Search

As society paves its way towards device miniaturization and precision medicine, micro-scale actuation and guided transport become increasingly prominent research fields with high impact in both technological and clinical contexts. In order to accomplish directed motion of micron-sized objects towards specific target sites, active biohybrid transport systems, such as motile living cells that act as smart biochemically-powered micro-carriers, have been suggested as an alternative to synthetic micro-robots. Inspired by the motility of leukocytes, we propose the amoeboid crawling of eukaryotic cells as a promising mechanism for transport of micron-sized cargoes and present an in-depth study of this novel type of composite active matter. Its transport properties result from the interactions of an active element (cell) and a passive one (cargo) and reveal an optimal cargo size that enhances the locomotion of the load-carrying cells, even exceeding their motility in the absence of cargo. The experimental findings are rationalized in terms of a biohybrid active matter theory that explains the emergent cell-cargo dynamics and enables us to derive the long-time transport properties of amoeboid micro-carries. As amoeboid locomotion is commonly observed for mammalian cells such as leukocytes, our results lay the foundations for the study of transport performance of other medically relevant cell types and for extending our findings to more advanced transport tasks in complex environments, such as tissues., Comment: 11 pages, 5 figures

Molecular motors walk along filaments until they detach stochastically with a force-dependent unbinding rate. Here, we show that this unbinding rate can be obtained from the analysis of experimental data of molecular motors moving in stationary optical traps. Two complementary methods are presented, based on the analysis of the distribution for the unbinding forces and of the motor's force traces. In the first method, analytically derived force distributions for slip bonds, slip-ideal bonds, and catch bonds are used to fit the cumulative distributions of the unbinding forces. The second method is based on the statistical analysis of the observed force traces. We validate both methods with stochastic simulations and apply them to experimental data for kinesin-1.

The adhesion of cell membranes is mediated by the binding of membrane-anchored receptor and ligand proteins. In this article, we review recent results from simulations and theory that lead to novel insights on how the binding equilibrium and kinetics of these proteins is affected by the membranes and by the membrane anchoring and molecular properties of the proteins. Simulations and theory both indicate that the binding equilibrium constant K2D and the on- and off-rate constants of anchored receptors and ligands in their 'two-dimensional' (2D) membrane environment strongly depend on the membrane roughness from thermally excited shape fluctuations on nanoscales. Recent theory corroborated by simulations provides a general relation between K2D} and the binding constant K3D of soluble variants of the receptors and ligands that lack the membrane anchors and are free to diffuse in three dimensions (3D)., Comment: Review article, 16 pages, 5 figures in Cell Adhesion & Migration, 2016

The adhesion of biological membranes is mediated by the binding of membrane-anchored receptor and ligand proteins. Central questions are how the binding kinetics of these proteins is affected by the membranes and by the membrane anchoring of the proteins. In this article, we (i) present detailed data for the binding of membrane-anchored proteins from coarse-grained molecular dynamics simulations, and (ii) provide a theory that describes how the binding kinetics depends on the average separation and thermal roughness of the adhering membranes, and on the anchoring, lengths, and length variations of the proteins. An important element of our theory is the tilt of bound receptor-ligand complexes and transition-state complexes relative to the membrane normals. This tilt results from an interplay of the anchoring energy and rotational entropy of the complexes and facilitates the formation of receptor-ligand bonds at membrane separations smaller than the preferred separation for binding. In our simulations, we have considered both lipid-anchored and transmembrane receptor and ligand proteins. We find that the binding equilibrium constant and binding on-rate constant of lipid-anchored proteins are considerably smaller than the binding constant and on-rate constant of rigid transmembrane proteins with identical binding domains., Comment: 13 pages, 6 figures; to appear in J. Chem. Phys

Adhesion processes of biological membranes that enclose cells and cellular organelles are essential for immune responses, tissue formation, and signaling. These processes depend sensitively on the binding constant K2D of the membrane-anchored receptor and ligand proteins that mediate adhesion, which is difficult to measure in the 'two-dimensional' (2D) membrane environment of the proteins. An important problem therefore is to relate K2D} to the binding constant K3D} of soluble variants of the receptors and ligands that lack the membrane anchors and are free to diffuse in three dimensions (3D). In this article, we present a general theory for the binding constants K2D and K3D of rather stiff proteins whose main degrees of freedom are translation and rotation, along membranes and around anchor points 'in 2D', or unconstrained 'in 3D'. The theory generalizes previous results by describing how K2D depends both on the average separation and thermal nanoscale roughness of the apposing membranes, and on the length and anchoring flexibility of the receptors and ligands. Our theoretical results for the ratio K2D/K3D of the binding constants agree with detailed results from Monte Carlo simulations without any data fitting, which indicates that the theory captures the essential features of the 'dimensionality reduction' due to membrane anchoring. In our Monte Carlo simulations, we consider a novel coarse-grained model of biomembrane adhesion in which the membranes are represented as discretized elastic surfaces, and the receptors and ligands as anchored molecules that diffuse continuously along the membranes and rotate at their anchor points., Comment: 17 pages, 11 figures; to appear in J. Chem. Phys

Cellular internalization of nanoparticles requires the full wrapping of the nanoparticles by the cell membrane. This wrapping process can occur spontaneously if the adhesive interactions between the nanoparticles and the membranes are sufficiently strong to compensate for the cost of membrane bending. In this article, we show that the membrane curvature prior to wrapping plays a key role for the wrapping process, besides the size and shape of the nanoparticles that have been investigated in recent years. For membrane segments that initially bulge away from nanoparticles by having a mean curvature of the same sign as the mean curvature of the particle surface, we find strongly stable partially wrapped states that can prevent full wrapping. For membrane segments that initially bulge towards the nanoparticles, in contrast, partially wrapped states can constitute a significant energetic barrier for the wrapping process., Comment: 6 pages, 4 figures; to appear in 'Soft Matter'

We investigate morphologies of semiflexible polymer rings, such as circular DNA, which are adsorbed onto topographically or chemically structured substrate surfaces. We classify all equilibrium morphologies for two striped surface structures, (i) topographical surface grooves and (ii) chemically structured surface domains. For both types of stripes, we find four equilibrium shapes: a round toroidal and a confined elongated shape as well as two shapes containing bulges. We determine the complete bifurcation diagram of these morphologies as a function of their contour length and the ratio of adhesive strength to bending rigidity. For more complex geometries consisting of several stripes we find a cascade of transitions between elongated shapes. Finally, we compare our findings to ring condensation by attractive interactions.

The bioactivity of nanoparticles crucially depends on their ability to cross biomembranes. Recent simulations indicate the cooperative wrapping and internalization of spherical nanoparticles in tubular membrane structures. In this article, we systematically investigate the energy gain of this cooperative wrapping by minimizing the energies of the rotationally symmetric shapes of the membrane tubes and of membrane segments wrapping single particles. We find that the energy gain for the cooperative wrapping of nanoparticles in membrane tubes relative to their individual wrapping as single particles strongly depends on the ratio of the particle radius and the range of the particle-membrane adhesion potential. For a potential range of the order of one nanometer, the cooperative wrapping in tubes is highly favorable for particles with a radius of tens of nanometers and intermediate adhesion energies, but not for particles that are significantly larger., Comment: 9 pages, 7 figures; to appear in Soft Matter

Motivated by unexpected morphologies of the emerging liquid phase (channels, bulges, droplets) at the edge of thin, melting alkane terraces, we propose a new heterogeneous nucleation pathway. The competition between bulk and interfacial energies and the boundary conditions determine the growth and shape of the liquid phase at the edge of the solid alkane terraces. Calculations and experiments reveal a "pre-critical" shape transition (channel-to-bulges) of the liquid before reaching its critical volume along a putative shape-conserving path. Bulk liquid emerges from the new shape, and depending on the degree of supersaturation, the new pathway may have two, one, or zero energy barriers. The findings are broadly relevant for many heterogeneous nucleation processes because the novel pathway is induced by common, widespread surface topologies (scratches, steps, etc.)., Comment: 5 figures, accepted for publication in Physical Review Letters (2012)

Osmotic deflation of vesicles enclosing two liquid phases can lead to bulging of one of the phases from the vesicle body. This budding process is preceded by a complete to partial wetting transition of one of the liquid phases on the membrane and depends on the membrane tensions and the tension of the interface between the enclosed liquid phases. These tensions dominate in different morphology regimes, the crossover of which initiates the budding process. In addition, the degree of budding can be controlled by aspiration via micropipettes. We also demonstrate that the budding direction can be reversed if there are two external phases in contact with the vesicle., Comment: 3 figures in the main text, 6 figures in the supporting information. Accepted for publication in The Journal of Physical Chemistry B (2012)

Motivated by recent experiments on biomimetic membranes exposed to several aqueous phases, we theoretically study the morphology of a membrane in contact with a liquid droplet formed via aqueous phase separation. We concentrate on membranes with negligible spontaneous curvature. At small droplet volume, bending energy dominates and the droplet is only partially wrapped by the membrane. At large volume, this configuration can become unstable and undergo a discontinuous transition to a state, in which the droplet is (almost) completely wrapped by the membrane. A morphology diagram, showing the parameter region where such budding transition occurs, is constructed as a function of the membrane tension and the intrinsic contact angle of the liquid with the membrane. The effects of spontaneous curvature are discussed qualitatively., Comment: 6 pages, 6 figures, Soft Matter, in press (2011)

We investigate the force generation by polymerizing bundles of filaments, which form because of short-range attractive filament interactions. We show that bundles can generate forces by a zipping mechanism, which is not limited by buckling and operates in the fully buckled state. The critical zipping force, i.e. the maximal force that a bundle can generate, is given by the adhesive energy gained during bundle formation. For opposing forces larger than the critical zipping force, bundles undergo a force-induced unbinding transition. For larger bundles, the critical zipping force depends on the initial configuration of the bundles. Our results are corroborated by Monte Carlo simulations.

The persistence length of semiflexible polymers and one-dimensional fluid membranes is obtained from the renormalization of their bending rigidity. The renormalized bending rigidity is calculated using an exact real-space functional renormalization group transformation based on a mapping to the one-dimensional Heisenberg model. The renormalized bending rigidity vanishes exponentially at large length scales and its asymptotic behaviour is used to define the persistence length. For semiflexible polymers, our result agrees with the persistence length obtained using the asymptotic behaviour of tangent correlation functions. Our definition differs from the one commonly used for fluid membranes, which is based on a perturbative renormalization of the bending rigidity., Comment: 7 pages

The polymerization of actin filaments is coupled to the hydrolysis of adenosine triphosphate (ATP), which involves both the cleavage of ATP and the release of inorganic phosphate. We describe hydrolysis by a reduced two-state model with a cooperative cleavage mechanism, where the cleavage rate depends on the state of the neighboring actin protomer in a filament. We obtain theoretical predictions of experimentally accessible steady state quantities such as the size of the ATP-actin cap, the size distribution of ATP-actin islands, and the cleavage flux for cooperative cleavage mechanisms., Comment: 6 pages

Directed polymers (strings) and semiflexible polymers (filaments) are one-dimensional objects governed by tension and bending energy, respectively. They undergo unbinding transitions in the presence of a short-range attractive potential. Using transfer matrix methods we establish a duality mapping for filaments and strings between the restricted partition sums in the absence and the presence of a short-range attraction. This allows us to obtain exact results for the critical exponents related to the unbinding transition, the transition point and transition order., Comment: 7 pages, eq. (20) corrected in this submission

We theoretically study the behaviour of a liquid bridge formed between a pair of rigid and parallel plates. The plates are smooth, they may either be homogeneous or decorated by circular patches of more hydrophilic domains, and they are generally not identical. We calculate the mechanical equilibrium distance of the liquid bridge as a function of liquid volume, contact angle and radius of the chemical domain. We show that a liquid bridge can be an equilibrium configuration as long as the sum of the contact angles at the two walls is larger than $180^\circ$. When comparisons are possible, our results agree well with recent analytical and molecular dynamics simulation results. We also derive the effective spring constant of the liquid bridge as it is perturbed from its equilibrium distance. The spring constant diverges when the sum of the contact angles is $180^\circ$ and is finite otherwise. The value of the spring constant decreases with increasing contact angle and volume, and the rate, at which it decreases, depends strongly on the properties of the two plates., Comment: 20 pages, 6 figures, To appear in Langmuir

The adhesion zone of immune cells, the 'immunological synapse', exhibits characteristic domains of receptor-ligand complexes. The domain formation is likely caused by a length difference of the receptor-ligand complexes, and has been investigated in experiments in which T cells adhere to supported membranes with anchored ligands. For supported membranes with two types of anchored ligands, MHCp and ICAM1, that bind to the receptors TCR and LFA1 in the cell membrane, the coexistence of domains of TCR-MHCp and LFA1-ICAM1 complexes in the cell adhesion zone has been observed for a wide range of ligand concentrations and affinities. For supported membranes with long and short ligands that bind to the same cell receptor CD2, in contrast, domain coexistence has been observed for a rather narrow ratio of ligand concentrations. In this article, we determine detailed phase diagrams for cells adhering to supported membranes with a statistical-physical model of cell adhesion. We find a characteristic difference between the adhesion scenarios in which two types of ligands in a supported membrane bind (i) to the same cell receptor or (ii) to two different cell receptors, which helps to explain the experimental observations. Our phase diagrams fully include thermal shape fluctuations of the cell membranes on nanometer scales, which lead to a critical point for the domain formation and to a cooperative binding of the receptors and ligands., Comment: 23 pages, 6 figures

We use stochastic computer simulations to study the transport of a spherical cargo particle along a microtubule-like track on a planar substrate by several kinesin-like processive motors. Our newly developed adhesive motor dynamics algorithm combines the numerical integration of a Langevin equation for the motion of a sphere with kinetic rules for the molecular motors. The Langevin part includes diffusive motion, the action of the pulling motors, and hydrodynamic interactions between sphere and wall. The kinetic rules for the motors include binding to and unbinding from the filament as well as active motor steps. We find that the simulated mean transport length increases exponentially with the number of bound motors, in good agreement with earlier results. The number of motors in binding range to the motor track fluctuates in time with a Poissonian distribution, both for springs and cables being used as models for the linker mechanics. Cooperativity in the sense of equal load sharing only occurs for high values for viscosity and attachment time., Comment: 40 pages, Revtex with 13 figures, to appear in Journal of Chemical Physics

We study the traffic of two types of molecular motors using the two-species symmetric simple exclusion process (ASEP) with periodic boundary conditions and with attachment and detachment of particles. We determine characteristic properties such as motor densities and currents by simulations and analytical calculations. For motors with different unbinding probabilities, mean field theory gives the correct bound density and total current of the motors, as shown by numerical simulations. For motors differing in their stepping probabilities, the particle-hole symmetry of the current-density relationship is broken and mean field theory fails drastically. The total motor current exhibits exponential finite-size scaling, which we use to extrapolate the total current to the thermodynamic limit. Finally, we also study the motion of a single motor in the background of many non-moving motors., Comment: 23 pages, 6 figures, latex

We present here exact results for a one-dimensional gas, or fluid, of hard-sphere particles with attractive boundaries. The particles, which can exchange with a bulk reservoir, mediate an interaction between the boundaries. A two-dimensional lattice of such one-dimensional gas `columns' represents a discrete approximation of a three-dimensional gas of particles between two surfaces. The effective particle-mediated interaction potential of the boundaries, or surfaces, is calculated from the grand-canonical partition function of the one-dimensional gas of particles, which is an extension of the well-studied Tonks gas. The effective interaction potential exhibits two minima. The first minimum at boundary contact reflects depletion interactions, while the second minimum at separations close to the particle diameter results from a single adsorbed particle that crosslinks the two boundaries. The second minimum is the global minimum for sufficiently large binding energies of the particles. Interestingly, the effective adhesion energy corresponding to this minimum is maximal at intermediate concentrations of the particles., Comment: to appear in Journal of Statistical Mechanics: Theory and Experiment

Cell membranes interact via anchored receptor and ligand molecules. Central questions on cell adhesion concern the binding affinity of these membrane-anchored molecules, the mechanisms leading to the receptor-ligand domains observed during adhesion, and the role of cytoskeletal and other active processes. In this review, these questions are addressed from a theoretical perspective. We focus on models in which the membranes are described as elastic sheets, and the receptors and ligands as anchored molecules. In these models, the thermal membrane roughness on the nanometer scale leads to a cooperative binding of anchored receptor and ligand molecules, since the receptor-ligand binding smoothens out the membranes and facilitates the formation of additional bonds. Patterns of receptor domains observed in Monte Carlo simulations point towards a joint role of spontaneous and active processes in cell adhesion. The interactions mediated by the receptors and ligand molecules can be characterized by effective membrane adhesion potentials that depend on the concentrations and binding energies of the molecules., Comment: Review article, 13 pages, 9 figures, to appear in Soft Matter

The adhesion of cells is mediated by receptors and ligands anchored in apposing membranes. A central question is how to characterize the binding affinity of these membrane-anchored molecules. For soluble molecules, the binding affinity is typically quantified by the binding equilibrium constant K3D in the linear relation [RL] = K3D [R][L] between the volume concentration [RL] of bound complexes and the volume concentrations [R] and [L] of unbound molecules. For membrane-anchored molecules, it is often assumed by analogy that the area concentration of bound complexes [RL] is proportional to the product [R][L] of the area concentrations for the unbound receptor and ligand molecules. We show here (i) that this analogy is only valid for two planar membranes immobilized on rigid surfaces, and (ii) that the thermal roughness of flexible membranes leads to cooperative binding of receptors and ligands. In the case of flexible membranes, the area concentration [RL] of receptor-ligand bonds is proportional to the square of [R][L] for typical lengths and concentrations of receptors and ligands in cell adhesion zones. The cooperative binding helps to understand why different experimental methods for measuring the binding affinity of membrane-anchored molecules have led to values differing by several orders of magnitude., Comment: 9 pages, 4 figures; to appear in Soft Matter

The transport by molecular motors along cytoskeletal filaments is studied theoretically in the presence of static defects. The movements of single motors are described as biased random walks along the filament as well as binding to and unbinding from the filament. Three basic types of defects are distinguished, which differ from normal filament sites only in one of the motors' transition probabilities. Both stepping defects with a reduced probability for forward steps and unbinding defects with an increased probability for motor unbinding strongly reduce the velocities and the run lengths of the motors with increasing defect density. For transport by single motors, binding defects with a reduced probability for motor binding have a relatively small effect on the transport properties. For cargo transport by motors teams, binding defects also change the effective unbinding rate of the cargo particles and are expected to have a stronger effect., Comment: 20 pages, latex, 7 figures, 1 table

Intracellular transport is mediated by molecular motors that pull cargos along cytoskeletal filaments. Many cargos move bidirectionally and are transported by two teams of motors which move into opposite directions along the filament. We have recently introduced a stochastic tug-of-war model for this situation. This model describes the motion of the cargo as a Markov process on a two-dimensional state space defined by the numbers of active plus and active minus motors. In spite of its simplicity, this tug-of-war model leads to a complex dependence of the cargo motility on the motor parameters. We present new numerical results for the dependence on the number of involved motors. In addition, we derive a simple and intuitive sharp maxima approximation, from which one obtains the cargo motility state from only four simple inequalities. This approach provides a fast and reliable method to determine the cargo motility for a given experimental system., Comment: 23 pages, latex, 12 figures, 1 table

We discuss effects of the stepping kinetics of molecular motors on their traffic behavior on crowded filaments using a simple two-state chemomechanical cycle. While the general traffic behavior is quite robust with respect to the detailed kinetics of the step, a few observable parameters exhibit a strong dependence on these parameters. Most strikingly, the effective unbinding rate of the motors may both increase and decrease with increasing traffic density, depending on the details of the motor step. Likewise the run length either exhibits a strong decrease or almost no dependence on the traffic density. We compare our theoretical results with recent experimental observations on motor traffic., Comment: 14 pages, 3 figures

In biomimetic and biological systems, interactions between surfaces are often mediated by adhesive molecules, nanoparticles, or colloids dispersed in the surrounding solution. We present here a general, statistical-mechanical model for two surfaces that interact via adhesive particles. The effective, particle-mediated interaction potential of the surfaces is obtained by integrating over the particles' degrees of freedom in the partition function. Interestingly, the effective adhesion energy of the surfaces exhibits a maximum at intermediate particle concentrations, and is considerably smaller both at low and high concentrations. The effective adhesion energy corresponds to a minimum in the interaction potential at surface separations slightly larger than the particle diameter, while a secondary minimum at surface contact reflects depletion interactions. Our results can be generalized to surfaces with specific receptors for solute particles, and have direct implications for the adhesion of biomembranes and for phase transitions in colloidal systems., Comment: 6 pages, 5 figures; to appear in Europhys. Lett

Molecular motors transport various cargos along cytoskeletal filaments, analogous to trucks on roads. In contrast to vehicles, however, molecular motors do not work alone but in small teams. We describe a simple model for the transport of a cargo by one team of motors and by two teams of motors, which walk into opposite directions. The cooperation of one team of motors generates long-range transport, which we observed experimentally in vitro. Transport by two teams of motors leads to a variety of bidirectional motility behaviour and to dynamic instabilities reminiscent of spontaneous symmetry breaking. We also discuss how cargo transport by teams of motors allows the cell to generate robust long-range bidirectional transport., Comment: 6 pages, latex, 1 figure, to appear in the Proceedings of "Traffic and Granular Flow '07" (Springer)

Intracellular transport is based on molecular motors that pull cargos along cytoskeletal filaments. One motor species always moves in one direction, e.g. conventional kinesin moves to the microtubule plus end, while cytoplasmic dynein moves to the microtubule minus end. However, many cellular cargos are observed to move bidirectionally, involving both plus-end and minus-end directed motors. The presumably simplest mechanism for such bidirectional transport is provided by a tug-of-war between the two motor species. This mechanism is studied theoretically using the load-dependent transport properties of individual motors as measured in single-molecule experiments. In contrast to previous expectations, such a tug-of-war is found to be highly cooperative and to exhibit seven different motility regimes depending on the precise values of the single motor parameters. The sensitivity of the transport process to small parameter changes can be used by the cell to regulate its cargo traffic., Comment: 17 pages, latex, 11 figures, 4 tables, includes Supporting Information

Multi-component membranes such as ternary mixtures of lipids and cholesterol can exhibit coexistence regions between two liquid phases. When such membranes adhere to a corrugated substrate, the phase separation process strongly depends on the interplay between substrate topography, bending rigidities, and line tension of the membrane domains as we show theoretically via energy minimization and Monte Carlo simulations. For sufficiently large bending rigidity contrast between the two membrane phases, the corrugated substrate truncates the phase separation process and leads to a stable pattern of membrane domains. Our theory is consistent with recent experimental observations and provides a possible control mechanism for domain patterns in biological membranes., Comment: to appear in Physical Review Letters

We review theoretical results for the adhesion-induced phase behavior of biomembranes. The focus is on models in which the membranes are represented as discretized elastic sheets with embedded adhesion molecules. We present several mechanism that lead to the formation of domains during adhesion, and discuss the time-dependent evolution of domain patterns obtained in Monte-Carlo simulations. The simulated pattern dynamics has striking similarities to the pattern evolution observed during T cell adhesion., Comment: 68 pages, 29 figures

Activity or spin patterns on random scale-free network are studied by mean field analysis and computer simulations. These activity patterns evolve in time according to local majority-rule dynamics which is implemented using (i) parallel or synchronous updating and (ii) random sequential or asynchronous updating. Our mean-field calculations predict that the relaxation processes of disordered activity patterns become much more efficient as the scaling exponent $\gamma$ of the scale-free degree distribution changes from $\gamma >5/2$ to $\gamma < 5/2$. For $\gamma > 5/2$, the corresponding decay times increase as $\ln(N)$ with increasing network size $N$ whereas they are independent of $N$ for $\gamma < 5/2$. In order to check these mean field predictions, extensive simulations of the pattern dynamics have been performed using two different ensembles of random scale-free networks: (A) multi-networks as generated by the configuration method, which typically leads to many self-connections and multiple edges, and (B) simple-networks without self-connections and multiple edges., Comment: 20 pages, 8 figures