The aim of this book volume is to explain the importance of Markov state models to molecular simulation, how they work, and how they can be applied to a range of problems.The Markov state model (MSM) approach aims to address two key challenges of molecular simulation:1) How to reach long timescales using short simulations of detailed molecular models.2) How to systematically gain insight from the resulting sea of data.MSMs do this by providing a compact representation of the vast conformational space available to biomolecules by decomposing it into states sets of rapidly interconverting conformations and the rates of transitioning between states. This kinetic definition allows one to[...]

An Introduction to Markov State Models and Their Application to Long Timescale Molecular Simulation

The time correlation functions of the electronic spin components of a metal ion without orbital degeneracy in solution are computed. The approach is based on the numerical solution of the time-dependent Schrodinger equation for a stochastic perturbing Hamiltonian which is simulated by a Monte Carlo algorithm using discrete time steps. The perturbing Hamiltonian is quite general, including the superposition of both the static mean crystal field contribution in the molecular frame and the usual transient ligand field term. The Hamiltonian of the static crystal field can involve the terms of all orders, which are invariant under the local group of the average geometry of the complex. In the laboratory frame, the random rotation of the complex is the only source of modulation of this Hamiltonian, whereas an additional Ornstein–Uhlenbeck process is needed to describe the time fluctuations of the Hamiltonian of the transient crystal field. A numerical procedure for computing the electronic paramagnetic resonance (EPR) spectra is proposed and discussed. For the [Gd(H2O)8]3+ octa-aqua ion and the [Gd(DOTA)(H2O)]– complex [DOTA = 1,4,7,10-tetrakis(carboxymethyl)-1,4,7,10-tetraazacyclo dodecane] in water, the predictions of the Redfield relaxation theory are compared with those of the Monte Carlo approach. The Redfield approximation is shown to be accurate for all temperatures and for electronic resonance frequencies at and above X-band, justifying the previous interpretations of EPR spectra. At lower frequencies the transverse and longitudinal relaxation functions derived from the Redfield approximation display significantly faster decays than the corresponding simulated functions. The practical interest of this simulation approach is underlined.

A general approach to the electronic spin relaxation of Gd(III) complexes in solutions. Monte Carlo simulations beyond the Redfield limit

Phospholipid hydroperoxides and phospholipid alcohols are two of the major forms of oxidatively modified phospholipids produced during oxidant stress and lipid peroxidation. The process of lipid peroxidation is known to affect the physiological function of membranes. We, therefore, investigated the effects of lipid peroxidation products on the molecular interactions in membranes. Our study was specifically focused on the effects of lipid peroxidation products on static membrane structure (molecular orientational order) and on the reorientational dynamics of the probe molecules in lipid bilayers. The study was done by performing angle-resolved fluorescence depolarization measurements (AFD) on the fluorescent probe diphenylhexatriene (DPH) and by performing angle-resolved electron spin resonance (A-ESR) measurements on cholestane (CSL) nitroxide spin probes embedded in macroscopically oriented planar bilayers consisting of 2-10% 1-palmitoyl-2-(9/13-hydroperoxylinoleoyl)phosphatidylcholine (PLPC-OOH) or 1-palmitoyl-2-(9/13-hydroxylinoleoyl)phosphatidylcholine (PLPC-OH) in 1-palmitoyl-2-linoleoylphosphatidylcholine (PLPC) or dilinoleoylphosphatidylcholine (DLPC). Both probe molecules have rigid cylindrical geometries and report on the overall molecular order and dynamics. However, being more polar, the nitroxide spin probe CSL is preferentially located near the surface of the membrane, while the less polar fluorescent probe DPH reports preferentially near the central hydrophobic region of the lipid bilayers. The results show that the presence of relatively small amounts of oxidatively modified phospholipids within the PLPC or DLPC membranes causes pronounced structural effects as the molecular orientational order of the probe molecules is strongly decreased. In contrast, the effect on membrane reorientational dynamics is minimal.

Structural and dynamic effects of oxidatively modified phospholipids in unsaturated lipid membranes.

The time correlation functions (TCFs) Gαα(t)≡⟨Sα(t)Sα(0)⟩ (α=x,y,z) of the electronic spin components of a complexed paramagnetic metal ion give information about the time fluctuations of its zero-field splitting (ZFS) Hamiltonian due to the random dynamics of the coordination polyhedron These TCFs reflect the electronic spin relaxation which plays an essential role in the inner- and outer-sphere paramagnetic relaxation enhancements of the various nuclear spins in solution When a static ZFS Hamiltonian is allowed by symmetry, its modulation by the random rotational motion of the complex has a great influence on the TCFs We discuss several attempts to describe this mechanism and show that subtle mathematical pitfalls should be avoided in order to obtain a theoretical framework, within which reliable adjustable parameters can be fitted through the interpretation of nuclear-magnetic relaxation dispersion experimental results We underline the advantage of the numerical simulation of the TCFs, which avoids the above difficulties and allows one to include the effect of the transient ZFS for all the relative magnitudes of the various terms in the electron-spin Hamiltonian and arbitrary correlation times This method is applied for various values of the magnetic field taken to be along the z direction At low field, contrary to previous theoretical expectations, if the transient ZFS has negligible influence, the longitudinal TCF G‖(t)≡Gzz(t) has a monoexponential decay with an electronic relaxation time T1e different from 1∕(2Dr), Dr being the rotational diffusion coefficient of the complex At intermediate and high field, the simulation results show that G‖(t) still has a monoexponential decay with a characteristic time T1e, which is surprisingly well approximated by a simple analytical expression derived from the Redfield perturbation approximation of the time-independent Zeeman Hamiltonian, even in the case of a strong ZFS where this approximation is expected to fail These results are illustrated for spins S=1, 3∕2, and 5∕2 in axial and rhombic symmetries Finally, the simulation method is applied to the reinterpretation of the water-proton relaxivity profile due to P760–Gd(III), an efficient blood pool contrast agent for magnetic-resonance imaging

Electronic relaxation of paramagnetic metal ions and NMR relaxivity in solution: critical analysis of various approaches and application to a Gd(III)-based contrast agent.

Protein, lipid, and DNA radicals to measure skin UVA damage and modulation by melanin.

Time-domain simulation of ESR spectra of nitroxide spin probes

A new approach for the simulation of ESR lineshapes over a large range of correlation times

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Time-domain simulation of ESR spectra of nitroxide spin probes

A new approach for the simulation of ESR lineshapes over a large range of correlation times