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.

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 ͑FFT͒. 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 ͑P 3 M), particle mesh Ewald ͑PME͒, 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 P 3 M approach, that we regard to be the most flexible. The issue of estimating the errors connected with particle mesh routines is reserved to paper II.

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 stiffness͒ can be widely tuned via a single parameter. In particular, bending rigidities in the experimentally relevant range are obtained, at least within 3 -30k 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. Lipid molecules in aqueous solution spontaneously assemble into bilayer membranes. In biological systems, such membranes are involved in tasks over an extraordinary range of length scales, from transport of water and ions at the scale of nanometers, up to phagocytosis, amoebal motion and cell budding at the scale of microns ͓1͔. Computer simulations designed to understand some aspects of this structural and functional range must be tailored to the specific length and timescales involved. Techniques that probe both the smallest ͓2͔ and largest ͓3͔ of these length and time scales are now well established; however, accessing intermediate regimes has proven far more difficult, and it is only recently that significant progress has been made in this regard. The need for a comprehensive suite of techniques to study lipid bilayers at the mesoscale is highlighted by the sheer number of relevant problems in this regime, which include viral budding, raft formation, fusion, phase separation of multicomponent systems, and protein sorting during vesiculation.Most existing approaches to mesoscale simulation employ coarse grained lipids and require explicit solvent particles to stabilize the bilayer. This strategy is convenient and natural, yet it comes at a high price: Already for small flat systems the solvent accounts for most of the computational effort, but the problem gets significantly worse when three dimensional objects such as vesicles are to be simulated. Membrane and solvent play the role of surface and bulk, respectively, hence, the solvent degrees of freedom vastly outnumber the lipids even for rather modest sized vesicles. An obvious solution to this problem is to replace the solvent by effective lipid interactions. Given the great success of this approach in polymer physics it is perhaps surprising that solvent-free bilayer simulations have so far failed to find widespread acceptance. The problem appears to be that naive choices for interparticle potentials ͑e.g., Lennard-Jones͒ do not lead to a fluid bilayer phase but only to ordered "solid" bilayers at low temperature and low density phases at high temperature. Many attempts to obtain a broadly stable fluid phase have been made with varying degrees of success. So far, however, none of these has result...

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.

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.

We investigate the phenomenon of counterion condensation in a solution of highly charged rigid polyelectrolytes within the cell model. A method is proposed which -based on the charge distribution function -identifies both the fraction of condensed ions and the radial extension of the condensed layer. Within salt-free Poisson-Boltzmann (PB) theory it reproduces the well known fraction 1 − 1/ξ of condensed ions for a Manning parameter ξ > 1. Furthermore, it predicts a weak salt dependence of this fraction and a breakdown of the concept of counterion condensation in the high salt limit. We complement our theoretical investigations with molecular dynamics simulations of a cell-like model, which constantly yield a stronger condensation than predicted by PB theory. While the agreement between theory and simulation is excellent in the monovalent, weakly charged case, it deteriorates with increasing electrostatic interaction strength and, in particular, increasing valence. For instance, at a high concentration of divalent salt and large ξ our computer simulations predict charge oscillations, which mean-field theory is unable to reproduce.

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.

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