The COMICS Tool - Computing Minimal Counterexamples for Discrete-time Markov Chains

This report presents the tool COMICS, which performs model checking and generates counterexamples for DTMCs. For an input DTMC, COMICS computes an abstract system that carries the model checking information and uses this result to compute a critical subsystem, which induces a counterexample. This abstract subsystem can be refined and concretized hierarchically. The tool comes with a command-line version as well as a graphical user interface that allows the user to interactively influence the refinement process of the counterexample

Interplay of Hydration and Protonation Dynamics in the K-Channel of Cytochrome c Oxidase

Cytochrome c oxidase is a membrane protein of the respiratory chain that consumes protons and molecular oxygen to produce water and uses the resulting energy to pump protons across the membrane. Our molecular dynamics simulations with an excess proton located at different positions in one of the proton-conducting channels, the K-channel, show a clear dependence of the number of water molecules inside the channel on the proton position. A higher hydration level facilitates the formation of hydrogen-bonded chains along which proton transfer can occur. However, a sufficiently high hydration level for such proton transport is observed only when the excess proton is located above S365, i.e., the lower third of the channel. From the channel entrance up to this point, proton transport is via water molecules as proton carriers. These hydronium ions move with their surrounding water molecules, up to K362, filling and widening the channel. The conformation of K362 depends on its own protonation state and on the hydration level, suggesting its role to be proton transport from a hydronium ion at the height of K362 to the upper part of the channel via a conformational change. The protonation-dependent conformational dynamics of E101 at the bottom of the channel renders proton transfer via E101 unlikely. Instead, its role is rather that of an amplifier of H96’s proton affinity, suggesting H96 as the initial proton acceptor

Protonation Dynamics in the K-Channel of Cytochrome c Oxidase Estimated from Molecular Dynamics Simulations

Proton transfer reactions are one of the most fundamental processes in biochemistry. We present a simplistic approach for estimating proton transfer probabilities in a membrane protein, cytochrome c oxidase. We combine short molecular dynamics simulations at discrete protonation states with a Monte Carlo approach to exchange between those states. Requesting for a proton transfer the existence of a hydrogen-bonded connection between the two source and target residues of the exchange, restricts the acceptance of transfers to only those in which a proton-relay is possible. Together with an analysis of the hydrogen-bonded connectivity in one of the proton-conducting channels of cytochrome c oxidase, this approach gives insight into the protonation dynamics of the hydrogen-bonded networks. The connectivity and directionality of the networks are coupled to the conformation of an important protein residue in the channel, K362, rendering proton transfer in the entire channel feasible in only one of the two major conformations. Proton transport in the channel can thus be regulated by K362 not only through its possible role as a proton carrier itself, but also by allowing or preventing proton transport via water residues

Effect of the Hydration Shell on the Carbonyl Vibration in the Ala-Leu-Ala-Leu Peptide

The vibrational spectrum of the Ala-Leu-Ala-Leu peptide in solution, computed from first-principles simulations, shows a prominent band in the amide I region that is assigned to stretching of carbonyl groups. Close inspection reveals combined but slightly different contributions by the three carbonyl groups of the peptide. The shift in their exact vibrational signature is in agreement with the different probabilities of these groups to form hydrogen bonds with the solvent. The central carbonyl group has a hydrogen bond probability intermediate to the other two groups due to interchanges between different hydrogen-bonded states. Analysis of the interaction energies of individual water molecules with that group shows that shifts in its frequency are directly related to the interactions with the water molecules in the first hydration shell. The interaction strength is well correlated with the hydrogen bond distance and hydrogen bond angle, though there is no perfect match, allowing geometrical criteria for hydrogen bonds to be used as long as the sampling is sufficient to consider averages. The hydrogen bond state of a carbonyl group can therefore serve as an indicator of the solvent’s effect on the vibrational frequency

Protonation-State Dependence of Hydration and Interactions in the Two Proton-Conducting Channels of Cytochrome c Oxidase

Cytochrome c Oxidase (CcO), a membrane protein of the respiratory chain, pumps protons against an electrochemical gradient by using the energy of oxygen reduction to water. The (“chemical”) protons required for this reaction and those pumped are taken up via two distinct channels, named D-channel and K-channel, in a step-wise and highly regulated fashion. In the reductive phase of the catalytic cycle, both channels transport protons so that the pumped proton passes the D-channel before the “chemical” proton has crossed the K-channel. By performing molecular dynamics simulations of CcO in the O→E redox state (after the arrival of the first reducing electron) with various combinations of protonation states of the D- and K-channels, we analysed the effect of protonation on the two channels. In agreement with previous work, the amount of water observed in the D-channel was significantly higher when the terminal residue E286 was not (yet) protonated than when the proton arrived at this end of the D-channel and E286 was neutral. Since a sufficient number of water molecules in the channel is necessary for proton transport, this can be understood as E286 facilitating its own protonation. K-channel hydration shows an even higher dependence on the location of the excess proton in the K-channel. Also in agreement with previous work, the K-channel exhibits a very low hydration level that likely hinders proton transfer when the excess proton is located in the lower part of the K-channel, that is, on the N-side of S365. Once the proton has passed S365 (towards the reaction site, the bi-nuclear centre (BNC)), the amount of water in the K-channel provides hydrogen-bond connectivity that renders proton transfer up to Y288 at the BNC feasible. No significant direct effect of the protonation state of one channel on the hydration level, hydrogen-bond connectivity, or interactions between protein residues in the other channel could be observed, rendering proton conductivity in the two channels independent of each other. Regulation of the order of proton uptake and proton passage in the two channels such that the “chemical” proton leaves its channel last must, therefore, be achieved by other means of communication, such as the location of the reducing electron

JGraph - A Java Based System for Drawing Graphs and Running Graph Algorithms

JGraph is a Java based system for drawing graphs and for running graph algorithms. A number of well-known algorithms are provided, including those for planarity testing and drawing planar graphs on a grid. The algorithms can be run with an animation feature where the user can see the intermediate steps as the algorithm executes. The system is extensible in that new algorithms can be easily added. The JGraph project was conceived and led by Jay Bagga. Several of his graduate students have made contributions. Aaron Nall designed the original version and the graphical user interface. The most recent version has been managed by Adrian Heinz who has added many new features and has also implemented algorithms for planarity testing and drawing of planar graphs on a grid. This system was initially created for students in computer science, mathematics, and other related disciplines who are learning graph theory and using graph algorithms. It can be used by anyone with an interest in graph drawing and graph algorithms. To draw a planar graph on a grid, we use the Shift Method of de Fraysseix et. al. [1,2