Kay Hamacher

Stochastic Tunneling Approach for Global Minimization of Complex Potential Energy Landscapes

We investigate a novel stochastic technique for the global optimization of complex potential energy surfaces (PES) that avoids the freezing problem of simulated annealing by allowing the dynamical process to tunnel energetically inaccessible regions of the PES by way of a dynamically adjusted nonlinear transformation of the original PES. We demonstrate the success of this approach, which is characterized by a single adjustable parameter, for three generic hard minimization problems.

Structure and Anonymity of the Bitcoin Transaction Graph

The Bitcoin network of decentralized payment transactions has attracted a lot of attention from both Internet users and researchers in recent years. Bitcoin utilizes a peer-to-peer network to issue anonymous payment transactions between different users. In the currently used Bitcoin clients, the full transaction history is available at each node of the network to prevent double spending without the need for a central authority, forming a valuable source for empirical research on network structure, network dynamics, and the implied anonymity challenges, as well as guidance on the future evolution of complex payment systems. We found dynamical effects of which some increase anonymity while others decrease it. Most importantly, several parameters of the Bitcoin transaction graph seem to have become stationary over the last 12–18 months. We discuss the implications.

Dependency map of proteins in the small ribosomal subunit

The assembly of the ribosome has recently become an interesting target for antibiotics in several bacteria. In this work, we extended an analytical procedure to determine native state fluctuations and contact breaking to investigate the protein stability dependence in the 30S small ribosomal subunit of Thermus thermophilus. We determined the causal influence of the presence and absence of proteins in the 30S complex on the binding free energies of other proteins. The predicted dependencies are in overall agreement with the experimentally determined assembly map for another organism, Escherichia coli. We found that the causal influences result from two distinct mechanisms: one is pure internal energy change, the other originates from the entropy change. We discuss the implications on how to target the ribosomal assembly most effectively by suggesting six proteins as targets for mutations or other hindering of their binding. Our results show that by blocking one out of this set of proteins, the association of other proteins is eventually reduced, thus reducing the translation efficiency even more. We could additionally determine the binding dependency of THX—a peptide not present in the ribosome of E. coli—and suggest its assembly path.

DOCKTITE—A Highly Versatile Step-by-Step Workflow for Covalent Docking and Virtual Screening in the Molecular Operating Environment

The formation of a covalent bond with the target is essential for a number of successful drugs, yet tools for covalent docking without significant restrictions regarding warhead or receptor classes are rare and limited in use. In this work we present DOCKTITE, a highly versatile workflow for covalent docking in the Molecular Operating Environment (MOE) combining automated warhead screening, nucleophilic side chain attachment, pharmacophore-based docking, and a novel consensus scoring approach. The comprehensive validation study includes pose predictions of 35 protein/ligand complexes which resulted in a mean RMSD of 1.74 Å and a prediction rate of 71.4% with an RMSD below 2 Å, a virtual screening with an area under the curve (AUC) for the receiver operating characteristics (ROC) of 0.81, and a significant correlation between predicted and experimental binding affinities (ρ = 0.806, R(2) = 0.649, p < 0.005).

Scaling behavior of stochastic minimization algorithms in a perfect funnel landscape

We determined scaling laws for the numerical effort to find the optimal configurations of a simple model potential energy surface (PES) with a perfect funnel structure that reflects key characteristics of the protein interactions. Generalized Monte-Carlo methods(MCM, STUN) avoid an enumerative search of the PES and thus provide a natural resolution of the Levinthal paradox. We find that the computational effort grows with approximately the eighth power of the system size for MCM and STUN, while a genetic algorithm was found to scale exponentially. The scaling behaviour of a derived lattice model is also rationalized.

Information theoretical measures to analyze trajectories in rational molecular design

We develop a new methodology to analyze molecular dynamics trajectories and other time series data from simulation runs. This methodology is based on an information measure of the difference between distributions of various data extract from such simulations. The method is fast as it only involves the numerical integration/summation of the distributions in one dimension while avoiding sampling issues at the same time. The method is most suitable for applications in which different scenarios are to be compared, e.g. to guide rational molecular design. We show the power of the proposed method in an application of rational drug design by reduced model computations on the BH3 motif in the apoptosis inducing BCL2 protein family.

Phycodnavirus Potassium Ion Channel Proteins Question the Virus Molecular Piracy Hypothesis

Phycodnaviruses are large dsDNA, algal-infecting viruses that encode many genes with homologs in prokaryotes and eukaryotes. Among the viral gene products are the smallest proteins known to form functional K+ channels. To determine if these viral K+ channels are the product of molecular piracy from their hosts, we compared the sequences of the K+ channel pore modules from seven phycodnaviruses to the K+ channels from Chlorella variabilis and Ectocarpus siliculosus, whose genomes have recently been sequenced. C. variabilis is the host for two of the viruses PBCV-1 and NY-2A and E. siliculosus is the host for the virus EsV-1. Systematic phylogenetic analyses consistently indicate that the viral K+ channels are not related to any lineage of the host channel homologs and that they are more closely related to each other than to their host homologs. A consensus sequence of the viral channels resembles a protein of unknown function from a proteobacterium. However, the bacterial protein lacks the consensus motif of all K+ channels and it does not form a functional channel in yeast, suggesting that the viral channels did not come from a proteobacterium. Collectively, our results indicate that the viruses did not acquire their K+ channel-encoding genes from their current algal hosts by gene transfer; thus alternative explanations are required. One possibility is that the viral genes arose from ancient organisms, which served as their hosts before the viruses developed their current host specificity. Alternatively the viral proteins could be the origin of K+ channels in algae and perhaps even all cellular organisms.

Structural model of the gas vesicle protein GvpA and analysis of GvpA mutants in vivo

Gas vesicles are gas‐filled protein structures increasing the buoyancy of cells. The gas vesicle envelope is mainly constituted by the 8 kDa protein GvpA forming a wall with a water excluding inner surface. A structure of GvpA is not available; recent solid‐state NMR results suggest a coil‐α‐β‐β‐α‐coil fold. We obtained a first structural model of GvpA by high‐performance de novo modelling. Attenuated total reflection (ATR)‐Fourier transform infrared spectroscopy (FTIR) supported this structure. A dimer of GvpA was derived that could explain the formation of the protein monolayer in the gas vesicle wall. The hydrophobic inner surface is mainly constituted by anti‐parallel β‐strands. The proposed structure allows the pinpointing of contact sites that were mutated and tested for the ability to form gas vesicles in haloarchaea. Mutations in α‐helix I and α‐helix II, but also in the β‐turn affected the gas vesicle formation, whereas other alterations had no effect. All mutants supported the structural features deduced from the model. The proposed GvpA dimers allow the formation of a monolayer protein wall, also consistent with protease treatments of isolated gas vesicles.

Research article: Estimating sufficient statistics in co-evolutionary analysis by mutual information

Mutual information (MI) is a standard measure in information theory to observe and quantify correlated signals and events in both, empirical data sets and theoretical models. In the field of computational biology the MI turned out to be particularly useful in studies on co-evolutionary signals of sites within biomolecules. A key issue in the applicability of the MI is, however, a correct reference system or null model to understand finite-size effects in the underlying, finite data set. Although some bioinformatics studies exist with rigorous results for theoretical, well-designed random distributions, data from real-world proteins was never used to quantify the effect of finite-size samples. The impact of real-world statistics is, however, most relevant for researchers in all fields concerned with detecting evolutionary signals within biological sequences. We present results on such effects in finite-sized biological data sets and point to future research directions. We are most of all concerned with bacterial, ribosomal proteins as a prototypical example in molecular evolution. We compare to previous published suggestions, give an empirical formula, and propose a protocol to guide future research projects.

BioPhysConnectoR: Connecting Sequence Information and Biophysical Models

BackgroundOne of the most challenging aspects of biomolecular systems is the understanding of the coevolution in and among the molecule(s).A complete, theoretical picture of the selective advantage, and thus a functional annotation, of (co-)mutations is still lacking. Using sequence-based and information theoretical inspired methods we can identify coevolving residues in proteins without understanding the underlying biophysical properties giving rise to such coevolutionary dynamics. Detailed (atomistic) simulations are prohibitively expensive. At the same time reduced molecular models are an efficient way to determine the reduced dynamics around the native state. The combination of sequence based approaches with such reduced models is therefore a promising approach to annotate evolutionary sequence changes.ResultsWith the R package BioPhysConnectoR we provide a framework to connect the information theoretical domain of biomolecular sequences to biophysical properties of the encoded molecules - derived from reduced molecular models. To this end we have integrated several fragmented ideas into one single package ready to be used in connection with additional statistical routines in R. Additionally, the package leverages the power of modern multi-core architectures to reduce turn-around times in evolutionary and biomolecular design studies. Our package is a first step to achieve the above mentioned annotation of coevolution by reduced dynamics around the native state of proteins.ConclusionsBioPhysConnectoR is implemented as an R package and distributed under GPL 2 license. It allows for efficient and perfectly parallelized functional annotation of coevolution found at the sequence level.