New Approach to Tolman’s Electronic Parameter Based on Local Vibrational Modes

Tolman’s electronic parameter (TEP) derived from the <i>A</i>₁-symmetrical CO stretching frequency of nickel–phosphine–tricarbonyl complexes, R₃PNi­(CO)₃, is brought to a new, improved level by replacing normal with local vibrational frequencies. CO normal vibrational frequencies are always flawed by mode–mode coupling especially with metal–carbon stretching modes, which leads to coupling frequencies as large as 100 cm^–1 and can become even larger when the transition metal and the number of ligands is changed. Local TEP (LTEP) values, being based on local CO stretching force constants rather than normal mode frequencies, no longer suffer from mode coupling and mass effects. For 42 nickel complexes of the type LNi­(CO)₃, it is shown that LTEP values provide a different ordering of ligand electronic effects as previously suggested by TEP and CEP values. The general applicability of the LTEP concept is demonstrated

Identifying Key Residues for Protein Allostery through Rigid Residue Scan

Allostery is a ubiquitous process for protein regulatory activity in which a binding event can change a protein’s function carried out at a distal site. Despite intensive theoretical and experimental investigation of protein allostery in the past five decades, effective methods have yet to be developed that can systematically identify key residues involved in allosteric mechanisms. In this study, we propose the rigid residue scan as a systematic approach to identify important allosteric residues. The third PDZ domain (PDZ3) in the postsynaptic density 95 protein (PSD-95) is used as a model system, and each amino acid residue is treated as a single rigid body during independent molecular dynamics simulations. Various indices based on cross-correlation matrices are used, which allow for two groups of residues with different functions to be identified. The first group is proposed as “switches” that are needed to “turn on” the binding effect of protein allostery. The second group is proposed as “wire residues” that are needed to propagate energy or information from the binding site to distal locations within the same protein. Among the nine residues suggested as important for PDZ3 intramolecular communication in this study, eight have been reported as critical for allostery in PDZ3. Therefore, the rigid residue scan approach is demonstrated to be an effective method for systemically identifying key residues in protein intramolecular communication and allosteric mechanisms

Description of Aromaticity with the Help of Vibrational Spectroscopy: Anthracene and Phenanthrene

A new approach is presented to determine π-delocalization and the degree of aromaticity utilizing measured vibrational frequencies. For this purpose, a perturbation approach is used to derive vibrational force constants from experimental frequencies and calculated normal mode vectors. The latter are used to determine the local counterparts of the vibrational modes. Next, relative bond strength orders (RBSO) are obtained from the local stretching force constants, which provide reliable descriptors of CC and CH bond strengths. Finally, the RBSO values for CC bonds are used to establish a modified harmonic oscillator model and an aromatic delocalization index AI, which is split into a bond weakening (strengthening) and bond alternation part. In this way, benzene, naphthalene, anthracene, and phenanthrene are described with the help of vibrational spectroscopy as aromatic systems with a slight tendency of peripheral π-delocalization. The 6.8 kcal/mol larger stability of phenanthrene relative to anthracene predominantly (84%) results from its higher resonance energy, which is a direct consequence of the topology of ring annelation. Previous attempts to explain the higher stability of phenanthrene via a maximum electron density path between the bay H atoms are misleading in view of the properties of the electron density distribution in the bay region

Heat maps of individual residue entropic contribution under rigid residue perturbation for unbound (left) and bound (right) states.

<p>The entropic contribution from each residue in unperturbed simulations (with index as 0 in both plots) is set as reference.</p

Quantitative Assessment of the Multiplicity of Carbon–Halogen Bonds: Carbenium and Halonium Ions with F, Cl, Br, and I

CX (X = F, Cl, Br, I) and CE bonding (E = O, S, Se, Te) was investigated for a test set of 168 molecules using the local CX and CE stretching force constants <i>k</i>^<i>a</i> calculated at the M06-2X/cc-pVTZ level of theory. The stretching force constants were used to derive a relative bond strength order (RBSO) parameter <i>n</i>. As alternative bond strength descriptors, bond dissociation energies (BDE) were calculated at the G3 level or at the two-component NESC (normalized elimination of the small component)/CCSD­(T) level of theory for molecules with X = Br, I or E = Se, Te. RBSO values reveal that both bond lengths and BDE values are less useful when a quantification of the bond strength is needed. CX double bonds can be realized for Br- or I-substituted carbenium ions where as suitable reference the double bond of the corresponding formaldehyde homologue is used. A triple bond cannot be realized in this way as the diatomic CX⁺ ions with a limited π-donor capacity for X are just double-bonded. The stability of halonium ions increases with the atomic number of X, which is reflected by a strengthening of the fractional (electron-deficient) CX bonds. An additional stability increase of up to 25 kcal/mol (X = I) is obtained when the X⁺ ion can form a bridged halonium ion with ethene such that a more efficient 2-electron–3-center bonding situation is created

Distributions of density of states for unperturbed unbound and bound states.

<p>Distributions of density of states for unperturbed unbound and bound states.</p

Key residues recognized based on protein entropic response to rigid body perturbation.

<p>Key residues recognized based on protein entropic response to rigid body perturbation.</p

Direct Measure of Metal–Ligand Bonding Replacing the Tolman Electronic Parameter

The Tolman electronic parameter (TEP) derived from the <i>A</i>₁-symmetrical CO stretching frequency of nickel-tricarbonyl complexes L–Ni­(CO)₃ with varying ligands L is misleading as (i) it is not based on a mode decoupled CO stretching frequency and (ii) a generally applicable and quantitatively correct or at least qualitatively reasonable relationship between the TEP and the metal–ligand bond strength does not exist. This is shown for a set of 181 nickel-tricarbonyl complexes using both experimental and calculated TEP values. Even the use of mode–mode decoupled CO stretching frequencies (L­(ocal)­TEPs) does not lead to a reliable description of the metal–ligand bond strength. This is obtained by introducing a new electronic parameter that is directly based on the metal–ligand local stretching force constant. For the test set of 181 nickel complexes, a direct metal–ligand electronic parameter (MLEP) in the form of a bond strength order is derived, which reveals that phosphines and related ligands (amines, arsines, stibines, bismuthines) are bonded to Ni both by σ-donation and π-back-donation. The strongest Ni–L bonds are identified for carbenes and cationic ligands. The new MLEP quantitatively assesses electronic and steric factors

Rigid Residue Scan Simulations Systematically Reveal Residue Entropic Roles in Protein Allostery

<div><p>Intra-protein information is transmitted over distances via allosteric processes. This ubiquitous protein process allows for protein function changes due to ligand binding events. Understanding protein allostery is essential to understanding protein functions. In this study, allostery in the second PDZ domain (PDZ2) in the human PTP1E protein is examined as model system to advance a recently developed rigid residue scan method combining with configurational entropy calculation and principal component analysis. The contributions from individual residues to whole-protein dynamics and allostery were systematically assessed via rigid body simulations of both unbound and ligand-bound states of the protein. The entropic contributions of individual residues to whole-protein dynamics were evaluated based on covariance-based correlation analysis of all simulations. The changes of overall protein entropy when individual residues being held rigid support that the rigidity/flexibility equilibrium in protein structure is governed by the La Châtelier’s principle of chemical equilibrium. Key residues of PDZ2 allostery were identified with good agreement with NMR studies of the same protein bound to the same peptide. On the other hand, the change of entropic contribution from each residue upon perturbation revealed intrinsic differences among all the residues. The quasi-harmonic and principal component analyses of simulations without rigid residue perturbation showed a coherent allosteric mode from unbound and bound states, respectively. The projection of simulations with rigid residue perturbation onto coherent allosteric modes demonstrated the intrinsic shifting of ensemble distributions supporting the population-shift theory of protein allostery. Overall, the study presented here provides a robust and systematic approach to estimate the contribution of individual residue internal motion to overall protein dynamics and allostery.</p></div

Average entropic response from each residue in all RRS simulations.

<p>Average entropic response from each residue in all RRS simulations.</p