Reinhard Lipowsky

Computer simulations of bilayer membranes: Self-assembly and interfacial tension

Binary Lennard-Jones fluids consisting of “solvent” and “surfactant” molecules are studied as simplified model systems for amphiphilic molecules in solution. Using Monte Carlo and molecular dynamics simulations, we observe the self-assembly of the surfactant molecules into bilayer membranes. These bilayers are fluid since the surfactants exhibit rapid lateral diffusion. We also measure the interfacial tension and the compressibility modulus of these bilayers. We show that they exhibit a tensionless state and characterize the corresponding stress profile. In this way, we bridge the gap between previous theoretical studies which were based (i) on discrete models with atomic resolution and (ii) on continuum models in which the bilayer membrane is treated as a smooth surface.

Tug-of-war as a cooperative mechanism for bidirectional cargo transport by molecular motors

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, whereas cytoplasmic dynein moves to the microtubule minus end. However, many cellular cargoes are observed to move bidirectionally, involving both plus- 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.

Equilibrium structure and lateral stress distribution of amphiphilic bilayers from dissipative particle dynamics simulations

The equilibrium structure and lateral stress profile of fluid bilayer membrane patches are investigated using the Dissipative Particle Dynamics simulation technique. Although there are no attractive forces between the model amphiphiles, they spontaneously aggregate into planar bilayers under suitable conditions of concentration and amphiphile architecture. Pure bilayers of single-chain and double-chain amphiphiles are simulated, and the amphiphile architecture and interaction parameters varied. We find that a strong chain stiffness potential is essential to create the lamellar order typical in natural lipid membranes. Single-chain amphiphiles form bilayers whose lamellar phase is destabilized by reductions in the tail stiffness. Double-chain amphiphiles form bilayers whose rigidity is sensitive to their architecture, and that remain well-ordered for smaller values of their tail stiffness than bilayers of single-chain linear amphiphiles with the same hydrophobic tail length. The lateral stress profile across the bilayers contains a detailed structure reflecting contributions from all the interaction potentials, as well as the amphiphile architecture. We measure the surface tension of the bilayers, and extract estimates of the membrane area stretch modulus and bending rigidity that are comparable to experimental values for typical lipid bilayers. The stress profile is similar to that found in coarse-grained Molecular Dynamics simulations, but requires a fraction of the computational cost. Dissipative Particle Dynamics therefore allows the study of the equilibrium behavior of fluid amphiphilic membranes hundreds of times larger than can be achieved using Molecular Dynamics simulations, and opens the way to the investigation of complex mesoscopic cellular phenomena.

Fluid Vesicles in Shear Flow.

The shape dynamics of fluid vesicles is governed by the coupling of the flow within the two-dimensional membrane to the hydrodynamics of the surrounding bulk fluid. We present a numerical scheme which is capable of solving this flow problem for arbitrarily shaped vesicles using the Oseen tensor formalism. For the particular problem of simple shear flow, stationary shapes are found for a large range of parameters. The dependence of the orientation of the vesicle and the membrane velocity on shear rate and vesicle volume can be understood from a simplified model.

Cooperative cargo transport by several molecular motors

The transport of cargo particles that are pulled by several molecular motors in a cooperative manner is studied theoretically in this article. The transport properties depend primarily on the maximal number N of motor molecules that may pull simultaneously on the cargo particle. Because each motor must unbind from the filament after a finite number of steps but can also rebind to it again, the actual number of pulling motors is not constant but varies with time between zero and N. An increase in the maximal number N leads to a strong increase of the average walking distance (or run length) of the cargo particle. If the cargo is pulled by up to N kinesin motors, for example, the walking distance is estimated to be 5(N-1)/N micrometers, which implies that seven or eight kinesin molecules are sufficient to attain an average walking distance in the centimeter range. If the cargo particle is pulled against an external load force, this force is shared between the motors, which provides a nontrivial motor-motor coupling and a generic mechanism for nonlinear force-velocity relationships. With increasing load force, the probability distribution of the instantaneous velocity is shifted toward smaller values, becomes broader, and develops several peaks. Our theory is consistent with available experimental data and makes quantitative predictions that are accessible to systematic in vitro experiments.

Shape Transformations of Giant Vesicles: Extreme Sensitivity to Bilayer Asymmetry

Shape transformations of vesicles of lecithin (DMPC) in water are induced by changing the temperature which effectively changes the volume-to-area ratio. Three different routes are found which include i) symmetric-asymmetric re-entrant transitions from a dumbbell to a pear-shaped state, ii) the expulsion of a smaller vesicle (budding), and iii) discocyte–stomatocyte transitions. All of these shape transformations are explained within a model for the bending energy of the bilayer which assumes i) that the two monolayers do not exchange lipid molecules, and ii) that the adjacent monolayers exhibit a small difference in their thermal expansivities which is easily produced, e.g., by residual impurities.

Time scales of membrane fusion revealed by direct imaging of vesicle fusion with high temporal resolution

Membrane fusion is a vital process of life involved, for example, in cellular secretion via exocytosis, signaling between nerve cells, and virus infection. In both the life sciences and bioengineering, controlled membrane fusion has many possible applications, such as drug delivery, gene transfer, chemical microreactors, or synthesis of nanomaterials. Until now, the fusion dynamics has been elusive because direct observations have been limited to time scales that exceed several milliseconds. Here, the fusion of giant lipid vesicles is induced in a controlled manner and monitored with a temporal resolution of 50 μs. Two different fusion protocols are used that are based on synthetic fusogenic molecules and electroporation. For both protocols, the opening of the fusion necks is very fast, with an average expansion velocity of centimeters per second. This velocity indicates that the initial formation of a single fusion neck can be completed in a few hundred nanoseconds.

Transport of Beads by Several Kinesin Motors

The movements of beads pulled by several kinesin-1 (conventional kinesin) motors are studied both theoretically and experimentally. While the velocity is approximately independent of the number of motors pulling the beads, the walking distance or run-length is strongly increased when more motors are involved. Run-length distributions are measured for a wide range of motor concentrations and matched to theoretically calculated distributions using only two global fit parameters. In this way, the maximal number of motors pulling the beads is estimated to vary between two and seven motors for total kinesin concentrations between 0.1 and 2.5 μg/ml or between 0.27 and 6.7 nM. In the same concentration regime, the average number of pulling motors is found to lie between 1.1 and 3.2 motors.

Domain-induced budding of fluid membranes

Domains within fluid membranes grow by the aggregation of molecules which diffuse laterally within the membrane matrix. A simple theoretical model is introduced which predicts that a flat or weakly curved domain becomes unstable at a certain limiting size and then undergoes a budding or invagination process. This instability is driven by the competition between the bending energy of the domain and the line tension of the domain edge. For lipid bilayers, the budding domain can rupture the membrane and then it pinches off from the matrix. The same mechanism should also drive the budding of non-coated domains in biomembranes, and could even be effective when these domains are covered by a coat of clathrin molecules.

Wetting morphologies on substrates with striped surface domains

The wetting and dewetting of chemically structured substrates with striped surface domains is studied theoretically. The lyophilic stripes and the lyophobic substrate are characterized by different contact angles θγ and θδ, respectively. We determine the complete bifurcation diagram for the wetting morphologies (i) on a single lyophilic stripe and (ii) on two neighboring stripes separated by a lyophobic one. We find that long channels can only be formed on the lyophilic stripes if the contact angle θγ is smaller than a certain threshold value θch(V) which depends only weakly on the volume V and attains the finite value θch(∞) in the limit of large V. This asymptotic value is equal to θch(∞)=arccos(π/4)≃38° for all lyophobic substrates with θδ⩾π/2. For a given value of θγ<θch(∞), the extended channels spread onto the lyophilic stripes with essentially constant cross section.