Markus Deserno

Aggregation and vesiculation of membrane proteins by curvature-mediated interactions

Membrane remodelling plays an important role in cellular tasks such as endocytosis, vesiculation and protein sorting, and in the biogenesis of organelles such as the endoplasmic reticulum or the Golgi apparatus. It is well established that the remodelling process is aided by specialized proteins that can sense as well as create membrane curvature, and trigger tubulation when added to synthetic liposomes. Because the energy needed for such large-scale changes in membrane geometry significantly exceeds the binding energy between individual proteins and between protein and membrane, cooperative action is essential. It has recently been suggested that curvature-mediated attractive interactions could aid cooperation and complement the effects of specific binding events on membrane remodelling. But it is difficult to experimentally isolate curvature-mediated interactions from direct attractions between proteins. Moreover, approximate theories predict repulsion between isotropically curving proteins. Here we use coarse-grained membrane simulations to show that curvature-inducing model proteins adsorbed on lipid bilayer membranes can experience attractive interactions that arise purely as a result of membrane curvature. We find that once a minimal local bending is realized, the effect robustly drives protein cluster formation and subsequent transformation into vesicles with radii that correlate with the local curvature imprint. Owing to its universal nature, curvature-mediated attraction can operate even between proteins lacking any specific interactions, such as newly synthesized and still immature membrane proteins in the endoplasmic reticulum.

How to Mesh up Ewald Sums. I. A Theoretical and Numerical Comparison of Various Particle Mesh Routines

Standard Ewald sums, which calculate, e.g., the electrostatic energy or the force in periodically closed systems of charged particles, can be efficiently speeded up by the use of the fast Fourier transformation (FFT). In this article we investigate three algorithms for the FFT-accelerated Ewald sum, which have attracted widespread attention, namely, the so-called particle–particle–particle mesh (P3M), particle mesh Ewald (PME), and smooth PME method. We present a unified view of the underlying techniques and the various ingredients which comprise those routines. Additionally, we offer detailed accuracy measurements, which shed some light on the influence of several tuning parameters and also show that the existing methods — although similar in spirit — exhibit remarkable differences in accuracy. We propose a set of combinations of the individual components, mostly relying on the P3M approach, that we regard to be the most flexible. The issue of estimating the errors connected with particle mesh routines i...

Tunable generic model for fluid bilayer membranes

We present a model for the efficient simulation of generic bilayer membranes. Individual lipids are represented by one head bead and two tail beads. By means of simple pair potentials these robustly self-assemble to a fluid bilayer state over a wide range of parameters, without the need for an explicit solvent. The model shows the expected elastic behavior on large length scales, and its physical properties (e.g., fluidity or bending stiffness) can be widely tuned via a single parameter. In particular, bending rigidities in the experimentally relevant range are obtained, at least within 3-30 k(B) T. The model is naturally suited to study many physical topics, including self-assembly, fusion, bilayer melting, lipid mixtures, rafts, and protein-bilayer interactions.

How to mesh up Ewald sums. II. An accurate error estimate for the particle–particle–particle-mesh algorithm

We construct an accurate estimate for the root mean square force error of the particle–particle–particle mesh (P3M) algorithm by extending a single particle pair error measure which has been given by Hockney and Eastwood. We also derive an easy to use analytic approximation to the error formula. This allows a straightforward and precise determination of the optimal splitting parameter (as a function of system specifications and P3M parameters) and hence knowledge of the force accuracy prior to the actual simulation. The high quality of the estimate is demonstrated in several examples.

Solvent-free model for self-assembling fluid bilayer membranes: Stabilization of the fluid phase based on broad attractive tail potentials

We present a simple and highly adaptable method for simulating coarse-grained lipid membranes without explicit solvent. Lipids are represented by one head bead and two tail beads, with the interaction between tails being of key importance in stabilizing the fluid phase. Two such tail-tail potentials were tested, with the important feature in both cases being a variable range of attraction. We examined phase diagrams of this range versus temperature for both functional forms of the tail-tail attraction and found that a certain threshold attractive width was required to stabilize the fluid phase. Within the fluid-phase region we find that material properties such as area per lipid, orientational order, diffusion constant, interleaflet flip-flop rate, and bilayer stiffness all depend strongly and monotonically on the attractive width. For three particular values of the potential width we investigate the transition between gel and fluid phases via heating or cooling and find that this transition is discontinuous with considerable hysteresis. We also investigated the stretching of a bilayer to eventually form a pore and found excellent agreement with recent analytic theory.

Elastic deformation of a fluid membrane upon colloid binding

When a colloidal particle adheres to a fluid membrane, it induces elastic deformations in the membrane which oppose its own binding. The structural and energetic aspects of this balance are investigated within the framework of a Helfrich Hamiltonian. Based on the full nonlinear shape equations for the membrane profile, a line of continuous binding transitions and a second line of discontinuous envelopment transitions are found, which meet at an unusual triple point. The regime of low tension is studied analytically using a small gradient expansion, while in the limit of large tension scaling arguments are derived which quantify the asymptotic behavior of phase boundary, degree of wrapping, and energy barrier. The maturation of animal viruses by budding is discussed as a biological example of such colloid-membrane interaction events.

Generic coarse-grained model for protein folding and aggregation.

A generic coarse-grained (CG) protein model is presented. The intermediate level of resolution (four beads per amino acid, implicit solvent) allows for accurate sampling of local conformations. It relies on simple interactions that emphasize structure, such as hydrogen bonds and hydrophobicity. Realistic alpha/beta content is achieved by including an effective nearest-neighbor dipolar interaction. Parameters are tuned to reproduce both local conformations and tertiary structures. The thermodynamics and kinetics of a three-helix bundle are studied. We check that the CG model is able to fold proteins with tertiary structures and amino acid sequences different from the one used for parameter tuning. By studying both helical and extended conformations we make sure the force field is not biased toward any particular secondary structure. The accuracy involved in folding not only the test protein but also other ones show strong evidence for amino acid cooperativity embedded in the model. Without any further adjustments or bias a realistic oligopeptide aggregation scenario is observed.

A novel method for measuring the bending rigidity of model lipid membranes by simulating tethers

The tensile force along a cylindrical lipid bilayer tube is proportional to the membranes bending modulus and inversely proportional to the tube radius. We show that this relation, which is experimentally exploited to measure bending rigidities, can be applied with even greater ease in computer simulations. Using a coarse-grained bilayer model we efficiently obtain bending rigidities that compare very well with complementary measurements based on an analysis of thermal undulation modes. We furthermore illustrate that no deviations from simple quadratic continuum theory occur up to a radius of curvature comparable to the bilayer thickness.

Wrapping of a spherical colloid by a fluid membrane

We theoretically study the elastic deformation of a fluid membrane induced by an adhering spherical colloidal particle within the framework of a Helfrich energy. Based on a full optimization of the membrane shape we find a continuous binding and a discontinuous envelopment transition, the latter displaying a potentially substantial energy barrier. A small-gradient approximation permits membrane shape and complex energy to be calculated analytically. While this only leads to a good representation of the complex geometry for very small degrees of wrapping, it still gives the correct phase boundaries in the regime of low tension.

Mesoscopic Membrane Physics: Concepts, Simulations, and Selected Applications

The window of a few tens to a few hundred nanometers in length scale is a booming field in lipid membrane research, owing largely to two reasons. First, many exciting biophysical and cell biological processes take place within it. Second, experimental techniques manage to zoom in on this sub-optical scale, while computer simulations zoom out to system sizes previously unattainable, and both will be meeting soon. This paper reviews a selection of questions and concepts in this field and demonstrates that they can often be favorably addressed with highly simplified simulation models. Among the topics discussed are membrane adhesion to substrates, mixed lipid bilayers, lipid curvature coupling, pore formation by antimicrobial peptides, composition-driven protein aggregation, and curvature driven vesiculation.