The "protein folding problem" consists of three closely related puzzles: (a) What is the folding code? (b) What is the folding mechanism? (c) Can we predict the native structure of a protein from its amino acid sequence? Once regarded as a grand challenge, protein folding has seen great progress in recent years. Now, foldable proteins and nonbiological polymers are being designed routinely and moving toward successful applications. The structures of small proteins are now often well predicted by computer methods. And, there is now a testable explanation for how a protein can fold so quickly: A protein solves its large global optimization problem as a series of smaller local optimization problems, growing and assembling the native structure from peptide fragments, local structures first.

Characterizing the equilibrium ensemble of folding pathways, including their relative probability, is one of the major challenges in protein folding theory today. Although this information is in principle accessible via all-atom molecular dynamics simulations, it is difficult to compute in practice because protein folding is a rare event and the affordable simulation length is typically not sufficient to observe an appreciable number of folding events, unless very simplified protein models are used. Here we present an approach that allows for the reconstruction of the full ensemble of folding pathways from simulations that are much shorter than the folding time. This approach can be applied to all-atom protein simulations in explicit solvent. It does not use a predefined reaction coordinate but is based on partitioning the state space into small conformational states and constructing a Markov model between them. A theory is presented that allows for the extraction of the full ensemble of transition pathways from the unfolded to the folded configurations. The approach is applied to the folding of a PinWW domain in explicit solvent where the folding time is two orders of magnitude larger than the length of individual simulations. The results are in good agreement with kinetic experimental data and give detailed insights about the nature of the folding process which is shown to be surprisingly complex and parallel. The analysis reveals the existence of misfolded trap states outside the network of efficient folding intermediates that significantly reduce the folding speed. D iscovering the mechanism by which proteins fold into their native 3D structure remains an intriguing problem (1, 2). Essential questions are: How does an ensemble of denatured molecules find the same native structure, starting from different conformations? Are there particular sequences in which the structural elements of a protein are formed (3-5)? Are there multiple parallel routes by which protein structure formation can proceed (6, 7)?Full answers to these questions require one to characterize the ensemble of folding pathways, including their relative probabilities. In principle, this detailed information is accessible via molecular dynamics (MD) simulations which, when used in concert with experimental evidence, are becoming an increasingly accepted tool to understanding structural details that are not easily accessible via the experimental observables (8). MD simulations with atomistic models of proteins have been used to study the dynamics of small proteins with folding times in the microsecond range (9-13). However, even though MD simulations make the full spatiotemporal detail accessible to observation, the characterization of the pathway ensemble is computationally difficult: A brute-force approach would start simulations from an equilibrium of unfolded structures, say A, and simulate until they relax into a set of folded state B. The analysis would then only be comprised of those trajectory segments that leave A and relax to B without...

Considering two rigid conical inclusions embedded in a membrane subject to lateral tension, we study the membrane-mediated interaction between these inclusions that originates from the hat-shaped membrane deformations associated with the cones. At nonvanishing lateral tensions, the interaction is found to depend on the orientation of the cones with respect to the membrane plane. The interaction of inclusions of equal orientation is repulsive at all distances between them, while the inclusions of opposite orientation repel each other at small separations, but attract each other at larger ones. Both the repulsive and attractive forces become stronger with increasing lateral tension. This is different from what has been predicted on the basis of the same static model for the case of vanishing lateral tension. Without tension, the inclusions repel each other at all distances independently of their relative orientation. We conclude that lateral tension may induce the aggregation of conical membrane inclusions.We consider a membrane with two embedded conical inclusions. The cross sections of the inclusions in the midplane of the membrane are circles of radius a. The centers of the two circles are separated by the distance R ͑see Fig. 3͒.

No abstract

Understanding and control of structures and rates involved in protein ligand binding are essential for drug design. Unfortunately, atomistic molecular dynamics (MD) simulations cannot directly sample the excessively long residence and rearrangement times of tightly binding complexes. Here we exploit the recently developed multi-ensemble Markov model framework to compute full protein-peptide kinetics of the oncoprotein fragment 25–109Mdm2 and the nano-molar inhibitor peptide PMI. Using this system, we report, for the first time, direct estimates of kinetics beyond the seconds timescale using simulations of an all-atom MD model, with high accuracy and precision. These results only require explicit simulations on the sub-milliseconds timescale and are tested against existing mutagenesis data and our own experimental measurements of the dissociation and association rates. The full kinetic model reveals an overall downhill but rugged binding funnel with multiple pathways. The overall strong binding arises from a variety of conformations with different hydrophobic contact surfaces that interconvert on the milliseconds timescale.

How nanoparticles interact with biomembranes is central for understanding their bioactivity. In this Letter, we report novel tubular membrane structures induced by adsorbed spherical nanoparticles, which we obtain from energy minimization. The membrane tubules enclose linear aggregates of particles and protrude into the vesicles. The high stability of the particle-filled tubules implies strongly attractive, membrane-mediated interactions between the particles. The tubular structures may provide a new route to encapsulate nanoparticles reversibly in vesicles.

The importance of curvature as a structural feature of biological membranes has been recognized for many years and has fascinated scientists from a wide range of different backgrounds. On the one hand, changes in membrane morphology are involved in a plethora of phenomena involving the plasma membrane of eukaryotic cells, including endo- and exocytosis, phagocytosis and filopodia formation. On the other hand, a multitude of intracellular processes at the level of organelles rely on generation, modulation, and maintenance of membrane curvature to maintain the organelle shape and functionality. The contribution of biophysicists and biologists is essential for shedding light on the mechanistic understanding and quantification of these processes. Given the vast complexity of phenomena and mechanisms involved in the coupling between membrane shape and function, it is not always clear in what direction to advance to eventually arrive at an exhaustive understanding of this important research area. The 2018 Biomembrane Curvature and Remodeling Roadmap of Journal of Physics D: Applied Physics addresses this need for clarity and is intended to provide guidance both for students who have just entered the field as well as established scientists who would like to improve their orientation within this fascinating area.

T cells form intriguing patterns during adhesion to antigen-presenting cells. The patterns are composed of two types of domains, which either contain short TCR/MHCp receptor-ligand complexes or the longer LFA-1/ICAM-1 complexes. The final pattern consists of a central TCR/MHCp domain surrounded by a ring-shaped LFA-1/ICAM-1 domain, whereas the characteristic pattern formed at intermediate times is inverted with TCR/MHCp complexes at the periphery of the contact zone and LFA-1/ICAM-1 complexes in the center. Several mechanisms have been proposed to explain the T-cell pattern formation. Whereas biologists have emphasized the role of active cytoskeletal processes, previous theoretical studies suggest that the pattern evolution may be caused by spontaneous self-assembly processes alone. Some of these studies focus on circularly symmetric patterns and propose a pivot mechanism for the formation of the intermediate inverted pattern. Here, we present a statistical-mechanical model which includes thermal fluctuations and the full range of spatial patterns. We confirm the observation that the intermediate inverted pattern may be formed by spontaneous self-assembly. However, we find a different self-assembly mechanism in which numerous TCR/MHCp microdomains initially nucleate throughout the contact zone. The diffusion of free receptors and ligands into the contact zone subsequently leads to faster growth of peripheral TCR/MHCp microdomains and to a closed ring for sufficiently large TCR/MHCp concentrations. At smaller TCR/MHCp concentrations, we observe a second regime of pattern formation with characteristic multifocal intermediates, which resemble patterns observed during adhesion of immature T cells or thymozytes. In contrast to other theoretical models, we find that the final T-cell pattern with a central TCR/MHCp domain is only obtained in the presence of active cytoskeletal transport processes.