Elucidation of the coupling between mechanical and biophysical properties of biological membranes

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Hwang, Hyea
Gumbart, James C.
Jacob, Karl I.
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The membranes of practically all living organisms and many viruses are made of a semipermeable lipid bilayer, which is composed of two layers of fatty acids, often containing many embedded proteins. This bilayer, a self-assembled soft material, can take on a multitude of shapes and sizes depending on its composition and its environment. It is responsible for maintaining the boundary of a cell, distinguishing inside from outside, and for selectively mediating the permeability of molecules across it. Quantifying the diverse functionality of membranes requires elucidating their mechanical properties and how those properties depend on their constituents. The cell envelope in Gram-negative bacteria comprises two distinct membranes with a cell wall between them. There has been a growing interest in the mechanical adaptation of this cell envelope to the osmotic pressure (or turgor pressure), which is generated by the difference in the concentration of solutes between the cytoplasm and the external environment. However, it remains unexplored how the cell wall, the inner membrane (IM), and the outer membrane (OM) effectively protect the cell from this pressure by bearing the resulting surface tension, thus preventing the formation of inner membrane bulges, abnormal cell morphology, spheroplasts and cell lysis. In this study, we have used molecular dynamics (MD) simulations combined with experiments to resolve how and to what extent models of the IM, OM, and cell wall respond to changes in surface tension. We calculated the area compressibility modulus of all three components in simulations from tension-area isotherms. Experiments on monolayers mimicking individual leaflets of the IM and OM were also used to characterize their compressibility.While the membranes become softer as they expand, the cell wall exhibits significant strain stiffening at moderate to high tensions. We integrate these results into a model of the cell envelope in which the OM and cell wall share the tension at low turgor pressure (0.3 atm) but the tension in the cell wall dominates at high values ( $>$ 1 atm). The second part of the proposed research involves an estimation of small-molecule permeation through membranes, which is of critical importance for the delivery of candidate drugs to an intracellular target. In this study, we consider the membrane deformation energy as the dominant factor in crossing the membrane into cells, as measured by in vitro cell-based experiments. We have investigated a new approach using the deformation free energy of a lipid bilayer based on the principle of a continuum theory. To gain atomistic insight into the passive permeability process, we have used physics-based methods, namely molecular dynamics simulations combined with the inhomogeneous solubility-diffusion model. The estimated permeabilities from our method are compared with other popular methods such as Parallel Artificial Membrane Permeability Assay (PAMPA) experiments. The third part of the proposed research introduces the method that can make the computational calculation faster than what it used to be required. The time step of atomistic molecular dynamics (MD) simulations is determined by the fastest motions in the system and is typically limited to 2 fs. An increasingly popular solution is to increase the mass of the hydrogen atoms to ~3 amu and decrease the mass of the parent atom by an equivalent amount. This approach, known as hydrogen-mass repartitioning (HMR), permits time steps up to 4 fs with reasonable simulation stability. While HMR has been applied in many published studies to date, it has not been extensively tested for membrane-containing systems. Here, we compare the results of simulations of a variety of membranes and membrane-protein systems run using a 2-fs time step and a 4-fs time step with HMR. For pure membrane systems, we find practically no difference in structural properties, such as area-per-lipid and order parameters, and very little difference in kinetic properties such as the diffusion constant. Conductance through a porin in an applied field, partitioning of a small peptide, hydrogen-bond dynamics, and membrane mixing also show very little dependence on HMR and the time step. We also tested a 9-Å cutoff compared to the standard CHARMM cutoff of 12 $\AA$, finding significant deviations in many properties tested. We conclude that HMR is a valid approach for membrane systems but a 9-A cutoff is often not.
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