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.

Parameter free evaluation of SN2 reaction rates for halide substitution in halomethane.

We estimate the kinetic constants of a series of archetypal SN2 reactions, i.e., the nucleophilic substitutions of halides in halomethane. A parameter free, multiscale approach recently developed [Campeggio et al., Phys. Chem. Chem. Phys., 2020, 22, 3455] is employed. The protocol relies on quantum mechanical calculations for the description of the energy profile along the intrinsic reaction coordinate, which is then mapped onto a reaction coordinate conveniently built for the reactive process. A Kramers-Klein equation is used to describe the stochastic time evolution of the reaction coordinate and its velocity; friction is parameterized using a hydrodynamic model and Kramers theory is used to derive the rate constant of the reaction. The method is here applied to six SN2 reactions in water at 295.15 K, which differ in the nucleophile and the leaving group. The computed reaction rates are in good agreement with the experimental data and correlate well with the trends observed for the activation energies.

Enabling Circular Economy: The Overlooked Role of Inorganic Materials Chemistry.

Circular economy is considered a new chance to build a more sustainable world from both the social and the economic point of view. In this Essay, the possible contribution of inorganic chemistry towards a smooth transition to circularity in inorganic materials design and production is discussed by adopting an interdisciplinary approach.

Stochastic Modelling of 13C NMR Spin Relaxation Experiments in Oligosaccharides.

A framework for the stochastic description of relaxation processes in flexible macromolecules including dissipative effects has been recently introduced, starting from an atomistic view, describing the joint relaxation of internal coordinates and global degrees of freedom, and depending on parameters recoverable from classic force fields (energetics) and medium modelling at the continuum level (friction tensors). The new approach provides a rational context for the interpretation of magnetic resonance relaxation experiments. In its simplest formulation, the semi-flexible Brownian (SFB) model has been until now shown to reproduce correctly correlation functions and spectral densities related to orientational properties obtained by direct molecular dynamics simulations of peptides. Here, for the first time, we applied directly the SFB approach to the practical evaluation of high-quality 13C nuclear magnetic resonance relaxation parameters, T1 and T2, and the heteronuclear NOE of several oligosaccharides, which were previously interpreted on the basis of refined ad hoc modelling. The calculated NMR relaxation parameters were in agreement with the experimental data, showing that this general approach can be applied to diverse classes of molecular systems, with the minimal usage of adjustable 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' 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, 679-705]. 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⊖ = 2.7 × 10-6 s-1 (with c⊖ = 1 M), which compares well to the experimental value of 3.3 × 10-6 s-1 [R. H. Bathgate and E. A. Melwyn-Hughes, J. Chem. Soc 1959, 2642-2648]. 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⊖ = 7.7 × 103 s-1. 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, 266-271].

Glycosidic linkage flexibility: The ψ torsion angle has a bimodal distribution in α-L-Rhap-(1→2)-α-L-Rhap-OMe as deduced from 13C NMR spin relaxation.

The molecular dynamics (MD) computer simulation technique is powerful for the investigation of conformational equilibrium properties of biomolecules. In particular, free energy surfaces of the torsion angles (those degrees of freedom from which the geometry mostly depends) allow one to access conformational states, as well as kinetic information, i.e., if the transitions between conformational states occur by simple jumps between wells or if conformational regions close to these states also are populated. The information obtained from MD simulations may depend substantially on the force field employed, and thus, a validation procedure is essential. NMR relaxation data are expected to be highly sensitive to the details of the torsional free energy surface. As a case-study, we consider the disaccharide α-l-Rhap-(1 → 2)-α-l-Rhap-OMe that features only two important torsion angles, ϕ and ψ, which define the interglycosidic orientation of the sugar residues relative to each other, governed mainly by the exo-anomeric effect and steric interactions, respectively. In water, a ψ- state is preferred, whereas in DMSO, it is a ψ+ state, suggesting inherent flexibility at the torsion angle. MD simulations indicated that bistable potentials describe the conformational region well. To test whether a unimodal distribution suffices or if a bimodal distribution better represents molecular conformational preferences, we performed an alchemical morphing of the torsional free energy surface and computed T1, T2, and NOE13C NMR relaxation data that were compared to experimental data. All three NMR observables are substantially affected by the morphing procedure, and the results strongly support a bimodal Boltzmann equilibrium density with a major and a minor conformational state bisected at ψ ≈ 0°, in accord with MD simulations in an explicit solvent.

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.

DiTe2: Calculating the diffusion tensor for flexible molecules.

We report on an extended hydrodynamic modeling of the friction tensorial properties of flexible molecules including all types of natural, Z-Matrix like, internal coordinates. We implement the new methodology by extending and updating the software DiTe [Barone et al. J. Comput. Chem. 30, 2 (2009)]. DiTe (DIffusion TEnsor) implements a hydrodynamic modeling of the generalized translational, rotational, and configurational friction and diffusion tensors of flexible molecules in which flexibility is described in terms of dihedral angles. The new tool, DiTe2, has been renewed to include also stretching and bending types of internal mobility. Furthermore, DiTe2 is able to calculate the friction and diffusion tensors along collective (or reaction) coordinates defined as linear combinations of the internal natural ones. A number of tests are reported to show the new features of DiTe2. As leitmotiv for the tests, the calmodulin protein is taken into consideration, described both at all-atom and coarse-grained levels. © 2018 Wiley Periodicals, Inc.

Evaluating rotation diffusion properties of molecules from short trajectories.

We show that under proper assumptions it is possible to estimate with good precision the principal values of the rotational diffusion tensor of proteins from the analysis of short (up to 2-3 ns) molecular dynamics trajectories. We apply this analysis to a few model cases: three polyalanine peptides (2, 5, and 10 aminoacids), the fragment B3 of protein G (GB3), the bovine pancreatic trypsin inhibitor (BPTI), the hen egg-white lysozyme (LYS), the B1 domain of plexin (PB1), and thrombin. The protocol is based on the analysis of the global angular momentum autocorrelation functions, complementing the standard approach based on rotational autocorrelation functions, which requires much longer trajectories. A comparison with values predicted by hydrodynamic modeling and available experimental data is presented.

Stochastic modeling of macromolecules in solution. II. Spectral densities.

In Paper I [Polimeno et al., J. Chem. Phys. 150, 184107 (2019)], we proposed a general approach for interpreting relaxation properties of a macromolecule in solution, derived from an atomistic description. A simple scheme (the semiflexible Brownian, SFB, model) has been defined for the case of limited internal flexibility, but retaining full coupling with external degrees of freedom, inclusion of all of the momenta, and dissipation. Here we discuss the application of the SFB model to the practical evaluation of orientation spectral densities, based on two complementary computational treatments.

Stochastic modeling of macromolecules in solution. I. Relaxation processes.

A framework for the stochastic description of relaxation processes in flexible macromolecules, including dissipative effects, is introduced from an atomistic point of view. Projection-operator techniques are employed to obtain multidimensional Fokker-Planck operators governing the relaxation of internal coordinates and global degrees of freedom and depending upon parameters fully recoverable from classic force fields (energetics) and continuum models (friction tensors). A hierarchy of approaches of different complexity is proposed in this unified context, aimed primarily at the interpretation of magnetic resonance relaxation experiments. In particular, a model based on a harmonic internal Hamiltonian is discussed as a test case.

Loop Electrostatics Asymmetry Modulates the Preexisting Conformational Equilibrium in Thrombin.

Thrombin exists as an ensemble of active (E) and inactive (E*) conformations that differ in their accessibility to the active site. Here we show that redistribution of the E*-E equilibrium can be achieved by perturbing the electrostatic properties of the enzyme. Removal of the negative charge of the catalytic Asp102 or Asp189 in the primary specificity site destabilizes the E form and causes a shift in the 215-217 segment that compromises substrate entrance. Solution studies and existing structures of D102N document stabilization of the E* form. A new high-resolution structure of D189A also reveals the mutant in the collapsed E* form. These findings establish a new paradigm for the control of the E*-E equilibrium in the trypsin fold.

Light-Induced Porphyrin-Based Spectroscopic Ruler for Nanometer Distance Measurements.

We present a novel pulsed electron paramagnetic resonance (EPR) spectroscopic ruler to test the performance of a recently developed spin-labeling method based on the photoexcited triplet state (S=1). Four-pulse electron double resonance (PELDOR) experiments are carried out on a series of helical peptides, labeled at the N-terminal end with the porphyrin moiety, which can be excited to the triplet state, and with the nitroxide at various sequence positions, spanning distances in the range 1.8-8 nm. The PELDOR traces provide accurate distance measurements for all the ruler series, showing deep envelope modulations at frequencies varying in a progressive way according to the increasing distance between the spin labels. The upper limit is evaluated and found to be around 8 nm. The PELDOR-derived distances are in excellent agreement with theoretical predictions. We demonstrate that high sensitivity is acquired using the triplet state as a spin label by comparison with Cu(II)-porphyrin analogues. The new labeling approach has a high potential for measuring nanometer distances in more complex biological systems due to the properties of the porphyrin triplet state.

Flexibility at a glycosidic linkage revealed by molecular dynamics, stochastic modeling, and (13)C NMR spin relaxation: conformational preferences of α-L-Rhap-α-(1 → 2)-α-L-Rhap-OMe in water and dimethyl sulfoxide solutions.

The monosaccharide L-rhamnose is common in bacterial polysaccharides and the disaccharide α-L-Rhap-α-(1 → 2)-α-L-Rhap-OMe represents a structural model for a part of Shigella flexneri O-antigen polysaccharides. Utilization of [1'-(13)C]-site-specific labeling in the anomeric position at the glycosidic linkage between the two sugar residues facilitated the determination of transglycosidic NMR (3)JCH and (3)JCC coupling constants. Based on these spin-spin couplings the major state and the conformational distribution could be determined with respect to the ψ torsion angle, which changed between water and dimethyl sulfoxide (DMSO) as solvents, a finding mirrored by molecular dynamics (MD) simulations with explicit solvent molecules. The (13)C NMR spin relaxation parameters T1, T2, and heteronuclear NOE of the probe were measured for the disaccharide in DMSO-d6 at two magnetic field strengths, with standard deviations ≤1%. The combination of MD simulation and a stochastic description based on the diffusive chain model resulted in excellent agreement between calculated and experimentally observed (13)C relaxation parameters, with an average error of <2%. The coupling between the global reorientation of the molecule and the local motion of the spin probe is deemed essential if reproduction of NMR relaxation parameters should succeed, since decoupling of the two modes of motion results in significantly worse agreement. Calculation of (13)C relaxation parameters based on the correlation functions obtained directly from the MD simulation of the solute molecule in DMSO as solvent showed satisfactory agreement with errors on the order of 10% or less.

General AMBER Force Field Parameters for Diphenyl Diselenides and Diphenyl Ditellurides.

The General AMBER Force Field (GAFF) has been extended to describe a series of selenium and tellurium diphenyl dichalcogenides. These compounds, besides being eco-friendly catalysts for numerous oxidations in organic chemistry, display peroxidase activity, i.e., can reduce hydrogen peroxide and harmful organic hydroperoxides to water/alcohols and as such are very promising antioxidant drugs. The novel GAFF parameters are tested in MD simulations in different solvents and the (77)Se NMR chemical shift of diphenyl diselenide is computed using structures extracted from MD snapshots and found in nice agreement with the measured value in CDCl3. The whole computational protocol is described in detail and integrated with in-house code to allow easy derivation of the force field parameters for analogous compounds as well as for Se/Te organocompounds in general.

Evidence for water-mediated triplet-triplet energy transfer in the photoprotective site of the peridinin-chlorophyll a-protein.

Experimental and theoretical studies indicate that water molecules between redox partners can significantly affect their electron-transfer and possibly also the triplet-triplet energy transfer (TTET) properties when in the vicinity of chromophores. In the present work, the interaction of an intervening water molecule with the peridinin triplet state in the peridinin-chlorophyll a-protein (PCP) from Amphidinium carterae is studied by using orientation selective (2)H electron spin echo envelope modulation (ESEEM) spectroscopy, in conjunction with quantum mechanical calculations. This water molecule is located at the interface between the chlorophyll and peridinin pigments involved in the photoprotection mechanism (Chl601(602)-Per614(624), for nomenclature see reference [1]), based on TTET. The characteristic deuterium modulation pattern is observed in the electron spin-echo envelopes for the PCP complex exchanged against (2)H2O. Simulations of the time- and frequency-domain two-pulse and three-pulse ESEEM require two types of coupled (2)H. The more strongly coupled (2)H has an isotropic coupling constant (aiso) of -0.4MHz. This Fermi contact contribution for one of the two water protons and the precise geometry of the water molecule at the interface between the chlorophyll and peridinin pigments, resulting from the analysis, provide experimental evidence for direct involvement of this structured water molecule in the mechanism of TTET. The PCP antenna, characterised by a unity efficiency of the process, represents a model for future investigations on protein- and solvent-mediated TTET in the field of natural/artificial photosynthesis.

Triplet-triplet energy transfer in fucoxanthin-chlorophyll protein from diatom Cyclotella meneghiniana: insights into the structure of the complex.

Although the major light harvesting complexes of diatoms, called FCPs (fucoxanthin chlorophyll a/c binding proteins), are related to the cab proteins of higher plants, the structures of these light harvesting protein complexes are much less characterized. Here, a structural/functional model for the "core" of FCP, based on the sequence homology with LHCII, in which two fucoxanthins replace the central luteins and act as quenchers of the Chl a triplet states, is proposed. Combining the information obtained by time-resolved EPR spectroscopy on the triplet states populated under illumination, with quantum mechanical calculations, we discuss the chlorophyll triplet quenching in terms of the geometry of the chlorophyll-carotenoid pairs participating to the process. The results show that local structural rearrangements occur in FCP, with respect to LHCII, in the photoprotective site.

Role of gamma carboxylated Glu47 in connexin 26 hemichannel regulation by extracellular Ca²âº: insight from a local quantum chemistry study.

Connexin hemichannels are regulated by several gating mechanisms, some of which depend critically on the extracellular Ca(2+) concentration ([Ca(2+)]e). It is well established that hemichannel activity is inhibited at normal (∼1 mM) [Ca(2+)]e, whereas lowering [Ca(2+)]e to micromolar levels fosters hemichannel opening. Atomic force microscopy imaging shows significant and reversible changes of pore diameter at the extracellular mouth of Cx26 hemichannels exposed to different [Ca(2+)]e, however, the underlying molecular mechanisms are not fully elucidated. Analysis of the crystal structure of connexin 26 (Cx26) gap junction channels, corroborated by molecular dynamics (MD) simulations, suggests that several negatively charged amino acids create a favorable environment for low-affinity Ca(2+) binding within the extracellular vestibule of the Cx26 hemichannel. In particular a highly conserved glutammic acid, found in position 47 in most connexins, is thought to undergo post translational gamma carboxylation (γGlu47), and is thus likely to play an important role in Ca(2+) coordination. γGlu47 may also form salt bridges with two conserved arginines (Arg75 and Arg184 in Cx26), which are considered important in stabilizing the structure of the extracellular region. Using a combination of quantum chemistry methods, we analyzed the interaction between γGlu47, Arg75 and Arg184 in a Cx26 hemichannel model both in the absence and in the presence of Ca(2+). We show that Ca(2+) imparts significant local structural changes and speculate that these modifications may alter the structure of the extracellular loops in Cx26, and may thus account for the mechanism of hemichannel closure in the presence of mM [Ca(2+)]e.

Energetics of oxo- and thio-dipeptide formation via amino acid condensation: a systematic computational analysis.

Oxo-dipeptides and thio-dipeptides are built via condensation between couples of amino acids and amino thioacids, the latter with the carbonyl oxygen replaced by an sp(2) sulfur. We explored via in silico methods (PBE0/6-31G(d,p) and PBE0/6-311G(d,p)) all the possible combinations and built 800 dipeptides, whose structures were fully optimized. Maps of condensation energies are presented to highlight optimal partners leading to stable dipeptides and critical situations for which lower stability or instability is predicted in terms of Gibbs reaction free energies. To validate the feasibility of our computational investigation, we synthesized and compared the stabilities of two thionated dimers, namely -Gly[Ψ(CSNH)]Gly- and -Phe[Ψ(CSNH)]Phe-, characterized by diverging physico-chemical properties. To the best of our knowledge, this is the first systematic analysis reported for dipeptides built from natural amino acids as well as for their corresponding thio-analogs.

Analysis of Velocity Autocorrelation Functions from Molecular Dynamics Simulations of a Small Peptide by the Generalized Langevin Equation with a Power-Law Kernel.

Internal motions play an essential role in the biological functions of proteins and have been the subject of numerous theoretical and spectroscopic studies. Such complex environments are associated with anomalous diffusion where, in contrast to the classical Brownian motion, the relevant correlation functions have power law decays with time. In this work, we investigate the presence of long memory stochastic processes through the analysis of atomic velocity autocorrelation functions. Analytical expressions of the velocity autocorrelation function spectrum obtained through a Mori-Zwanzig projection approach were shown to be compatible with molecular dynamics simulations of a small helical peptide (8-polyalanine).