Engineered molecular sensors for quantifying cell surface crowding.

Cells mediate interactions with the extracellular environment through a crowded assembly of transmembrane proteins, glycoproteins and glycolipids on their plasma membrane. The extent to which surface crowding modulates the biophysical interactions of ligands, receptors, and other macromolecules is poorly understood due to the lack of methods to quantify surface crowding on native cell membranes. In this work, we demonstrate that physical crowding on reconstituted membranes and live cell surfaces attenuates the effective binding affinity of macromolecules such as IgG antibodies in a surface crowding-dependent manner. We combine experiment and simulation to design a crowding sensor based on this principle that provides a quantitative readout of cell surface crowding. Our measurements reveal that surface crowding decreases IgG antibody binding by 2 to 20 fold in live cells compared to a bare membrane surface. Our sensors show that sialic acid, a negatively charged monosaccharide, contributes disproportionately to red blood cell surface crowding via electrostatic repulsion, despite occupying only ~1% of the total cell membrane by mass. We also observe significant differences in surface crowding for different cell types and find that expression of single oncogenes can both increase and decrease crowding, suggesting that surface crowding may be an indicator of both cell type and state. Our high-throughput, single-cell measurement of cell surface crowding may be combined with functional assays to enable further biophysical dissection of the cell surfaceome.

Soft confinement of self-propelled rods: simulation and theory.

We present an analytical framework for evolving the dynamics of active rods under any periodic external potential, including confining channels and arrays of harmonic traps. As a proof of concept, we analyze the structure and dispersion of self-propelled rods under a soft, periodic one-dimensional (1D) confinement potential and under a two-dimensional (2D) periodic radial harmonic trap. While passive rods and polymers nematically order under 1D confinement, their diffusive transport along the director is limited by thermal diffusion. In contrast, self-propelled rods can generate large convective fluxes when combined with nematic ordering, producing a strong dispersion along the director. Combining theory and simulation, we demonstrate that nematic alignment and self-propulsion generates an exponential enhancement in active diffusivity along the director, in contrast to passive rods that experience at most a 2-fold increase.

Dynamic surfactants drive anisotropic colloidal assembly.

Colloidal building blocks with re-configurable shapes and dynamic interactions can exhibit unusual self-assembly behaviors and pathways. In this work, we consider the phase behavior of colloids coated with surface-mobile polymer brushes that behave as "dynamic surfactants." Unlike traditional polymer-grafted colloids, we show that colloids coated with dynamic surfactants can acquire anisotropic macroscopic assemblies, even for spherical colloids with isotropic attractive interactions. We use Brownian Dynamics simulations and dynamic density functional theory to demonstrate that time-dependent reorganization of the dynamic surfactants leads to phase diagrams with anisotropic assemblies. We observed that the microscopic polymer distributions impose unique geometric constraints between colloids that control their packing into lamellar, string, and vesicle phases. Our work may help discover versatile building blocks and provide extensive design freedom for assembly out of thermodynamic equilibrium.

Active Surface Flows Accelerate the Coarsening of Lipid Membrane Domains.

Phase separation of multicomponent lipid membranes is characterized by the nucleation and coarsening of circular membrane domains that grow slowly in time as ∼t^{1/3}, following classical theories of coalescence and Ostwald ripening. In this Letter, we study the coarsening kinetics of phase-separating lipid membranes subjected to nonequilibrium forces and flows transmitted by motor-driven gliding actin filaments. We experimentally observe that the activity-induced surface flows trigger rapid coarsening of noncircular membrane domains that grow as ∼t^{2/3}, a 2x acceleration in the growth exponent compared to passive coalescence and Ostwald ripening. We analyze these results by developing analytical theories based on the Smoluchowski coagulation model and the phase field model to predict the domain growth in the presence of active flows. Our Letter demonstrates that active matter forces may be used to control the growth and morphology of membrane domains driven out of equilibrium.

Nonequilibrium interactions between multi-scale colloids regulate the suspension microstructure and rheology.

Understanding nonequilibrium interactions of multi-component colloidal suspensions is critical for many dynamical settings such as self-assembly and material processing. A key question is how the nonequilibrium distributions of individual components influence the effective interparticle interactions and flow behavior. In this work, we develop a first-principle framework to study a bidisperse suspension of colloids and depletants using a Smoluchowski equation and corroborated by Brownian dynamics (BD) simulations. Using nonlinear microrheology as a case study, we demonstrate that effective depletion interactions between driven colloids are sensitive to particle timescales out of equilibrium and cannot be predicted by equilibrium-based pair potentials like Asakura-Oosawa. Furthermore, we show that the interplay between Brownian relaxation timescales of different species plays a critical role in governing the viscosity of multi-component suspensions. Our model highlights the limitations of using equilibrium pair potentials to approximate interparticle interactions in nonequilibrium processes such as hydrodynamic flows and presents a useful framework for studying the transport of driven, interacting suspensions.

Boundary design regulates the diffusion of active matter in heterogeneous environments.

Physical boundaries play a key role in governing the overall transport properties of nearby self-propelled particles. In this work, we develop dispersion theories and conduct Brownian dynamics simulations to predict the coupling between surface accumulation and effective diffusivity of active particles in boundary-rich media. We focus on three models that are well-understood for passive systems: particle transport in (i) an array of fixed volume-excluding obstacles; (ii) a pore with spatially heterogeneous width; and (iii) a tortuous path with kinks and corners. While the impact of these entropic barriers on passive particle transport is well established, we find that these classical models of porous media flows break down due to the unique interplay between activity and the microstructure of the internal geometry. We study the activity-induced slowdown of effective diffusivity by formulating a Smoluchowski description of long-time self diffusivity which contains contributions from the density and fluctuation fields of the active particles. Particle-based and finite element simulations corroborate this perspective and reveal important nonequilibrium considerations of active transport.

Dynamic interfaces for contact-time control of colloidal interactions.

Understanding pairwise interactions between colloidal particles out of equilibrium has a profound impact on dynamical processes such as colloidal self assembly. However, traditional colloidal interactions are effectively quasi-static on colloidal timescales and cannot be modulated out of equilibrium. A mechanism to dynamically tune the interactions during colloidal contacts can provide new avenues for self assembly and material design. In this work, we develop a framework based on polymer-coated colloids and demonstrate that in-plane surface mobility and mechanical relaxation of polymers at colloidal contact interfaces enable an effective, dynamic interaction. Combining analytical theory, simulations, and optical tweezer experiments, we demonstrate precise control of dynamic pair interactions over a range of pico-Newton forces and seconds timescales. Our model helps further the general understanding of out-of-equilibrium colloidal assemblies while providing extensive design freedom via interface modulation and nonequilibrium processing.

Molecular height measurement by cell surface optical profilometry (CSOP).

The physical dimensions of proteins and glycans on cell surfaces can critically affect cell function, for example, by preventing close contact between cells and limiting receptor accessibility. However, high-resolution measurements of molecular heights on native cell membranes have been difficult to obtain. Here we present a simple and rapid method that achieves nanometer height resolution by localizing fluorophores at the tip and base of cell surface molecules and determining their separation by radially averaging across many molecules. We use this method, which we call cell surface optical profilometry (CSOP), to quantify the height of key multidomain proteins on a model cell, as well as to capture average protein and glycan heights on native cell membranes. We show that average height of a protein is significantly smaller than its contour length, due to thermally driven bending and rotation on the membrane, and that height strongly depends on local surface and solution conditions. We find that average height increases with cell surface molecular crowding but decreases with solution crowding by solutes, both of which we confirm with molecular dynamics simulations. We also use experiments and simulations to determine the height of an epitope, based on the location of an antibody, which allows CSOP to profile various proteins and glycans on a native cell surface using antibodies and lectins. This versatile method for profiling cell surfaces has the potential to advance understanding of the molecular landscape of cells and the role of the molecular landscape in cell function.

Active Contact Forces Drive Nonequilibrium Fluctuations in Membrane Vesicles.

We analyze the nonequilibrium shape fluctuations of giant unilamellar vesicles encapsulating motile bacteria. Owing to bacteria-membrane collisions, we experimentally observe a significant increase in the magnitude of membrane fluctuations at low wave numbers, compared to the well-known thermal fluctuation spectrum. We interrogate these results by numerically simulating membrane height fluctuations via a modified Langevin equation, which includes bacteria-membrane contact forces. Taking advantage of the lengthscale and timescale separation of these contact forces and thermal noise, we further corroborate our results with an approximate theoretical solution to the dynamical membrane equations. Our theory and simulations demonstrate excellent agreement with nonequilibrium fluctuations observed in experiments. Moreover, our theory reveals that the fluctuation-dissipation theorem is not broken by the bacteria; rather, membrane fluctuations can be decomposed into thermal and active components.

A theory for the phase behavior of mixtures of active particles.

Systems at equilibrium like molecular or colloidal suspensions have a well-defined thermal energy kBT that quantifies the particles' kinetic energy and gauges how "hot" or "cold" the system is. For systems far from equilibrium, such as active matter, it is unclear whether the concept of a "temperature" exists and whether self-propelled entities are capable of thermally equilibrating like passive Brownian suspensions. Here we develop a simple mechanical theory to study the phase behavior and "temperature" of a mixture of self-propelled particles. A mixture of active swimmers and passive Brownian particles is an ideal system for discovery of the temperature of active matter and the quantities that get shared upon particle collisions. We derive an explicit equation of state for the active/passive mixture to compute a phase diagram and to generalize thermodynamic concepts like the chemical potential and free energy for a mixture of nonequilibrium species. We find that different stability criteria predict in general different phase boundaries, facilitating considerations in simulations and experiments about which ensemble of variables are held fixed and varied.

Swim stress, motion, and deformation of active matter: effect of an external field.

We analyze the stress, dispersion, and average swimming speed of self-propelled particles subjected to an external field that affects their orientation and speed. The swimming trajectory is governed by a competition between the orienting influence (i.e., taxis) associated with the external (e.g., magnetic, gravitational, thermal, nutrient concentration) field versus the effects that randomize the particle orientations (e.g., rotary Brownian motion and/or an intrinsic tumbling mechanism like the flagella of bacteria). The swimmers' motion is characterized by a mean drift velocity and an effective translational diffusivity that becomes anisotropic in the presence of the orienting field. Since the diffusivity yields information about the micromechanical stress, the anisotropy generated by the external field creates a normal stress difference in the recently developed "swim stress" tensor [Takatori, Yan, and Brady, Phys. Rev. Lett., 2014]. This property can be exploited in the design of soft, compressible materials in which their size, shape, and motion can be manipulated and tuned by loading the material with active swimmers. Since the swimmers exert different normal stresses in different directions, the material can compress/expand, elongate, and translate depending on the external field strength. Such an active system can be used as nano/micromechanical devices and motors. Analytical solutions are corroborated by Brownian dynamics simulations.

Dynamic swarms regulate the morphology and distribution of soft membrane domains.

We study the dynamic structure of lipid domain inclusions embedded within a phase-separated reconstituted lipid bilayer in contact with a swarming flow of gliding filamentous actin. Passive circular domains transition into highly deformed morphologies that continuously elongate, rotate, and pinch off into smaller fragments, leading to a dynamic steady state with ≈23× speedup in the relaxation of the intermediate scattering function compared with passive membrane domains driven by purely thermal forces. To corroborate experimental results, we develop a phase-field model of the lipid domains with two-way coupling to the Toner-Tu equations. We report phase domains that become entrained in the chaotic eddy patterns, with oscillating waves of domains that correlate with the dominant wavelengths of the Toner-Tu flow fields.

Surface Topography Induces and Orients Nematic Swarms of Active Filaments: Considerations for Lab-On-A-Chip Devices.

Surface-bound molecular motors can drive the collective motion of cytoskeletal filaments in the form of nematic bands and polar flocks in reconstituted gliding assays. Although these "swarming transitions" are an emergent property of active filament collisions, they can be controlled and guided by tuning the surface chemistry or topography of the substrate. To date, the impact of surface topography on collective motion in active nematics is only partially understood, with most experimental studies focusing on the escape of a single filament from etched channels. Since the late 1990s, significant progress has been made to utilize the nonequilibrium properties of active filaments and create a range of functional nanodevices relevant to biosensing and parallel computation; however, the complexity of these swarming transitions presents a challenge when attempting to increase filament surface concentrations. In this work, we etch shallow, linear trenches into glass substrates to induce the formation of swarming nematic bands and investigate the mechanisms by which surface topography regulates the two-dimensional (2D) collective motion of driven filamentous actin (F-actin). We demonstrate that nematic swarms only appear at intermediate trench spacings and vanish if the trenches are made too narrow, wide, or tortuous. To rationalize these results, we simulate the F-actin as self-propelled, semiflexible chains subject to a soft, spatially modulated potential that encodes the energetic cost of bending a filament along the edge of a trench. In our model, we hypothesize that an individual filament experiences a penalty when its projected end-to-end distance is smaller than the trench spacing ("bending and turning"). However, chains that span the channel width glide above the trenches in a force- and torque-free manner ("crowd-surfing"). Our simulations demonstrate that collections of filaments form nematic bands only at intermediate trench spacings, consistent with our experimental findings.

Colloidal transport phenomena in dynamic, pulsating porous materials.

We study the transport phenomena of colloidal particles embedded within a moving array of obstacles that mimics a dynamic, time-varying porous material. While colloidal transport in an array of stationary obstacles ("passive" porous media) has been well studied, we lack the fundamental understanding of colloidal diffusion in a nonequilibrium porous environment. We combine Taylor dispersion theory, Brownian dynamics simulations, and optical tweezer experiments to study the transport of tracer colloidal particles in an oscillating lattice of obstacles. We discover that the dispersion of tracer particles is a non-monotonic function of oscillation frequency and exhibits a maximum that exceeds the Stokes-Einstein-Sutherland diffusivity in the absence of obstacles. By solving the Smoluchowski equation using a generalized dispersion framework, we demonstrate that the enhanced transport of the tracers depends critically on both the direct interparticle interactions with the obstacles and the fluid-mediated, hydrodynamic interactions generated by the moving obstacles.

Bio-enabled Engineering of Multifunctional "Living" Surfaces.

Through the magic of "active matter"─matter that converts chemical energy into mechanical work to drive emergent properties─biology solves a myriad of seemingly enormous physical challenges. Using active matter surfaces, for example, our lungs clear an astronomically large number of particulate contaminants that accompany each of the 10,000 L of air we respire per day, thus ensuring that the lungs' gas exchange surfaces remain functional. In this Perspective, we describe our efforts to engineer artificial active surfaces that mimic active matter surfaces in biology. Specifically, we seek to assemble the basic active matter components─mechanical motor, driven constituent, and energy source─to design surfaces that support the continuous operation of molecular sensing, recognition, and exchange. The successful realization of this technology would generate multifunctional, "living" surfaces that combine the dynamic programmability of active matter and the molecular specificity of biological surfaces and apply them to applications in biosensors, chemical diagnostics, and other surface transport and catalytic processes. We describe our recent efforts in bio-enabled engineering of living surfaces through the design of molecular probes to understand and integrate native biological membranes into synthetic materials.

Enhanced dispersion in an oscillating array of harmonic traps.

Experiment, theory, and simulation are employed to understand the dispersion of colloidal particles in a periodic array of oscillating harmonic traps generated by optical tweezers. In the presence of trap oscillation, a nonmonotonic and anisotropic dispersion is observed. Surprisingly, the stiffest traps produce the largest dispersion at a critical frequency, and the particles diffuse significantly faster in the direction of oscillation than those undergoing passive Stokes-Einstein-Sutherland diffusion. Theoretical predictions for the effective diffusivity of the particles as a function of trap stiffness and oscillation frequency are developed using generalized Taylor dispersion theory and Brownian dynamics simulations. Both theory and simulation demonstrate excellent agreement with the experiments, and reveal a "slingshot" mechanism that predicts a significant enhancement of colloidal diffusion in dynamic external fields.

Antibody binding reports spatial heterogeneities in cell membrane organization.

The spatial organization of cell membrane glycoproteins and glycolipids is critical for mediating the binding of ligands, receptors, and macromolecules on the plasma membrane. However, we currently do not have the methods to quantify the spatial heterogeneities of macromolecular crowding on live cell surfaces. In this work, we combine experiment and simulation to report crowding heterogeneities on reconstituted membranes and live cell membranes with nanometer spatial resolution. By quantifying the effective binding affinity of IgG monoclonal antibodies to engineered antigen sensors, we discover sharp gradients in crowding within a few nanometers of the crowded membrane surface. Our measurements on human cancer cells support the hypothesis that raft-like membrane domains exclude bulky membrane proteins and glycoproteins. Our facile and high-throughput method to quantify spatial crowding heterogeneities on live cell membranes may facilitate monoclonal antibody design and provide a mechanistic understanding of plasma membrane biophysical organization.

Acoustic trapping of active matter.

Confinement of living microorganisms and self-propelled particles by an external trap provides a means of analysing the motion and behaviour of active systems. Developing a tweezer with a trapping radius large compared with the swimmers' size and run length has been an experimental challenge, as standard optical traps are too weak. Here we report the novel use of an acoustic tweezer to confine self-propelled particles in two dimensions over distances large compared with the swimmers' run length. We develop a near-harmonic trap to demonstrate the crossover from weak confinement, where the probability density is Boltzmann-like, to strong confinement, where the density is peaked along the perimeter. At high concentrations the swimmers crystallize into a close-packed structure, which subsequently 'explodes' as a travelling wave when the tweezer is turned off. The swimmers' confined motion provides a measurement of the swim pressure, a unique mechanical pressure exerted by self-propelled bodies.

In vivo corneal oxygen uptake during soft-contact-lens wear.

PURPOSE: We develop a new method to compute in situ corneal oxygen uptake during soft-contact-lens (SCL) wear using a micro-polarographic Clark electrode. METHODS: After steady SCL wear and subsequent removal, a membrane-covered polarographic microelectrode is immediately placed onto the cornea. The resulting polarographic signal is related to the steady-state corneal oxygen uptake rate during soft-contact-lens wear. We devise a new analysis to quantify oxygen uptake into the cornea during lens wear. The proposed procedure is applied to new polarographic data for 10 human subjects with 12 different commercial lenses during open eye. We compare our results with recent theory. RESULTS: Average corneal oxygen uptake rates at open eye during SCL wear for 10 subjects wearing 12 different commercial lenses vary from 2 to 10 µL(STP)/cm(2)/h. High oxygen permeability lenses have uptake rates of -10 µL(STP)/cm(2)/h, in close agreement with our previously obtained no-lens human uptake rates of 9 to 13 µL(STP)/cm(2)/h at open eye.(40) Application of the classical data-interpretation procedure to our experimental data gives corneal-uptake results that are approximately three to five times smaller than those obtained with our new interpretation scheme. CONCLUSIONS: We provide a simple and reliable tool to quantify corneal-oxygen-uptake rates during in vivo soft-contact-lens wear. Comparison of our newly measured in vivo oxygen uptakes to model prediction for SCLs of varying oxygen transmissibility is in good agreement with available theory.

A quasi-2-dimensional model for respiration of the cornea with soft contact lens wear.

PURPOSE: Because neither the human cornea nor a soft contact lens (SCL) is of constant thickness, corneal oxygenation varies locally. To quantify the importance of cornea/SCL thickness variations on oxygen demand, we develop a quasi-2-dimensional (2D) respiration model that accounts for aerobic and anaerobic metabolism and bicarbonate buffering. METHODS: Because metabolism is critical to oxygen demand, we extend the 1-dimensional (1D), 6-layer oxygen metabolic model of Chhabra et al. Lateral diffusion is shown to be negligible. Accordingly, we adopt the 1D reactive-diffusion metabolic model but apply it locally along the cornea/lens extent. This "quasi-2D" approximation permits 2D assessment of oxygen consumption, including the effects of carbon dioxide, glucose, and lactate, bicarbonate, and hydrogen ions. We use both an oxygen deficiency factor and an excess lactate factor to gauge corneal health after accounting for both cornea and contact lens thickness variations. RESULTS: The quasi-2D respiration model provides quantitative spatial resolution of corneal oxygenation with minimal expenditure of computation time. When only aerobic oxygen loss is included, our quasi-2D approach is in excellent agreement with the fully 2D results of Alvord et al. However, the quasi-2D model predicts 2D concentration profiles of glucose, lactate ions, bicarbonate ions, hydrogen ions, and carbon dioxide, as well as oxygen. Neglect of metabolic reactions and/or thickness variations leads to inaccurate prediction of oxygen demand, especially near the lens periphery. CONCLUSIONS: The quasi-2D respiration model indicates that lateral thickness variations and respiration kinetics are critical for assessing on-eye physiologic performance of an SCL. We find that oxygen deficiency factor and excess lactate factor are useful indices to gauge corneal hypoxia. A user-friendly computer program of the quasi-2D respiration model is available for lens design.