Substrate stiffness tunes the dynamics of polyvalent rolling motors

Rational engineering of DNA-nanoparticle motor with high speed and processivity comparable to motor proteins

DNA-nanoparticle motor is a burnt-bridge Brownian ratchet moving on RNA-modified surface driven by Ribonuclease H (RNase H), and one of the fastest nanoscale artificial motors. However, its speed is still much lower than those of motor proteins. Here we resolve elementary processes of motion and reveal long pauses caused by slow RNase H binding are the bottleneck. As RNase H concentration ([RNase H]) increases, pause lengths shorten from ~70 s to ~0.2 s, while step sizes (displacements between two consecutive pauses) are constant ( ~ 20 nm). At high [RNase H], speed reaches ~100 nm s-1, however, processivity (total number of steps before detachment), run-length, and unidirectionality largely decrease. A geometry-based kinetic simulation reveals switching of bottleneck from RNase H binding to DNA/RNA hybridization at high [RNase H], and trade-off mechanism between speed and other performances. An engineered motor with 3.8-times larger DNA/RNA hybridization rate simultaneously achieves 30 nm s-1 speed, 200 processivity, and 3 μm run-length comparable to motor proteins.

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.

Within-host evolution of SARS-CoV-2: how often are de novo mutations transmitted from symptomatic infections?

Despite a relatively low mutation rate, the large number of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) infections has allowed for substantial genetic change, leading to a multitude of emerging variants. Using a recently determined mutation rate (per site replication), as well as within-host parameter estimates for symptomatic SARS-CoV-2 infection, we apply a stochastic transmission-bottleneck model to describe the survival probability of de novo SARS-CoV-2 mutations as a function of bottleneck size and selection coefficient. For narrow bottlenecks, we find that mutations affecting per-target-cell attachment rate (with phenotypes associated with fusogenicity and ACE2 binding) have similar transmission probabilities to mutations affecting viral load clearance (with phenotypes associated with humoral evasion). We further find that mutations affecting the eclipse rate (with phenotypes associated with reorganization of cellular metabolic processes and synthesis of viral budding precursor material) are highly favoured relative to all other traits examined. We find that mutations leading to reduced removal rates of infected cells (with phenotypes associated with innate immune evasion) have limited transmission advantage relative to mutations leading to humoral evasion. Predicted transmission probabilities, however, for mutations affecting innate immune evasion are more consistent with the range of clinically estimated household transmission probabilities for de novo mutations. This result suggests that although mutations affecting humoral evasion are more easily transmitted when they occur, mutations affecting innate immune evasion may occur more readily. We examine our predictions in the context of a number of previously characterized mutations in circulating strains of SARS-CoV-2. Our work offers both a null model for SARS-CoV-2 mutation rates and predicts which aspects of viral life history are most likely to successfully evolve, despite low mutation rates and repeated transmission bottlenecks.

Limits on the Precision of Catenane Molecular Motors: Insights from Thermodynamics and Molecular Dynamics Simulations

Thermodynamic uncertainty relations (TURs) relate precision to the dissipation rate, yet the inequalities can be far from saturation. Indeed, in catenane molecular motor simulations, we record precision far below the TUR limit. We further show that this inefficiency can be anticipated by four physical parameters: the thermodynamic driving force, fuel decomposition rate, coupling between fuel decomposition and motor motion, and rate of undriven motor motion. The physical insights might assist in designing molecular motors in the future.

Adhesive Dynamics Simulations of Highly Polyvalent DNA Motors

Molecular motors, such as myosin and kinesin, perform diverse tasks ranging from vesical transport to bulk muscle contraction. Synthetic molecular motors may eventually be harnessed to perform similar tasks in versatile synthetic systems. The most promising type of synthetic molecular motor, the DNA walker, can undergo processive motion but generally exhibits low speeds and virtually no capacity for force generation. However, we recently showed that highly polyvalent DNA motors (HPDMs) can rival biological motors by translocating at micrometer per minute speeds and generating 100+ pN of force. Accordingly, DNA nanotechnology-based designs may hold promise for the creation of synthetic, force-generating nanomotors. However, the dependencies of HPDM speed and force on tunable design parameters are poorly understood and difficult to characterize experimentally. To overcome this challenge, we present RoloSim, an adhesive dynamics software package for fine-grained simulations of HPDM translocation. RoloSim uses biophysical models for DNA duplex formation and dissociation kinetics to explicitly model tens of thousands of molecular scale interactions. These molecular interactions are then used to calculate the nano- and microscale motions of the motor. We use RoloSim to uncover how motor force and speed scale with several tunable motor properties such as motor size and DNA duplex length. Our results support our previously defined hypothesis that force scales linearly with polyvalency. We also demonstrate that HPDMs can be steered with external force, and we provide design parameters for novel HPDM-based molecular sensor and nanomachine designs.

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.

Physics of self-rolling viruses

Viruses are right at the interface of inanimate matter and life. However, recent experiments [Sakai et al., J. Virol. 92, e01522-17 (2018)0022-538X10.1128/JVI.01522-17] have shown that some influenza strains can actively roll on glycan-covered surfaces. In a previous letter [Ziebert and Kulić, Phys. Rev. Lett. 126, 218101 (2021)0031-900710.1103/PhysRevLett.126.218101] we suggested this to be a form of viral surface metabolism: a collection of spike proteins that attach to and cut the glycans act as a self-organized mechano-chemical motor. Here we study in more depth the physics of the emergent self-rolling states. We give scaling arguments how the motion arises, substantiated by a detailed analytical theory that yields the full torque-angular velocity relation of the self-organized motor. Stochastic Gillespie simulations are used to validate the theory and to quantify stochastic effects like virus detachment and reversals of its direction. Finally, we also cross-check several approximations made previously and show that the proposed mechanism is very robust. All these results point together to the statistical inevitability of viral rolling in the presence of enzymatic activity.

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.

Durotaxis of Passive Nanoparticles on Elastic Membranes

The transport of macromolecules and nanoscopic particles to a target cellular site is a crucial aspect in many physiological processes. This directional motion is generally controlled via active mechanical and chemical processes. Here we show, by means of molecular dynamics simulations and an analytical theory, that completely passive nanoparticles can exhibit directional motion when embedded in nonuniform mechanical environments. Specifically, we study the motion of a passive nanoparticle adhering to a mechanically nonuniform elastic membrane. We observe a nonmonotonic affinity of the particle to the membrane as a function of the membrane's rigidity, which results in the particle transport. This transport can be both up or down the rigidity gradient, depending on the absolute values of the rigidities that the gradient spans across. We conclude that rigidity gradients can be used to direct average motion of passive macromolecules and nanoparticles on deformable membranes, resulting in the preferential accumulation of the macromolecules in regions of certain mechanical properties.

Toward Chemotactic Supramolecular Nanoparticles: From Autonomous Surface Motion Following Specific Chemical Gradients to Multivalency-Controlled Disassembly

Nature designs chemotactic supramolecular structures that can selectively bind specific groups present on surfaces, autonomously scan them moving along density gradients, and react once a critical concentration is encountered. Since such properties are key in many biological functions, these also offer inspirations for designing artificial systems capable of similar bioinspired autonomous behaviors. One approach is to use soft molecular units that self-assemble in an aqueous solution generating nanoparticles (NPs) that display specific chemical groups on their surface, enabling multivalent interactions with complementarily functionalized surfaces. However, a first challenge is to explore the behavior of these assemblies at sufficiently high-resolution to gain insights on the molecular factors controlling their behaviors. Here, by coupling coarse-grained molecular models and advanced simulation approaches, we show that it is possible to study the (autonomous or driven) motion of self-assembled NPs on a receptor-grafted surface at submolecular resolution. As an example, we focus on self-assembled NPs composed of facially amphiphilic oligomers. We observe how tuning the multivalent interactions between the NP and the surface allows to control of the NP binding, its diffusion along chemical surface gradients, and ultimately, the NP reactivity at determined surface group densities. In silico experiments provide physical-chemical insights on key molecular features in the self-assembling units which determine the dynamic behavior and fate of the NPs on the surface: from adhesion, to diffusion, and disassembly. This offers a privileged point of view into the chemotactic properties of supramolecular assemblies, improving our knowledge on how to design new types of materials with bioinspired autonomous behaviors.

Durotaxis of Passive Nanoparticles on Elastic Membranes

The transport of macromolecules and nanoscopic particles to a target cellular site is a crucial aspect in many physiological processes. This directional motion is generally controlled via active mechanical and chemical processes. Here we show, by means of molecular dynamics simulations and an analytical theory, that completely passive nanoparticles can exhibit directional motion when embedded in nonuniform mechanical environments. Specifically, we study the motion of a passive nanoparticle adhering to a mechanically nonuniform elastic membrane. We observe a nonmonotonic affinity of the particle to the membrane as a function of the membrane's rigidity, which results in the particle transport. This transport can be both up or down the rigidity gradient, depending on the absolute values of the rigidities that the gradient spans across. We conclude that rigidity gradients can be used to direct average motion of passive macromolecules and nanoparticles on deformable membranes, resulting in the preferential accumulation of the macromolecules in regions of certain mechanical properties.

Burnt bridge ratchet motor force scales linearly with polyvalency: a computational study

Nano- and micro-scale burnt bridge ratchet motors, which translocate via "guide" molecules that bind to and degrade a field of "fuel" molecules, have recently emerged in several biological and engineering contexts. The capacity of these motors to generate mechanical forces remains an open question. Here, chemomechanical modeling suggests that BBR force scales linearly with the steady-state number of guide-fuel bonds.

Multivalent Diffusive Transport

We present here a model for multivalent diffusive transport whereby a central point-like hub is coupled to multiple feet, which bind to complementary sites on a two-dimensional landscape. The available number of binding interactions is dependent on the number of feet (multivalency) and on their allowed distance from the central hub (span). Using Monte Carlo simulations that implement the Gillespie algorithm, we simulate multivalent diffusive transport processes for 100 distinct walker designs. Informed by our simulation results, we derive an analytical expression for the diffusion coefficient of a general multivalent diffusive process as a function of multivalency, span, and dissociation constant K_d. Our findings can be used to guide the experimental design of multivalent transporters, in particular, providing insight into how to overcome trade-offs between diffusivity and processivity.

AutoSmarTrace: Automated chain tracing and flexibility analysis of biological filaments

Single-molecule imaging is widely used to determine statistical distributions of molecular properties. One such characteristic is the bending flexibility of biological filaments, which can be parameterized via the persistence length. Quantitative extraction of persistence length from images of individual filaments requires both the ability to trace the backbone of the chains in the images and sufficient chain statistics to accurately assess the persistence length. Chain tracing can be a tedious task, performed manually or using algorithms that require user input and/or supervision. Such interventions have the potential to introduce user-dependent bias into the chain selection and tracing. Here, we introduce a fully automated algorithm for chain tracing and determination of persistence lengths. Dubbed "AutoSmarTrace," the algorithm is built off a neural network, trained via machine learning to identify filaments within images recorded using atomic force microscopy. We validate the performance of AutoSmarTrace on simulated images with widely varying levels of noise, demonstrating its ability to return persistence lengths in agreement with input simulation parameters. Persistence lengths returned from analysis of experimental images of collagen and DNA agree with previous values obtained from these images with different chain-tracing approaches. Although trained on atomic-force-microscopy-like images, the algorithm also shows promise to identify chains in other single-molecule imaging approaches, such as rotary-shadowing electron microscopy and fluorescence imaging.