Franci Merzel

Is the first hydration shell of lysozyme of higher density than bulk water

Characterization of the physical properties of protein surface hydration water is critical for understanding protein structure and folding. Here, using molecular dynamics simulation, we provide an explanation of recent x-ray and neutron solution scattering data that indicate that the density of water on the surface of lysozyme is significantly higher than that of bulk water. The simulation-derived scattering profiles are in excellent agreement with the experiment. In the simulation, the 3-Å-thick first hydration layer is 15% denser than bulk water. About two-thirds of this increase is the result of a geometric contribution that would also be present if the water was unperturbed from the bulk. The remaining third arises from modification of the water structure and dynamics, involving approximately equal contributions from shortening of the average water–water O–O distance and an increase in the coordination number. Variation in the first hydration shell density is shown to be determined by topographical and electrostatic properties of the protein surface. On average, denser water is found in depressions on the surface in which the water dipoles tend to be aligned parallel to each other by the electrostatic field generated by the protein atoms.

Molecular dynamics integration and molecular vibrational theory. I. New symplectic integrators

New symplectic integrators have been developed by combining molecular dynamics integration with the standard theory of molecular vibrations to solve the Hamiltonian equations of motion. The presented integrators analytically resolve the internal high-frequency molecular vibrations by introducing a translating and rotating internal coordinate system of a molecule and calculating normal modes of an isolated molecule only. The translation and rotation of a molecule are treated as vibrational motions with the vibrational frequency zero. All types of motion are thus described in terms of the normal coordinates. The methods time reversibility requirement was used to determine the equations of motion for internal coordinate system of a molecule. The calculation of long-range forces is performed numerically within the generalized second-order leap-frog scheme, in the same way as in standard second-order symplectic methods. The new methods for integrating classical equations of motion using normal mode analysis allow us to use a long integration step and are applicable to any system of molecules with one equilibrium configuration.

SASSIM: a method for calculating small‐angle X‐ray and neutron scattering and the associated molecular envelope from explicit‐atom models of solvated proteins

A method is presented to calculate efficiently small-angle neutron and X-ray solution scattering intensities from explicit-atom models of macromolecules and the surrounding solvent. The method is based on a multipole expansion of the scattering amplitude. It is particularly appropriate for extensive configurational averaging, as is required for calculations based on computer-simulation results. In test calculations, excellent agreement with experiment is found between neutron and X-ray scattering profiles calculated from a molecular-dynamics simulation of lysozyme in water. The question of definition of the protein surface is also addressed. For comparison with the continuum model, an analytical envelope around the protein is defined in terms of spherical harmonics and is calculated using a Lebedev grid. The analytical surface thus defined is shown to reproduce well the scattering profile calculated from the explicit-atom model of the protein.

Liquid-ordered phase formation in cholesterol/sphingomyelin bilayers: all-atom molecular dynamics simulations.

This paper reports an all-atom molecular dynamics simulation of lipid bilayers with different cholesterol/sphingomyelin molar ratios. Our results reveal structural and dynamic changes suggesting the random distribution of lipids along the bilayer planes is supplanted at cholesterol concentrations above 30 mol % by the formation of a liquid-ordered phase, which is thought to be the precursor to lipid raft formation. The packing of molecules in the bilayer is shown to be associated with the hydrogen bonding between cholesterol and sphingomyelin. The molecules tend to migrate toward distributions in which the sphingomyelin molecule forms on average one hydrogen bond with a cholesterol molecule. The threshold for activation of this packing trend coincides with the experimentally determined threshold membrane activity of a cytolytic protein ostreolysin, which binds to and permeabilizes cholesterol-sphingomyelin bilayers containing more than 30 mol % cholesterol.

Protein hydration water: Structure and thermodynamics

Abstract Characterization of the physical properties of protein surface hydration water is critical for understanding protein structure and folding. Recent X-ray and neutron solution scattering data indicate that the density of water on the surface of lysozyme is significantly higher than that of bulk water. Recent molecular dynamics simulation work shows also that variation in the first hydration shell density is determined by electrostatic properties of the protein surface and local surface topography. The thermodynamics of binding of well-ordered structural water to proteins is also examined. Using normal mode analysis, the vibrational entropy change on burial of a crystallographically well-ordered water molecule in Bovine Pancreatic Trypsin Inhibitor (BPTI) is calculated. The vibrational entropy content of the complex is 13.4 cal/mol/K higher than that of the unbound protein. An analysis is performed of how the translational and rotational degrees of freedom of the isolated water molecule are transformed into vibrational modes in the complex.

Origin of hydrophobicity and enhanced water hydrogen bond strength near purely hydrophobic solutes

Significance Hydrophobicity governs a wide range of fundamental physicochemical processes, but its physical origin is unclear. The classical explanation of hydrophobicity is that tiny “icebergs” are formed near such solutes; however, no experimental proof has been advanced for their existence. Here, we used four small purely hydrophobic solutes (methane, ethane, krypton, and xenon) in water to study hydrophobicity at the most fundamental level. We present unequivocal experimental proof for strengthened water hydrogen bonds near purely hydrophobic solutes, matching those in ice and clathrates. The water molecules involved in the enhanced hydrogen bonds display extensive structural ordering resembling that in clathrates, thus indicating the fundamental interconnection between electrostatic screening (shielding) and the hydrophobic effect. Hydrophobicity plays an important role in numerous physicochemical processes from the process of dissolution in water to protein folding, but its origin at the fundamental level is still unclear. The classical view of hydrophobic hydration is that, in the presence of a hydrophobic solute, water forms transient microscopic “icebergs” arising from strengthened water hydrogen bonding, but there is no experimental evidence for enhanced hydrogen bonding and/or icebergs in such solutions. Here, we have used the redshifts and line shapes of the isotopically decoupled IR oxygen–deuterium (O-D) stretching mode of HDO water near small purely hydrophobic solutes (methane, ethane, krypton, and xenon) to study hydrophobicity at the most fundamental level. We present unequivocal and model-free experimental proof for the presence of strengthened water hydrogen bonds near four hydrophobic solutes, matching those in ice and clathrates. The water molecules involved in the enhanced hydrogen bonds display extensive structural ordering resembling that in clathrates. The number of ice-like hydrogen bonds is 10–15 per methane molecule. Ab initio molecular dynamics simulations have confirmed that water molecules in the vicinity of methane form stronger, more numerous, and more tetrahedrally oriented hydrogen bonds than those in bulk water and that their mobility is restricted. We show the absence of intercalating water molecules that cause the electrostatic screening (shielding) of hydrogen bonds in bulk water as the critical element for the enhanced hydrogen bonding around a hydrophobic solute. Our results confirm the classical view of hydrophobic hydration.

AN EFFICIENT SYMPLECTIC INTEGRATION ALGORITHM FOR MOLECULAR DYNAMICS SIMULATIONS

A new explicit symplectic integration algorithm for molecular dynamics (MD) simulations is described. The method involves splitting of the total Hamiltonian of the system into the harmonic part and the remaining part in such a way that both parts can be efficiently computed. The Hamilton equations of motion are then solved using the second order generalized leap-frog integration scheme in which the high-frequency motions are treated analytically by the normal mode analysis which is carried out only once, at the beginning of the calculation. The proposed algorithm requires only one force evaluation per integration step, the computation cost per integration step is approximately the same as that of the standard leap-frog-Verlet method, and it allows an integration time step ten times larger than can be used by other methods of the same order. It was applied to MD simulations of the linear molecule of the form H-(CEC),-H and was by an order of magnitude faster than the standard leap-frog-Verlet method. The approach for MD simulations described here is general and applicable to any molecular system.

Vibrational softening of a protein on ligand binding.

Neutron scattering experiments have demonstrated that binding of the cancer drug methotrexate softens the low-frequency vibrations of its target protein, dihydrofolate reductase (DHFR). Here, this softening is fully reproduced using atomic detail normal-mode analysis. Decomposition of the vibrational density of states demonstrates that the largest contributions arise from structural elements of DHFR critical to stability and function. Mode-projection analysis reveals an increase of the breathing-like character of the affected vibrational modes consistent with the experimentally observed increased adiabatic compressibility of the protein on complexation.

Modus operandi of controlled release from mesoporous matrices: a theoretical perspective.

The ability to alter the rate at which molecules are released from pores by manipulating structural and surface properties of mesoporous materials was demonstrated consistently in numerous studies. Yet an understanding of the role of pore size, attraction to pore walls and of the release mechanism in general has still been elusive. Here we address these issues by means of a simple 2-dimensional (2D) model of ordered porous matrices with various pore sizes and strengths of molecule-wall attractions. The system dynamics are described with a 2D Fokker-Planck equation which is solved numerically for various cases of initial concentration distribution. We show that the interactions with walls play an essential and fundamental role in controlled release from mesoporous materials, regardless of whether they are additionally functionalized or not. They affect the relative cross-section where the local flux has a non-vanishing axial component and accordingly the effective transfer rate into bulk solution. Furthermore the inclusion of molecule-wall attractions into the theoretical description turns out to be the missing piece of the puzzle that explains the origin of the experimentally observed dependence of release kinetics on the pore size. Our results enable us to reinterpret existing experimental findings and provide a revised view of the mechanism of controlled release from ordered porous matrices.

Probing amyloid-beta fibril stability by increasing ionic strengths.

Previous experimental studies have demonstrated changing the ionic strength of the solvent to have a great impact on the mechanism of aggregation of amyloid-beta (Aβ) protein leading to distinct fibril morphology at high and low ionic strength. Here, we use molecular dynamics simulations to elucidate the ionic strength-dependent effects on the structure and dynamics of the model Aβ fibril. The change in ionic strength was brought forth by varying the NaCl concentration in the environment surrounding the Aβ fibril. Comparison of the calculated vibrational spectra of Aβ derived from 40 ns all-atom molecular dynamics simulations at different ionic strength reveals the fibril structure to be stiffer with increasing ionic strength. This finding is further corroborated by the calculation of the stretching force constants. Decomposition of binding and dynamical properties into contributions from different structural segments indicates the elongation of the fibril at low ionic strength is most likely promoted by hydrogen bonding between N-terminal parts of the fibril, whereas aggregation at higher ionic strength is suggested to be driven by the hydrophobic interaction.