Shape variation of bilayer membrane daughter vesicles induced by anisotropic membrane inclusions

Mesoscale computational studies of membrane bilayer remodeling by curvature-inducing proteins

Biological membranes constitute boundaries of cells and cell organelles. These membranes are soft fluid interfaces whose thermodynamic states are dictated by bending moduli, induced curvature fields, and thermal fluctuations. Recently, there has been a flood of experimental evidence highlighting active roles for these structures in many cellular processes ranging from trafficking of cargo to cell motility. It is believed that the local membrane curvature, which is continuously altered due to its interactions with myriad proteins and other macromolecules attached to its surface, holds the key to the emergent functionality in these cellular processes. Mechanisms at the atomic scale are dictated by protein-lipid interaction strength, lipid composition, lipid distribution in the vicinity of the protein, shape and amino acid composition of the protein, and its amino acid contents. The specificity of molecular interactions together with the cooperativity of multiple proteins induce and stabilize complex membrane shapes at the mesoscale. These shapes span a wide spectrum ranging from the spherical plasma membrane to the complex cisternae of the Golgi apparatus. Mapping the relation between the protein-induced deformations at the molecular scale and the resulting mesoscale morphologies is key to bridging cellular experiments across the various length scales. In this review, we focus on the theoretical and computational methods used to understand the phenomenology underlying protein-driven membrane remodeling. Interactions at the molecular scale can be computationally probed by all atom and coarse grained molecular dynamics (MD, CGMD), as well as dissipative particle dynamics (DPD) simulations, which we only describe in passing. We choose to focus on several continuum approaches extending the Canham - Helfrich elastic energy model for membranes to include the effect of curvature-inducing proteins and explore the conformational phase space of such systems. In this description, the protein is expressed in the form of a spontaneous curvature field. The approaches include field theoretical methods limited to the small deformation regime, triangulated surfaces and particle-based computational models to investigate the large-deformation regimes observed in the natural state of many biological membranes. Applications of these methods to understand the properties of biological membranes in homogeneous and inhomogeneous environments of proteins, whose underlying curvature fields are either isotropic or anisotropic, are discussed. The diversity in the curvature fields elicits a rich variety of morphological states, including tubes, discs, branched tubes, and caveola. Mapping the thermodynamic stability of these states as a function of tuning parameters such as concentration and strength of curvature induction of the proteins is discussed. The relative stabilities of these self-organized shapes are examined through free-energy calculations. The suite of methods discussed here can be tailored to applications in specific cellular settings such as endocytosis during cargo trafficking and tubulation of filopodial structures in migrating cells, which makes these methods a powerful complement to experimental studies.

Modulation of the pHLIP transmembrane helix insertion pathway

The membrane-associated folding/unfolding of pH (low) insertion peptide (pHLIP) provides an opportunity to study how sequence variations influence the kinetics and pathway of peptide insertion into bilayers. Here, we present the results of steady-state and kinetics investigations of several pHLIP variants with different numbers of charged residues, with attached polar cargoes at the peptide's membrane-inserting end, and with three single-Trp variants placed at the beginning, middle, and end of the transmembrane helix. Each pHLIP variant exhibits a pH-dependent interaction with a lipid bilayer. Although the number of protonatable residues at the inserting end does not affect the ultimate formation of helical structure across a membrane, it correlates with the time for peptide insertion, the number of intermediate states on the folding pathway, and the rates of unfolding and exit. The presence of polar cargoes at the peptide's inserting end leads to the appearance of intermediate states on the insertion pathway. Cargo polarity correlates with a decrease of the insertion rate. We conclude that the existence of intermediate states on the folding and unfolding pathways is not mandatory and, in the simple case of a polypeptide with a noncharged and nonpolar inserting end, the folding and unfolding appears as an all-or-none transition. We propose a model for membrane-associated insertion/folding and exit/unfolding and discuss the importance of these observations for the design of new delivery agents for direct translocation of polar therapeutic and diagnostic cargo molecules across cellular membranes.

Systems biology and physical biology of clathrin-mediated endocytosis

In this review, we describe the application of experimental data and modeling of intracellular endocytic trafficking mechanisms with a focus on the process of clathrin-mediated endocytosis. A detailed parts-list for the protein-protein interactions in clathrin-mediated endocytosis has been available for some time. However, recent experimental, theoretical, and computational tools have proved to be critical in establishing a sequence of events, cooperative dynamics, and energetics of the intracellular process. On the experimental front, total internal reflection fluorescence microscopy, photo-activated localization microscopy, and spinning-disk confocal microscopy have focused on assembly and patterning of endocytic proteins at the membrane, while on the theory front, minimal theoretical models for clathrin nucleation, biophysical models for membrane curvature and bending elasticity, as well as methods from computational structural and systems biology, have proved insightful in describing membrane topologies, curvature mechanisms, and energetics.

Energetics of peptide (pHLIP) binding to and folding across a lipid bilayer membrane

The pH low-insertion peptide (pHLIP) serves as a model system for peptide insertion and folding across a lipid bilayer. It has three general states: (I) soluble in water or (II) bound to the surface of a lipid bilayer as an unstructured monomer, and (III) inserted across the bilayer as a monomeric alpha-helix. We used fluorescence spectroscopy and isothermal titration calorimetry to study the interactions of pHLIP with a palmitoyloleoylphosphatidylcholine (POPC) lipid bilayer and to calculate the transition energies between states. We found that the Gibbs free energy of binding to a POPC surface at low pHLIP concentration (state I-state II transition) at 37 degrees C is approximately -7 kcal/mol near neutral pH and that the free energy of insertion and folding across a lipid bilayer at low pH (state II-state III transition) is nearly -2 kcal/mol. We discuss a number of related thermodynamic parameters from our measurements. Besides its fundamental interest as a model system for the study of membrane protein folding, pHLIP has utility as an agent to target diseased tissues and translocate molecules through the membrane into the cytoplasm of cells in environments with elevated levels of extracellular acidity, as in cancer and inflammation. The results give the amount of energy that might be used to move cargo molecules across a membrane.

Bilayer interactions of pHLIP, a peptide that can deliver drugs and target tumors

The pH-dependent insertion of pHLIP across membranes is proving to be a useful property for targeting acidic tissues or tumors and delivering drugs attached to its C-terminus. It also serves as a model peptide for studies of protein insertion into membranes, so further elucidation of the insertion mechanism of pHLIP and its features is desirable. We examine how the peptide perturbs a model phosphatidylcholine membrane and how it associates with the lipid bilayer using an array of fluorescence techniques, including fluorescence anisotropy measurements of TMA-DPH anchored in bilayers, quenching of pHLIP fluorescence by brominated lipids and acrylamide, and measurements of energy transfer between aromatic residues of pHLIP and TMA-DPH. When pHLIP is bound to the surface of bilayers near neutral pH, the membrane integrity is preserved whereas the elastic properties of bilayers are changed as reported by an increase of membrane viscosity. When it is inserted, there is little perturbation of the lipids. The results also suggest that pHLIP can bind to the membrane surface in a shallow or a deep mode depending on the phase state of the lipids. Using parallax analysis, the change of the penetration depth of pHLIP was estimated to be 0.4 A from the bilayer center and 2.8 A from the membrane surface after the liquid-to-gel phase transition.