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The aim of the present work is the development and implementation of new simulation
possibilities for the CAST program package. Development included, among other
things, the partial parallelization of the already existing force fields, extension of the
treatment of electrostatic interactions and implementation of molecular dynamics and
free energy algorithms.
The most time consuming part of force field calculations is the evaluation of the nonbonded
interactions. The calculation of these interactions has been parallelized and
it could be shown to yield a significant speed up for multi-core calculations compared
to the serial execution on only one CPU. For both, simple energy/gradient as well as
molecular dynamics simulations the computational time could be significantly reduced.
To further increase the performance of calculations employing a cutoff radius, a linkedcell
algorithm was implemented which is able to build up the non-bonded interaction
list up to 7 times faster than the original algorithm.
To provide access to dynamic properties based on the natural time evolution of a system,
a molecular dynamics code has been implemented. The MD implementation features
two integration schemes for the equations of motion which are able to generate stable
trajectories. The basic MD algorithm as described in Section 1.2 leads to the sampling
in the microcanonical (NVE) ensemble. The practical use of NVE simulations is limited
though because it does not correspond to any experimentally realistic situation.
More realistic simulation conditions are found in the isothermal (NVT) and isothermalisobaric
(NPT) ensembles. To generate those ensembles, temperature and pressure
control has been implemented. The temperature can be controlled in two ways: by direct
velocity scaling and by a Nose-Hoover thermostat which produces a real canonical
ensemble. The pressure coupling is realized by implementation of a Berendsen barostat.
The pressure coupling can be used for isotropic or anisotropic box dimensions with the
restriction that the angles of the box need to be 90. A crucial simulation parameter in
MD simulations is the length of the timestep. The timestep is usually in the rang of 1fs.
Increasing the timestep beyond 1fs can lead to unstable trajectories since the fastest
motion in the system, usually the H-X stretch vibration can not be sampled anymore.
A way to allow for bigger timesteps is the use of a constraint algorithm which constrains the H-X bonds to the equilibrium distance. For this the RATTLE algorithm has been
implemented in the CAST program. The velocity Verlet algorithm in combination with
the RATTLE algorithm has been shown to yield stable trajectories for an arbitrary
length of simulation time. In a first application the MD implementation is used in conjunction
with the MOPAC interface for the investigation of PBI sidechains and their
rigidity. The theoretical investigations show a nice agreement with experimentally obtained
results. Based on the MD techniques two algorithms for the determination of free
energy differences have been implemented. The umbrella sampling algorithm can be
used to determine the free energy change along a reaction coordinate based on distances
or dihedral angles. The implementation was tested on the stretching of a deca-L-alanine
and the rotation barrier of butane in vacuum. The results are in nearly perfect agreement
with literature values. For the FEP implementation calculations were performed
for a zero-sum transformation of ethane in explicit solvent, the charging of a sodium
ion in explicit solvent and the transformations of a tripeptide in explicit solvent. All
results are in agreement with benchmark calculations of the NAMD program as well
as literature values. The FEP formalism was then applied to determine the relative
binding free energies between two inhibitors in an inhibitor-protein complex.
Next to force fields, ab-initio methods can be used for simulations and global optimizations.
Since the performance of such methods is usually significantly poorer than force
field applications, the use for global optimizations is limited. Nevertheless significant
progress has been made by porting these codes to GPUs. In order to make use of these
developments a MPI interface has been implemented into CAST for communication
with the DFT code TeraChem. The CAST/TeraChem combination has been tested
on the $H_2 O_{10}$ cluster as well as the polypeptide met-Enkephalin. The pure ab-initio
calculations showed a superior behavior compared to the standard procedure where the
force field results are usually refined using quantum chemical methods.
KasA is a key enzyme which plays an essential part in the biosynthetic pathway of mycolic acids, the building block of cell wall in Mycobacterium tuberculosis. Its importance was demonstrated by the finding that the depletion of KasA leads to the cell lysis of Mycobacterium tuberculosis. Since Mycobacterium tuberculosis is a pathogen of tuberculosis, the second leading cause of death from an infectious disease worldwide, KasA has drawn attention as one of the attractive drug targets against tuberculosis. Due to the emergence of extensively drug-resistant strains which make most of the known antibiotics for treating tuberculosis ineffective, it became an urgent issue to develop new drugs against tuberculosis. In chapter 3.1, the protonation state of the catalytic residues in the resting state was mainly addressed. The FEP computation and MD simulations were employed for this investigation, and the results showed that the zwitterionic state is most probable. To underpin this conclusion with more solid data, The PESs for the proton transfer between the neutral and zwitterionic state were computed in the context of QM/MM. However, due to the strong dependency of the QM/MM optimization on the initial structure, it was not possible to obtain consistent results from these computations. To circumvent this problem, QM/MM based umbrella sampling was carried out with a semi-empirical method (RM1), and the resulting PMF surface indicated that the zwitterionic state is more stable than the neutral state. In chapter 3.2, the protonation state of significant residues in the acyl-enzyme state was investigated. Unlike other catalytic residues, the protonation state of His311 is ambiguous in the acyl-enzyme state, and different decarboxylation mechanisms can be derived depending on the protonation state of His311 in the acyl-enzyme state. Therefore, FEP computations were carried out to find most probable protonation state of His311 in terms of free energy, and the results showed that the pKa value at Nδ is considerably lowered by the enzyme environment while that of Nε is not. Additionally, the PMF profiles for the proton transfer between Lys340 and Glu354 were computed using QM/MM based umbrellas sampling method, and the results showed that the property of the Lys340/Glu354 pair is neutral rather than ionic when His311 is protonated at Nε. Moreover, a relatively larger ionic character of the Lys340/Glu354 pair when His311 is doubly protonated provides a valuable insight into how the Lys340/Glu354 pair plays a role in shifting the protonated state from Nδ to Nε in His311 after the acyl-transfer step. Overall, the results demonstrated that His311 is neutral and protonated at Nε, and the Lys340/Glu354 pair is also neutral in the acyl-enzyme state. Those computational results lead to the conclusion that the decarboxylation reaction is facilitated by an oxyanion hole which is comprised of two catalytic histidines. In chapter 3.3, the protonation state of catalytic residues in the resting state was revisited because a recent benchmark study showed that the employed semi-empirical method (RM1) in chapter 3.1 tends to overestimate the stabilization of the zwitterionic state. Furthermore, the Lys340/Glu354 pair was considered as purely ionic in chapter 3.1, while it actually has a mixed neutral and ionic character as demonstrated in chapter 3.2. The new investigations employed a larger QM region including the Lys340/Glu354 pair with the BLYP/6-31G** approach, which was proven to be accurate enough for the present purpose by benchmark computations. The new results from the QM/MM MD and FEP computations indicated the catalytic residues to be neutral most probably in the resting state, and this in turn brought up the question how KasA can be activated to initiate the catalytic reaction. On the basis of the results from the MD simulations and FEP computations for the His311Ala mutant in chapter 3.1, we hypothesized that the open conformation of Phe404 would trigger the activation of the catalytic residues by the formation of a strong hydrogen bond. The QM/MM MD simulation proved that the activation of the catalytic residues can indeed be accomplished by the open conformation of Phe404 we suggested, and the corresponding force field based PMF profile also indicated that this conformational change is energetically feasible. The distribution of hydrophilic and hydrophobic residues in the malonyl binding pocket in conjunction with our computational results further provided a valuable insight into the detailed process how the catalytic residues is activated upon the substrate entering.
Although known about and investigated since the late 1970’s, the picture of the basic principles governing inhibitor strengths and the structure-activity relationships of the cysteine protease inhibition mechanism is still very incomplete. Computational approaches can be a very useful tool for investigating such questions, as they allow the inspection of single, specific effects in isolation from all others, in a manner very difficult to achieve experimentally. The ab initio treatments of such large systems like proteins are still not feasible. However, there is a vast number of computational approaches capable of dealing with protein structures with reasonable accuracy. This work presents a summary of theoretical investigations into cysteine protease cathepsin B using a range of methods. We have concentrated on the investigation of cysteine protease inhibition by epoxide- and aziridine-based inhibitors in order to obtain better insight into these important topics. Various model systems are simulated by means of pure quantum mechanical methods and by hybrid (QM/MM) methods. Both approaches provide a static picture. Dynamical effects are then accounted for by additional molecular dynamics (MD) simulations, using both classical and QM/MM MD approaches. The quantum mechanical approach was used to study very small model systems consisting only of the electrophilic warhead of the inhibitor (both substitituted and not) and molecular moieties simulating a very simplified protein active site (methylthiolate instead of Cys29 and methylimidazolium instead of His199 residue) and solvent surroundings (two waters or two ammonium ions, in combination with a continuum solvent model). Although simple, such a system provides a good description of the most important interactions involved in the inhibition reaction. It also allows investigation of the influence of the properties of the electrophilic warhead on the reaction rate. Beside the properties of the electrophilic warhead, the protein and solvent environment is also an important factor in the irreversible deactivation of the enzyme active site by the inhibitor. The non-covalent interactions of the inhibitor with the oxyanion hole and other subsites of the enzyme, as well as its interaction with the solvent molecules, need to be explicitly taken into account in the calculations, because of their possible impact on the reaction profile. As molecular modeling methods allow the treatment of such large systems, but lack the possibility of describing covalent interactions, our method of choice was the combined quantum mechanics/molecular modeling approach. By splitting the system into a smaller part that undergoes the bond cleavage/formation process and must be treated quantum mechanically, and a larger part, comprised of the rest of the protein, which could be treated using force fields, we managed to simulate the system at the desired precision. Our investigations concentrated on the role of His199 in the inhibition mechanism as well as on the structure-reactivity relationships between cysteine protease and various inhibitors, yielding new insight into the kinetics, regio- and stereospecificity of the inhibition. In particular, our calculations provide the following insights: i.) an explanation for the regioselectivity of the reaction, and original insight into which interactions affect the stereoselectivity; ii.) a clear model which explains the known structure-activity relationships and connects these effects with the pH-dependency of the inhibition; iii.) our computations question the generally accepted two-step model by showing that substituent effects accelerate the irreversible step to such an extent that the achievement of an equilibrium in the first step is doubtful; iv.) by way of theoretical characterizations of aziridine models, the reasons for similarities and differences in the mode of action of epoxide- and aziridine-based inhibitors are elucidated; and finally, v.) combining our results with experimental knowledge will allow rational design of new inhibitors. To account for dynamical effects as well, molecular dynamics (MD) computations were also performed. In these calculations the potential energy was computed at the force field level. The results not only supported and clarified the QM/MM results, but comparison with previous X-ray structures helped correct existing errors in the available geometrical models and resolved inconsistencies in the weighting of various factors governing the inhibition. In the work the first QM/MM MD calculations on the active site of the cysteine proteases are presented. In contrast to the MD simulations, these calculations used potential energies computed at the QM/MM-level. With the help of these computations we sought to address strongly disputed questions about the reasons for the existence of the active site ion pair and its role in the high activity of the enzyme.