How things get stuck: kinetics, elastohydrodynamics, and soft adhesion

Size-Dependent Diffusion and Dispersion of Particles in Mucin

Mucus, composed significantly of glycosylated mucins, is a soft and rheologically complex material that lines respiratory, reproductive, and gastrointestinal tracts in mammals. Mucus may present as a gel, as a highly viscous fluid, or as a viscoelastic fluid. Mucus acts as a barrier to the transport of harmful microbes and inhaled atmospheric pollutants to underlying cellular tissue. Studies on mucin gels have provided critical insights into the chemistry of the gels, their swelling kinetics, and the diffusion and permeability of molecular constituents such as water. The transport and dispersion of micron and sub-micron particles in mucin gels and solutions, however, differs from the motion of small molecules since the much larger tracers may interact with microstructure of the mucin network. Here, using brightfield and fluorescence microscopy, high-speed particle tracking, and passive microrheology, we study the thermally driven stochastic movement of 0.5-5.0 μm tracer particles in 10% mucin solutions at neutral pH, and in 10% mucin mixed with industrially relevant dust; specifically, unmodified limestone rock dust, modified limestone, and crystalline silica. Particle trajectories are used to calculate mean square displacements and the displacement probability distributions; these are then used to assess tracer diffusion and transport. Complex moduli are concomitantly extracted using established microrheology techniques. We find that under the conditions analyzed, the reconstituted mucin behaves as a weak viscoelastic fluid rather than as a viscoelastic gel. For small- to moderately sized tracers with a diameter of lessthan 2 μm, we find that effective diffusion coefficients follow the classical Stokes-Einstein relationship. Tracer diffusivity in dust-laden mucin is surprisingly larger than in bare mucin. Probability distributions of mean squared displacements suggest that heterogeneity, transient trapping, and electrostatic interactions impact dispersion and overall transport, especially for larger tracers. Our results motivate further exploration of physiochemical and rheological mechanisms mediating particle transport in mucin solutions and gels.

Matrix Stiffness Modulates Mechanical Interactions and Promotes Contact between Motile Cells

The mechanical micro-environment of cells and tissues influences key aspects of cell structure and function, including cell motility. For proper tissue development, cells need to migrate, interact, and form contacts. Cells are known to exert contractile forces on underlying soft substrates and sense deformations in them. Here, we propose and analyze a minimal biophysical model for cell migration and long-range cell–cell interactions through mutual mechanical deformations of the substrate. We compute key metrics of cell motile behavior, such as the number of cell-cell contacts over a given time, the dispersion of cell trajectories, and the probability of permanent cell contact, and analyze how these depend on a cell motility parameter and substrate stiffness. Our results elucidate how cells may sense each other mechanically and generate coordinated movements and provide an extensible framework to further address both mechanical and short-range biophysical interactions.

Synchronized oscillations, traveling waves, and jammed clusters induced by steric interactions in active filament arrays

Autonomous active, elastic filaments that interact with each other to achieve cooperation and synchrony underlie many critical functions in biology. The mechanisms underlying this collective response and the essential ingredients for stable synchronization remain a mystery. Inspired by how these biological entities integrate elasticity with molecular motor activity to generate sustained oscillations, a number of synthetic active filament systems have been developed that mimic oscillations of these biological active filaments. Here, we describe the collective dynamics and stable spatiotemporal patterns that emerge in such biomimetic multi-filament arrays, under conditions where steric interactions may impact or dominate the collective dynamics. To focus on the role of steric interactions, we study the system using Brownian dynamics, without considering long-ranged hydrodynamic interactions. The simulations treat each filament as a connected chain of self-propelling colloids. We demonstrate that short-range steric inter-filament interactions and filament roughness are sufficient - even in the absence of inter-filament hydrodynamic interactions - to generate a rich variety of collective spatiotemporal oscillatory, traveling and static patterns. We first analyze the collective dynamics of two- and three-filament clusters and identify parameter ranges in which steric interactions lead to synchronized oscillations and strongly occluded states. Generalizing these results to large one-dimensional arrays, we find rich emergent behaviors, including traveling metachronal waves, and modulated wavetrains that are controlled by the interplay between the array geometry, filament activity, and filament elasticity. Interestingly, the existence of metachronal waves is non-monotonic with respect to the inter-filament spacing. We also find that the degree of filament roughness significantly affects the dynamics - specifically, filament roughness generates a locking-mechanism that transforms traveling wave patterns into statically stuck and jammed configurations. Taken together, simulations suggest that short-ranged steric inter-filament interactions could combine with complementary hydrodynamic interactions to control the development and regulation of oscillatory collective patterns. Furthermore, roughness and steric interactions may be critical to the development of jammed spatially periodic states; a spatiotemporal feature not observed in purely hydrodynamically interacting systems.

Kinetic of Adhesion of S. epidermidis with Different EPS Production on Ti6Al4V Surfaces

Controlling initial bacterial adhesion is essential to prevent biofilm formation and implant-related infection. The search for surface coatings that prevent initial adhesion is a powerful strategy to obtain implants that are more resistant to infection. Tracking the progression of adhesion on surfaces from the beginning of the interaction between bacteria and the surface provides a deeper understanding of the initial adhesion behavior. To this purpose, we have studied the progression over time of bacterial adhesion from a laminar flow of a bacterial suspension, using a modified Robbins device (MRD). Comparing with other laminar flow devices, such as the parallel plate flow chamber, MRD allows the use of diverse substrata under the same controlled flow conditions simultaneously. Two different surfaces of Ti6Al4V and two strains of Staphylococcus epidermidis with different exopolymer production were tested. In addition, the modified Robbins device was examined for its convenience and suitability for the purpose of this study. Results were analyzed according to a pseudofirst order kinetic. The values of the parameters obtained from this model make it possible to discriminate the adhesive behavior of surfaces and bacteria. One of the fitting parameters depends on the bacterial strain and the other only on the surface properties of the substrate.

Mechanical Contact Spectroscopy: Characterizing Nanoscale Adhesive Contacts via Thermal Forces

The adhesion of micro- and nanoparticles to solid substrates immersed in liquids is a problem of great scientific and technological importance. However, the quantitative characterization of such nanoscale adhesive contacts without rupturing them still presents a major experimental challenge. In this article, we introduce mechanical contact spectroscopy (MCS), an experimental technique for the nondestructive probing of particle adhesion in liquid environments. With MCS, the strength of adhesive contacts is inferred from residual position fluctuations of adherent particles excited by thermal forces. In particular, the strength of adhesion is correlated with the standard deviation of the particle lateral position x, with smaller position standard deviations [Formula: see text] indicating higher adhesive strength. For a given combination of particles, substrate, and immersion medium, the adhesion is characterized by the mechanical contact spectrum, which is a histogram of ξ values obtained from tracking an ensemble of adherent particles. Because the energy of thermal excitation at room temperature is very small in comparison to the typical total energy of adhesive contacts, the studied contacts remain in equilibrium during the measurement. Using MCS, we study the adhesion of micrometer-sized particles to planar solid substrates under a wide range of environmental conditions, including liquid immersion media of varying ionic strength and adhesion substrates with different chemical functionality of their surfaces. These experiments provide evidence that MCS is capable of reproducibly detecting minute changes in the particle-substrate work of adhesion while at the same time covering the range of adhesive contact strength relevant in the context of surface chemistry, biology, and microfabrication.

Hydrodynamics of transient cell-cell contact: The role of membrane permeability and active protrusion length

In many biological settings, two or more cells come into physical contact to form a cell-cell interface. In some cases, the cell-cell contact must be transient, forming on timescales of seconds. One example is offered by the T cell, an immune cell which must attach to the surface of other cells in order to decipher information about disease. The aspect ratio of these interfaces (tens of nanometers thick and tens of micrometers in diameter) puts them into the thin-layer limit, or "lubrication limit", of fluid dynamics. A key question is how the receptors and ligands on opposing cells come into contact. What are the relative roles of thermal undulations of the plasma membrane and deterministic forces from active filopodia? We use a computational fluid dynamics algorithm capable of simulating 10-nanometer-scale fluid-structure interactions with thermal fluctuations up to seconds- and microns-scales. We use this to simulate two opposing membranes, variously including thermal fluctuations, active forces, and membrane permeability. In some regimes dominated by thermal fluctuations, proximity is a rare event, which we capture by computing mean first-passage times using a Weighted Ensemble rare-event computational method. Our results demonstrate a parameter regime in which the time it takes for an active force to drive local contact actually increases if the cells are being held closer together (e.g., by nonspecific adhesion), a phenomenon we attribute to the thin-layer effect. This leads to an optimal initial cell-cell separation for fastest receptor-ligand binding, which could have relevance for the role of cellular protrusions like microvilli. We reproduce a previous experimental observation that fluctuation spatial scales are largely unaffected, but timescales are dramatically slowed, by the thin-layer effect. We also find that membrane permeability would need to be above physiological levels to abrogate the thin-layer effect.

Modeling the relative dynamics of DNA-coated colloids

We construct a theoretical model for the dynamics of a microscale colloidal particle, modeled as an interval, moving horizontally on a DNA-coated surface, modelled as a line coated with springs that can stick to the interval. Averaging over the fast DNA dynamics leads to an evolution equation for the particle in isolation, which contains both friction and diffusion. The DNA-induced friction coefficient depends on the physical properties of the DNA, and substituting parameter values typical of a 1 μm colloid coated densely with weakly interacting DNA gives a coefficient about 100 times larger than the corresponding coefficient of hydrodynamic friction. We use a mean-field extension of the model to higher dimensions to estimate the friction tensor for a disc rotating and translating horizontally along a line. When the DNA strands are very stiff and short, the friction coefficient for the disc rolling approaches zero while the friction for the disc sliding remains large. Together, these results could have significant implications for the dynamics of DNA-coated colloids or other ligand-receptor systems, implying that DNA-induced friction between colloids can be stronger than hydrodynamic friction and should be incorporated into simulations, and that it depends nontrivially on the type of relative motion, possibly causing the particles to assemble into out-of-equilibrium metastable states governed by the pathways with the least friction.

Long ligands reinforce biological adhesion under shear flow

In this work, computer modeling has been used to show that longer ligands allow biological cells (e.g., blood platelets) to withstand stronger flows after their adhesion to solid walls. A mechanistic model of polymer-mediated ligand-receptor adhesion between a microparticle (cell) and a flat wall has been developed. The theoretical threshold between adherent and non-adherent regimes has been derived analytically and confirmed by simulations. These results lead to a deeper understanding of numerous biophysical processes, e.g., arterial thrombosis, and to the design of new biomimetic colloid-polymer systems.

Rolling and aging in temperature-ramp soft adhesion

Immediately before adsorption to a horizontal substrate, sinking polymer-coated colloids can undergo a complex sequence of landing, jumping, crawling, and rolling events. Using video tracking, we studied the soft adhesion to a horizontal flat plate of micron-size colloids coated by a controlled molar fraction f of the poly(lysine)-grafted-poly(N-isopropylacrylamide) (PLL-g-PNIPAM) which is a temperature-sensitive polymer. We ramp the temperature from below to above T_{c}=32±1^{∘}C, at which the PNIPAM polymer undergoes a transition, triggering attractive interaction between microparticles and surface. The adsorption rate, the effective in-plane (x-y) diffusion constant, and the average residence time distribution over z were extracted from the Brownian motion records during last seconds before immobilization. Experimental data are understood within a rate-equations-based model that includes aging effects and includes three populations: the untethered, the rolling, and the arrested colloids. We show that preadsorption dynamics casts a characteristic scaling function α(f) proportional to the number of available PNIPAM patches met by soft contact during Brownian rolling. In particular, the increase of in-plane diffusivity with increasing f is understood: The stickiest particles have the shortest rolling regime prior to arrest, so that their motion is dominated by the untethered phase.

Stochastic disks that roll

We study a model of rolling particles subject to stochastic fluctuations, which may be relevant in systems of nano- or microscale particles where rolling is an approximation for strong static friction. We consider the simplest possible nontrivial system: a linear polymer of three disks constrained to remain in contact and immersed in an equilibrium heat bath so the internal angle of the polymer changes due to stochastic fluctuations. We compare two cases: one where the disks can slide relative to each other and the other where they are constrained to roll, like gears. Starting from the Langevin equations with arbitrary linear velocity constraints, we use formal homogenization theory to derive the overdamped equations that describe the process in configuration space only. The resulting dynamics have the formal structure of a Brownian motion on a Riemannian or sub-Riemannian manifold, depending on if the velocity constraints are holonomic or nonholonomic. We use this to compute the trimer's equilibrium distribution with and without the rolling constraints. Surprisingly, the two distributions are different. We suggest two possible interpretations of this result: either (i) dry friction (or other dissipative, nonequilibrium forces) changes basic thermodynamic quantities like the free energy of a system, a statement that could be tested experimentally, or (ii) as a lesson in modeling rolling or friction more generally as a velocity constraint when stochastic fluctuations are present. In the latter case, we speculate there could be a "roughness" entropy whose inclusion as an effective force could compensate the constraint and preserve classical Boltzmann statistics. Regardless of the interpretation, our calculation shows the word "rolling" must be used with care when stochastic fluctuations are present.

Ligand-mediated adhesive mechanics of two static, deformed spheres

A self-consistent model is developed to investigate attachment/detachment kinetics of two static, deformable microspheres with irregular surface and coated with flexible binding ligands. The model highlights how the microscale binding kinetics of these ligands as well as the attractive/repulsive potential of the charged surface affects the macroscale static deformed configuration of the spheres. It is shown that in the limit of smooth, neutrally charged surface (i.e., the dimensionless inverse Debye length, [Formula: see text]), interacting via elastic binders (i.e., the dimensionless stiffness coefficient, [Formula: see text]) the adhesion mechanics approaches the regime of application of the JKR theory, and in this particular limit, the contact radius, R_c, scales with the particle radius, R, according to the scaling law, [Formula: see text]. We show that static, deformed, highly charged, ligand-coated surface of micro-spheres exhibit strong adhesion. Normal stress distribution within the contact area adjusts with the binder stiffness coefficient, from a maximum at the center to a maximum at the periphery of the region. Although reported in some in vitro experiments involving particle adhesion, until now a physical interpretation for this variation of the stress distribution for deformable, charged, ligand-coated microspheres is missing. Surface roughness results in a diminished adhesion with a distinct reduction in the pull-off force, larger separation gap, weaker normal stress and limited area of adhesion. These results are in agreement with the published experimental findings.

Hydrogel-colloid interfacial interactions: a study of tailored adhesion using optical tweezers

Dynamics of colloidal particles adhering to soft, deformable substrates, such as tissues, biofilms, and hydrogels play a key role in many biological and biomimetic processes. These processes, including, but not limited to colloid-based delivery, stitching, and sorting, involve microspheres exploring the vicinity of soft, sticky materials in which the colloidal dynamics are affected by the fluid environment (e.g., viscous coupling), inter-molecular interactions between the colloids and substrates (e.g., Derjaguin-Landau-Verwey-Overbeek (DLVO) theory), and the viscoelastic properties of contact region. To better understand colloidal dynamics at soft interfaces, an optical tweezers back-focal-plane interferometry apparatus was developed to register the transverse Brownian motion of a silica microsphere in the vicinity of polyacrylamide (PA) hydrogel films. The time-dependent mean-squared displacements are well described by a single exponential relaxation, furnishing measures of the transverse interfacial diffusion coefficient and binding stiffness. Substrates with different elasticities were prepared by changing the PA crosslinking density, and the inter-molecular interactions were adjusted by coating the microspheres with fluid membranes. Stiffer PA hydrogels (with bulk Young's moduli ≈1-10 kPa) immobilize the microspheres more firmly (lower diffusion coefficient and position variance), and coating the particles with zwitterionic lipid bilayers (DOPC) completely eliminates adhesion, possibly by repulsive dispersion forces. Remarkably, embedding polyethylene glycol-grafted lipid bilayers (DSPE-PEG2k-Amine) in the zwitterionic fluid membranes produces stronger adhesion, possibly because of polymer-hydrogel attraction and entanglement. This study provides new insights to guide the design of nanoparticles and substrates with tunable adhesion, leading to smarter delivery, sorting, and screening of micro- and nano-systems.

Surface deformation and shear flow in ligand mediated cell adhesion

We present a unified, multiscale model to study the attachment/detachment dynamics of two deforming, charged, near spherical cells, coated with binding ligands and subject to a slow, homogeneous shear flow in a viscous, ionic fluid medium. The binding ligands on the surface of the cells experience both attractive and repulsive forces in an ionic medium and exhibit finite resistance to rotation via bond tilting. The microscale drag forces and couples describing the fluid flow inside the small separation gap between the cells, are calculated using a combination of methods in lubrication theory and previously published numerical results. For a selected range of material and fluid parameters, a hysteretic transition of the sticking probability curves (i.e., the function [Formula: see text]) between the adhesion phase (when [Formula: see text]) and the fragmentation phase (when [Formula: see text]) is attributed to a nonlinear relation between the total nanoscale binding forces and the separation gap between the cells. We show that adhesion is favoured in highly ionic fluids, increased deformability of the cells, elastic binders and a higher fluid shear rate (until a critical threshold value of shear rate is reached). Within a selected range of critical shear rates, the continuation of the limit points (i.e., the turning points where the slope of [Formula: see text] changes sign) predict a bistable region, indicating an abrupt switching between the adhesion and the fragmentation regimes. Although, bistability in the adhesion-fragmentation phase diagram of two deformable, charged cells immersed in an ionic aqueous environment has been identified by some in vitro experiments, but until now, has not been quantified theoretically.

Pressure-driven occlusive flow of a confined red blood cell

When red blood cells (RBCs) move through narrow capillaries in the microcirculation, they deform as they flow. In pathophysiological processes such as sickle cell disease and malaria, RBC motion and flow are severely restricted. To understand this threshold of occlusion, we use a combination of experiment and theory to study the motion of a single swollen RBC through a narrow glass capillary of varying inner diameter. By tracking the movement of the squeezed cell as it is driven by a controlled pressure drop, we measure the RBC velocity as a function of the pressure gradient as well as the local capillary diameter, and find that the effective blood viscosity in this regime increases with both decreasing RBC velocity and tube radius by following a power-law that depends upon the length of the confined cell. Our observations are consistent with a simple elasto-hydrodynamic model and highlight the role of lateral confinement in the occluded pressure-driven slow flow of soft confined objects.

Elastohydrodynamics and Kinetics of Protein Patterning in the Immunological Synapse

We propose a minimal mathematical model for the physical basis of membrane protein patterning in the immunological synapse (IS), which encompass membrane mechanics, protein binding kinetics and motion, and fluid flow in the synaptic cleft. Our theory leads to simple predictions for the spatial and temporal scales of protein cluster formation, growth and arrest as a function of membrane stiffness, rigidity and kinetics of the adhesive proteins, and the fluid flow in the synaptic cleft. Numerical simulations complement these scaling laws by quantifying the nucleation, growth and stabilization of proteins domains on the size of the cell. Direct comparison with experiment shows that passive elastohydrodynamics and kinetics of protein binding in the synaptic cleft can describe the short-time formation and organization of protein clusters, without evoking any active processes in the cytoskeleton. Despite the apparent complexity of the process, our analysis shows that just two dimensionless parameters characterize the spatial and temporal evolution of the protein pattern: a ratio of membrane elasticity to protein stiffness, and the ratio of a hydrodynamic time scale for fluid flow relative to the protein binding rate. A simple phase diagram encompasses the variety of patterns that can arise.

The speed of an inclined ruck

Steady rucks in an elastic beam can roll at constant speed down an inclined plane. We examine the dynamics of these travelling-wave structures and argue that their speed can be dictated by a combination of the physical conditions arising in the vicinity of the 'contact points' where the beam is peeled off the underlying plane and stuck back down. We provide three detailed models for the contact dynamics: viscoelastic fracture, a thermodynamic model for bond formation and detachment and adhesion mediated by a thin liquid film. The results are compared with experiments.

Sticky surface: sphere-sphere adhesion dynamics

We present a multi-scale model to study the attachment of spherical particles with a rigid core, coated with binding ligands and suspended in the surrounding, quiescent fluid medium. This class of fluid-immersed adhesion is widespread in many natural and engineering settings, particularly in microbial surface adhesion. Our theory highlights how the micro-scale binding kinetics of these ligands, as well as the attractive/repulsive surface potential in an ionic medium affects the eventual macro-scale size distribution of the particle aggregates (flocs). The bridge between the micro-macro model is made via an aggregation kernel. Results suggest that the presence of elastic ligands on the particle surface lead to the formation of larger floc aggregates via efficient inter-floc collisions (i.e. non-zero sticking probability, g). Strong electrolytic composition of the surrounding fluid favours large floc formation as well. The kernel for the Brownian diffusion for hard spheres is recovered in the limit of perfect binding effectiveness (g→1) and in a neutral solution with no dissolved salts.

Impact of flow on ligand-mediated bacterial flocculation

To understand the adhesion-fragmentation dynamics of bacterial aggregates (i.e., flocs), we model the aggregates as two ligand-covered rigid spheres. We develop and investigate a model for the attachment/detachment dynamics in a fluid subject to a homogeneous planar shear-flow. The binding ligands on the surface of the flocs experience attractive and repulsive surface forces in an ionic medium and exhibit finite resistance to rotation (via bond tilting). For certain range of material and fluid parameters, our results predict a nonlinear or hysteretic relationship between the binding/unbinding of the floc surface and the net floc velocity (translational plus rotational velocity). We show that the surface adhesion is promoted by increased fluid flow until a critical value, beyond which the bonds starts to yield. Moreover, adhesion is not promoted in a medium with low ionic strength, or flocs with bigger size or higher binder stiffness. The numerical simulations of floc-aggregate number density studies support these findings.

Hysteretically reversible phase transition in a molecular glass

Pressure induced densification in a molecular arsenic sulfide glass is studied at ambient temperature using x-ray scattering, absorption and Raman spectroscopic techniques in situ in a diamond anvil cell. The relatively abrupt changes in the position of the first sharp diffraction peak, FSDP, and the pressure-volume equation of state near ∼2 GPa suggest a phase transition between low- and high-density amorphous phases characterized by different densification mechanisms and rates. Raman spectroscopic results provide clear evidence that the phase transition corresponds to a topological transformation between a low-density molecular structure and a high-density network structure via opening of the constituent As(4)S(3) cage molecules and bond switching. Pressure induced mode softening of the high density phase suggests a low dimensional nature of the network. The phase transformation is hysteretically reversible, and therefore, reminiscent of a first-order phase transition.