Paweł Grochowski

The role of hydrogen bonding in the enzymatic reaction catalyzed by HIV-1 protease.

The hydrogen‐bond network in various stages of the enzymatic reaction catalyzed by HIV‐1 protease was studied through quantum‐classical molecular dynamics simulations. The approximate valence bond method was applied to the active site atoms participating directly in the rearrangement of chemical bonds. The rest of the protein with explicit solvent was treated with a classical molecular mechanics model. Two possible mechanisms were studied, general‐acid/general‐base (GA/GB) with Asp 25 protonated at the inner oxygen, and a direct nucleophilic attack by Asp 25. Strong hydrogen bonds leading to spontaneous proton transfers were observed in both reaction paths. A single‐well hydrogen bond was formed between the peptide nitrogen and outer oxygen of Asp 125. The proton was diffusely distributed with an average central position and transferred back and forth on a picosecond scale. In both mechanisms, this interaction helped change the peptide‐bond hybridization, increased the partial charge on peptidyl carbon, and in the GA/GB mechanism, helped deprotonate the water molecule. The inner oxygens of the aspartic dyad formed a low‐barrier, but asymmetric hydrogen bond; the proton was not positioned midway and made a slightly elongated covalent bond, transferring from one to the other aspartate. In the GA/GB mechanism both aspartates may help deprotonate the water molecule. We observed the breakage of the peptide bond and found that the protonation of the peptidyl amine group was essential for the peptide‐bond cleavage. In studies of the direct nucleophilic mechanism, the peptide carbon of the substrate and oxygen of Asp 25 approached as close as 2.3 Å.

MOLECULAR AND ELECTROSTATIC PROPERTIES OF THE N-METHYLATED NUCLEIC ACID BASES BY DENSITY FUNCTIONAL THEORY

Abstract Complete geometry optimizations using a density functional theory (DFT) with the combined Becke3 and LYP functional potentials (B3-LYP) and the conventional ab initio Hartree-Fock (HF) method with the 6-31G(d,p) basis set were carried out for the fundamental tautomeric forms of nucleic acid bases (cytosine, thymine, guanine and adenine) and their derivatives methylated at the N1 (pyrimidines) or N9 (purines) positions. At the HF/6-31G(d,p) geometries, the dipole moments, electronic densities and molecular electrostatic potentials (MEPs) were computed using the HF/6-31G(d,p), MP2(fc)/6-31G(d,p), DFT(B3-LYP)/6-31G(d,p), DFT(B3-LYP)/6-31 + + G(d,p) methods and DFT with inclusion of Becke nonlocal, gradient-corrected exchange energy terms (DFT(NLE) method) with the numerical DNP basis set. The same properties were also computed using the DFT(B3-LYP)/6-31G(d,p) method for the corresponding optimized geometries of the molecules. The charges that reproduce the MEP maps from the ab initio (HF, MP2) and DFT calculations were fitted and compared. The ground state molecular parameters (rotational constants, dipole moments) of the methylated bases are compared with the molecular parameters calculated at the same level for the nonmethylated DNA bases and with available experimental data. The results show that the DFT calculations reproduce well the MP2 results for the MEPs, the ESP charges and the dipole moments of the DNA bases and their N-methylated derivatives.

Quantum-Dynamical Picture of a Multistep Enzymatic Process: Reaction Catalyzed by Phospholipase A 2

A quantum-classical molecular dynamics model (QCMD), applying explicit integration of the time-dependent Schrödinger equation (QD) and Newtonian equations of motion (MD), is presented. The model is capable of describing quantum dynamical processes in complex biomolecular systems. It has been applied in simulations of a multistep catalytic process carried out by phospholipase A(2) in its active site. The process includes quantum-dynamical proton transfer from a water molecule to histidine localized in the active site, followed by a nucleophilic attack of the resulting OH(-) group on a carbonyl carbon atom of a phospholipid substrate, leading to cleavage of an adjacent ester bond. The process has been simulated using a parallel version of the QCMD code. The potential energy function for the active site is computed using an approximate valence bond (AVB) method. The dynamics of the key proton is described either by QD or classical MD. The coupling between the quantum proton and the classical atoms is accomplished via Hellmann-Feynman forces, as well as the time dependence of the potential energy function in the Schrödinger equation (QCMD/AVB model). Analysis of the simulation results with an Advanced Visualization System revealed a correlated rather than a stepwise picture of the enzymatic process. It is shown that an sp(2)--> sp(3) configurational change at the substrate carbonyl carbon is mostly responsible for triggering the activation process.

Implementation of a symplectic multiple-time-step molecular dynamics algorithm, based on the united-residue mesoscopic potential energy function.

A symplectic multiple-time-step (MTS) algorithm has been developed for the united-residue (UNRES) force field. In this algorithm, the slow-varying forces (which contain most of the long-range interactions and are, therefore, expensive to compute) are integrated with a larger time step, termed the basic time step, and the fast-varying forces are integrated with a shorter time step, which is an integral fraction of the basic time step. Based on the split operator formalism, the equations of motion were derived. Separation of the fast- and slow-varying forces leads to stable molecular dynamics with longer time steps. The algorithms were tested with the Ala(10) polypeptide chain and two versions of the UNRES force field: the current one in which the energy components accounting for the energetics of side-chain rotamers (U(rot)) can lead to numerically unstable forces and a modified one in which the the present U(rot) was replaced by a numerically stable expression which, at present, is parametrized only for polyalanine chains. With the modified UNRES potential, stable trajectories were obtained even when extending the basic time step to 15 fs and, with the original UNRES potentials, the basic time step is 1 fs. An adaptive multiple-time-step (A-MTS) algorithm is proposed to handle instabilities in the forces; in this method, the number of substeps in the basic time step varies depending on the change of the magnitude of the acceleration. With this algorithm, the basic time step is 1 fs but the number of substeps and, consequently, the computational cost are reduced with respect to the MTS algorithm. The use of the UNRES mesoscopic energy function and the algorithms derived in this work enables one to increase the simulation time period by several orders of magnitude compared to conventional atomic-resolution molecular dynamics approaches and, consequently, such an approach appears applicable to simulating protein-folding pathways, protein functional dynamics in a real molecular environment, and dynamical molecular recognition processes.

Quantum-Classical Molecular Dynamics. Models and Applications

Time-dependent, quantum mechanical models and theories play an important role in studies of enzyme catalysis, interactions of enzymes with chemotherapeutic agents, electron and proton tunneling in condensed media and in liquids, electron and proton transfer in biomolecular systems, photosynthesis, photodissociation processes, unimolecular decay reactions, tautomerism of nucleic acid bases, phosphorylation processes in biomolecular systems, and other molecular and biomolecular processes. Analytical models of time—dependent processes in quantum systems are limited to relatively simple objects. Several examples are discussed in the next chapter. Systems with a slightly more complicated structure can be studied using purely quantum-mechanical simulations, i.e. by numerically solving the time—dependent Schroedinger equation. In the case of larger systems, like enzymes, a quantum-classical description of their structure and dynamics is a useful strategy. A large part of such systems can be described using classical theories, whereas a small portion, typically their active sites, should be described in a quantum—dynamical way.

Molecular Dynamics Simulations of the First Steps of the Reaction Catalyzed by HIV-1 Protease

The mechanism of the first steps of the reaction catalyzed by HIV-1 protease was studied through molecular dynamics simulations. The potential energy surface in the active site was generated using the approximate valence bond method. The approximate valence bond (AVB) method was parameterized based on density functional calculations. The surrounding protein and explicit water environment was modeled with conventional, classical force field. The calculations were performed based on HIV-1 protease complexed with the MVT-101 inhibitor that was modified to a model substrate. The protonation state of the catalytic aspartates was determined theoretically. Possible reaction mechanisms involving the lytic water molecule are accounted for in this study. The modeled steps include the dissociation of the lytic water molecule and proton transfer onto Asp-125, the nucleophilic attack followed by a proton transfer onto peptide nitrogen. The simulations show that in the active site most preferable energetically are structures consisting of ionized or polarized molecular fragments that are not accounted for in conventional molecular dynamics. The mobility of the lytic water molecule, the dynamics of the hydrogen bond network, and the conformation of the aspartates in the active center were analyzed.

Extended Hellmann-Feynman forces, canonical representations, and exponential propagators in the mixed quantum-classical molecular dynamics

Analytical expressions of the Hellmann–Feynman (HF) forces in the quantum-classical molecular dynamics (QCMD) are evaluated and analyzed. The conventional expression of the HF forces is valid in the differential form of the QCMD evolution equations, but the extended formula appears in the context of approximate, time-step propagators. The canonical Hamilton representation of QCMD, and its symplectic and nonsymplectic exponential propagators, are reviewed. Tests for a model proton transfer system are performed in order to compare efficiency of the proposed integration schemes. The most efficient scheme results from separation of either different time scales or different approximation orders for the quantum and classical parts, and also from correct accumulation of the HF forces, corresponding to an improved extended HF formula. We derive the canonical representation and propagators of QCMD in the adiabatic basis set. If the classical and quantum parts of the propagator are separated in that representation,...

The Poisson-Boltzmann model for tRNA: Assessment of the calculation set-up and ionic concentration cutoff

Using tRNA molecule as an example, we evaluate the applicability of the Poisson‐Boltzmann model to highly charged systems such as nucleic acids. Particularly, we describe the effect of explicit crystallographic divalent ions and water molecules, ionic strength of the solvent, and the linear approximation to the Poisson‐Boltzmann equation on the electrostatic potential and electrostatic free energy. We calculate and compare typical similarity indices and measures, such as Hodgkin index and root mean square deviation. Finally, we introduce a modification to the nonlinear Poisson‐Boltzmann equation, which accounts in a simple way for the finite size of mobile ions, by applying a cutoff in the concentration formula for ionic distribution at regions of high electrostatic potentials. We test the influence of this ionic concentration cutoff on the electrostatic properties of tRNA.

Advanced Calculations and Visualization of Enzymatic Reactions with the Combined Quantum Classical Molecular Dynamics Code

The parallel version of the Quantum Classical Molecular Dynamics code is presented. The execution time scales almost linearly with the number of processors. The measured overhead of the parallelization paradigm is extremely small which ensures the high efficiency of the presented method. Tools based on the Advanced Visualization System (AVS) framework were developed for visualization and analysis of the QCMD simulations.

Parallel Version of a Quantum Classical Molecular Dynamics Code for Complex Molecular and Biomolecular Systems

A Quantum-Classical Molecular Dynamics model (QCMD) and its parallel version are presented. PFortran and MPI were used in the parallelization process. The code was tested on Cray T3D and Cray T3E computers. The execution time scales almost linearly with the number of processors. which ensures the high efficiency of the presented method.