Role of Shape in Particle-Lipid Membrane Interactions: From Surfing to Full Engulfment.

Understanding and manipulating the interactions between foreign bodies and cell membranes during endo- and phagocytosis is of paramount importance, not only for the fate of living cells but also for numerous biomedical applications. This study aims to elucidate the role of variables such as anisotropic particle shape, curvature, orientation, membrane tension, and adhesive strength in this essential process using a minimal experimental biomimetic system comprising giant unilamellar vesicles and rod-like particles with different curvatures and aspect ratios. We find that the particle wrapping process is dictated by the balance between the elastic free energy penalty and adhesion free energy gain, leading to two distinct engulfment pathways, tip-first and side-first, emphasizing the significance of the particle orientation in determining the pathway. Moreover, our experimental results are consistent with theoretical predictions in a state diagram, showcasing how to control the wrapping pathway from surfing to partial to complete wrapping by the interplay between membrane tension and adhesive strength. At moderate particle concentrations, we observed the formation of rod clusters, which exhibited cooperative and sequential wrapping. Our study contributes to a comprehensive understanding of the mechanistic intricacies of endocytosis by highlighting how the interplay between the anisotropic particle shape, curvature, orientation, membrane tension, and adhesive strength can influence the engulfment pathway.

Enhanced diffusion of tracer particles in nonreciprocal mixtures.

We study the diffusivity of a tagged particle in a binary mixture of Brownian particles with nonreciprocal interactions. Numerical simulations reveal that, for a broad class of interaction potentials, nonreciprocity can significantly increase the long-time diffusion coefficient of tracer particles and that this diffusion enhancement is associated with a breakdown of the Einstein relation. These observations are quantified and confirmed via two different and complementary analytical approaches: (i) a linearized stochastic density field theory, which is particularly accurate in the limit of soft interactions, and (ii) a reduced two-body description, which is exact at leading order in the density of particles. The latter reveals that diffusion enhancement can be attributed to the formation of transiently propelled dimers of particles, whose cohesion and speed are controlled by the nonreciprocal interactions.

Dynamical Pattern Formation without Self-Attraction in Quorum-Sensing Active Matter: The Interplay between Nonreciprocity and Motility.

We study a minimal model involving two species of particles interacting via quorum-sensing rules. Combining simulations of the microscopic model and linear stability analysis of the associated coarse-grained field theory, we identify a mechanism for dynamical pattern formation that does not rely on the standard route of intraspecies effective attractive interactions. Instead, our results reveal a highly dynamical phase of chasing bands induced only by the combined effects of self-propulsion and nonreciprocity in the interspecies couplings. Turning on self-attraction, we find that the system may phase separate into a macroscopic domain of such chaotic chasing bands coexisting with a dilute gas. We show that the chaotic dynamics of bands at the interfaces of this phase-separated phase results in anomalously slow coarsening.

Network Effects Lead to Self-Organization in Metabolic Cycles of Self-Repelling Catalysts.

Mixtures of particles that interact through phoretic effects are known to aggregate if they belong to species that exhibit attractive self-interactions. We study self-organization in a model metabolic cycle composed of three species of catalytically active particles that are chemotactic toward the chemicals that define their connectivity network. We find that the self-organization can be controlled by the network properties, as exemplified by a case where a collapse instability is achieved by design for self-repelling species. Our findings highlight a possibility for controlling the intricate functions of metabolic networks by taking advantage of the physics of phoretic active matter.

Self-organization of primitive metabolic cycles due to non-reciprocal interactions.

One of the greatest mysteries concerning the origin of life is how it has emerged so quickly after the formation of the earth. In particular, it is not understood how metabolic cycles, which power the non-equilibrium activity of cells, have come into existence in the first instances. While it is generally expected that non-equilibrium conditions would have been necessary for the formation of primitive metabolic structures, the focus has so far been on externally imposed non-equilibrium conditions, such as temperature or proton gradients. Here, we propose an alternative paradigm in which naturally occurring non-reciprocal interactions between catalysts that can partner together in a cyclic reaction lead to their recruitment into self-organized functional structures. We uncover different classes of self-organized cycles that form through exponentially rapid coarsening processes, depending on the parity of the cycle and the nature of the interaction motifs, which are all generic but have readily tuneable features.

Pair Interaction between Two Catalytically Active Colloids.

Due to the intrinsically complex non-equilibrium behavior of the constituents of active matter systems, a comprehensive understanding of their collective properties is a challenge that requires systematic bottom-up characterization of the individual components and their interactions. For self-propelled particles, intrinsic complexity stems from the fact that the polar nature of the colloids necessitates that the interactions depend on positions and orientations of the particles, leading to a 2d - 1 dimensional configuration space for each particle, in d dimensions. Moreover, the interactions between such non-equilibrium colloids are generically non-reciprocal, which makes the characterization even more complex. Therefore, derivation of generic rules that enable us to predict the outcomes of individual encounters as well as the ensuing collective behavior will be an important step forward. While significant advances have been made on the theoretical front, such systematic experimental characterizations using simple artificial systems with measurable parameters are scarce. Here, two different contrasting types of colloidal microswimmers are studied, which move in opposite directions and show distinctly different interactions. To facilitate the extraction of parameters, an experimental platform is introduced in which these parameters are confined on a 1D track. Furthermore, a theoretical model for interparticle interactions near a substrate is developed, including both phoretic and hydrodynamic effects, which reproduces their behavior. For subsequent validation, the degrees of freedom are increased to 2D motion and resulting trajectories are predicted, finding remarkable agreement. These results may prove useful in characterizing the overall alignment behavior of interacting self-propelling active swimmer and may find direct applications in guiding the design of active-matter systems involving phoretic and hydrodynamic interactions.

Dependence of diffusion in Escherichia coli cytoplasm on protein size, environmental conditions, and cell growth.

Inside prokaryotic cells, passive translational diffusion typically limits the rates with which cytoplasmic proteins can reach their locations. Diffusion is thus fundamental to most cellular processes, but the understanding of protein mobility in the highly crowded and non-homogeneous environment of a bacterial cell is still limited. Here, we investigated the mobility of a large set of proteins in the cytoplasm of Escherichia coli, by employing fluorescence correlation spectroscopy (FCS) combined with simulations and theoretical modeling. We conclude that cytoplasmic protein mobility could be well described by Brownian diffusion in the confined geometry of the bacterial cell and at the high viscosity imposed by macromolecular crowding. We observed similar size dependence of protein diffusion for the majority of tested proteins, whether native or foreign to E. coli. For the faster-diffusing proteins, this size dependence is well consistent with the Stokes-Einstein relation once taking into account the specific dumbbell shape of protein fusions. Pronounced subdiffusion and hindered mobility are only observed for proteins with extensive interactions within the cytoplasm. Finally, while protein diffusion becomes markedly faster in actively growing cells, at high temperature, or upon treatment with rifampicin, and slower at high osmolarity, all of these perturbations affect proteins of different sizes in the same proportions, which could thus be described as changes of a well-defined cytoplasmic viscosity.

Catalysis-Induced Phase Separation and Autoregulation of Enzymatic Activity.

We present a thermodynamically consistent model describing the dynamics of a multicomponent mixture where one enzyme component catalyzes a reaction between other components. We find that the catalytic activity alone can induce phase separation for sufficiently active systems and large enzymes, without any equilibrium interactions between components. In the limit of fast reaction rates, binodal lines can be calculated using a mapping to an effective free energy. We also explain how this catalysis-induced phase separation can act to autoregulate the enzymatic activity, which points at the biological relevance of this phenomenon.

Response to Comment on "Following Molecular Mobility during Chemical Reactions: No Evidence for Active Propulsion" and "Molecular Diffusivity of Click Reaction Components: The Diffusion Enhancement Question".

In their Comment (DOI: 10.1021/jacs.2c02965) on two related publications by our group (J. Am. Chem. Soc. 2022, 144, 1380-1388; DOI: 10.1021/jacs.1c11754) and another (J. Am. Chem. Soc. 2021, 143, 20884-20890; DOI: 10.1021/jacs.1c09455), Huang and Granick refer to the diffusion NMR measurements of molecules during a copper-catalyzed azide-alkyne cycloaddition (CuAAC) "click" reaction. Here we respond to their comments and maintain that no measurable diffusion enhancement was observed during the reaction. We expand on the physical arguments presented in our original JACS Article regarding the appropriate reference state for the diffusion coefficient and present new data showing that the use of other reference states, as suggested by Huang and Granick, will still support our conclusion that the two reactants and one product of the CuAAC reaction do not exhibit boosted mobility during the reaction.

Chemotactic self-caging in active emulsions.

A common feature of biological self-organization is how active agents communicate with each other or their environment via chemical signaling. Such communications, mediated by self-generated chemical gradients, have consequences for both individual motility strategies and collective migration patterns. Here, in a purely physicochemical system, we use self-propelling droplets as a model for chemically active particles that modify their environment by leaving chemical footprints, which act as chemorepulsive signals to other droplets. We analyze this communication mechanism quantitatively both on the scale of individual agent-trail collisions as well as on the collective scale where droplets actively remodel their environment while adapting their dynamics to that evolving chemical landscape. We show in experiment and simulation how these interactions cause a transient dynamical arrest in active emulsions where swimmers are caged between each other's trails of secreted chemicals. Our findings provide insight into the collective dynamics of chemically active particles and yield principles for predicting how negative autochemotaxis shapes their navigation strategy.

Molecular Diffusivity of Click Reaction Components: The Diffusion Enhancement Question.

Micrometer-sized objects are widely known to exhibit chemically driven motility in systems away from equilibrium. Experimental observation of reaction-induced motility or enhancement in diffusivity at the much shorter length scale of small molecules is, however, still a matter of debate. Here, we investigate the molecular diffusivity of reactants, catalyst, and product of a model reaction, the copper-catalyzed azide-alkyne cycloaddition click reaction, and develop new NMR diffusion approaches that allow the probing of reaction-induced diffusion enhancement in nanosized molecular systems with higher accuracy than the state of the art. Following two different approaches that enable the accounting of time-dependent concentration changes during NMR experiments, we closely monitored the diffusion coefficient of reaction components during the reaction. The reaction components showed distinct changes in the diffusivity: while the two reactants underwent a time-dependent decrease in their diffusivity, the diffusion coefficient of the product gradually increased and the catalyst showed only slight diffusion enhancement within the range expected for reaction-induced sample heating. The decrease in diffusion coefficient of the alkyne, one of the two reactants of click reaction, was not reproduced during its copper coordination when the second reactant, azide, was absent. Our results do not support the catalysis-induced diffusion enhancement of the components of the click reaction and, instead, point to the role of a relatively large intermediate species within the reaction cycle with diffusivity lower than that of both the reactants and product molecule.

Synchronization and Enhanced Catalysis of Mechanically Coupled Enzymes.

We examine the stochastic dynamics of two enzymes that are mechanically coupled to each other, e.g., through an elastic substrate or a fluid medium. The enzymes undergo conformational changes during their catalytic cycle, which itself is driven by stochastic steps along a biased chemical free energy landscape. We find conditions under which the enzymes can synchronize their catalytic steps, and discover that the coupling can lead to a significant enhancement in their overall catalytic rate. Both effects can be understood as arising from a global bifurcation in the underlying dynamical system at sufficiently strong coupling. Our findings suggest that, despite their molecular scale, enzymes can be cooperative and improve their performance in metabolic clusters.

Non-equilibrium phase separation in mixtures of catalytically active particles: size dispersity and screening effects.

Biomolecular condensates in cells are often rich in catalytically active enzymes. This is particularly true in the case of the large enzymatic complexes known as metabolons, which contain different enzymes that participate in the same catalytic pathway. One possible explanation for this self-organization is the combination of the catalytic activity of the enzymes and a chemotactic response to gradients of their substrate, which leads to a substrate-mediated effective interaction between enzymes. These interactions constitute a purely non-equilibrium effect and show exotic features such as non-reciprocity. Here, we analytically study a model describing the phase separation of a mixture of such catalytically active particles. We show that a Michaelis-Menten-like dependence of the particles' activities manifests itself as a screening of the interactions, and that a mixture of two differently sized active species can exhibit phase separation with transient oscillations. We also derive a rich stability phase diagram for a mixture of two species with both concentration-dependent activity and size dispersity. This work highlights the variety of possible phase separation behaviours in mixtures of chemically active particles, which provides an alternative pathway to the passive interactions more commonly associated with phase separation in cells. Our results highlight non-equilibrium organizing principles that can be important for biologically relevant liquid-liquid phase separation.

Should I bend or should I grow: the mechanisms of droplet-mediated autophagosome formation.

Phase-separated droplets with liquid-like properties can be degraded by macroautophagy/autophagy, but the mechanism underlying this degradation is poorly understood. We have recently derived a physical model to investigate the interaction between autophagic membranes and such droplets, uncovering that intrinsic wetting interactions underlie droplet-membrane contacts. We found that the competition between droplet surface tension and the increasing tendency of growing membrane sheets to bend determines whether a droplet is completely engulfed or isolated in a piecemeal fashion, a process we term fluidophagy. Intriguingly, we found that another critical parameter of droplet-membrane interactions, the spontaneous curvature of the membrane, determines whether the droplet is degraded by autophagy or - counterintuitively - serves as a platform from which autophagic membranes expand into the cytosol. We also discovered that the interaction of membrane-associated LC3 with the LC3-interacting region (LIR) found in the autophagic cargo receptor protein SQSTM1/p62 and many other autophagy-related proteins influences the preferred bending directionality of forming autophagosomes in living cells. Our study provides a physical account of how droplet-membrane wetting underpins the structure and fate of forming autophagosomes.

Wetting regulates autophagy of phase-separated compartments and the cytosol.

Compartmentalization of cellular material in droplet-like structures is a hallmark of liquid-liquid phase separation1,2, but the mechanisms of droplet removal are poorly understood. Evidence suggests that droplets can be degraded by autophagy3,4, a highly conserved degradation system in which membrane sheets bend to isolate portions of the cytoplasm within double-membrane autophagosomes5-7. Here we examine how autophagosomes sequester droplets that contain the protein p62 (also known as SQSTM1) in living cells, and demonstrate that double-membrane, autophagosome-like vesicles form at the surface of protein-free droplets in vitro through partial wetting. A minimal physical model shows that droplet surface tension supports the formation of membrane sheets. The model also predicts that bending sheets either divide droplets for piecemeal sequestration or sequester entire droplets. We find that autophagosomal sequestration is robust to variations in the droplet-sheet adhesion strength. However, the two sides of partially wetted sheets are exposed to different environments, which can determine the bending direction of autophagosomal sheets. Our discovery of this interplay between the material properties of droplets and membrane sheets enables us to elucidate the mechanisms that underpin droplet autophagy, or 'fluidophagy'. Furthermore, we uncover a switching mechanism that allows droplets to act as liquid assembly platforms for cytosol-degrading autophagosomes8 or as specific autophagy substrates9-11. We propose that droplet-mediated autophagy represents a previously undescribed class of processes that are driven by elastocapillarity, highlighting the importance of wetting in cytosolic organization.

Particle engulfment by strongly asymmetric membranes with area reservoirs.

Biological cells are capable of undergoing extensive shape transformations thanks to the existence of membrane area reservoirs from which they can pull out membrane when required. A particularly relevant example of such membrane remodelling is given by endocytic and phagocytic processes, during which the cell membrane engulfs nano- and micrometer sized particles. Recently, it was shown that cell-like membrane reservoirs can be mimicked in giant vesicles with nanotubes stabilized by strong bilayer asymmetry, as quantified by the membrane's spontaneous curvature. Here, we theoretically investigate particle engulfment by such strongly-asymmetric membranes. We find that, depending on the sign of the spontaneous curvature, the engulfment transition may be continuous or discontinuous. Moreover, we find that, in the case of particle engulfment, the presence of asymmetry-stabilized reservoirs is not well captured by the constant-tension model typically used to describe cell-membrane deformations. This highlights the need for a better understanding of the nature of cellular membrane reservoirs, in order to accurately describe membrane remodelling processes.

Wrapping of Microparticles by Floppy Lipid Vesicles.

Lipid membranes, the barrier defining living cells and many of their subcompartments, bind to a wide variety of nano- and micrometer sized objects. In the presence of strong adhesive forces, membranes can strongly deform and wrap the particles, an essential step in crossing the membrane for a variety of healthy and disease-related processes. A large body of theoretical and numerical work has focused on identifying the physical properties that underly wrapping. Using a model system of micron-sized colloidal particles and giant unilamellar lipid vesicles with tunable adhesive forces, we measure a wrapping phase diagram and make quantitative comparisons to theoretical models. Our data are consistent with a model of membrane-particle interactions accounting for the adhesive energy per unit area, membrane bending rigidity, particle size, and vesicle radius.

Cooperatively enhanced reactivity and "stabilitaxis" of dissociating oligomeric proteins.

Many functional units in biology, such as enzymes or molecular motors, are composed of several subunits that can reversibly assemble and disassemble. This includes oligomeric proteins composed of several smaller monomers, as well as protein complexes assembled from a few proteins. By studying the generic spatial transport properties of such proteins, we investigate here whether their ability to reversibly associate and dissociate may confer on them a functional advantage with respect to nondissociating proteins. In uniform environments with position-independent association-dissociation, we find that enhanced diffusion in the monomeric state coupled to reassociation into the functional oligomeric form leads to enhanced reactivity with localized targets. In nonuniform environments with position-dependent association-dissociation, caused by, for example, spatial gradients of an inhibiting chemical, we find that dissociating proteins generically tend to accumulate in regions where they are most stable, a process that we term "stabilitaxis."

Engulfment of ellipsoidal nanoparticles by membranes: full description of orientational changes.

We study the engulfment of ellipsoidal nanoparticles by membranes. It has been previously predicted that wrapping by the membrane can induce reorientation of the particle, however, previous studies only considered the wrapping process constrained to either side-oriented or tip-oriented particles. In contrast, we consider here the full two-dimensional energy landscape for engulfment, where the two degrees of freedom represent (i) the amount of wrapping and (ii) the particle orientation. In this way, we obtain access to the stability limits of the differently-oriented states, as well as to the energy barriers between them. We find that prolate and oblate particles undergo qualitatively different engulfment transitions, and show that the initial orientation of the particle at first contact with the membrane influences its fate.