Udo Seifert

Configurations of fluid membranes and vesicles

Abstract Vesicles consisting of a bilayer membrane of amphiphilic lipid molecules are remarkably flexible surfaces that show an amazing variety of shapes of different symmetry and topology. Owing to the fluidity of the membrane, shape transitions such as budding can be induced by temperature changes or the action of optical tweezers. Thermally excited shape fluctuations are both strong and slow enough to be visible by video microscopy. Depending on the physical conditions, vesicles adhere to and unbind from each other or a substrate. This article describes the systematic physical theory developed to understand the static and dynamic aspects of membrane and vesicle configurations. The preferred shapes arise from a competition between curvature energy, which derives from the bending elasticity of the membrane, geometrical constraints such as fixed surface area and fixed enclosed volume, and a signature of the bilayer aspect. These shapes of lowest energy are arranged into phase diagrams, which separate regi...

Stochastic thermodynamics, fluctuation theorems and molecular machines

Stochastic thermodynamics as reviewed here systematically provides a framework for extending the notions of classical thermodynamics such as work, heat and entropy production to the level of individual trajectories of well-defined non-equilibrium ensembles. It applies whenever a non-equilibrium process is still coupled to one (or several) heat bath(s) of constant temperature. Paradigmatic systems are single colloidal particles in time-dependent laser traps, polymers in external flow, enzymes and molecular motors in single molecule assays, small biochemical networks and thermoelectric devices involving single electron transport. For such systems, a first-law like energy balance can be identified along fluctuating trajectories. For a basic Markovian dynamics implemented either on the continuum level with Langevin equations or on a discrete set of states as a master equation, thermodynamic consistency imposes a local-detailed balance constraint on noise and rates, respectively. Various integral and detailed fluctuation theorems, which are derived here in a unifying approach from one master theorem, constrain the probability distributions for work, heat and entropy production depending on the nature of the system and the choice of non-equilibrium conditions. For non-equilibrium steady states, particularly strong results hold like a generalized fluctuation-dissipation theorem involving entropy production. Ramifications and applications of these concepts include optimal driving between specified states in finite time, the role of measurement-based feedback processes and the relation between dissipation and irreversibility. Efficiency and, in particular, efficiency at maximum power can be discussed systematically beyond the linear response regime for two classes of molecular machines, isothermal ones such as molecular motors, and heat engines such as thermoelectric devices, using a common framework based on a cycle decomposition of entropy production.

Entropy production along a stochastic trajectory and an integral fluctuation theorem.

For stochastic nonequilibrium dynamics like a Langevin equation for a colloidal particle or a master equation for discrete states, entropy production along a single trajectory is studied. It involves both genuine particle entropy and entropy production in the surrounding medium. The integrated sum of both Delatas(tot) is shown to obey a fluctuation theorem (exp([-Deltas(tot) = 1 for arbitrary initial conditions and arbitrary time-dependent driving over a finite time interval.

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.

Rupture of multiple parallel molecular bonds under dynamic loading.

Biological adhesion often involves several pairs of specific receptor-ligand molecules. Using rate equations, we study theoretically the rupture of such multiple parallel bonds under dynamic loading assisted by thermal activation. For a simple generic type of cooperativity, both the rupture time and force exhibit several different scaling regimes. The dependence of the rupture force on the number of bonds is predicted to be either linear, like a square root, or logarithmic.

Stochastic thermodynamics: principles and perspectives

Stochastic thermodynamics provides a framework for describing small systems like colloids or biomolecules driven out of equilibrium but still in contact with a heat bath. Both, a first-law like energy balance involving exchanged heat and entropy production entering refinements of the second law can consistently be defined along single stochastic trajectories. Various exact relations involving the distribution of such quantities like integral and detailed fluctuation theorems for total entropy production and the Jarzynski relation follow from such an approach based on Langevin dynamics. Analogues of these relations can be proven for any system obeying a stochastic master equation like, in particular, (bio)chemically driven enzyms or whole reaction networks. The perspective of investigating such relations for stochastic field equations like the Kardar-Parisi-Zhang equation is sketched as well.

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.

Efficiency at maximum power : An analytically solvable model for stochastic heat engines

We study a class of cyclic Brownian heat engines in the framework of finite-time thermodynamics. For infinitely long cycle times, the engine works at the Carnot efficiency limit producing, however, zero power. For the efficiency at maximum power, we find a universal expression, different from the endoreversible Curzon-Ahlborn efficiency. Our results are illustrated with a simple one-dimensional engine working in and with a time-dependent harmonic potential.

Viscous modes of fluid bilayer membranes

We determine the dispersion relation for a fluid bilayer membrane, taking into account the coupling between bending and the local density of the two monolayers. Apart from important corrections to the conventional bending mode, we obtain a second slow mode which is essentially a fluctuation in the density difference of the two monolayers, damped by inter-monolayer friction. Estimates for a stack of membranes show reasonable agreement with a recent spin-echo study of membrane undulations.

Thermodynamics of a colloidal particle in a time-dependent nonharmonic potential.

We study the motion of an overdamped colloidal particle in a time-dependent nonharmonic potential. We demonstrate the first lawlike balance between applied work, exchanged heat, and internal energy on the level of a single trajectory. The observed distribution of applied work is distinctly non-Gaussian in good agreement with numerical calculations. Both the Jarzynski relation and a detailed fluctuation theorem are verified with good accuracy.