Jürgen Schlitter

Estimation of absolute and relative entropies of macromolecules using the covariance matrix

Abstract A new method is reported for estimating absolute and relative entropies of conformers of a macromolecule. It is based on the evaluation of the covariance matrix of Cartesian positional coordinates obtainable by computer simulation and requires only calculation of a determinant. The approximation for the absolute entropy is derived using a quantum-mechanical approach and represents an upper limit for the quantum-mechanical entropy. Together with the easily accessible energy it offers a new way to calculate absolute and relative free energies of conformers. The numerical apllication of the method, which is of particular interest in the field of protein research, is demonstrated with the example of a short ∝-helical polypeptide.

Targeted molecular dynamics simulation of conformational change: application to the T↔R transition in insulin

Abstract A novel method to calculate transition pathways between two known protein conformations is presented. It is based on a molecular dynamics simulation starting from one conformational state as initial structure and using the other for a directing constraint. The method is exemplified with the T ↔ R transition of insulin. The most striking difference between these conformational states is that in T the 8 N-terminal residues of the B chain are arranged as an extended strand whereas in R they are forming a helix. Both the transition from T to R and from R to T were simulated. The method proves capable of finding a continuous pathway for each direction which are moderately different. The refolding processes are illustrated by a series of transient structures and pairs of O, ψ angles selected from the time course of the simulations. In the T → R direction the helix is formed in the →last third of the transition, while in the R → T direction it is preserved during more than half of the simulation period....

Targeted molecular dynamics: A new approach for searching pathways of conformational transitions

Molecular dynamics simulations have proven to be a valuable tool to investigate the dynamic behavior of stable macromolecules at finite temperatures. However, considerable conformational transitions take place during a simulation only accidentally or at exceptionally high temperatures far from the range of experimental conditions. Targeted molecular dynamics (TMD) is a method to induce a conformational change to a known target structure at ordinary temperature by applying a time-dependent, purely geometrical constraint. The transition is enforced independently of the height of energy barriers, while the dynamics of the molecule is only minimally influenced by the constraint. Simulations of decaalanine and insulin show the ability of the method to explore the configurational space for pathways accessible at a given temperature. The transitions studied at insulin comprise unfolding of an alpha-helical portion and, in the reverse direction, refolding from an extended conformation. A possible application of TMD is the search for energy barriers and stable intermediates from rather local changes up to protein denaturation.

Dynamics of Water Molecules in the Bacteriorhodopsin Trimer in Explicit Lipid/Water Environment

Protonated networks of internal water molecules appear to be involved in proton transfer in various integral membrane proteins. High-resolution x-ray studies of protein crystals at low temperature deliver mean positions of most internal waters, but only limited information about fluctuations within such H-bonded networks formed by water and residues. The question arises as to how water molecules behave inside and on the surface of a fluctuating membrane protein under more physiological conditions. Therefore, as an example, long-time molecular dynamics simulations of bacteriorhodopsin were performed with explicit membrane/water environment. Based on a recent x-ray model the bacteriorhodopsin trimer was inserted in a fully solvated 16 x 16 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC)-bilayer patch, resulting in a system of approximately 84,000 atoms. Unrestrained molecular dynamics calculations of 5 ns were performed using the GROMACS package and force field. Mean water densities were computed to describe the anisotropic distribution of internal water molecules. In the whole protein two larger areas of higher water density are identified. They are located between the central proton binding site, the Schiff base, and the extracellular proton release site. Separated by Arg-82 these water clusters could provide a proton release pathway in a Grotthus-like mechanism as indicated by a continuum absorbance change observed during the photocycle by time-resolved Fourier transform infrared spectroscopy. Residues are identified which are H-bonded to the water clusters and are therefore facilitating proton conduction. Their influence on proton transfer via the H-bonded network as indicated by the continuum absorbance change is predicted. This may explain why several site-directed mutations alter the proton release kinetics without a direct involvement in proton transfer.

Calculation of pathways for the conformational transition between the GTP- and GDP-bound states of the Ha-ras-p21 protein: Calculations with explicit solvent simulations and comparison with calculations in vacuum

The transitions between the water‐equilibrated structures of the GTP and GDP forms of Ha‐ras‐p21 have been calculated by using the targeted molecular dynamics (TMD) method (Schlitter et al., Mol. Sim. 10:291–309, 1993) both in vacuo and with explicit solvent simulation. These constrained molecular dynamics calculations result in different pathways, depending on the nucleotide bound. Each pathway consists in a sequence of transitions affecting six segments of the protein, four of them forming a hydrophilic cleft around the nucleotide. The transitions are initiated by the removal or introduction of the γ‐phosphate of the nucleotide and proceed sequentially, crossing several low‐energy transition states. The movements are transmitted either by direct interactions between the segments or through the nucleotide. The GTP to GDP pathway is initiated by the removal of the nucleotide γ‐phosphate. This gives some space to Gly12, Gly13, and Val14. Their movement is transmitted to the target recognition domain and the switch II region, forcing these segments to adopt another position. In a second step the target recognition domain and the switch II region undergo conformational transitions to reach an intermediate conformation. Finally, there is a relaxation of the target recognition domain to its final state that forces the switch II region to reach its target conformation. The calculated pathways allow the identification of many residues that play an important role in the conformational changes, explain the altered transformation properties of some, and suggest mutations to alter the pathway. Proteins 28:434–451, 1997.

Ras and GTPase-activating protein (GAP) drive GTP into a precatalytic state as revealed by combining FTIR and biomolecular simulations

Members of the Ras superfamily regulate many cellular processes. They are down-regulated by a GTPase reaction in which GTP is cleaved into GDP and Pi by nucleophilic attack of a water molecule. Ras proteins accelerate GTP hydrolysis by a factor of 105 compared to GTP in water. GTPase-activating proteins (GAPs) accelerate hydrolysis by another factor of 105 compared to Ras alone. Oncogenic mutations in Ras and GAPs slow GTP hydrolysis and are a factor in many cancers. Here, we elucidate in detail how this remarkable catalysis is brought about. We refined the protein-bound GTP structure and protein-induced charge shifts within GTP beyond the current resolution of X-ray structural models by combining quantum mechanics and molecular mechanics simulations with time-resolved Fourier-transform infrared spectroscopy. The simulations were validated by comparing experimental and theoretical IR difference spectra. The reactant structure of GTP is destabilized by Ras via a conformational change from a staggered to an eclipsed position of the nonbridging oxygen atoms of the γ- relative to the β-phosphates and the further rotation of the nonbridging oxygen atoms of α- relative to the β- and γ-phosphates by GAP. Further, the γ-phosphate becomes more positive although two of its oxygen atoms remain negative. This facilitates the nucleophilic attack by the water oxygen at the phosphate and proton transfer to the oxygen. Detailed changes in geometry and charge distribution in the ligand below the resolution of X-ray structure analysis are important for catalysis. Such high resolution appears crucial for the understanding of enzyme catalysis.

A new concise expression for the free energy of a reaction coordinate

For processes that can be parametrized by a reaction coordinate, the calculation of the free energy against this coordinate is the first step towards equilibrium constants and transition rates. We present a new concise expression for the free energy that is computed from data sampled at a fixed (constrained) reaction coordinate. It is consistent with previous theories and satisfies a more general criterion for free energy profiles.

Role of the arginine finger in Ras·RasGAP revealed by QM/MM calculations

In the Ras·RasGAP complex, hydrolysis of guanosine triphosphate is strongly accelerated GAP as compared to Ras alone. This is largely attributed to the arginine finger R789GAP pointing to AlFx in the transition state analogue. We performed QM/MM simulations where triphosphate was treated using the quantum mechanical method of density functional theory, while the protein complex and water environment were described classically using MD. Compared to Ras, the crucial electron shift, bond stretching and distortion towards an eclipsed γ‐to‐β orientation are much more pronounced. The arginine finger is shown to act by displacing water out of the binding niche. The resulting enhanced electrostatic field catalyses the cleavage step.

Simulations of a G protein-coupled receptor homology model predict dynamic features and a ligand binding site

A computational approach to predict structures of rhodopsin‐like G protein‐coupled receptors (GPCRs) is presented and evaluated by comparison to the X‐ray structural models. By combining sequence alignment, the rhodopsin crystal structure, and point mutation data on the β2 adrenoreceptor (b2ar), we predict a (−)‐epinephrine‐bound computational model of the β2 adrenoreceptor. The model is evaluated by molecular dynamics simulations and by comparison with the recent X‐ray structures of b2ar. The overall correspondence between the predicted and the X‐ray structural model is high. Especially the prediction of the ligand binding site is accurate. This shows that the proposed dynamic homology modelling approach can be used to create reasonable models for the understanding of structure and dynamics of other rhodopsin‐like GPCRs.

The role of magnesium for geometry and charge in GTP hydrolysis, revealed by quantum mechanics/molecular mechanics simulations.

The coordination of the magnesium ion in proteins by triphosphates plays an important role in catalytic hydrolysis of GTP or ATP, either in signal transduction or energy conversion. For example, in Ras the magnesium ion contributes to the catalysis of GTP hydrolysis. The cleavage of GTP to GDP and P(i) in Ras switches off cellular signaling. We analyzed GTP hydrolysis in water, Ras, and Ras·Ras-GTPase-activating protein using quantum mechanics/molecular mechanics simulations. By comparison of the theoretical IR-difference spectra for magnesium ion coordinated triphosphate to experimental ones, the simulations are validated. We elucidated thereby how the magnesium ion contributes to catalysis. It provides a temporary storage for the electrons taken from the triphosphate and it returns them after bond cleavage and P(i) release back to the diphosphate. Furthermore, the Ras·Mg(2+) complex forces the triphosphate into a stretched conformation in which the β- and γ-phosphates are coordinated in a bidentate manner. In this conformation, the triphosphate elongates the bond, which has to be cleaved during hydrolysis. Furthermore, the γ-phosphate adopts a more planar structure, driving the conformation of the molecule closer to the hydrolysis transition state. GTPase-activating protein enhances these changes in GTP conformation and charge distribution via the intruding arginine finger.