Research topics

Inferential structure determination

In structural biology, many experiments like SAXS and NMR experiments measure observables averaged over ensembles of structures. Even if there is a single structure underlying the data, the information content of these observables is often too low to reconstruct a high-resolution structural model. The situation is even more complicated in cases where observables are averaged over an ensemble of dynamic and diverse molecular structures.

In these cases, ensemble refinement makes it possible to take advantage of the high distinguishing power of averaged experimental observables. We combine simulations of flexible and dynamic biological macromolecules like proteins, DNA, and RNA with the experimentally measured data. For example, we used the EROS (Boura et al. Structure 2011) method to refine simulation ensembles of structures of the Atg1-complex and its sub-complexes Atg1-Atg13 and Atg17-Atg31-Atg29 using SAXS data (Koefinger et al. Cell 2015).

In general and not restricted to ensemble refinement, simulations ideally summarize everything that is known about the system before the new data is available. This information comprises prior experimental information like crystal or NMR structures of sub-domains, cross-linking information, and biochemical data, for example. Moreover, simulations contain physical information like interaction potentials between atoms and knowledge from statistical mechanics, i.e., that states are distributed according to Boltzmann’s distribution.

When new data becomes available, we can use this data in two different ways. We can steer the simulations to explore the true phase space underlying the data more effciently or we use the data to refine an already existing simulation ensemble. Recently we have shown that the EROS method and refinement by replica simulations lead to the same ensemble in the limit of large numbers of replicas (Hummer and Koefinger, J. Chem. Phys. 2015). By combining the two approaches we can overcome the limitation of the individual approaches. In his bachelor thesis, Sebastian Roy implemented a Python wrapper to perform replica simulations and applied them to coarse-grained simulations of a disordered peptide.

However, ensemble refinement is not restrictured to ensembles generated in simulations. Recently we have shown how spin-label rotamer refinement can be used to obtain precision distances from DEER experiments (Reichel et al. J. Phys. Chem. Letters 2018)

Atomic-resolution structural information from SAXS/WAXS experiments

Solution scattering experiments provide signatures of the atomistic structures of biological macromolecules like proteins, DNA molecules, and RNA molecules under near-physiological conditions. Small-angle scattering (SAXS and SANS for x-rays and neutrons, respectively) experiments probe the size and shape of the macromoleculeswhereas wide-angle x-ray scattering (WAXS) provides higher resolution structural information. For example, wide-angle scattering experiments on proteins report onsecondary structure and fold.

The maximum amount of structural information probed by solution scattering experiments is contained in the pair-distance distribution function. In experiments, however, only their Fourier transform is measured over a restricted range of scattering angles. To quantify the maximum structural information content, we developed a novelmethod to calculate not only accurate and precise scattering intensities from fully atomistic molecular dynamics simulations, but also the underlying pair-distance distribution functions. In contrast to previous methods, the latter are calculated directly from the real-space information provided by molecular dynamics simulations without invoking inverse Fourier transform methods.

On the right, we show a comparison of a typical experimental pair-distance distribution function (blue) for hen egg-white lysozyme and our theoretical result (red). The experimental pair-distance distribution function has been obtained by inverse Fourier transformation of the intensity measured over a restricted range of scattering angles(left panel). The experimental pair-distance distribution function is rather smooth and lacks the rich sub-nanometer structural features of our theoretical result, which accesses the maximum amount of structural information. In our work, we also provide guidance for the design of scattering experiments to probe this high resolution structural information. This information can then be extracted from the measured scattering intensities using molecular dynamics simulations in combination with our method.

Single-file water in nanopores

Water molecules in narrow nanopores arrange in single-file where they form hydrogen bonded chains. In biological cells, such pores are formed by membrane spanning proteins like aquaporin and gramicidin A, which regulate the efficient transport of water, protons, and other ions. The special transport properties of these quasi one-dimensional water chains might be exploited in desalination devices, molecular filters, and fuel cells. Possible building blocks for such devices are carbon and boron-nitride nanotubes.

On the right, you can see a snapshot of a molecular dynamics simulation of water in a narrow carbon nanotube. The water molecules form tight hydrogen bonds and the chain is orientationally ordered as each water molecule donates a hydrogen bond to its neighbor on the right and accepts one from its neighbor on the left. This orientational order is a precondition for fast proton transport. For long tubes, however, defects are bound to occur that will destroy the order and hinder proton transport. The question arises how long these chains can be such that they are still predominately ordered.

This question was answered in my PhD thesis, supervised by Dr. Christoph Dellago (University of Vienna, Austria) and in cooperation with Dr. Gerhard Hummer (National Institutes of Health, U.S.A.). I developed a model for single-file water, which facilitates computer simulations of tubes with lengths ranging from nanometers to millimeters. Also, this model serves as a theoretical framework for analytical calculations.

We showed that single-file water remains ordered up to tube lengths of ~0.1 mm, which is in the range of the diameters of human hair. We modified our model to study the response of nanopore water to electric fields that vary with time. We found that single-file water reacts sensitively to small electric fields along the tube axis, which can be exploited to determine the fundamental microscopic properties of water experimentally. Also, our results indicate that single-file water might serve in capacitors for future sensing devices.

Phase behavior of fluid mixtures

Nearly all liquids of every day life are mixtures, often of a large number of components like paint, blood, drugs, drinks, gas, and oil. The knowledge of the phase behavior is important for production processes, technical applications, the design of liquids with certain properties, and for the development of new drugs to give a few examples.

In my master thesis, under the supervision of Dr. Gerhard Kahl (Vienna TU, Austria) and in cooperation with Dr. Nigel B. Wilding (University of Bath, UK), I applied integral equation theory and advanced Monte Carlo simulation methods to study the fluid phase behavior of binary fluid mixtures.

Using integral equation theory, I was able to obtain the full phase diagram in the three-dimensional thermodynamic space of density, concentration, and temperature (right) for two different types of phase behavior. The system shows rich phase behavior with critical lines, critical end points, triple lines, and a tricritical point. Our extensive simulations of these systems confirmed the validity of the applied integral theory and showed that advanced Monte Carlo methods are capable of resolving the complex phase behavior of such mixtures.