress has been made in creating artificial molecular motors. However, the dream of harnessing proteins - the building blocks selected by nature - to design autonomous motors has so far remained elusive. Here we report the synthesis and characterization of the Lawnmower, an autonomous, protein-based artificial molecular motor comprised of a spherical hub decorated with proteases. Its "burnt-bridge" motion is directed by cleavage of a peptide lawn, promoting motion towards unvisited substrate. We find that Lawnmowers exhibit directional motion with average speeds of up to 80 nm/s, comparable to biological motors. By selectively patterning the peptide lawn on microfabricated tracks, we furthermore show that the Lawnmower is capable of track-guided motion. Our work opens an avenue towards nanotechnology applications of artificial protein motors.

Through the Eyes of Creators: Observing Artificial Molecular Motors

Inspired by molecular motors in biology, there has been significant progress in building artificial molecular motors, using a number of quite distinct approaches. As the constructs become more sophisticated, there is also an increasing need to directly observe the motion of artificial motors at the nanoscale and to characterize their performance. Here, we review the most used methods that tackle those tasks. We aim to help experimentalists with an overview of the available tools used for different types of synthetic motors and to choose the method most suited for the size of a motor and the desired measurements, such as the generated force or distances in the moving system. Furthermore, for many envisioned applications of synthetic motors, it will be a requirement to guide and control directed motions. We therefore also provide a perspective on how motors can be observed on structures that allow for directional guidance, such as nanowires and microchannels. Thus, this Review facilitates the future research on synthetic molecular motors, where observations at a single-motor level and a detailed characterization of motion will promote applications.

Sliding across a surface: Particles with fixed and mobile ligands

A quantitative model of the mobility of ligand-presenting particles at the interface is pivotal to understanding important systems in biology and nanotechnology. In this work, we investigate the emerging dynamics of particles featuring ligands that selectively bind receptors decorating an interface. The formation of a ligand-receptor complex leads to a molecular bridge anchoring the particle to the surface. We consider systems with reversible bridges in which ligand-receptor pairs bind/unbind with finite reaction rates. For a given set of bridges, the particle can explore a tiny fraction of the surface as the extensivity of the bridges is finite. We show how, at timescales longer than the bridges' lifetime, the average position of the particle diffuses away from its initial value. We distill our findings into two analytic equations for the sliding diffusion constant of particles carrying mobile and fixed ligands. We quantitatively validate our theoretical predictions using reaction-diffusion simulations. We compare our findings with results from recent literature studies and discuss the molecular parameters that likely affect the particle's mobility most. Our results, along with recent literature studies, will allow inferring the microscopic parameters at play in complex biological systems from experimental trajectories.

The nanocaterpillar's random walk: diffusion with ligand-receptor contacts

Particles with ligand-receptor contacts bind and unbind fluctuating "legs" to surfaces, whose fluctuations cause the particle to diffuse. Quantifying the diffusion of such "nanoscale caterpillars" is a challenge, since binding events often occur on very short time and length scales. Here we derive an analytical formula, validated by simulations, for the long time translational diffusion coefficient of an overdamped nanocaterpillar, under a range of modeling assumptions. We demonstrate that the effective diffusion coefficient, which depends on the microscopic parameters governing the legs, can be orders of magnitude smaller than the background diffusion coefficient. Furthermore it varies rapidly with temperature, and reproduces the striking variations seen in existing data and our own measurements of the diffusion of DNA-coated colloids. Our model gives insight into the mechanism of motion, and allows us to ask: when does a nanocaterpillar prefer to move by sliding, where one leg is always linked to the surface, and when does it prefer to move by hopping, which requires all legs to unbind simultaneously? We compare a range of systems (viruses, molecular motors, white blood cells, protein cargos in the nuclear pore complex, bacteria such as Escherichia coli, and DNA-coated colloids) and present guidelines to control the mode of motion for materials design.