Stochastic modeling of macromolecules in solution. II. Spectral densities

Bootstrap Aggregation for Model Selection in the Model-free Formalism

The ability to make robust inferences about the dynamics of biological macromolecules using NMR spectroscopy depends heavily on the application of appropriate theoretical models for nuclear spin relaxation. Data analysis for NMR laboratory-frame relaxation experiments typically involves selecting one of several model-free spectral density functions using a bias-corrected fitness test. Here, advances in statistical model selection theory, termed bootstrap aggregation or bagging, are applied to ¹⁵N spin relaxation data, developing a multimodel inference solution to the model-free selection problem. The approach is illustrated using data sets recorded at four static magnetic fields for the bZip domain of the S. cerevisiae transcription factor GCN4.

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.

Structural Dynamics by NMR in the Solid State: The Unified MOMD Perspective Applied to Organic Frameworks with Interlocked Molecules

The microscopic-order-macroscopic-disorder (MOMD) approach for NMR lineshape analysis has been applied to the University of Windsor Dynamic Materials (UWDM) of types 1, 2, α-3, β-3, and 5, which are metal-organic frameworks (MOFs) comprising mobile mechanically interlocked molecules (MIMs). The mobile MIM components are selectively deuterated crown ether macrocycles - 24C6, 22C6, and B24C6. Their motion is described in MOMD by an effective/collective dynamic mode characterized by a diffusion tensor, R, a restricting/ordering potential, u, expanded in the Wigner rotation matrix elements, D_0, K^L, and features of local geometry. Experimental ²H lineshapes are available over 220 K (on average) and in some cases 320 K. They are reproduced with axial R, u given by the terms D_0,0² and D_0,|2|², and established local geometry. For UWDM of types 1, β-3, and 5, where the macrocycle resides in a relatively loose space, u is in the 1-3 kT, R_∥ in the (1.0-2.5) × 10⁶ s^-1, and R_⊥ in the (0.4-2.5) × 10⁴ s^-1 range; the deuterium atom is bonded to a carbon atom with tetrahedral coordination character. For UWDM of types 2 and α-3, where the macrocycle resides in a much tighter space, a substantial change in the symmetry of u and the coordination character of the ²H-bonded carbon are detected at higher temperatures. The activation energies for R_∥ and R_⊥ are characteristic of each system. The MOMD model is general; effective/collective dynamic modes are treated. The characteristics of motion, ordering, and geometry are physically well-defined; they differ from case to case in extent and symmetry but not in essence. Physical clarity and consistency provide new insights. A previous interpretation of the same experimental data used models consisting of collections of independent simple motions. These models are specific to each case and temperature. Within their scope, generating consistent physical pictures and comparing cases are difficult; possible collective modes are neglected.

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].

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.