Gerhard Stock

Monomer adds to preformed structured oligomers of Aβ-peptides by a two-stage dock–lock mechanism

Nonfibrillar soluble oligomers, which are intermediates in the transition from monomers to amyloid fibrils, may be the toxic species in Alzheimers disease. To monitor the early events that direct assembly of amyloidogenic peptides we probe the dynamics of formation of (Aβ16–22)n by adding a monomer to a preformed (Aβ16–22)n−1 (n = 4–6) oligomer in which the peptides are arranged in an antiparallel β-sheet conformation. All atom molecular dynamics simulations in water and multiple long trajectories, for a cumulative time of 6.9 μs, show that the oligomer grows by a two-stage dock–lock mechanism. The largest conformational change in the added disordered monomer occurs during the rapid (≈50 ns) first dock stage in which the β-strand content of the monomer increases substantially from a low initial value. In the second slow-lock phase, the monomer rearranges to form in register antiparallel structures. Surprisingly, the mobile structured oligomers undergo large conformational changes in order to accommodate the added monomer. The time needed to incorporate the monomer into the fluid-like oligomer grows even when n = 6, which suggests that the critical nucleus size must exceed six. Stable antiparallel structure formation exceeds hundreds of nanoseconds even though frequent interpeptide collisions occur at elevated monomer concentrations used in the simulations. The dock–lock mechanism should be a generic mechanism for growth of oligomers of amyloidogenic peptides.

Energy landscape of a small peptide revealed by dihedral angle principal component analysis

A 100 ns molecular dynamics simulation of penta‐alanine in explicit water is performed to study the reversible folding and unfolding of the peptide. Employing a standard principal component analysis (PCA) using Cartesian coordinates, the resulting free‐energy landscape is found to have a single minimum, thus suggesting a simple, relatively smooth free‐energy landscape. Introducing a novel PCA based on a transformation of the peptide dihedral angles, it is found, however, that there are numerous free energy minima of comparable energy (≲ 1 kcal/mol), which correspond to well‐defined structures with characteristic hydrogen‐bonding patterns. That is, the true free‐energy landscape is actually quite rugged and its smooth appearance in the Cartesian PCA represents an artifact of the mixing of internal and overall motion. Well‐separated minima corresponding to specific conformational structures are also found in the unfolded part of the free energy landscape, revealing that the unfolded state of penta‐alanine is structured rather than random. Performing a connectivity analysis, it is shown that neighboring states are connected by low barriers of similar height and that each state typically makes transitions to three or four neighbor states. Several principal pathways for helix nucleation are identified and discussed in some detail. Proteins 2005.

Hydrogen-bond lifetime measured by time-resolved 2D-IR spectroscopy: N-methylacetamide in methanol

Abstract 2D vibrational spectroscopy is applied to investigate the equilibrium dynamics of hydrogen bonding of N-methylacetamide (NMA) dissolved in methanol-d4. For this particular solute–solvent system, roughly equal populations are found for two conformers of the solute–solvent complex, one of which forms a hydrogen bond from the CO group of NMA to the surrounding solvent, and one of which does not. Using time-resolved 2D-IR spectroscopy on the amide I band of NMA, the exchange between both conformers is resolved. Equilibration of each conformer is completed after 4.5 ps, while the formation and breaking of the hydrogen bond occurs on a slower, 10–15 ps time scale. This interpretation is supported by classical molecular-dynamics simulations of NMA in methanol. The calculations predict a 64% population of the hydrogen-bonded conformer and an average hydrogen-bond lifetime of ≈12 ps.

Surface-hopping modeling of photoinduced relaxation dynamics on coupled potential-energy surfaces

A mixed quantum-classical description of nonadiabatic photoreactions such as internal conversion and electron transfer is outlined. In particular the validity and limitations of Tully’s surface-hopping (SH) model [J. Chem. Phys. 93, 1061 (1990)] is investigated in the case of photoinduced relaxation processes which are triggered by a multidimensional conical intersection (or avoided crossing) of two potential-energy surfaces. Detailed numerical studies are presented, adopting (i) a three-mode model of the S2→S1 internal-conversion process in pyrazine, (ii) a multimode model of ultrafast intramolecular electron-transfer, (iii) a model exhibiting nonadiabatic photoisomerization dynamics, and (iv) various spin-boson-type models with an Ohmic bath for the description of electron-transfer in solution. The SH simulations are compared to exact quantum-mechanical calculations as well as to results obtained by an alternative mixed quantum-classical description, that is, the self-consistent classical-path method. I...

Peptide conformational heterogeneity revealed from nonlinear vibrational spectroscopy and molecular-dynamics simulations

Nonlinear time-resolved vibrational spectroscopy is used to compare spectral broadening of the amide I band of the small peptide trialanine with that of N-methylacetamide, a commonly used model system for the peptide bond. In contrast to N-methylacetamide, the amide I band of trialanine is significantly inhomogeneously broadened. Employing classical molecular-dynamics simulations combined with density-functional-theory calculations, the origin of the spectral inhomogeneity is investigated. While both systems exhibit similar hydrogen-bonding dynamics, it is found that the conformational dynamics of trialanine causes a significant additional spectral broadening. In particular, transitions between the poly(Gly)II and the αR conformations are identified as the main source of the additional spectral inhomogeneity of trialanine. The experimental and computational results suggest that trialanine adopts essentially two conformations: poly(Gly)II (80%) and αR (20%). The potential of the joint experimental and computational approach to explore conformational dynamics of peptides is discussed.

Dihedral angle principal component analysis of molecular dynamics simulations

It has recently been suggested by Mu et al. [Proteins 58, 45 (2005)] to use backbone dihedral angles instead of Cartesian coordinates in a principal component analysis of molecular dynamics simulations. Dihedral angles may be advantageous because internal coordinates naturally provide a correct separation of internal and overall motion, which was found to be essential for the construction and interpretation of the free energy landscape of a biomolecule undergoing large structural rearrangements. To account for the circular statistics of angular variables, a transformation from the space of dihedral angles {phi(n)} to the metric coordinate space {x(n)=cos phi(n),y(n)=sin phi(n)} was employed. To study the validity and the applicability of the approach, in this work the theoretical foundations underlying the dihedral angle principal component analysis (dPCA) are discussed. It is shown that the dPCA amounts to a one-to-one representation of the original angle distribution and that its principal components can readily be characterized by the corresponding conformational changes of the peptide. Furthermore, a complex version of the dPCA is introduced, in which N angular variables naturally lead to N eigenvalues and eigenvectors. Applying the methodology to the construction of the free energy landscape of decaalanine from a 300 ns molecular dynamics simulation, a critical comparison of the various methods is given.

Nonperturbative approach to femtosecond spectroscopy: General theory and application to multidimensional nonadiabatic photoisomerization processes

A general nonperturbative approach to calculate femtosecond pump‐probe (PP) signals is proposed, which treats both the intramolecular couplings and the field‐matter interaction (numerically) exactly. Experimentally as well as in a perturbative calculation it is straightforward to distinguish between different spectroscopic processes through the direction of the wave vector of the emitted radiation. A nonperturbative calculation, on the other hand, yields the overall polarization of the system, which is the sum of all these contributions. We present a general and practical method that allows to extract the individual spectroscopic signals, which are resolved in time, frequency, and direction of the emission, from the overall polarization. We briefly derive the basic expressions for the time‐ and frequency‐resolved PP signals under consideration, and discuss in detail the simplifications that arise when the usual assumptions (i.e., weak laser fields, nonoverlapping pulses, slowly‐varying envelope assumption...

Semiclassical description of nonadiabatic quantum dynamics: Application to the S1–S2 conical intersection in pyrazine

A recently proposed semiclassical approach to the description of nonadiabatic quantum dynamics [G. Stock and M. Thoss, Phys. Rev. Lett. 78, 578 (1997), X. Sun and W. H. Miller, J. Chem. Phys. 106, 916 (1997)] is applied to the S1–S2 conical intersection in pyrazine. This semiclassical method is based on a transformation of discrete quantum variables to continuous variables, thereby bypassing the problem of a classical treatment of discrete quantum degrees of freedom such as electronic states. Extending previous work on small systems, we investigate the applicability of the semiclassical method to larger systems with strong vibronic coupling. To this end, we present results for several pyrazine models of increasing dimensionality and complexity. In particular, we discuss the quality and performance of the semiclassical approach when the number of nuclear degrees of freedom is increased. Comparison with quantum-mechanical calculations and experimental results shows that the semiclassical method is able to d...

Subpicosecond conformational dynamics of small peptides probed by two-dimensional vibrational spectroscopy

The observation of subpicosecond fluctuations in the conformation of a small peptide in water is demonstrated. We use an experimental method that is specifically sensitive to conformational dynamics taking place on an ultrafast time scale. Complementary molecular-dynamics simulations confirm that the conformational fluctuations exhibit a subpicosecond component, the time scale and amplitude of which agree well with those derived from the experiment.

Energy transport in peptide helices

We investigate energy transport through an α-aminoisobutyric acid-based 310-helix dissolved in chloroform in a combined experimental-theoretical approach. Vibrational energy is locally deposited at the N terminus of the helix by ultrafast internal conversion of a covalently attached, electronically excited, azobenzene moiety. Heat flow through the helix is detected with subpicosecond time resolution by employing vibrational probes as local thermo meters at various distances from the heat source. The experiment is supplemented by detailed nonequilibrium molecular dynamics (MD) simulations of the process, revealing good qualitative agreement with experiment: Both theory and experiment exhibit an almost instantaneous temperature jump of the reporter units next to the heater which is attributed to the direct impact of the isomerizing azobenzene moiety. After this impact event, helix and azobenzene moiety appear to be thermally decoupled. The energy deposited in the helix thermalizes on a subpicosecond timescale and propagates along the helix in a diffusive-like process, accompanied by a significant loss into the solvent. However, in terms of quantitative numbers, theory and experiment differ. In particular, the MD simulation seems to overestimate the heat diffusion constant (2 Å2 ps−1 from the experiment) by a factor of five.