Diego Frezzato

Toward quantitative estimates of binding affinities for protein–ligand systems involving large inhibitor compounds: A steered molecular dynamics simulation route

Understanding binding mechanisms between enzymes and potential inhibitors and quantifying protein–ligand affinities in terms of binding free energy is of primary importance in drug design studies. In this respect, several approaches based on molecular dynamics simulations, often combined with docking techniques, have been exploited to investigate the physicochemical properties of complexes of pharmaceutical interest. Even if the geometric properties of a modeled protein–ligand complex can be well predicted by computational methods, it is still challenging to rank with chemical accuracy a series of ligand analogues in a consistent way. In this article, we face this issue calculating relative binding free energies of a focal adhesion kinase, an important target for the development of anticancer drugs, with pyrrolopyrimidine‐based ligands having different inhibitory power. To this aim, we employ steered molecular dynamics simulations combined with nonequilibrium work theorems for free energy calculations. This technique proves very powerful when a series of ligand analogues is considered, allowing one to tackle estimation of protein–ligand relative binding free energies in a reasonable time. In our cases, the calculated binding affinities are comparable with those recovered from experiments by exploiting the Michaelis–Menten mechanism with a competitive inhibitor.

Exploiting Configurational Freezing in Nonequilibrium Monte Carlo Simulations.

To achieve acceptable accuracy in fast-switching free energy estimates by Jarzynski equality [ Phys. Rev. Lett. 1997 , 78 , 2690 ] or Crooks fluctuation theorem [ J. Stat. Phys. 1998 , 90 , 1481 ], it is often necessary to realize a large number of externally driven trajectories. This is basically due to inefficient calculation of path-ensemble averages arising from the work dissipated during the nonequilibrium paths. We propose a computational technique, addressed to Monte Carlo simulations, to improve free energy estimates by lowering the dissipated work. The method is inspired by the dynamical freezing approach, recently developed in the context of molecular dynamics simulations [ Phys. Rev. E 2009 , 80 , 041124 ]. The idea is to limit the configurational sampling to particles of a well-established region of the sample (namely, the region where dissipation is supposed to occur), while leaving fixed (frozen) the other particles. Therefore, the method, called configurational freezing, is based on the reasonable assumption that dissipation is a local phenomenon in single-molecule nonequilibrium processes, a statement which is satisfied by most processes, including folding of biopolymers, molecular docking, alchemical transformations, etc. At variance with standard simulations, in configurational freezing simulations the computational cost is not correlated with the size of the whole system, but rather with that of the reaction site. The method is illustrated in two examples, i.e., the calculation of the water to methane relative hydration free energy and the calculation of the potential of mean force of two methane molecules in water solution as a function of their distance.

Deuterium NMR Evidences of Slow Dynamics in the Nematic Phase of a Banana-Shaped Liquid Crystal

Experimental evidences of the slow dynamic behaviour of a banana-shaped liquid crystal (LC) detected by means of Deuterium Nuclear Magnetic Resonance (DNMR) in its nematic phase are reported. Deuterium line-shape and line-width trends of DNMR spectra of three selectively deuterium-labelled isotopomers of 4-chloro 1,3-phenylene bis 4-4′-(11-undecenyloxy) benzoyloxy benzoate (ClPbis11BB) are discussed in comparison with those of a deuterated probe dissolved in ClPbis11BB, used as LC solvent. Different dynamic regimes are observed for the central and lateral aromatic rings of the probe. These experimental remarks are discussed in terms of overall and internal molecular motions.

Dynamics of liquid benzene: A cage analysis

Dynamics of single molecules in liquids, inspected in the picosecond time scale by means of spectroscopic measurements or molecular-dynamics (MD) simulations, reveals a complex behavior which can be addressed as due to local confinement (cage). This work is devoted to the analysis of cage structures in liquid benzene, obtained from MD simulations. According to a paradigm proposed for previous analysis of atomic and molecular liquids [see, for example, A. Polimeno, G. J. Moro, and J. H. Freed, J. Chem. Phys. 102, 8094 (1995)], the istantaneous cage structure is specified by the frame of axes which identifies the molecular configuration at the closest minimum on the potential-energy landscape. In addition, the modeling of the interaction potential between probe molecule and molecular environment, based on symmetry considerations, and its parametrization from the MD trajectories, allows the estimation of the structural parameters which quantify the strength of molecular confinement. Roto-translational dynamics of probe and related cage with respect to a laboratory frame, dynamics of the probe within the cage (vibrations, librations, re-orientational motions), and the restructuring processes of the cage itself are analyzed in terms of selected time self-correlation functions. A time-scale separation between the processes is established. Moreover, by exploiting the evidence of fast vibrational motions of the probe with respect to the cage center, an orientational effective potential is derived to describe the caging in the time scale longer than approximately 0.2 ps.

Looking for some free energy? Call JEFREE (…).

In this communication, we present the Jarzynskis Equality FREe Energy (JEFREE) library, an efficient and easy‐to‐use C++ library targeted to the calculation of the free energy profile along a selected generalized coordinate of a system, within the framework of the nonequilibrium steered transformations as introduced by Jarzynski [Phys. Rev. E, 1997, 56, 5018]. JEFREE can be readily integrated into any code, since both C and FORTRAN wrappers have been developed, and easily customizable by a user thanks to the object‐oriented programming paradigm offered by the C++ language. Also, JEFREE implements the novel idea of making a total “morphing” of the system energy landscape before initiating the proper steering stage. This proves to be an efficient mean to overtake the problematic sampling of the initial equilibrium state when the number of degrees of freedom is high and the landscape owns many local minima separated by large energy barriers. The calculation of the free energy profile for the rotation along torsion angles in alkyl chains is presented as an example of application of our tool.

Transverse nuclear spin relaxation induced by director fluctuations in a nematic liquid crystal polymer. Evaluation of the anisotropic elastic constants

Transverse deuteron spin relaxation measurements, employing Carr–Purcell–Meiboom–Gill (CP) sequences, have been used to determine the anisotropic elastic constants of a thermotropic main chain/side chain liquid crystal polymer (LCP) in the nematic phase. The observed relaxation rates, R2CP(ω), exhibit a square root dependence on the inverse pulse frequency, ω, i.e., R2CP(ω)∝ω−1/2, over more than one order of magnitude in ω in the kHz regime. This is precisely the dispersion law expected for nematic director fluctuations. Analysis of the experimental dispersion profile is performed using a slow-motional model for director fluctuations, in which five independent Leslie viscosities and three Frank elastic constants are considered. Using additional information from a step-rotation rheo-nuclear magnetic resonance (NMR) experiment, the analysis provides absolute values for the splay, bend, and twist elastic constant of the studied LCP. It is the first time that such data are available for this class of polymers. The splay elastic constant of K1∼8×10−8 N exceeds that of monomers by four orders of magnitude, in substantial agreement with theoretical predictions. The values for the bend and twist elastic constant of K2∼K3≃5×10−10 N are by a factor of 100 larger than those of low molecular weight liquid crystals. The results show that transverse NMR relaxation measurements involving CP sequences represent a powerful tool for the study of the anisotropic viscoelastic properties of LCPs.Transverse deuteron spin relaxation measurements, employing Carr–Purcell–Meiboom–Gill (CP) sequences, have been used to determine the anisotropic elastic constants of a thermotropic main chain/side chain liquid crystal polymer (LCP) in the nematic phase. The observed relaxation rates, R2CP(ω), exhibit a square root dependence on the inverse pulse frequency, ω, i.e., R2CP(ω)∝ω−1/2, over more than one order of magnitude in ω in the kHz regime. This is precisely the dispersion law expected for nematic director fluctuations. Analysis of the experimental dispersion profile is performed using a slow-motional model for director fluctuations, in which five independent Leslie viscosities and three Frank elastic constants are considered. Using additional information from a step-rotation rheo-nuclear magnetic resonance (NMR) experiment, the analysis provides absolute values for the splay, bend, and twist elastic constant of the studied LCP. It is the first time that such data are available for this class of polymers...

Predicting the paramagnet-enhanced NMR relaxation of H2 encapsulated in endofullerene nitroxides by density-functional theory calculations

We have investigated the structure and nuclear magnetic resonance (NMR) spectroscopic properties of some dihydrogen endofullerene nitroxides by means of density-functional theory (DFT) calculations. Quantum versus classical roto-translational dynamics of H2 have been characterized and compared. Geometrical parameters and hyperfine couplings calculated by DFT have been input to the Solomon–Bloembergen equations to predict the enhancement of the NMR longitudinal relaxation of H2 due to coupling with the unpaired electron. Estimating the rotational correlation time via computed molecular volumes leads to a fair agreement with experiment for the simplest derivative; the estimate is considerably improved by recourse to the calculation of the diffusion tensor. For the other more flexible congeners, the agreement is less good, which may be due to an insufficient sampling of the conformational space. In all cases, relaxation by Fermi contact and Curie mechanisms is predicted to be negligible.

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.

Transverse nuclear spin relaxation due to director fluctuations in liquid crystals. II. Second-order contributions of the fluctuating director

Recently, we have introduced a slow-motional theory for transverse nuclear spin relaxation due to director fluctuations [D. Frezzato, G. Kothe, and G. J. Moro, J. Phys. Chem. B 105, 1281 (2001)]. This method is now generalized to second-order contributions of the fluctuating director. We consider the specific case in which the director is aligned orthogonal to the magnetic field. By exploiting the Gaussian character of director fluctuations, the stochastic Liouville equation for the coupled spin and director dynamics is solved in terms of a characteristic function whose time dependence is determined by a nonlinear integral equation. A convenient solution of the integral equation is obtained by decomposing the characteristic function according to the relaxation rates of the director fluctuations. In a first application, we evaluate the free induction decay and the corresponding absorption spectrum for quadrupolar probe nuclei in nematic liquid crystals. It is shown that the transverse magnetization is well...

Distribution and Dynamic Properties of Xenon Dissolved in the Ionic Smectic Phase of [C16mim][NO3]: MD Simulation and Theoretical Model

We have investigated the structural and dynamic properties of Xe dissolved in the ionic liquid crystal (ILC) phase of 1-hexadecyl-3-methylimidazolium nitrate using classical molecular dynamics (MD) simulations. Xe is found to be preferentially dissolved within the hydrophobic environment of the alkyl chains rather than in the ionic layers of the smectic phase. The structural parameters and the estimated local diffusion coefficients concerning the short-time motion of Xe are used to parametrize a theoretical model based on the Smoluchowski equation for the macroscopic dynamics across the smectic layers, a feature which cannot be directly obtained from the relatively short MD simulations. This protocol represents an efficient combination of computational and theoretical tools to obtain information on slow processes concerning the permeability and diffusivity of the xenon in smectic ILCs.