Kinetics and Dynamics

In this chapter we present an overview of what is known today about the reactivity of Ca²⁺ with different species, both from the theoretical and the experimental points of view. We have paid particular attention to the bonding characteristics of Ca²⁺ complexes and to the electron density re-distribution undergone by the neutral interacting with this doubly charged metal, due to the quite intense electric field around it, which results sometimes in, dramatic polarization effects. Another important question is related with the stability of Ca²⁺ complexes in the gas phase, in clear contrast with the instability of analogous complexes involving other metal dications, such as Cu²⁺ or Pb²⁺, which only produce singly charged species when interacting with neutral bases. The last part of this chapter will be devoted to review the different combined experimental and theoretical studies of several reactions involving Ca²⁺. This survey will include a comparison of the reactivity exhibited by Ca²⁺ with respect to the reactivity shown by other divalent metal ions, as well as some preliminary results of the reaction of Ca²⁺ with uracil. Particular attention will be also paid to the catalytic effect of Ca²⁺ in the tautomeric process of these kinds of biochemical compounds.

We present a review of our recent developments in computational modeling of hydrogen-bonding-induced phenomena in a series of biologically relevant bifunctional proton donor–acceptor heteroazaaromatic compounds. Different types of hydrogen-bonded solvates, in which water or alcohol molecules form a bridge connecting the proton donor (pyrrole NH group) and the acceptor (pyridine or quinoline nitrogen) atoms of bifunctional solutes, are explored by combining density functional theory (DFT) and molecular dynamics (MD) simulation approaches. Structure and dynamics of multiple hydrogen-bonded solute-solvent complexes are studied starting from isolated complexes in the gas phase, elucidating their solvation dynamics in solutions and, finally, in a heterogeneous environment of a lipid bilayer. Our results indicate that the structure, stoichiometry and hydrogen bond strength in such solvates are tuned by local topologies of the hydrogen-bonding sites of a bifunctional proton donor–acceptor molecule. A role of such solvates in hydrogen-bond-dependent photophysics and in controlling excited-state behavior of heteroazaaromatic compounds is discussed.

Dynamics simulations are an essential step in exploring ultrafast phenomena in photochemistry and photobiology. In this chapter we present results of photodynamics studies for some model compounds for the peptide bond using the on-the-fly surface hopping method. The mechanism of photodissociation of formamide, its protonated forms and methyl substituted derivatives in their lowest singlet excited states in the gas phase is discussed in detail. Merits and demerits of using these simple molecules as models in exploring photochemical and photophysical properties of more complex systems, like peptides and proteins, are emphasized. It is found that in all examined model molecules the major deactivation process after excitation to the S₁ state is dissociation of the peptide C–N bond. The same holds for the deactivation path from the S₂ state, with exception of the O- protonated formamide in which C–O dissociation becomes the major deactivation process. Furthermore, it is shown that substitution by the methyl group(s), as well as protonation, strongly influence the lifetime of both excited states. In the last section application of the newly developed hybrid nonadiabatic photodynamics QM/MM approach in calculating photodissociation of formamide in argon matrix is illustrated.

The current decade being a golden era in the history of organocatalysis, designing new organocatalysts for synthetically valuable reactions is of high importance. A fine blend of theoretical techniques and knowledge gathered from the experimental observations can help one design highly selective organocatalysts. The present chapter summarizes our efforts in designing organocatalysts for two synthetically important reactions; namely, the aldol reaction and sulfur ylide mediated ring formation reactions. In order to identify the crucial elements that affect the stereoselection process, detailed mechanistic studies are performed initially. Thus, factors controlling the vital energy differences between the diastereomeric transition states are identified and rationalized. Later on, insights from these model studies are utilized toward designing the new catalyst framework. In the last stage, the catalytic efficiency with the designed catalysts is evaluated for selected reactions. Conformationally constrained catalysts designed in this manner are predicted to be more effective with improved selectivities in comparison to the experimentally employed analogues.

Describing chemical reactions is one of the most challenging aspects of current computational approaches to chemistry. In this chapter established (EVB, ReaxFF) and novel (MMPT, ARMD) approaches are discussed that allow to study bond forming and bond breaking processes in a variety of chemical and biological environments. Particular emphasis is put on methods that enable investigating the dynamics of chemical reactions. For MMPT and ARMD methods, a number of model studies are discussed in more detail. They include the kinetics of NO rebinding to Myoglobin and the conformational transition in Neuroglobin which explores the full functionality of ARMD. The chapter closes with an outlook of possible generalizations of the methods discussed.

In this review, the applicability of computational chemistry procedures for modelling of macromolecules and large macromolecular systems is shortly reviewed. In particular, the recent achievements in studying the reactions leading to polymers by quantum chemical and molecular mechanical methods are presented.

The kinetics of chemical reactions characterizes the rates of chemical processes, i.e. distribution of all reactants, intermediates and products over time. This information is of vital importance for all areas of chemistry: chemical technology to control organic or inorganic syntheses, chemical construction of nanomaterials, as well as for the investigation of biochemical processes. The chemical kinetics data provide a possibility to investigate the effect of different chemical, physical and environmental factors on the rate of a reaction, final products and by-products distribution, and even the direction of a chemical process. In the first part of the chapter the general introduction to the kinetics of chemical reactions is given. The classical kinetics of chemical reactions uses the outcome from experimental measurement of reaction rates. However, currently available reliable computational ab initio methods provide an alternative efficient way for estimation of the rate constants even for stepwise and multidirectional reactions. Another benefit of the computational investigations is the possibility to simulate a wide range of processes with duration from picoseconds to hours, days, or even for much longer time scales. Contemporary ab initio methods have been used for estimation and prediction of reaction rates for a number of different chemical reactions. Until recently most of the theoretical studies on kinetic parameters have not been extended beyond the calculations of the rate constants of chemical reactions. In the present review we describe the simulation of the chemical kinetics of proton transfer (tautomerization) in nucleic acid bases and their complexes with metal ions, also in the presence of water molecules. The considered models are based on the ab initio calculated rate constants of chemical reactions. Then, such predicted rate constants are used for further kinetic simulations. Biological consequences of investigated processes are also discussed.

The phenomenon of charge migration in DNA has attracted considerable interest of experimental as well as computational research in the last decade. It poses a huge challenge for simulation, due to the large system size and the long relevant time scales. Simple modeling frameworks may miss or overapproximate several important factors influencing the charge transfer in DNA, most prominently the dynamical and solvent effects. Therefore, modern approaches make use of multi-scale coarse-grained computational schemes, which have been developed in several labs recently. These techniques combine empirical force fields to capture the DNA dynamics and quantum-chemical methods to describe the actual charge transfer events. The performed simulations show that the dynamics and solvent effects play a major role in DNA charge transfer.

Computational studies of biological macromolecules are challenging due to large size of biomolecules, their conformational flexibility, and the need in explicit water solvation in order to simulate conditions close to experiment. Under these circumstances studying molecular systems via quantum-mechanical calculations becomes exceedingly difficult. Natural is the attempt to reduce the complex quantum-mechanical picture to a more tractable one by accommodating classical-mechanical principles. However, the simplified models may overlook important physics details of atomic interactions. To avoid such potential pitfalls higher level of theory methods should be available to conduct validation studies. Using semiempirical linear scaling quantum-mechanical LocalSCF method we performed molecular dynamics simulation of ubiquitin in explicit water. The simulation revealed various deviations from the classical mechanics picture. The average charge on amino acids varied depending on their environment. We observed charge transfer channels transmitting electric charge between amino acids in sync with protein motion. We also noticed that the excess charge transferred from protein to water creates a charge cloud around the protein. The observed global dynamic effects of charge transfer represent a new previously unaccounted degree of freedom of biomolecules which requires QM treatment in order to obtain more accurate dynamics of biomolecules at atomic resolution.

The role transition structures (TSs) and vectors have played in discussing issues associated to enzyme catalysis is examined with focus on RubisCO; computations belong to standard semi-classic Born-Oppenheimer model with one-electron orbitals located at nuclear position coordinates. Here, theory is brought a step beyond starting from exact quantum schemes to get types of semi-classic Hamiltonians allowing for clear definitions of electronuclear separable models. Electronuclear quantum states (QSs) are given by linear superpositions over eigenfunctions of semi-classic Hamiltonians; base state functions are products of space and spin components. For frozen nuclei models amplitudes depend on nuclear configuration multiplying electronic diabatic base functions characterized by nodal pattern distributions. QS’ time evolution requires couplings to external fields and does not necessarily conserve total spin. RubisCO’s dioxygen and ethene-fragment quantum reactivity are examined and generalized. Conservation of nodal patterns permits links to exact semi-classic schemes ensuring correct presentation of bond forming processes; possible failures of LCAO-based computations without nodal control are discussed. These issues are examined in relation to catalysis representation. Pauling’s idea that TS signals bent out of equilibrium shape of reactant and product is framed in terms of transition QSs. A full quantum catalysis model is introduced.

The application of molecular dynamics (MD) simulations is now firmly established as a strategy to help understanding the activity of biological systems, being routinely applied to investigate the structure, dynamics and thermodynamics of biological molecules and their complexes. Commonly available biomolecular force fields like AMBER, CHARMM, OPLS, and GROMOS contain sets of molecular mechanical parameters for the 20 natural amino acid residues and for a limited set of additional structural elements, allowing accurate MD simulations to be performed for a vast number of proteins and enzymes that are composed simply by such elements. For more diverse biological systems, such as those containing covalently bound metal atoms, no parameters are normally available to describe the specific interactions formed between the metal and the amino acid residues, limiting in practice the direct application of MD simulations to the study of these systems. This chapter presents the typical difficulties normally encountered when trying to run MD simulations on a metalloenzyme, and introduces common solutions and strategies to circumvent these problems, illustrating also the wide range of catalytic relevant properties that can be obtained from such simulations. The zinc metalloenzyme farnesyltransferase is used to illustrate these aspects.

Combined quantum mechanical/molecular mechanical (QM/MM) models have been established as efficient approaches to simulate chemical reactions in complex molecular systems including enzymes. The QM/MM Hamiltonian is defined based on partitioning a molecular system into a reactive center and its surrounding, namely, the QM and MM regions. How to properly treat the QM/MM interface, which involves both covalent and non-covalent interactions, has been one of the central focuses in QM/MM method development. Techniques for energy minimization and conformational sampling based on QM/MM Hamiltonians have also been continuously developed, with the goal to determine reaction paths and potential/free energy surfaces of complex molecular systems efficiently and reliably. Accompanying method development, there have been an increasing number of studies applying QM/MM to various enzyme systems and providing new insights into their mechanisms.

Lactate dehydrogenases, LDH, catalyzed reaction has been used in this chapter as a conductor wire to present the evolution and difficulties on computing methods to model chemical reactions in enzymes, since the early calculations based at semiempirical level carried out in gas phase to the recent sophisticated simulations based on hybrid Quantum Mechanical/Molecular Mechanics Dynamics (QM/MM MD) schemes. LDH catalyzes the reversible transformation of pyruvate into lactate. The chemical step consists in a hydride and a proton transfer from the cofactor (NADH) and a protonated histidine (His195), respectively. This fact has generated a lot of controversy about the timing of both transfers in the active site, as well as the role of the different aminoacids of the active site and problems related with the flexibility of the protein. We herein show how an adequate method within a realistic model, taking into account the pKa of the titratable aminoacids, the flexibility of the protein, the size of the MM and QM region or the level of theory used to describe the QM region, must be used to obtain reliable conclusions. Finally, and keeping in mind the size of the system under study, it has been demonstrated the need of performing statistical simulations to sample the full conformational space of all states involved in the reaction, that allow getting free energies and averaged properties directly compared with experimental data.

Molecular modelling and simulation are making increasingly important contributions to the study of the structure and function of biological macromolecules. An area of particular current interest and debate is that of enzyme catalysis, and the role of protein dynamics in enzyme-catalysed reactions. Simulations allow enzyme catalytic mechanisms and protein dynamics to be investigated at the atomic level (e.g. with combined quantum mechanics/molecular mechanics (QM/MM) calculations and atomistic molecular dynamics simulations). This level of detailed analysis is beyond what is currently possible in experiments for reactions in enzymes, and simulations therefore have a crucial role to play in testing hypotheses and aiding in the interpretation of experimental data. Biomolecular simulations will therefore be crucial in resolving current controversies about the role of protein dynamics in enzyme catalysis. In this chapter we describe some recent simulations which have contributed to an understanding of enzyme mechanism, dynamics and function.

Computational approaches at various levels have been used to elucidate the mechanism of the ammonium/ammonia transport process through the Escherichia coli AmtB membrane protein. Molecular dynamics (MD) simulations at the classical molecular mechanical (MM) level confirmed that only NH₃ can transport through the highly hydrophobic AmtB channel. Thus, NH₄ ⁺, which is predominant in solution, must deprotonate before crossing the channel. Significantly, conformational analyses revealed that in the end of the recruitment vestibule, there is a hydrogen bond wire between NH₄ ⁺ and the carboxylate group of Asp160 via two water molecules. Thus, Asp160 is most likely the proton acceptor from NH₄ ⁺. This explains the high conservation of Asp160 in Amt proteins and why the D160A mutant would completely quench the activity of AmtB. The proposed deprotonation mechanism was further examined by the combined QM/MM methods. Computations at both QM(DFT)/MM and QM(PM3)/MM levels concur that the proton transfer starts from a lose of a proton from a nearby water to Asp160 to form a hydroxide anion in the intermediate state, followed by a proton transfer from NH₄ ⁺ to the hydroxide ion through a water molecule.

A model is presented which relates kinetic isotope effects and their temperature dependence to physical parameters governing enzymatic carbon–hydrogen cleavage, a reaction that typically exhibits a large isotope effect indicative of tunneling. The model aims to replace the Arrhenius equation, which is not valid for tunneling reactions, and the one-dimensional Bell model, which excludes skeletal vibrations. Cast in the form of three user-friendly analytical equations, it applies directly to the observed rate constants and effective activation energies, for both adiabatic and nonadiabatic hydrogen transfer. The approach has the dual aim of establishing criteria to probe whether a set of data can be assigned to a single rate-limiting tunneling step and to find numerical values for the proton or hydrogen transfer distance and for properties of the tunneling mode as well as skeletal modes involved in this step. It is applied to several enzymatic (model) reactions, including free-radical reactions catalyzed by cofactor B₁₂ and phenylalanine hydroxylase, and electron-assisted proton-transfer reactions catalyzed by soybean lipoxygenase-1 and methylamine dehydrogenase.

The accurate evaluation of quantum effects is of great importance in many reaction processes. Variational transition state theory with multidimensional tunneling is the natural choice for the study of these reactions, because it incorporates quantum effects through a multiplicative transmission coefficient and it can deal with large systems. Currently, the main approximation used for taking into account tunneling is the small-curvature approximation, mainly because the large curvature and the least-action approximations are computationally very demanding and their use it is usually associated to small systems. Here we describe two algorithms based on splines under tension, which allow the evaluation of these two transmission coefficients for large systems. The analysis of kinetic isotope effects on a model reaction show that the least-action transmission coefficient should be used instead of the more inexpensive, but probably less accurate small-curvature transmission coefficient.

We review the role of dynamics in enzyme catalysed H-tunnelling reactions with particular focus on the integration of computational methods with experimental and numerical modelling studies. We show that H-tunnelling requires compressive motion along the H-transfer coordinate and these reactions can be modelled successfully using vibrationally-coupled H-tunnelling models in which barrier compression is driven by fast motions within the enzyme–substrate complex.