03 Fakultät Chemie
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Item Open Access Are different stoichiometries feasible for complexes between lymphotoxin-alpha and tumor necrosis factor receptor 1?(2012) Mascarenhas, Nahren Manuel; Kästner, JohannesBackground Tumor necrosis factors, TNF and lymphotoxin-α (LT), are cytokines that bind to two receptors, TNFR1 and TNFR2 (TNF-receptor 1 and 2) to trigger their signaling cascades. The exact mechanism of ligand-induced receptor activation is still unclear. It is generally assumed that three receptors bind to the homotrimeric ligand to trigger a signaling event. Recent evidence, though, has raised doubts if the ligand:receptor stoichiometry should indeed be 3:3 for ligand-induced cellular response. We used molecular dynamics simulations, elastic network models, as well as MM/PBSA to analyze this question. Results Applying MM/PBSA methodology to different stoichiometric complexes of human LT-(TNFR1)n=1,2,3 the free energy of binding in these complexes has been estimated by single-trajectory and separate-trajectory methods. Simulation studies rationalized the favorable binding energy in the LT-(TNFR1)1 complex, as evaluated from single-trajectory analysis to be an outcome of the interaction of cysteine-rich domain 4 (CRD4) and the ligand. Elastic network models (ENMs) help to associate the difference in the global fluctuation of the receptors in these complexes. Functionally relevant transformation associated with these complexes reveal the difference in the dynamics of the receptor when free and in complex with LT. Conclusions MM/PBSA predicts complexes with a ligand-receptor molar ratio of 3:1 and 3:2 to be energetically favorable. The high affinity associated with LT-(TNFR1)1 is due to the interaction between the CRD4 domain with LT. The global dynamics ascertained from ENMs have highlighted the differential dynamics of the receptor in different states.Item Open Access Using umbrella integration to find minimum free energy paths(2015) Bohner, Matthias Ulrich; Kästner, Johannes (Prof. Dr.)The analysis of the detailed mechanism of chemical reactions is a key task of computational chemistry. The detailed knowledge may help to improve known processes or even contribute to the development of new ones. In this way ecological and economic demands can be reduced. Furthermore, the course of a reaction path also plays an important role in the action of drugs. Understanding the binding of the active ingredient to receptors, such as proteins, can make it possible to optimize drugs by reducing side effects, or even to find new effects. Unfortunately, chemical reactions are usually too fast to observe intermediate states by experimental methods. This is where theoretical chemistry joins the game. In theoretical chemistry we combine the coordinates of all atoms with the configuration space. The potential energy forms a hypersurface in this space. Minima represent stable or metastable states. Saddle points represent transition states which are the most unfavourable configurations occurring on the most favourable path between two minima. If the path of a reaction is known, all intermediate states can be observed by theoretical methods. However, these calculations are usually computationally costly. This is the reason why, in contrast to experimental methods, it is in general impossible to sample the whole configuration space. This would in most cases exceed the available computational resources. It is therefore necessary to use techniques enabling a reaction path to be found without sampling the whole configuration space. In the case of a thermodynamic ensemble, e.g. the contents of a test tube, statistical information has to be included. The corresponding potential is the so-called free energy landscape, for which some degrees of freedom of the configuration space are thermostatistically integrated out. Consequently this function includes statistical and energetic properties. The free energy can in general only be calculated by statistical simulations (Monte--Carlo or molecular dynamics). Unfortunately, the transition states in which we have a special interest are rarely sampled. Special methods have to be applied to get sufficient sampling as well in areas of these rare events. In this work a non-physical quadratic potential is used to bias the equation of motion of the particles while doing molecular dynamics simulations. In this way unfavourable areas in the configuration space can also be sampled sufficiently. This technique is called umbrella sampling. The bias is applied to one or more coordinates which describe the reaction and therefore are called reaction coordinates. An umbrella sampling run will result in a distribution of the reaction coordinates. The expectation value of this distribution will be located close to the minimum of the bias function without in general corresponding to it. The difference between the minimum of the bias function and the expectation value can be used to calculate the gradient of the underlying free energy surface. Similarly, the covariance of the distribution of the reaction coordinate can be used to calculate the Hessian of the free energy surface. This method of interpreting the data gained by umbrella sampling is called umbrella integration. At first these values are used for an iterative search of the saddle points, which represent the transition states. From these configurations, free energy paths can be constructed by following the gradient down to the minima. This algorithm was successfully tested for the alanine dipeptide system. This simple method has the disadvantages that it works serially and that one needs good initial guesses for the saddle points in order to find them. Therefore, in a second part of the work, the established method of nudged elastic band optimization (NEB) is extended for use in the free energy surface. NEB optimization searches for a reaction path. This path is discretized into a number configurations, so-called images. For the sake of equal distribution of the images along the path a non-physical spring force between the images is used. The force, which is actually minimized during the NEB optimisation, consists of the projection of the real force of the underlying potential perpendicular to the path, and the projection of the spring force parallel to the path. An optimizer is developed which archives quadratic convergence of NEB optimizations in the noise-free potential energy surface of some test systems. This optimiser uses gradients and Hessians at each step. For the free energy surface both values can be calculated by umbrella integration as mentioned above. NEB optimizations within the free energy are performed in this work in the following way: at first a guess path is assumed, e.g. a straight line between two points in the configuration space, usually minima. This path is discretized into a number of images. Molecular dynamics umbrella sampling simulations are performed on each image. The gradient and Hessian from the umbrella integration are fed into the newly developed NEB optimizer. This way one does not need good starting guesses for the saddle points but an interpolation between the much more easily accessible minima is sufficient. Furthermore, the need for independent molecular dynamics runs at each image makes the method intrinsically parallel. The whole method is applied to the well-studied alanine dipeptide system and compared with the results from the serial method. Subsequently the algorithm is applied to a much more costly system of binding a ligand to its receptor in water.Item Open Access Accurate force- and Hessian predictions from neural network potentials(2020) Cooper, April Mae; Kästner, Johannes (Prof. Dr.)Item Open Access Improvements to the instanton method : tunneling rates in the enzyme glutamate mutase(2012) Rommel, Judith Barbara; Kästner, Johannes (Jun.-Prof.)Atom tunneling occurs in many chemical reactions involving hydrogen transfers. Tunneling increases the reaction rate compared to the classical over-the-barrier model especially at low temperature. In many enzymes tunneling of hydrogen atoms influences the reaction rate even at room temperature which can experimentally be observed by unusually high kinetic isotope effects (KIEs). A high KIE shows that tunneling accelerates the rate limiting step. Computer simulations can directly quantify the effect of tunneling in a reaction by switching it on and off. The enzyme glutamate mutase catalyzes the radical conversion mechanism of (S)-glutamate to (2S,3S)-3-methylaspartate including two hydrogen transfer steps. The protium/deuterium KIEs measured in glutamate mutase range from 4.1 to 35 at 10°C. Thus, it is unclear whether tunneling is involved or important for the catalytic process. Glutamate mutase is studied by a multiscale approach combining quantum mechanics with molecular mechanics (QM/MM), with quantum mechanical (QM) calculations used for the atoms directly involved in bond rearrangements and force field calculations (MM) for the environment. The QM part is investigated with density functional theory and coupled cluster theory. The results of the QM/MM simulations show new details of the catalyzed reaction and lead to an improved understanding of the catalysis by glutamate mutase: the conversion of (S)-glutamate to (2S,3S)-3-methylaspartate is found to proceed via a fragmentation-recombination mechanism. The involved hydrogen atom transfer steps exhibit the highest barrier, 101 kJ/mol (M06 functional). The barriers of the hydrogen transfers match for density functional theory (M06 functional) and coupled cluster (LUCCSD(T)) calculations. It turned out that the influence of the enzyme is mainly electrostatical and to a lesser degree sterical. The calculations shed light on the atomistic details of the reaction mechanism. The well-known arginine claw (Arg 66, Arg 100, and Arg 149) and Glu 171 are found to have the strongest influence on the reaction. The arginine claw keeps the intermediate fragments in place, and is important for the recombination process. However, significant catalytic roles of amino acids close to the active center, e.g., Glu 214, Lys 322, Gln 147, Glu 330, Lys 326, and Met 294 are found as well. These results predict new promising experimental targets. The role of tunneling in the enzyme glutamate mutase is investigated by QM/MM simulations based on instanton theory with up to 78 atoms allowed to tunnel. Primary protium/deuterium KIEs of hydrogen transfers are in good agreement with experiment. The secondary tritium KIEs hint that coupled motions on a ribose ring of the cofactor are part of the tunneling motions. The enzyme uses both classical and tunneling motions for a successful catalysis. The instanton method (also called imaginary free energy method) is based on Feynman's path integral formalism. The instanton is the most-likely tunneling path. The instanton is also a first-order saddle point of the Euclidean action. The problem of finding an instanton is addressed as a saddle-point search problem. Four algorithms implemented to locate instantons are compared: a modified Newton-Raphson method, the partitioned rational function optimization algorithm, the dimer method, and a newly proposed mode-following algorithm. These algorithms are tested on three chemical systems. Overall, the Newton-Raphson turns out to be the most promising method, consistently efficient and stable, with the newly proposed mode-following method being the fall-back option. Two bottlenecks are challenging in instanton rate calculations: (1) Hessian calculations subsequent to the instanton optimization are expensive for large systems like enzymes. (2) At lower temperature more and more discretization points (images) on the equidistantly discretized path tend to accumulate at the ends of the instanton path. Thus, methods that allow to use fewer discretization points for the same quality in the rates are required. The development of a quadratically convergent optimizer significantly increases the efficiency of instanton optimizations. In combination with a new, flexible, and variable discretization of the integration along the instanton, the computational costs are reduced by one or two orders of magnitude.Item Open Access Development of full configuration interaction quantum Monte Carlo methods for strongly correlated electron systems(2019) Dobrautz, Werner; Alavi, Ali (Prof. Dr.)Full Configuration Interaction Quantum Monte Carlo (FCIQMC) is a prominent method to calculate the exact solution of the Schrödinger equation in a finite antisymmetric basis and gives access to physical observables through an efficient stochastic sampling of the wavefunction that describes a quantum mechanical system. Although system-agnostic (black-box-like) and numerically exact, its effectiveness depends crucially on the compactness of the wavefunction: a property that gradually decreases as correlation effects become stronger. In this work, we present two -conceptually distinct- approaches to extend the applicability of FCIQMC towards larger and more strongly correlated systems. In the first part, we investigate a spin-adapted formulation of the FCIQMC algorithm, based on the Unitary Group Approach. Exploiting the inherent symmetries of the nonrelativistic molecular Hamiltonian results in a dramatic reduction of the effective Hilbert space size of the problem. The use of a spin-pure basis explicitly resolves the different spin-sectors, even when degenerate, and the absence of spin-contamination ensures the sampled wavefunction is an eigenfunction of the total spin operator. Moreover, targeting specific many-body states with conserved total spin allows an accurate description of chemical processes governed by the intricate interplay of them. We apply the above methodology to obtain results, not otherwise attainable with conventional approaches, for the spin-gap of the high-spin cobalt atom ground- and low-spin excited state and the electron affinity of scandium within chemical accuracy to experiment. Furthermore we establish the ordering of the scandium anion bound states, which has until now not been experimentally determined. In the second part, we investigate a methodology to explicitly incorporate electron correlation into the initial Ansatz of the ground state wavefunction. Such an Ansatz induces a compact description of the wavefunction, which ameliorates the sampling of the configuration space of a system with FCIQMC. Within this approach, we investigate the two-dimensional Hubbard model near half-filling in the intermediate interaction regime, where such an Ansatz can be exactly incorporated by a nonunitary similarity transformation of the Hamiltonian based on a Gutzwiller correlator. This transformation generates novel three-body interactions, tractable due to the stochastic nature of FCIQMC, and leads to a non-Hermitian effective Hamiltonian with extremely compact right eigenvectors. The latter fact allows application of FCIQMC to larger lattice sizes, well beyond the reach of the method applied to the original Hubbard Hamiltonian.Item Open Access Calculation of reaction rate constants via instanton theory in the canonical and microcanonical ensemble(2018) Löhle, Andreas; Kästner, Johannes (Prof. Dr.)Item Open Access Kopplung von Dichtefunktional- und ab-initio-Methoden(2008) Goll, Erich; Stoll, Hermann (Prof. Dr.)Im Rahmen der Doktorarbeit wurde untersucht, inwieweit die Kopplung von Dichtefunktionalmethoden und ab-initio-Korrelationsmethoden der Quantenchemie eine Verbesserung bezüglich beider Grenzmethoden erbringt. Die Kopplung erfolgt durch eine Aufspaltung des interelektronischen Hamiltonoperators (abstoßende Coulombwechselwirkung). Die kurzreichweitige Wechselwirkung wird mit Dichtefunktionaltheorie behandelt, die langreichweitige mit Hilfe von ab-initio-Methoden. Diese Aufteilung soll dazu dienen, die Berechnung der interelektronischen Singularität (Cusp), die für die große Basissatzabhängigkeit der ab-initio-Methoden verantwortlich ist, auf DFT abzuwälzen. Gleichzeitig sollen langreichweitige Effekte im Rahmen der ab-initio-Methoden behandelt werden, wofür sich diese wiederum besser als DFT eignen. Zum Zweck der Kopplung wurden auf der DFT-Seite verschiedene kurzreichweitige Spindichtefunktionale (PBE und TPSS mit und ohne exakten Austausch) implementiert, auf der ab-initio-Seite Hartree-Fock, Configuration Interaction, Møller-Plesset-Störungstheorie und Coupled-Cluster-Methoden. Es zeigt sich, daß die gemischte DFT/ab-initio-Methode für mittelgroße Basissätze den beiden Grenzfällen überlegen ist. So lassen sich schwach gebundene Systeme mit guter Genauigkeit beschreiben. Auch bei der Berechnung von Moleküleigenschaften konnten erhebliche Verbesserungen erzielt werden.Item Open Access Machine-learning techniques for geometry optimization(2023) Born, Daniel; Kästner, Johannes (Prof. Dr.)Geometry optimization in computational chemistry is still a challenging task. The bottleneck is the computationally expensive ab initio calculations. Thus reducing the total amount of these calculations to accelerate minimization and transition state search is essential. In recent years machine-learning techniques, like Gaussian process regression or neural networks, became popular among scientists. These can be used to calculate the surrogate surface of the potential energy surface and perform geometry optimization there. Another important aspect of geometry optimization is the choice of coordinate system. While Cartesian coordinates describe uniquely a molecule, they are highly coupled. To reduce the coupling between the coordinates, the so-called internal coordinates were developed a long time ago. In addition, these coordinates are non-redundant. With these types of coordinates, a speedup of geometry optimization was obtained. Combining internal coordinates with machine-learning technique has thus the potential to significantly improve geometry optimization. In this thesis, the improvement is demonstrated.Item Open Access Theoretical investigations of atom tunneling in the interstellar medium(2018) Meisner, Jan; Kästner, Johannes (Prof. Dr.)