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).

Intrinsic Flexibility beyond the Highly Ordered DNA Tetrahedron: An Integrative Spectroscopic and Molecular Dynamics Approach.

Since the introduction of DNA-based architectures, in the past decade, DNA tetrahedrons have aroused great interest. Applications of such nanostructures require structural control, especially in the perspective of their possible functionalities. In this work, an integrated approach for structural characterization of a tetrahedron structure is proposed with a focus on the fundamental biophysical aspects driving the assembly process. To address such an issue, spin-labeled DNA sequences are chemically synthesized, self-assembled, and then analyzed by Continuous-Wave (CW) and pulsed Electron Paramagnetic Resonance (EPR) spectroscopy. Interspin distance measurements based on PELDOR/DEER techniques combined with molecular dynamics (MD) thus revealed unexpected dynamic heterogeneity and flexibility of the assembled structures. The observation of flexibility in these ordered 3D structures demonstrates the sensitivity of this approach and its effectiveness in accessing the main dynamic and structural features with unprecedented resolution.

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.

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.

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.

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.

Similarity and Specificity of Chlorophyll b Triplet State in Comparison to Chlorophyll a as Revealed by EPR/ENDOR and DFT Calculations.

An investigation of the photoexcited triplet state of chlorophyll (Chl) b has been carried out by means of electron nuclear double resonance, both in a frozen organic solvent and in a protein environment provided by the water-soluble chlorophyll protein of Lepidium virginicum. Density functional theory calculations have allowed the complete assignment of the observed hyperfine couplings corresponding to the methine protons and the methyl groups, leading to a complete picture of the spin density distribution of the triplet state in the tetrapyrrole macrocycle. The triplet-state properties of Chl b are found to be similar, in many respects, to those previously reported for Chl a, although some specificities have been highlighted. Concerning the spin density distribution, the differences are mainly localized on the carbon atoms close to the formyl group which, in Chl b, replaces the methyl group of Chl a.

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.

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.

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 ß-d-Glcp-(1→3)[ß-d-Glcp-(1→2)]-α-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 the acquisition of high-quality 13C NMR relaxation parameters, T1 and T2, and heteronuclear NOE, with standard deviations of ≤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 a very good agreement with experimental data, deviating <3%. The resulting dynamics are described by correlation times of 196 and 174 ps for the ß-(1→2)- and ß-(1→3)-linked glucosyl residues, respectively, i.e., different and linkage dependent. Notably, the devised computational protocol was performed without any fitting of parameters.

Integrated Computational Approach to the Electron Paramagnetic Resonance Characterization of Rigid 310-Helical Peptides with TOAC Nitroxide Spin Labels.

We address the interpretation, via an integrated computational approach, of the experimental continuous-wave electron paramagnetic resonance (cw-EPR) spectra of a complete set of conformationally highly restricted, stable 310-helical peptides from hexa- to nonamers, each bis-labeled with nitroxide radical-containing TOAC (4-amino-1-oxyl-2,2,6,6-tetramethylpiperidine-4-carboxylic acid) residues. The usefulness of TOAC for this type of analysis has been shown already to be due to its cyclic piperidine side chain, which is rigidly connected to the peptide backbone α-carbon. The TOAC α-amino acids are separated by two, three, four, and five intervening residues. This set of compounds has allowed us to modulate both the radical···radical distance and the relative orientation parameters. To further validate our conclusion, a comparative analysis has been carried out on three singly TOAC-labeled peptides of similar main-chain length.

Decomposition of Proteins into Dynamic Units from Atomic Cross-Correlation Functions.

In this article, we present a clustering method of atoms in proteins based on the analysis of the correlation times of interatomic distance correlation functions computed from MD simulations. The goal is to provide a coarse-grained description of the protein in terms of fewer elements that can be treated as dynamically independent subunits. Importantly, this domain decomposition method does not take into account structural properties of the protein. Instead, the clustering of protein residues in terms of networks of dynamically correlated domains is defined on the basis of the effective correlation times of the pair distance correlation functions. For these properties, our method stands as a complementary analysis to the customary protein decomposition in terms of quasi-rigid, structure-based domains. Results obtained for a prototypal protein structure illustrate the approach proposed.

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.

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.

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.