Variational Methods for Biomolecular Modeling

Structure, function and dynamics of many biomolecular systems can be characterized by the energetic variational principle and the corresponding systems of partial differential equations (PDEs). This principle allows us to focus on the identification of essential energetic components, the optimal parametrization of energies, and the efficient computational implementation of energy variation or minimization. Given the fact that complex biomolecular systems are structurally non-uniform and their interactions occur through contact interfaces, their free energies are associated with various interfaces as well, such as solute-solvent interface, molecular binding interface, lipid domain interface, and membrane surfaces. This fact motivates the inclusion of interface geometry, particular its curvatures, to the parametrization of free energies. Applications of such interface geometry based energetic variational principles are illustrated through three concrete topics: the multiscale modeling of biomolecular electrostatics and solvation that includes the curvature energy of the molecular surface, the formation of microdomains on lipid membrane due to the geometric and molecular mechanics at the lipid interface, and the mean curvature driven protein localization on membrane surfaces. By further implicitly representing the interface using a phase field function over the entire domain, one can simulate the dynamics of the interface and the corresponding energy variation by evolving the phase field function, achieving significant reduction of the number of degrees of freedom and computational complexity. Strategies for improving the efficiency of computational implementations and for extending applications to coarse-graining or multiscale molecular simulations are outlined.Comment: 36 page

Transmembrane but not soluble helices fold inside the ribosome tunnel

Integral membrane proteins are assembled into the ER membrane via a continuous ribosome-translocon channel. The hydrophobicity and thickness of the core of the membrane bilayer leads to the expectation that transmembrane (TM) segments minimize the cost of harbouring polar polypeptide backbones by adopting a regular pattern of hydrogen bonds to form α-helices before integration. Co-translational folding of nascent chains into an α-helical conformation in the ribosomal tunnel has been demonstrated previously, but the features governing this folding are not well understood. In particular, little is known about what features influence the propensity to acquire α-helical structure in the ribosome. Using in vitro translation of truncated nascent chains trapped within the ribosome tunnel and molecular dynamics simulations, we show that folding in the ribosome is attained for TM helices but not for soluble helices, presumably facilitating SRP (signal recognition particle) recognition and/or a favourable conformation for membrane integration upon translocon entry

Molecular imaging of glycan chains couples cell-wall polysaccharide architecture to bacterial cell

Biopolymer composite cell walls maintain cell shape and resist forces in plants, fungi and bacteria. Peptidoglycan, a crucial antibiotic target and immunomodulator, performs this role in bacteria. The textbook structural model of peptidoglycan is a highly ordered, crystalline material. Here we use atomic force microscopy (AFM) to image individual glycan chains in peptidoglycan from Escherichia coli in unprecedented detail. We quantify and map the extent to which chains are oriented in a similar direction (orientational order), showing it is much less ordered than previously depicted. Combining AFM with size exclusion chromatography, we reveal glycan chains up to 200 nm long. We show that altered cell shape is associated with substantial changes in peptidoglycan biophysical properties. Glycans from E. coli in its normal rod shape are long and circumferentially oriented, but when a spheroid shape is induced (chemically or genetically) glycans become short and disordered

SecA, a remarkable nanomachine

Biological cells harbor a variety of molecular machines that carry out mechanical work at the nanoscale. One of these nanomachines is the bacterial motor protein SecA which translocates secretory proteins through the protein-conducting membrane channel SecYEG. SecA converts chemically stored energy in the form of ATP into a mechanical force to drive polypeptide transport through SecYEG and across the cytoplasmic membrane. In order to accommodate a translocating polypeptide chain and to release transmembrane segments of membrane proteins into the lipid bilayer, SecYEG needs to open its central channel and the lateral gate. Recent crystal structures provide a detailed insight into the rearrangements required for channel opening. Here, we review our current understanding of the mode of operation of the SecA motor protein in concert with the dynamic SecYEG channel. We conclude with a new model for SecA-mediated protein translocation that unifies previous conflicting data

Arginine in Membranes: The Connection Between Molecular Dynamics Simulations and Translocon-Mediated Insertion Experiments

Several laboratories have carried out molecular dynamics (MD) simulations of arginine interactions with lipid bilayers and found that the energetic cost of placing arginine in lipid bilayers is an order of magnitude greater than observed in molecular biology experiments in which Arg-containing transmembrane helices are inserted across the endoplasmic reticulum membrane by the Sec61 translocon. We attempt here to reconcile the results of the two approaches. We first present MD simulations of guanidinium groups alone in lipid bilayers, and then, to mimic the molecular biology experiments, we present simulations of hydrophobic helices containing single Arg residues at different positions along the helix. We discuss the simulation results in the context of molecular biology results and show that the energetic discrepancy is reduced, but not eliminated, by considering free energy differences between Arg at the interface and at the center of the model helices. The reduction occurs because Arg snorkeling to the interface prevents Arg from residing in the bilayer center where the energetic cost of desolvation is highest. We then show that the problem with MD simulations is that they measure water-to-bilayer free energies, whereas the molecular biology experiments measure the energetics of partitioning from translocon to bilayer, which raises the fundamental question of the relationship between water-to-bilayer and water-to-translocon partitioning. We present two thermodynamic scenarios as a foundation for reconciliation of the simulation and molecular biology results. The simplest scenario is that translocon-to-bilayer partitioning is independent of water-to-bilayer partitioning; there is no thermodynamic cycle connecting the two paths

A unified model for BAM function that takes into account type Vc secretion and species differences in BAM composition

Transmembrane proteins in the outer membrane of Gram-negative bacteria are almost exclusively β-barrels. They are inserted into the outer membrane by a conserved and essential protein complex called the BAM (for β-barrel assembly machinery). In this commentary, we summarize current research into the mechanism of this protein complex and how it relates to type V secretion. Type V secretion systems are autotransporters that all contain a β-barrel transmembrane domain inserted by BAM. In type Vc systems, this domain is a homotrimer. We argue that none of the current models are sufficient to explain BAM function particularly regarding type Vc secretion. We also find that current models based on the well-studied model system Escherichia coli mostly ignore the pronounced differences in BAM composition between different bacterial species. We propose a more holistic view on how all OMPs, including autotransporters, are incorporated into the lipid bilayer