Wouter K. den Otter

The Generation of Curved Clathrin Coats from Flat Plaques

Flat clathrin lattices or ‘plaques’ are commonly believed to be the precursors to clathrin‐coated buds and vesicles. The sequence of steps carrying the flat hexagonal lattice into a highly curved polyhedral cage with exactly 12 pentagons remains elusive, however, and the large numbers of disrupted interclathrin connections in previously proposed conversion pathways make these scenarios rather unlikely. The recent notion that clathrin can make controlled small conformational transitions opens new avenues. Simulations with a self‐assembling clathrin model suggest that localized conformational changes in a plaque can create sufficiently strong stresses for a dome‐like fragment to break apart. The released fragment, which is strongly curved but still hexagonal, may subsequently grow into a cage by recruiting free triskelia from the cytoplasm, thus building all 12 pentagonal faces without recourse to complex topological changes. The critical assembly concentration in a slightly acidic in vitro solution is used to estimate the binding energy of a cage at 25–40 kBT/clathrin.

Simulations of Skin Barrier Function: Free Energies of Hydrophobic and Hydrophilic Transmembrane Pores in Ceramide Bilayers

Transmembrane pore formation is central to many biological processes such as ion transport, cell fusion, and viral infection. Furthermore, pore formation in the ceramide bilayers of the stratum corneum may be an important mechanism by which penetration enhancers such as dimethylsulfoxide (DMSO) weaken the barrier function of the skin. We have used the potential of mean constraint force (PMCF) method to calculate the free energy of pore formation in ceramide bilayers in both the innate gel phase and in the DMSO-induced fluidized state. Our simulations show that the fluid phase bilayers form archetypal water-filled hydrophilic pores similar to those observed in phospholipid bilayers. In contrast, the rigid gel-phase bilayers develop hydrophobic pores. At the relatively small pore diameters studied here, the hydrophobic pores are empty rather than filled with bulk water, suggesting that they do not compromise the barrier function of ceramide membranes. A phenomenological analysis suggests that these vapor pores are stable, below a critical radius, because the penalty of creating water-vapor and tail-vapor interfaces is lower than that of directly exposing the strongly hydrophobic tails to water. The PMCF free energy profile of the vapor pore supports this analysis. The simulations indicate that high DMSO concentrations drastically impair the barrier function of the skin by strongly reducing the free energy required for pore opening.

Accurate and unbiased estimation of power-law exponents from single-emitter blinking data

Single emitter blinking with a power-law distribution for the on and off times has been observed on a variety of systems including semiconductor nanocrystals, conjugated polymers, fluorescent proteins, and organic fluorophores. The origin of this behavior is still under debate. Reliable estimation of power exponents from experimental data is crucial in validating the various models under consideration. We derive a maximum likelihood estimator for power-law distributed data and analyze its accuracy as a function of data set size and power exponent both analytically and numerically. Results are compared to least-squares fitting of the double logarithmically transformed probability density. We demonstrate that least-squares fitting introduces a severe bias in the estimation result and that the maximum likelihood procedure is superior in retrieving the correct exponent and reducing the statistical error. For a data set as small as 50 data points, the error margins of the maximum likelihood estimator are already below 7%, giving the possibility to quantify blinking behavior when data set size is limited, e.g., due to photobleaching.

Free energies of stable and metastable pores in lipid membranes under tension

The free energy profile of pore formation in a lipid membrane, covering the entire range from a density fluctuation in an intact bilayer to a large tension-stabilized pore, has been calculated by molecular dynamics simulations with a coarse-grained lipid model. Several fixed elongations are used to obtain the Helmholtz free energy as a function of pore size for thermodynamically stable, metastable, and unstable pores, and the system-size dependence of these elongations is discussed. A link to the Gibbs free energy at constant tension, commonly known as the Litster model, is established by a Legendre transformation. The change of genus upon pore formation is exploited to estimate the saddle-splay modulus or Gaussian curvature modulus of the membrane leaflets. Details are provided of the simulation approach, which combines the potential of mean constraint force method with a reaction coordinate based on the local lipid density.The free energy profile of pore formation in a lipid membrane, covering the entire range from a density fluctuation in an intact bilayer to a large tension-stabilized pore, has been calculated by molecular dynamics simulations with a coarse-grained lipid model. Several fixed elongations are used to obtain the Helmholtz free energy as a function of pore size for thermodynamically stable, metastable, and unstable pores, and the system-size dependence of these elongations is discussed. A link to the Gibbs free energy at constant tension, commonly known as the Litster model, is established by a Legendre transformation. The change of genus upon pore formation is exploited to estimate the saddle-splay modulus or Gaussian curvature modulus of the membrane leaflets. Details are provided of the simulation approach, which combines the potential of mean constraint force method with a reaction coordinate based on the local lipid density.

An elementary singularity-free Rotational Brownian Dynamics algorithm for anisotropic particles

Brownian Dynamics is the designated technique to simulate the collective dynamics of colloidal particles suspended in a solution, e.g., the self-assembly of patchy particles. Simulating the rotational dynamics of anisotropic particles by a first-order Langevin equation, however, gives rise to a number of complications, ranging from singularities when using a set of three rotational coordinates to subtle metric and drift corrections. Here, we derive and numerically validate a quaternion-based Rotational Brownian Dynamics algorithm that handles these complications in a simple and elegant way. The extension to hydrodynamic interactions is also discussed.

Rotational Brownian Dynamics simulations of clathrin cage formation

The self-assembly of nearly rigid proteins into ordered aggregates is well suited for modeling by the patchy particle approach. Patchy particles are traditionally simulated using Monte Carlo methods, to study the phase diagram, while Brownian Dynamics simulations would reveal insights into the assembly dynamics. However, Brownian Dynamics of rotating anisotropic particles gives rise to a number of complications not encountered in translational Brownian Dynamics. We thoroughly test the Rotational Brownian Dynamics scheme proposed by Naess and Elsgaeter [Macromol. Theory Simul. 13, 419 (2004); Naess and Elsgaeter Macromol. Theory Simul. 14, 300 (2005)], confirming its validity. We then apply the algorithm to simulate a patchy particle model of clathrin, a three-legged protein involved in vesicle production from lipid membranes during endocytosis. Using this algorithm we recover time scales for cage assembly comparable to those from experiments. We also briefly discuss the undulatory dynamics of the polyhedral cage.

Revisiting the Exact Relation between Potential of Mean Force and Free-Energy Profile

Constraints are convenient in the calculation of free energy profiles via molecular dynamics simulations, but they subtly alter the phase space distribution. In a recent letter of a related title in this journal, Wong and York [J. Chem. Theory Comput. 2012, 8, 3998-4003] suggest replacing Fixmans mass-metric correction with its inverse and adding a Jacobian contribution to the potential of mean constraint force. This letter refutes both suggestions, discusses the underlying interpretation problems, and provides supporting numerical simulations.

Can Confinement-Induced Variations in the Viscous Dissipation be Measured?

Liquids confined to molecular scales become anisotropic and often show pronounced self-organization such as layering. Although this effect is well accepted, it is still debated if confinement induces measurable changes of viscous friction. We use molecular dynamics to address this issue by simulating a Lennard-Jones liquid confined between a solid cylinder and an atomically smooth surface. The simulations reproduce the well-established variations of normal force, density, and diffusivity with the distance between wall and cylinder. We find high diffusivity and low density when the numbers of layers is in between integers. This observation seems to contradict most experimental results on the effective damping between atomic force microscope tips and substrates when interpreting them within continuum hydrodynamics used to connect liquid viscosity and diffusivity. This contradiction is resolved by directly extracting the damping that the tip experiences, which we achieve by using the fluctuation-dissipation theorem; as in experiment, we find local minima in the damping near integer numbers of molecular layers and maxima in between. These variations correlate with distinct structural changes in the microscopic order of the fluid. We reconfirm that constitutive equations valid at macroscopic scales cannot be used to interpret confined liquids and finally conclude that viscous friction displays measurable, non-monotonic behavior with the degree of confinement.

Clathrin Assembly Regulated by Adaptor Proteins in Coarse-Grained Models

The assembly of clathrin triskelia into polyhedral cages during endocytosis is regulated by adaptor proteins (APs). We explore how APs achieve this by developing coarse-grained models for clathrin and AP2, employing a Monte Carlo click interaction, to simulate their collective aggregation behavior. The phase diagrams indicate that a crucial role is played by the mechanical properties of the disordered linker segment of AP. We also present a statistical-mechanical theory for the assembly behavior of clathrin, yielding good agreement with our simulations and experimental data from the literature. Adaptor proteins are found to regulate the formation of clathrin coats under certain conditions, but can also suppress the formation of cages.

Coarse-Grained Simulations of Three-Armed Star Polymer Melts and Comparison with Linear Chains

Melts of three-armed star polymers have been simulated using a coarse-grained model parameterized by atomistic simulations of polyethylene. The bonds between the highly coarse-grained, and hence soft, polymer beads are explicitly prevented from crossing by the TWENTANGLEMENT algorithm. The three melts of symmetric stars, differing in the lengths of the arms, are compared against five melts of linear polymers with comparable dimensions to study the impact of branched architecture on self-diffusion and bulk rheological properties. Differently from the power-law relation between the viscosity and molecular mass of linear chains, the star polymers in our simulations follow an exponential mass-viscosity relation and show qualitative agreement with the storage and loss moduli for stars with far longer arms from experiments. The stress relaxation dynamics of the stars are also compared with theoretical analysis in terms of Rouse modes.