Curvature as a Collective Coordinate in Enhanced Sampling Membrane Simulations

Predicting binding events in very flexible, allosteric, multi-domain proteins

Knowledge of the structures formed by proteins and small ligands is of fundamental importance for understanding molecular principles of chemotherapy and for designing new and more effective drugs. Due to the still high costs and to the several limitations of experimental techniques, it is most often desirable to predict these ligand-protein complexes in silico , particularly when screening for new putative drugs from databases of millions of compounds. While virtual screening based on molecular docking is widely used for this purpose, it generally fails in mimicking binding events associated with large conformational changes in the protein, particularly when the latter involve multiple domains. In this work, we describe a new methodology aimed at generating bound-like conformations of very flexible and allosteric proteins bearing multiple binding sites. Validation was performed on the enzyme adenylate kinase (ADK), a paradigmatic example of proteins that undergo very large conformational changes upon ligand binding. By only exploiting the unbound structure and the putative binding sites of the protein, we generated a significant fraction of bound-like structures, which employed in ensemble-docking calculations allowed to find native-like poses of substrates, inhibitors, and catalytically incompetent binders. Our protocol provides a general framework for the generation of bound-like conformations of flexible proteins that are suitable to host different ligands, demonstrating high sensitivity to the fine chemical details that regulate protein's activity. We foresee applications in virtual screening for difficult targets, prediction of the impact of amino acid mutations on structure and dynamics, and protein engineering.

Determination of Elastic Parameters of Lipid Membranes with Molecular Dynamics: A Review of Approaches and Theoretical Aspects

Lipid membranes are abundant in living organisms, where they constitute a surrounding shell for cells and their organelles. There are many circumstances in which the deformations of lipid membranes are involved in living cells: fusion and fission, membrane-mediated interaction between membrane inclusions, lipid-protein interaction, formation of pores, etc. In all of these cases, elastic parameters of lipid membranes are important for the description of membrane deformations, as these parameters determine energy barriers and characteristic times of membrane-involved phenomena. Since the development of molecular dynamics (MD), a variety of in silico methods have been proposed for the determination of elastic parameters of simulated lipid membranes. These MD methods allow for the consideration of details unattainable in experimental techniques and represent a distinct scientific field, which is rapidly developing. This work provides a review of these MD approaches with a focus on theoretical aspects. Two main challenges are identified: (i) the ambiguity in the transition from the continuum description of elastic theories to the discrete representation of MD simulations, and (ii) the determination of intrinsic elastic parameters of lipid mixtures, which is complicated due to the composition-curvature coupling effect.

Membrane curvature as a signal to ensure robustness of diverse cellular processes

An increasing corpus of research has demonstrated that membrane shape, generated either by the external environment of the cell or by intrinsic mechanisms such as cytokinesis and vesicle or organelle formation, is an important parameter in the control of diverse cellular processes. In this review we discuss recent findings that demonstrate how membrane curvature (from nanometer to micron length-scales) alters protein function. We describe an expanding toolkit for experimentally modulating membrane curvature to reveal effects on protein function, and discuss how membrane curvature - far from being a passive consequence of the physical environment and the internal protein activity of a cell - is an important signal that controls protein affinity and enzymatic activity to ensure robust forward progression of key processes within the cell.

Molecular Dynamics Simulations of Curved Lipid Membranes

Eukaryotic cells contain membranes with various curvatures, from the near-plane plasma membrane to the highly curved membranes of organelles, vesicles, and membrane protrusions. These curvatures are generated and sustained by curvature-inducing proteins, peptides, and lipids, and describing these mechanisms is an important scientific challenge. In addition to that, some molecules can sense membrane curvature and thereby be trafficked to specific locations. The description of curvature sensing is another fundamental challenge. Curved lipid membranes and their interplay with membrane-associated proteins can be investigated with molecular dynamics (MD) simulations. Various methods for simulating curved membranes with MD are discussed here, including tools for setting up simulation of vesicles and methods for sustaining membrane curvature. The latter are divided into methods that exploit scaffolding virtual beads, methods that use curvature-inducing molecules, and methods applying virtual forces. The variety of simulation tools allow researcher to closely match the conditions of experimental studies of membrane curvatures.

Simulating realistic membrane shapes

Biological membranes exhibit diversity in their shapes and complexity in chemical compositions that are linked to many cellular functions. These two central features of biomembranes have been the subject of numerous simulation studies, using a diverse range of computational techniques. Currently, the field is able to capture this complexity at increasing levels of realism and connect the microscopic view on protein-lipid interactions to cellular morphologies at the level of entire organelles. Here we highlight recent advances in this topic, identify current bottlenecks, and sketch possible ways ahead.

How proteins open fusion pores: insights from molecular simulations

Fusion proteins can play a versatile and involved role during all stages of the fusion reaction. Their roles go far beyond forcing the opposing membranes into close proximity to drive stalk formation and fusion. Molecular simulations have played a central role in providing a molecular understanding of how fusion proteins actively overcome the free energy barriers of the fusion reaction up to the expansion of the fusion pore. Unexpectedly, molecular simulations have revealed a preference of the biological fusion reaction to proceed through asymmetric pathways resulting in the formation of, e.g., a stalk-hole complex, rim-pore, or vertex pore. Force-field based molecular simulations are now able to directly resolve the minimum free-energy path in protein-mediated fusion as well as quantifying the free energies of formed reaction intermediates. Ongoing developments in Graphics Processing Units (GPUs), free energy calculations, and coarse-grained force-fields will soon gain additional insights into the diverse roles of fusion proteins.

Density Field Thermodynamic Integration (DFTI): A "Soft" Approach to Calculate the Free Energy of Surfactant Self-Assemblies

Thermodynamic integration is one of the most established methods to quantify excess free energies between different metastable states. Excess intermolecular interactions in surfactant assemblies are on the scale of the energy of thermal fluctuations. Therefore, these materials can be deformed and topologically altered via relatively small mechanical stresses. It is thus intuitive to design reaction paths and associated order parameters that exploit the "soft" nature of these materials to mechanically rather than alchemically morph surfactant assemblies from state to state. Here, we propose a novel method coined "density field thermodynamic integration" (DFTI) that adopts the universality and transferability of alchemical methods while simultaneously exploiting the soft excess interactions between surfactant molecules. DFTI was designed for a rapid quantification of the free energy differences between different metastable structures in soft fluid materials. The DFTI method uses an external field coupled to the local density to mechanically morph the system between metastable states of interest. Here, we explored the capability of the DFTI method to swiftly and accurately calculate free energy differences between states. To this aim, we studied two different coarse-grained lipidic surfactant systems: (i) a fusion stalk and (ii) a worm-like micelle. Our results illustrate that DFTI can provide an efficient, versatile, and rather reliable method to calculate the free energy differences between surfactant assemblies.