The roto-conformational diffusion tensor as a tool to interpret molecular flexibility

Stochastic modeling approaches can be used to rationalize complex molecular dynamical behaviours in solution, helping to interpret the coupling mechanisms among internal and external degrees of freedom, providing insight into reaction mechanisms and extracting structural and dynamical data from spectroscopic observables. However, the definition of comprehensive models is usually limited by (i) the difficulty in defining – without resorting to phenomenological assumptions – a representative reduced ensemble of molecular coordinates able to capture essential dynamical properties and (ii) the complexity of numerical or approximate treatments of the resulting equations. In this paper, we address the first of these two issues. Building on a previously defined systematic approach to construct rigorous stochastic models of flexible molecules in solutions from basic principles, we define a manageable diffusive framework leading to a Smoluchowski equation determined by one main tensorial parameter, namely the scaled roto-conformational diffusion tensor, which accounts for the influence of both conservative and dissipative forces and describes the molecular mobility via a precise definition of internal–external and internal–internal couplings. We then show the usefulness of the roto-conformational scaled diffusion tensor as an efficient gauge of molecular flexibility through the analysis of a set of molecular systems of increasing complexity ranging from dimethylformamide to a protein domain

Differential Dynamics at Glycosidic Linkages of an Oligosaccharide as Revealed by 13C NMR Spin Relaxation and Stochastic Modeling

Among biomolecules, carbohydrates are unique in that not only can linkages be formed through different positions but the structures may also be branched. The trisaccharide \uf062-D-Glcp-(1\uf0ae3)[\uf062-D-Glcp-(1\uf0ae2)]-\uf061-D-Manp-OMe represents a model of a branched vicinally disubstituted structure. A 13C site-specific isotopologue with labeling in each of the two terminal glucosyl residues enabled acquisition of high-quality 13C NMR relaxation parameters T1, T2 and heteronuclear NOE, with standard deviations of \uf0a3 0.5%. For interpretation of the experimental NMR data a diffusive chain model was used in which the dynamics of the glycosidic linkages is coupled to the global reorientation motion of the trisaccharide. Brownian dynamics simulations relying on the potential of mean force at the glycosidic linkages were employed to evaluate spectral densities of the spin probes. Calculated NMR relaxation parameters showed very good agreement with experimental data, deviating < 3%. The resulting dynamics is described by correlation times of 196 ps and 174 ps for the \uf062-(1\uf0ae2)- and \uf062-(1\uf0ae3)-linked glucosyl residues, respectively, i.e., different and linkage dependent. Notably, the devised computational protocol was performed without any fitting of parameters

Multiscale modeling of reaction rates: application to archetypal SN2 nucleophilic substitutions

We propose an approach to the evaluation of kinetic rates of elementary chemical reactions within Kramers\u2019 theory based on the definition of the reaction coordinate as a linear combination of natural, pseudo Z-matrix, internal coordinates of the system. The element of novelty is the possibility to evaluate the friction along the reaction coordinate, within a hydrodynamic framework developed recently [J. Campeggio et al., J. Comput. Chem. 2019, 40, 679\u2013705]. This, in turn, allows to keep into account barrier recrossing, i.e. the transmission coefficient that is employed in correcting transition state theory evaluations. To test the capabilities and the flaws of the approach we use as case studies two archetypal SN2 reactions. First, we consider to the standard substitution of chloride ion to bromomethane. The rate constant at 295.15 K is evaluated to k/c 96 = 2.7 7 10 126 s 121 (with c 96 = 1 M), which compares well to the experimental value of 3.3 7 10 126 s 121 [R. H. Bathgate and E. A. Melwyn-Hughes, J. Chem. Soc 1959, 2642\u20132648]. Then, the method is applied to the SN2 reaction of methylthiolate to dimethyl disulfide in water. In biology, such an interconversion of thiols and disulfides is an important metabolic topic still not entirely rationalized. The predicted rate constant is k/c 96 = 7.7 7 103 s 121. No experimental data is available for such a reaction, but it is in accord with the fact that the alkyl thiolates to dialkyl disulfides substitutions in water have been found to be fast reactions [S. M. Bachrach, J. M. Hayes, T. Dao and J. L. Mynar, Theor. Chem. Acc. 2002, 107, 266\u2013271]

flexibility at a glycosidic linkage revealed by molecular dynamics stochastic modeling and 13c nmr spin relaxation conformational preferences of α l rhap α 1 2 α l rhap ome in water and dimethyl sulfoxide solutions

Coupling between global reorientation and local motion is essential for reproducing NMR relaxation parameters of a flexible molecule

Changes in the fraction of strongly attached cross bridges in mouse atrophic and hypertrophic muscles as revealed by continuous wave electron paramagnetic resonance.

Electron paramagnetic resonance (EPR), coupled with site-directed spin labeling, has been proven to be a particularly suitable technique to extract information on the fraction of myosin heads strongly bound to actin upon muscle contraction. The approach can be used to investigate possible structural changes occurring in myosin of fiber s altered by diseases and aging. In this work, we labeled myosin at position Cys707, located in the SH1-SH2 helix in the myosin head cleft, with iodoacetamide spin label, a spin label that is sensitive to the reorientational motion of this protein during the ATPase cycle and characterized the biochemical states of the labeled myosin head by means of continuous wave EPR. After checking the sensitivity and the power of the technique on different muscles and species, we investigated whether changes in the fraction of strongly bound myosin heads might explain the contractile alterations observed in atrophic and hypertrophic murine muscles. In both conditions, the difference in contractile force could not be justified simply by the difference in muscle mass. Our results showed that in atrophic muscles the decrease in force generation was attributable to a lower fraction of strongly bound cross bridges during maximal activation. In contrast in hypertrophic muscles, the increase in force generation was likely due to several factors, as pointed out by the comparison of the EPR experiments with the tension measurements on single skinned fibers

Evaluation of translational friction coefficients of micro-sized spherical probes in nematic liquid crystals

We study the translational friction coefficients of a spherical micrometric probe moving in nematic liquid crystalline fluids, by solving numerically the constitutive hydrodynamic equations of uncompressible isothermal nematic fluids (Leslie–Ericksen equations). The nematic medium is described by a vector field, which specifies the director orientation at each point and by the velocity vector field. Simulations of director dynamics surrounding the moving probe are presented, and the dependence of translational diffusion upon liquid crystal viscoelastic parameters is discussed. The time evolution of director field is studied in the presence of an orienting magnetic field in two characteristic situations, i.e. direction of motion parallel and perpendicular to field. In particular, a detailed analysis is given for the case of a spherical probe in rectilinear motion in nematic MBBA (4-methoxibenzylidene-4′-n-butylaniline), together with a comparison with other nematogens

A stochastic cage model for linear solutes

A stochastic cage model describing a linear solute reorienting under the action of a librational potential due to neighboring solvent molecules is presented. The fluctuations of the cage structure are taken into account by means of a suitable distribution of the Librational frequency, Moreover, a detailed description of the cage dynamics is introduced by considering both the cage rotation and its restructuring through randomizations of the Librational frequency and of the equilibrium orientation of the solute. With a suitable choice of the basis functions for the representation of the time evolution operator, the cage model can be solved numerically in order to compute different types of dynamical observables: angular momentum and orientational correlation functions, frequency dependent dielectric permittivity, and far-infrared spectra. Typical behavior of such observables in normal liquids is recovered from the cage model, thus demonstrating its capability of describing experimental observations at quite different time scales. (C) 1997 American Institute of Physics

Separation of fast and slow processes from a stochastic cage model of molecular dynamics

The linear solute cage model (LSCM) has been proposed in the past [Moro, G. J., Polimeno, A. J. Chem. Phys. 1997, 107, 7884] to account for the action of the confining potential generated by neighboring solvent molecules on a linear solute, in the presence of fluctuations of the resulting cage structure. Rotational correlation functions, directly related to spectroscopic observables such as dielectric permittivity and far-infrared spectra in molecular liquids, can be calculated from the numerical solution of the model. However, to understand the influence of different relaxation processes on the solute dynamics, it is useful to explore semianalytical approximations, able to connect directly predictions with physical ingredients of the model. In this work, we present a detailed analysis of LSCM based on the application of a Born-Oppenheimer time-scale separation procedure, which allows a complete description of the probe fast libration motions and the cage slow rotation and restructuring modes

Computational Electron Paramagnetic Resonance SpectroscopyReference Module in Chemistry, Molecular Sciences and Chemical Engineering

In this article, we want to review computational approach to the interpretation of EPR observables. We shall limit our discussion only to cw-EPR spectroscopy, leaving out, by necessity, advanced EPR spectroscopies like time domain multiple-pulse spin echo and double resonance methods. Also, we shall address here only examples and systems for which a clear separation can be drawn between fast local motions of solvent-related properties and large-amplitude molecular relaxation processes. Within this hypothesis, which actually can be said to encompass most experimental situations, averaging of magnetic properties with respect to rapidly relaxing solvent local motions is allowed, thus implying that constant principal values of all involved magnetic tensors can be used in the SLE per se. A relevant exception is given by highly polar and protic solvents, like water and ethanol, where the presence of specific directional H-bonds may lead to a residual explicit dynamic dependence of the magnetic properties from local solvent coordinates (e.g., the average number of H-bonds) to be included in the SL