Characterising the diffusion of biological nanoparticles on fluid and cross-linked membranes

An optically fabricated gradient nanochannel array to access the translocation dynamics of T4-phage DNA through nanoconfinement

It has been widely recognized that nanostructures in natural biological materials play important roles in regulating life machinery. Even though nanofabrication techniques such as two-photon polymerization (TPP) provide sub-100 nm fabrication resolution, it remains technologically challenging to produce 3D nanoscale features modeling the complexity in vivo. We herein demonstrate that a nanochannel array carrying different sizes and nanostructures with gradually transitioning dimensions can be easily produced on a slightly tilted nano-stage. Using the gradient nanochannel array, we systematically investigate the factors affecting the dynamics of DNA translocation through nanoconfinement, including the size of biomolecules and geometrical features of the physical environment, which resembles the selectivity of nanopores in the cell membrane. It is observed that T4-phage DNA shows distinctive conformational transition dynamics during translocation through nanochannels driven by electric field or flow, and the deformation energy required for DNA to enter the nanochannels depends on both chemical environmental conditions, i.e., the ionic strength regulating DNA persistence length and nanochannel dimension. In the electric field, DNA repeatedly gets stretched and compressed during its migration through the nanochannel, reflected by elevated fluctuation in extension, which is substantially greater than the thermal fluctuation. However, driven by flow, DNA remains stretched during translocation through nanochannels, and shows variances in extension of merely a few hundred nanometers. These results indicate that the optically fabricated gradient nanochannel array is a suitable platform for optimizing the experimental conditions for biomedical applications such as gene mapping, and verify that production of complex three dimensional (3D) nanostructures can be greatly simplified by including slight inclination during TPP fabrication.

Computational modeling of passive transport of functionalized nanoparticles

Functionalized nanoparticles (NPs) are complex objects present in a variety of systems ranging from synthetic grafted nanoparticles to viruses. The morphology and number of the decorating groups can vary widely between systems. Thus, the modeling of functionalized NPs typically considers simplified spherical objects as a first-order approximation. At the nanoscale label, complex hydrodynamic interactions are expected to emerge as the morphological features of the particles change, and they can be further amplified when the NPs are confined or near walls. Direct estimation of these variations can be inferred via diffusion coefficients of the NPs. However, the evaluation of the coefficients requires an improved representation of the NPs morphology to reproduce important features hidden by simplified spherical models. Here, we characterize the passive transport of free and confined functionalized nanoparticles using the Rigid Multi-Blob (RMB) method. The main advantage of RMB is its versatility to approximate the mobility of complex structures at the nanoscale with significant accuracy and reduced computational cost. In particular, we investigate the effect of functional groups' distribution, size, and morphology over nanoparticle translational and rotational diffusion. We identify that the presence of functional groups significantly affects the rotational diffusion of the nanoparticles; moreover, the morphology of the groups and number induce characteristic mobility reduction compared to non-functionalized nanoparticles. Confined NPs also evidenced important alterations in their diffusivity, with distinctive signatures in the off-diagonal contributions of the rotational diffusion. These results can be exploited in various applications, including biomedical, polymer nanocomposite fabrication, drug delivery, and imaging.

Membrane-Mediated Interactions Between Nonspherical Elastic Particles

The transport of particles across lipid-bilayer membranes is important for biological cells to exchange information and material with their environment. Large particles often get wrapped by membranes, a process which has been intensively investigated in the case of hard particles. However, many particles in vivo and in vitro are deformable, e.g., vesicles, filamentous viruses, macromolecular condensates, polymer-grafted nanoparticles, and microgels. Vesicles may serve as a generic model system for deformable particles. Here, we study nonspherical vesicles with various sizes, shapes, and elastic properties at initially planar lipid-bilayer membranes. Using the Helfrich Hamiltonian, triangulated membranes, and energy minimization, we predict the interplay of vesicle shapes and wrapping states. Increasing particle softness enhances the stability of shallow-wrapped and deep-wrapped states over nonwrapped and complete-wrapped states. The free membrane mediates an interaction between partial-wrapped vesicles. For the pair interaction between deep-wrapped vesicles, we predict repulsion. For shallow-wrapped vesicles, we predict attraction for tip-to-tip orientation and repulsion for side-by-side orientation. Our predictions may guide the design and fabrication of deformable particles for efficient use in medical applications, such as targeted drug delivery.

Protein-coated nanoparticles exhibit Lévy flights on a suspended lipid bilayer

Lateral diffusion of nano-objects on lipid membranes is a crucial process in cell biology. Recent studies indicate that nanoparticle lateral diffusion is affected by the presence of membrane proteins and deviates from Brownian motion. Gold nanoparticles (Au NPs) stabilized by short thiol ligands were dispersed near a free-standing bilayer formed in a 3D microfluidic chip. Using dark-field microscopy, the position of single NPs at the bilayer surface was tracked over time. Numerical analysis of the NP trajectories shows that NP diffusion on the bilayer surface corresponds to Brownian motion. The addition of bovine serum albumin (BSA) protein to the solution led to the formation of a protein corona on the NP surface. We found that protein-coated NPs show anomalous superdiffusion and that the distribution of their relative displacement obeys Lévy flight statistics. This superdiffusive motion is attributed to a drastic reduction in adhesive energies between the NPs and the bilayer in the presence of the protein corona. This hypothesis was confirmed by numerical simulations mimicking the random walk of a single particle near a weakly adhesive surface. These results may be generalized to other classes of nano-objects that experience adsorption-desorption behaviour with a weakly adhesive surface.

Transport of a self-propelled tracer through a hairy cylindrical channel: interplay of stickiness and activity

Active transport of biomolecules assisted by motor proteins is imperative for the proper functioning of cellular activities. Inspired by the diffusion of active agents in crowded cellular channels, we computationally investigate the transport of an active tracer through a polymer grafted cylindrical channel by varying the activity of the tracer and stickiness of the tracer to the polymers. Our results reveal that the passive tracer exhibits profound subdiffusion with increasing stickiness by exploring deep into the grafted polymeric zone, while purely repulsive one prefers to diffuse through the pore-like space created along the cylindrical axis of the channel. In contrast, the active tracer shows faster dynamics and intermediate superdiffusion even though the tracer preferentially stays close to the dense polymeric region. This observation is further supported by the sharp peaks in the density profile of the probability of radial displacement of the tracer. We discover that the activity plays an important role in deciding the pathway that the tracer takes through the narrow channel. Interestingly, increasing the activity washes out the effect of stickiness. Adding to this, van-Hove functions manifest that the active tracer dynamics deviates from Gaussianity, and the degree of deviation grows with the activity. Our work has direct implications on how effective transportation and delivery of cargo can be achieved through a confined medium where activity, interactions, and crowding are interplaying. Looking ahead, these factors will be crucial for understanding the mechanism of artificial self-powered machines navigating through the cellular channels and performing in vivo challenging tasks.

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.

Physical modeling of multivalent interactions in the nuclear pore complex

In the nuclear pore complex, intrinsically disordered proteins (FG Nups), along with their interactions with more globular proteins called nuclear transport receptors (NTRs), are vital to the selectivity of transport into and out of the cell nucleus. Although such interactions can be modeled at different levels of coarse graining, in vitro experimental data have been quantitatively described by minimal models that describe FG Nups as cohesive homogeneous polymers and NTRs as uniformly cohesive spheres, in which the heterogeneous effects have been smeared out. By definition, these minimal models do not account for the explicit heterogeneities in FG Nup sequences, essentially a string of cohesive and noncohesive polymer units, and at the NTR surface. Here, we develop computational and analytical models that do take into account such heterogeneity in a minimal fashion and compare them with experimental data on single-molecule interactions between FG Nups and NTRs. Overall, we find that the heterogeneous nature of FG Nups and NTRs does play a role in determining equilibrium binding properties but is of much greater significance when it comes to unbinding and binding kinetics. Using our models, we predict how binding equilibria and kinetics depend on the distribution of cohesive blocks in the FG Nup sequences and of the binding pockets at the NTR surface, with multivalency playing a key role. Finally, we observe that single-molecule binding kinetics has a rather minor influence on the diffusion of NTRs in polymer melts consisting of FG-Nup-like sequences.

Non-Normalizable Quasi-Equilibrium Solution of the Fokker-Planck Equation for Nonconfining Fields

We investigate the overdamped Langevin motion for particles in a potential well that is asymptotically flat. When the potential well is deep as compared to the temperature, physical observables, like the mean square displacement, are essentially time-independent over a long time interval, the stagnation epoch. However, the standard Boltzmann-Gibbs (BG) distribution is non-normalizable, given that the usual partition function is divergent. For this regime, we have previously shown that a regularization of BG statistics allows for the prediction of the values of dynamical and thermodynamical observables in the non-normalizable quasi-equilibrium state. In this work, based on the eigenfunction expansion of the time-dependent solution of the associated Fokker–Planck equation with free boundary conditions, we obtain an approximate time-independent solution of the BG form, being valid for times that are long, but still short as compared to the exponentially large escape time. The escaped particles follow a general free-particle statistics, where the solution is an error function, which is shifted due to the initial struggle to overcome the potential well. With the eigenfunction solution of the Fokker–Planck equation in hand, we show the validity of the regularized BG statistics and how it perfectly describes the time-independent regime though the quasi-stationary state is non-normalizable.