Critical Transitions In a Model of a Genetic Regulatory System

We consider a model for substrate-depletion oscillations in genetic systems, based on a stochastic differential equation with a slowly evolving external signal. We show the existence of critical transitions in the system. We apply two methods to numerically test the synthetic time series generated by the system for early indicators of critical transitions: a detrended fluctuation analysis method, and a novel method based on topological data analysis (persistence diagrams).Comment: 19 pages, 8 figure

Molecular Dynamics Simulations of the Bacterial Outer Membrane Channels TolC and OprM & dxTuber, a Biomolecular Cavity Detection Tool based on Protein and Solvent Dynamics

The multidrug resistance of bacteria is a serious phenomenon in current medical treatment. Beginning with the introduction of antibiotics more and more bacterial strains achieved resistance against these chemical compounds and over the years a competition between antibiotic drug discovery and bacterial drug resistance arose. The well studied Gram-negative bacteria Escherichia coli and Pseudomonas aeruginosa serve in this work as a model organisms for bacterial resistance against antibiotics. Both bacteria evolved multidrug resistant strains through several strategies, including the expelling of harming compounds through efflux systems. The over expression of these efflux systems in the bacterial membranes are responsible for resistance against many antibiotic compounds. The AcrA/B-TolC efflux system induces resistance of E.coli against a broad range of antibiotics. Ranging from the inner membrane towards the outer membrane, the efflux system spans the entire periplasmic space. The system consists of the inner membrane transporter AcrB, the membrane fusion protein AcrA and the outer membrane channel TolC. TolC itself cooperates with several inner membrane transporters and facilitates the export of harming compounds across the outer membrane. Due to this versatility TolC could become a target of drug treatment. A disabled or blocked TolC could prevent drug extrusion via systems that use TolC as an exit gate. At the time of writing the gating functionality of TolC is not known in detail. To gain insights into TolC functionality two series of unbiased molecular dynamics (MD) simulations were performed. Whereas the first series was carried out in absence of AcrB the second one was executed in presence of the AcrB docking domain (AcrB-DD). For the first series unbiased MD simulations between 150-300 ns in a Palmitoyloleoylphosphatidylethanolamine (POPE) / NaCl / water environment were calculated. In most of these simulations TolC opens and closes freely on extracellular side hinting at the absence of a gating functionality on this side. On periplasmic side a double aspartate ring restricts substrate passage in all simulations and grasping-like motions were noticed for the tip loops of helix 7 & 8. A consecutive binding of two sodium ions inside the lower periplasmic part of TolC occured in one simulation, which induced a stabilized closed state on periplasmic side. TolC remained closed on periplasmic side unless all ions were removed from the simulation box indicating a sodium dependent lock on this side. For the second series of MD simulations we added the AcrB-DD to the previously described system setup based on orientations of a previously published data driven modeled structure. Four unbiased 150 ns MD simulations were calculated and in one of these simulations the docking domain spontaneously docks onto TolC. The latter simulation was extended to a simulation time of 1.05 μs resulting in a tighter binding between AcrB and TolC with regards to the modeled structure. A preferred open conformation on extracellular hints analogue to TolC only simulations at the absence of a lock on extracellular side. On the AcrB-facing side TolC's tip loops located at helix 7 & 8 opened up and were stabilized by the AcrB docking domain. However, the double aspartate ring remained closed until the end of the simulation, meaning that either the simulation time is too short to observe an opening of TolC or that another part of the AcrA/B-TolC efflux system is missing to open TolC. In Pseudomonas aeruginosa OprM had been identified as a TolC homologue protein. OprM is part of the multidrug efflux system MexA/B-OprM and acts as an exit duct for several inner membrane transporters. Also for OprM the gating mechanisms are not known in detail at time of writing. To explore OprM's gating mechanisms it has been simulated in a POPE / NaCl / water environment. During all five 200 ns long MD simulations OprM opens and closes freely on extracellular side suggesting also for OprM the absence of a gating mechanism on extracellular side. The tip loops of helix 7 & 8 on periplasmic side open up in a way comparable to TolC simulations and in contrast to TolC no closing motions were noticed for these helices for OprM. In OprM a single aspartate ring limits substrate passage on the inner membrane facing side of OprM. In contrast to TolC simulations a slight opening of this aspartate ring was measured in all five simulations. The absence of heightened sodium densities near the periplasmic entrance regions could mean that either longer simulation time is needed to observe a sodium induced closure of OprM or that the periplasmic access is regulated only by the aspartate ring. Despite the absence of heightened sodium densities in the aspartate ring region, clear peaks of high sodium densities identified sodium pockets between the equatorial region and the aspartate ring region formed by Asp171 and Asp230. Voids inside of proteins can indicate substrate binding sites, ion pockets, pathways through channel proteins, their open and closed states and active sites. Over the years numerous cavity detection tools have been introduced to identify and highlight these voids. All available cavity detection tools were based on static structures and present cavities for single protein conformations only. With dxTuber we developed and introduced a novel cavity detection tool based on an ensemble of protein conformations. It uses averaged protein and solvent density maps, which are derived from MD trajectories, as input. With this technique protein dynamics are taken into account and cavities are detected through the separation of protein external solvent from protein internal solvent. Protein internal solvent can be grouped into cavities and stored in the commonly used PDB file format. Individual cavities can be separated via the atom name field of the PDB file format. dxTuber itself can calculate cavity volume and the cross-sectional area of a single cavity along a principle axis. For convenience a graphical user interface (GUI) and a command line interface (CLI) of dxTuber are released under the GPL v2

A single mutation in a tunnel to the active site changes the mechanism and kinetics of product release in haloalkane dehalogenase LinB

Many enzymes have buried active sites. The properties of the tunnels connecting the active site with bulk solvent affect ligand binding and unbinding and, therefore, also the catalytic properties. Here, we investigate ligand passage in the haloalkane dehalogenase enzyme LinB, and the effect of replacing leucine by a bulky tryptophan at a tunnel-lining position. Transient kinetic experiments show that the mutation significantly slows down the rate of product release. Moreover, the mechanism of bromide ion release is changed from a one-step process in the wild type enzyme to a two-step process in the mutant. The rate constant of bromide ion release corresponds to the overall steady-state turnover rate constant, suggesting that product release became the rate-limiting step of catalysis in the mutant. We explain the experimental findings by investigating the molecular details of the process computationally. Analysis of trajectories from molecular dynamics simulations with the CAVER 3.0 program reveals differences in the tunnels available for ligand egress. Corresponding differences are seen in simulations of product egress using the Random Acceleration Molecular Dynamics technique. The differences in the free energy barriers for egress of a bromide ion calculated using the Adaptive Biasing Force method are in good agreement with the differences in rates obtained from the transient kinetic experiments. Interactions of the bromide ion with the introduced tryptophan are shown to affect the free energy barrier for its passage. The study demonstrates how the mechanism of an enzymatic catalytic cycle and reaction kinetics can be engineered by modification of protein tunnels

Investigating domain-selective angiotensin converting enzyme inhibition and oxidative inactivation

Angiotensin converting enzyme (ACE) is a zinc metalloprotease comprised of two highly homologous, catalytically active domains (90% active site identity and 60% sequence similarity). The C-domain is responsible for blood pressure regulation via angiotensin I cleavage while the N-domain inactivates an antifibrotic peptide Acetyl-Ser-Asp-Lys-Pro (AcSDKP). Since selective N-domain inhibition will result in AcSDKP accumulation, it shows promise for the treatment of fibrosis without affecting blood pressure. Low bioavailability, however, precludes the use of currently available N-selective ACE inhibitors in a clinical setting. Inhibition of ACE by a phosphinic, peptidomimetic compound, 33RE, was characterized using a continuous assay with quenched fluorogenic substrate. The N-domain displayed nanomolar (Ki = 11.21±0.74nM) and the C-domain micromolar (Ki = 11 278±410nM) inhibition, thus 1000-fold selectivity. Residues predicted to contribute to selectivity based on the N-domain-33RE co-crystal structure were subsequently mutated to their C-domain counterparts. S2 subsite mutation with resulting loss of a hydrogen bond drastically decreased 33RE affinity (Ki = 2794±156nM), yet did not entirely account for the selectivity. Additional substitution of all unique S2’ residues, however, completely abolished N-selectivity (Ki = 10 009±157nM). Interestingly, these residues do not directly bind 33RE. All mutants were therefore subjected to molecular dynamics (MD) simulations in the presence and absence of 33RE in addition to co-crystallization of 33RE with the N-domain mutant having all S2 and S2’ residues mutated. Trajectory analyses highlighted the S2’ residues’ importance in formation of a favourable interface between the ACE subdomains and thus a closed, ligand-bound complex. This was supported by X-ray crystallography and provides a molecular basis for the inter-subsite synergism governing 33RE’s 1000-fold N-domain selectivity. Enzyme kinetics were also used to study the concentration-dependent competitive inhibition and time-dependent irreversible oxidative inactivation of ACE catalysed by the Cu-Gly-GlyHis-lisinopril (CuGGHLis) metallodrug. Although both domains displayed nanomolar affinity for metallodrug binding (N-domain Ki = 44.94±1.84nM and C-domain Ki = 15.57±1.30nM), rapid and complete CuGGHLis-mediated inactivation occurred exclusively in the N-domain upon incubation with ascorbate and H2O2 redox co-reactants (k2 = 59 710 M-1 min-1 ). Michaelis-Menten characterization of the residual activity after partial N-domain inactivation revealed a decreased rate for hydrolysis of a non-domain selective substrate. This suggests that although CuGGHLis binds with similar affinity to both domains, the metal-chelate is optimally orientated in the N- but not the C-domain to catalyze oxidation of residues involved in substrate hydrolysis. The C-domain, in contrast, showed increased susceptibility to oxidative inactivation by diffuse radicals. This is of physiological significance as C-domain inactivation in normotensive individuals could result in accumulation of pro-inflammatory peptides. Since the N-domain is more heavily glycosylated, the potential role of unique glycans in diffuse radical shielding was studied using glycoprotein MD simulations. Unique C-domain solvent tunnels were identified that could increase diffuse radical access and, additionally, the mechanism whereby glycosylation contributes to ACE thermal stability was described for each site. This has implications for future ACE crystallography studies and the design of ACE-modulating agents with potential anti-inflammatory activity. This study demonstrated the utility of combining in vitro and in silico approaches to reveal how subtle amino acid or glycosylation site differences between the highly homologous domains control dynamic behaviour. It furthermore elucidated how two inhibitors with different mechanisms of action selectively target the N-domain active site by exploiting these differences and provided valuable insight for future anti-fibrotic ACE inhibitor design

Classical And Quantum Mechanical Simulations Of Condensed Systems And Biomolecules

This work describes the fundamental study of two enzymes of Fe(II)/-KG super family enzymes (TET2 and AlkB) by applying MD and QM/MM approaches, as well as the development of multipolar-polarizable force field (AMOEBA/GEM-DM) for condensed systems (ionic liquids and water). TET2 catalytic activity has been studied extensively to identify the potential source of its substrate preference in three iterative oxidation steps. Our MD results along with some experimental data show that the wild type TET2 active site is shaped to enable higher order oxidation. We showed that the scaffold stablished by Y1902 and T1372 is required for iterative oxidation. The mutation of these residues perturbs the alignment of the substrate in the active site, resulting in “5hmC-stalling” phenotype in some of the mutants. We provided more details on 5hmC to 5fC oxidation mechanism for wild type and one of the “5hmC-stallling” mutants (E mutant). We showed that 5hmC oxidizes to 5fC in the wild type via three steps. The first step is the hydrogen atom abstraction from hydroxyl group of 5hmC, while the second hydrogen is transferred from methylene group of 5hmC through the third transition state as a proton. Our results suggest that the oxidation in E mutant is kinetically unfavorable due to its high barrier energy. Many analyses have been performed to qualitatively describe our results and we believed our results can be used as a guide for other researchers. In addition, two MD approaches (explicit ligand sampling and WHAM) are used to study the oxygen molecule diffusion into the active site of AlkB. Our results showed that there are two possible channels for oxygen diffusion, however, diffusion through one of them is thermodynamically favorable. We also applied multipolar-polarizable force field to describe the oxygen diffusion along the preferred tunnel. We showed that the polarizable force field can describe the behavior of the highly polarizable systems accurately. We also developed a new multipolar-polarizable force field (AMOEBA/GEM-DM) to calculate the properties of imidazolium- and pyrrolidinium- based ionic liquids and water in a range of temperature. Our results agree well with the experimental data. The good agreement between our results and experimental data is because our new parameters provide an accurate description of non-bonded interactions. We fit all the non-bonded parameters against QM. We use the multipoles extracted from fitted electron densities (GEM) and we consider both inter- and intra-molecular polarization. We believe this method can accurately calculate the properties of condensed systems and can be helpful for designing new systems such as electrolytes

Engineering the protein dynamics of an ancestral luciferase.

Protein dynamics are often invoked in explanations of enzyme catalysis, but their design has proven elusive. Here we track the role of dynamics in evolution, starting from the evolvable and thermostable ancestral protein AncHLD-RLuc which catalyses both dehalogenase and luciferase reactions. Insertion-deletion (InDel) backbone mutagenesis of AncHLD-RLuc challenged the scaffold dynamics. Screening for both activities reveals InDel mutations localized in three distinct regions that lead to altered protein dynamics (based on crystallographic B-factors, hydrogen exchange, and molecular dynamics simulations). An anisotropic network model highlights the importance of the conformational flexibility of a loop-helix fragment of Renilla luciferases for ligand binding. Transplantation of this dynamic fragment leads to lower product inhibition and highly stable glow-type bioluminescence. The success of our approach suggests that a strategy comprising (i) constructing a stable and evolvable template, (ii) mapping functional regions by backbone mutagenesis, and (iii) transplantation of dynamic features, can lead to functionally innovative proteins