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Nonadiabatic molecular dynamics simulations of correlated electrons in solution. 1. Full configuration interaction (CI) excited-state relaxation dynamics of hydrated dielectrons.

The hydrated dielectron is composed of two excess electrons dissolved in liquid water that occupy a single cavity; in both its singlet and triplet spin states there is a significant exchange interaction so the two electrons cannot be considered to be independent. In this paper and the following paper,we present the results of mixed quantum/classical molecular dynamics simulations of the nonadiabatic relaxation dynamics of photoexcited hydrated dielectrons, where we use full configuration interaction (CI) to solve for the two-electron wave function at every simulation time step. To the best of our knowledge, this represents the first systematic treatment of excited-state solvation dynamics where the multiple-electron problem is solved exactly. The simulations show that the effects of exchange and correlation contribute significantly to the relaxation dynamics. For example, spin-singlet dielectrons relax to the ground state on a time scale similar to that of single electrons excited at the same energy, but spin-triplet dielectrons relax much faster. The difference in relaxation dynamics is caused by exchange and correlation: The Pauli exclusion principle imposes very different electronic structure when the electrons' spins are singlet paired than when they are triplet paired, altering the available nonadiabatic relaxation pathways. In addition, we monitor how electronic correlation changes dynamically during nonadiabatic relaxation and show that solvent dynamics cause electron correlation to evolve quite differently for singlet and triplet dielectrons. Despite such differences, our calculations show that both spin states are stable to excited-state dissociation, but that the excited-state stability has different origins for the two spin states. For singlet dielectrons, the stability depends on whether the solvent structure can rearrange to create a second cavity before the ground state is reached. For triplet dielectrons, in contrast, electronic correlation ensures that the two electrons do not dissociate, even if the dielectron is artificially kept from reaching the ground state. In addition, both singlet and triplet dielectrons change shape dramatically during relaxation, so that linear response fails to describe the solvation dynamics for either spin state. In the following paper (Larsen, R. E.; Schwartz, B. J. J. Phys. Chem. B 2006, 110, 9692), we use these simulations to calculate the pump-probe spectroscopic signal expected for photoexcited hydrated dielectrons and to predict an experiment to observe hydrated dielectrons directly.

Computer Simulation↗

Optimized Verlet-like algorithms for molecular dynamics simulations.

Explicit velocity- and position-Verlet-like algorithms of the second order are proposed to integrate the equations of motion in many-body systems. The algorithms are derived on the basis of an extended decomposition scheme at the presence of a free parameter. The nonzero value for this parameter is obtained by reducing the influence of truncated terms to a minimum. As a result, the proposed algorithms appear to be more efficient than the original Verlet versions that correspond to a particular case when the introduced parameter is equal to zero. Like the original versions, the extended counterparts are symplectic and time reversible, but lead to an improved accuracy in the generated solutions at the same overall computational costs. The advantages of the optimized algorithms are demonstrated in molecular dynamics simulations of a Lennard-Jones fluid.

Journal Article↗

Hydrophobic attraction as revealed by AFM force measurements and molecular dynamics simulation.

Spherical calcium dioleate particles ( approximately 10 mum in diameter) were used as AFM (atomic force microscope) probes to measure interaction forces of the collector colloid with calcite and fluorite surfaces. The attractive AFM force between the calcium dioleate sphere and the fluorite surface is strong and has a longer range than the DLVO (Derjaguin-Landau-Verwey-Overbeek) prediction. The AFM force between the calcium dioleate sphere and the mineral surfaces does not agree with the DLVO prediction. Consideration of non-DLVO forces, including the attractive hydrophobic force and the repulsive hydration force, was necessary to explain the experimental results. The non-DLVO interactions considered were justified by the different interfacial water structures at calcite- and fluorite-water interfaces as revealed by the numerical computation experiments with molecular dynamics simulation.

Journal Article↗

Conformational flexibility of the MHC class I alpha1-alpha2 domain in peptide bound and free states: a molecular dynamics simulation study.

Major histocompatibility complex class I proteins play a key role in the recognition and presentation of peptide antigens to the host immune system. The structure of various major histocompatibility complex class I proteins has been determined experimentally in complex with several antigenic peptides. However, the structure in the unbound (empty) form is not known. To study the conformational dynamics of the empty major histocompatibility complex class I molecule comparative molecular dynamics simulations have been performed starting from the crystal structure of a peptide bound class I peptide-binding domain in the presence and absence of a peptide ligand. Simulations including the bound peptide stayed close to the experimental start structure at both simulation temperatures (300 and 355 K) during the entire simulation of 26 ns. Several independent simulations in the absence of peptide indicate that the empty domain may not adopt a single defined conformation but is conformationally significantly more heterogeneous in particular within the alpha-helices that flank the peptide binding cleft. The calculated conformational dynamics along the protein chain correlate well with available spectroscopic data and with the observed site-specific sensitivity of the empty class I protein to proteolytic digestion. During the simulations at 300 K the binding region for the peptide N-terminus stayed close to the conformation in the bound state, whereas the anchor region for the C-terminus showed significantly larger conformational fluctuations. This included a segment at the beginning of the second alpha-helix in the domain that is likely to be involved in the interaction with the chaperone protein tapasin during the peptide-loading process. The simulation studies further indicate that peptide binding at the C- and N-terminus may follow different mechanisms that involve different degrees of induced conformational changes in the peptide-binding domain. In particular binding of the peptide C-terminus may require conformational stabilization by chaperone proteins during peptide loading.

Binding Sites↗

Molecular dynamics simulation studies of the wild-type, I21V, and I16T mutants of isoniazid-resistant Mycobacterium tuberculosis enoyl reductase (InhA) in complex with NADH: toward the understanding of NADH-InhA different affinities.

The increasing prevalence of tuberculosis in many areas of the world, associated with the rise in drug-resistant Mycobacterium tuberculosis (MTB) strains, presents a major threat to global health. InhA, the enoyl-ACP reductase from MTB, catalyzes the nicotinamide adenine dinucleotide (NADH)-dependent reduction of long-chain trans-2-enoyl-ACP fatty acids, an intermediate in mycolic acid biosynthesis. Mutations in the structural gene for InhA are associated with isoniazid resistance in vivo due to a reduced affinity for NADH, suggesting that the mechanism of drug resistance may be related to specific interactions between enzyme and cofactor within the NADH binding site. To compare the molecular events underlying ligand affinity in the wild-type, I21V, and I16T mutant enzymes and to identify the molecular aspects related to resistance, molecular dynamics simulations of fully solvated NADH-InhA (wild-type and mutants) were performed. Although very flexible, in the wild-type InhA-NADH complex, the NADH molecule keeps its extended conformation firmly bound to the enzyme's binding site. In the mutant complexes, the NADH pyrophosphate moiety undergoes considerable conformational changes, reducing its interactions with its binding site and probably indicating the initial phase of ligand expulsion from the cavity. This study should contribute to our understanding of specific molecular mechanisms of drug resistance, which is central to the design of more potent antimycobacterial agents for controlling tuberculosis.

Amino Acid Sequence↗

500 picosecond molecular dynamics simulation of amphiphilic polypeptide Ac(LKKL)4 NHEt with 1,2 di-mysristoyl-sn-glycero-3-phosphorylcholine (DMPC) molecules.

Molecular dynamics (MD) simulation of the interaction between amphiphilic polypeptide Ac(LKKL)4NHEt and 4 DMPC (1,2 di-mysristoyl-sn-glycero-3-phosphorylcholine) molecules has been carried out at 310 K for 500 picoseconds (ps) using AMBER 4.0. Interaction energy and a number of conformational parameters are calculated for the subaveraged coordinates, using P-CURVES 3.1 and our MD trajectory analysis program ANALMD. No significant change in DMPC headgroup conformation was observed. However, the mobility of P atoms was found to be restricted. The chains were quite flexible and their flexibility increased towards the ends. They interacted amongst themselves. The polypeptide remained predominantly in alpha-helical conformation. Leu1 and Lys2 at the N terminus and Leu13 to Leu16 at C terminus assumed non helical conformation and were quite flexible. Average interaction energy between the polypeptide and DMPC molecules was found to be -151.828 kcal*mol-1. The main contributory factor was electrostatic interaction of Lys NH3+ groups with the DMPC phosphates. On an average one Lys chain interacted with 1.5 DMPC molecules. Central region of the polypeptide had better contact with DMPC molecules. A model for the fusogenic properties of the polypeptide is presented on the basis of MD results.

Amino Acid Sequence↗

Qmd-plot: a graphical utility for rapid preliminary analysis of time series of fluctuating data, developed in the context of molecular dynamics simulations.

Qmd-plot is a utility to obtain rapid information about past or on-going simulations, or real-time data collections, in the form of graphs of recorded variables (x, y, ...), as x-y plots or as a function of simulated or real time. Time series records in the data file must be named. Variable names and their locations in the data file are initially unknown to the program, but are identified in a first scan, in which header records are located on the basis of a predefined key (that can be changed interactively). The names of the time series are then presented in an interactive menu, from which the user can repeatedly specify a graph to be viewed. Qmd-plot has been developed in the context of molecular dynamics simulations. We give examples of time series and x-y plots made from output of the sigma program. Qmd-plot code is a Java application; source and class files can be obtained free from the authors.

Journal Article↗

Dimerization of the p53 oligomerization domain: identification of a folding nucleus by molecular dynamics simulations.

Dimerization of the p53 oligomerization domain involves coupled folding and binding of monomers. To examine the dimerization, we have performed molecular dynamics (MD) simulations of dimer folding from the rate-limiting transition state ensemble (TSE). Among 799 putative transition state structures that were selected from a large ensemble of high-temperature unfolding trajectories, 129 were identified as members of the TSE via calculation of a 50% transmission coefficient from at least 20 room-temperature simulations. This study is the first to examine the refolding of a protein dimer using MD simulations in explicit water, revealing a folding nucleus for dimerization. Our atomistic simulations are consistent with experiment and offer insight that was previously unobtainable.

Computer Simulation↗

Mechanism of intracellular block of the KcsA K+ channel by tetrabutylammonium: insights from X-ray crystallography, electrophysiology and replica-exchange molecular dynamics simulations.

The mechanism of intracellular blockade of the KcsA potassium channel by tetrabutylammonium (TBA) is investigated through functional, structural and computational studies. Using planar-membrane electrophysiological recordings, we characterize the binding kinetics as well as the dependence on the transmembrane voltage and the concentration of the blocker. It is found that the apparent affinity of the complex is significantly greater than that of any of the eukaryotic K(+) channels studied previously, and that the off-rate increases with the applied transmembrane voltage. In addition, we report a crystal structure of the KcsA-TBA complex at 2.9 A resolution, with TBA bound inside the large hydrophobic cavity located at the center of the channel, consistent with the results of previous functional and structural studies. Of particular interest is the observation that the presence of TBA has a negligible effect on the channel structure and on the position of the potassium ions occupying the selectivity filter. Inspection of the electron density corresponding to TBA suggests that the ligand may adopt more than one conformation in the complex, though the moderate resolution of the data precludes a definitive interpretation on the basis of the crystallographic refinement methods alone. To provide a rationale for these observations, we carry out an extensive conformational sampling of an atomic model of TBA bound in the central cavity of KcsA, using the Hamiltonian replica-exchange molecular dynamics simulation method. Comparison of the simulated and experimental density maps indicates that the latter does reflect at least two distinct binding orientations of TBA. The simulations show also that the relative population of these binding modes is dependent on the ion configuration occupying the selectivity filter, thus providing a clue to the nature of the voltage-dependence of the binding kinetics.

Alanine↗

Rheological and structural studies of liquid decane, hexadecane, and tetracosane under planar elongational flow using nonequilibrium molecular-dynamics simulations.

We report for the first time rheological and structural properties of liquid decane, hexadecane, and tetracosane using nonequilibrium molecular-dynamics (NEMD) simulations under planar elongational flow (PEF). The underlying NEMD algorithm employed is the so-called p-SLLOD algorithm [C. Baig, B. J. Edwards, D. J. Keffer, and H. D. Cochran, J. Chem. Phys. 122, 114103 (2005)]. Two elongational viscosities are measured, and they are shown not to be equal to each other, indicating two independent viscometric functions in PEF. With an appropriate definition, it is observed that the two elongational viscosities converge to each other at very low elongation rates, i.e., in the Newtonian regime. For all three alkanes, tension-thinning behavior is observed. At high elongation rates, chains appear to be fully stretched. This is supported by the result of the mean-square end-to-end distance of chains (R(ete2)) and the mean-square radius of gyration of chains (R(g2)), and further supported by the result of the intramolecular Lennard-Jones (LJ) potential energy. It is also observed that (R(ete2)) and (R(g2)) show a different trend as a function of strain rate from those in shear flow: after reaching a plateau value, (R(ete2)) and (R(g2)) are found to increase further as elongation rate increases. A minimum in the hydrostatic pressure is observed for hexadecane and tetracosane at about epsilon(msigma2/epsilon)1/2=0.02. This phenomenon is shown to be associated with the intermolecular LJ potential energy. The bond-bending and torsional energies display similar trends, but a different behavior is observed for the bond-stretching energy. An important observation common in these three bonded-intramolecular interactions is that all three modes are suppressed to a small value at high elongation rates. We conjecture that a liquid-crystal-like, nematic structure is present in these systems at high elongation rates, which is characterized by a strong chain alignment with a fully stretched conformation.

Journal Article↗

Adsorption of acetic acid on ice: experiments and molecular dynamics simulations.

Adsorption study of acetic acid on ice surfaces was performed by combining experimental and theoretical approaches. The experiments were conducted between 193 and 223 K using a coated wall flow tube coupled to a mass spectrometric detection. Under our experimental conditions, acetic acid was mainly dimerized in the gas phase. The surface coverage increases with decreasing temperature and with increasing concentrations of acetic acid dimers. The obtained experimental surface coverages were fitted according to the BET theory in order to determine the enthalpy of adsorption deltaH(ads) and the mololayer capacity N(M(dimers)) of the acetic acid dimers on ice: deltaH(ads) = (-33.5 +/- 4.2) kJ mol(-1), N(M(dimers)) = (l1.27 +/- 0.25) x 10(14) dimers cm(-2). The adsorption characteristics of acetic acid on an ideal ice I(n)(0001) surface were also studied by means of classical molecular dynamics simulations in the same temperature range. The monolayer capacity, the configurations of the molecules in their adsorption sites, and the corresponding adsorption energies have been determined for both acetic acid monomers and dimers, and compared to the corresponding data obtained from the experiments. In addition, the theoretical results show that the interaction with the ice surface could be strong enough to break the acetic acid dimers that exist in the gas phase and leads to the stabilization of acetic acid monomers on ice.

Journal Article↗

Functional conformations of the L11-ribosomal RNA complex revealed by correlative analysis of cryo-EM and molecular dynamics simulations.

The interaction between the GTPase-associated center (GAC) and the aminoacyl-tRNA.EF-Tu.GTP ternary complex is of crucial importance in the dynamic process of decoding and tRNA accommodation. The GAC includes protein L11 and helices 43-44 of 23S rRNA (referred to as L11-rRNA complex). In this study, a method of fitting based on a systematic comparison between cryo-electron microscopy (cryo-EM) density maps and structures obtained by molecular dynamics simulations has been developed. This method has led to the finding of atomic models of the GAC that fit the EM maps with much improved cross-correlation coefficients compared with the fitting of the X-ray structure. Two types of conformations of the L11-rRNA complex, produced by the simulations, match the cryo-EM maps representing the states either bound or unbound to the aa-tRNA.EF-Tu.GTP ternary complex. In the bound state, the N-terminal domain of L11 is extended from its position in the crystal structure, and the base of nucleotide A1067 in the 23S ribosomal RNA is flipped out. This position of the base allows the RNA to reach the elbow region of the aminoacyl-tRNA when the latter is bound in the A/T site. In the unbound state, the N-terminal domain of L11 is rotated only slightly, and A1067 of the RNA is flipped back into the less-solvent-exposed position, as in the crystal structure. By matching our experimental cryo-EM maps with much improved cross-correlation coefficients compared to the crystal structure, these two conformations prove to be strong candidates of the two functional states.

Amino Acid Sequence↗

The [Lys(-2)-Arg(-1)-des(17-21)]-endothelin-1 peptide retains the specific Arg(-1)-Asp8 salt bridge but reveals discrepancies between NMR data and molecular dynamics simulations.

The [des(17-21)]-endothelin-1 (CSH-ET) and [Lys(-)(2)-Arg(-)(1)-des(17-21)]-endothelin-1 (KR-CSH-ET) peptides, designed by removing the five-residue hydrophobic tail from the endothelin-1 (ET-1) and [Lys(-)(2)-Arg(-)(1)]-endothelin-1 (KR-ET-1) peptides, respectively, were synthesized. Previous studies on KR-ET-1 showed that, in contrast to ET-1, this engineered compound displays a pH-dependent conformational change related to the formation of a stabilizing salt bridge between the Arg(-)(1) and Asp(8) side chains. CD and NMR spectra indicate that CSH-ET and KR-CSH-ET display conformational behavior similar to those of ET-1 and KR-ET-1, respectively. The short salt bridge-stabilized KR-CSH-ET peptide therefore appears to be an attractive elementary scaffold for drug design. The solution structure of the salt-bridged form of KR-CSH-ET was determined by NMR at pH 4.5 and is very similar to the corresponding form of the parent KR-ET-1 peptide. Molecular dynamics simulations of the salt-bridged form of KR-CSH-ET were performed using both the GB/SA implicit solvation scheme or an explicit solvation and the particle-mesh Ewald method for long-range electrostatic calculation. Unexpectedly, the Arg(-)(1)-Asp(8) salt bridge does not display in the simulation the stability that could be expected from the experimental data. The cooperative involvement of a cation-pi interaction in formation of the salt bridge has been hypothesized. Difficulties in accurately simulating cation-pi interactions might be responsible for the lack of stability in the simulation. At this time, however, no definitive explanation for the observed discrepancy between experiments and simulations is available, and further experimental studies appear to be necessary to fully understand in atomic detail the pH-dependent conformational change observed in the KR-ET-1 series.

Amino Acid Motifs↗

Influence of a mutation in the transmembrane domain of the p185c-erbB2 oncogene-encoded protein studied by molecular dynamics simulations.

The c-erbB2 proto-oncogene encodes for a protein of 185kDa (p185) which becomes transforming upon the Val-->Glu transmembrane amino acid substitution. The transforming ability seems to be due to a substitution-resulting constitutive activation of the tyrosine kinase cytosolic domain of the protein. These observations prompted us to evaluate the structural and dynamical behavior of the transmembrane region of the wild and transforming p185 protein in order to understand the role of this region in the transduction mechanism. 160 ps molecular dynamics simulations in vacuo have been performed on two peptides corresponding to the sequence [651-679] of p185c-erbB2 protein and its transforming mutant Val659-->Glu659. These two sequences include the transmembrane domain and are initially postulated to be in an alpha-helix conformation. Noticeable differences in the flexibility of the two peptides are shown. The nontransforming sequence seems rather flexible and several conformational changes are detected at the junction of the mutation point [658-659] and at position Val665-Val666 during the 160 ps simulations. On the contrary, no transitions were observed for the mutated sequence which adopts a stable alpha-helix conformation. This difference in flexibility could be hypothesized as a factor involved in the regulation of the tyrosine kinase activity of p185c-erbB2.

Amino Acid Sequence↗

Molecular dynamics simulations of a beta-hairpin fragment of protein G: balance between side-chain and backbone forces.

How is the native structure encoded in the amino acid sequence? For the traditional backbone centric view, the dominant forces are hydrogen bonds (backbone) and phi-psi propensity. The role of hydrophobicity is non-specific. For the side-chain centric view, the dominant force of protein folding is hydrophobicity. In order to understand the balance between backbone and side-chain forces, we have studied the contributions of three components of a beta-hairpin peptide: turn, backbone hydrogen bonding and side-chain interactions, of a 16-residue fragment of protein G. The peptide folds rapidly and cooperatively to a conformation with a defined secondary structure and a packed hydrophobic cluster of aromatic side-chains. Our strategy is to observe the structural stability of the beta-hairpin under systematic perturbations of the turn region, backbone hydrogen bonds and the hydrophobic core formed by the side-chains, respectively. In our molecular dynamics simulations, the peptides are solvated. with explicit water molecules, and an all-atom force field (CFF91) is used. Starting from the original peptide (G41EWTYDDATKTFTVTE56), we carried out the following MD simulations. (1) unfolding at 350 K; (2) forcing the distance between the C(alpha) atoms of ASP47 and LYS50 to be 8 A; (3) deleting two turn residues (Ala48 and Thr49) to form a beta-sheet complex of two short peptides, GEWTYDD and KTFTVTE; (4) four hydrophobic residues (W43, Y45, F52 and T53) are replaced by a glycine residue step-by-step; and (5) most importantly, four amide hydrogen atoms (T44, D46, T53, and T55, which are crucial for backbone hydrogen bonding), are substituted by fluorine atoms. The fluorination not only makes it impossible to form attractive hydrogen bonding between the two beta-hairpin strands, but also introduces a repulsive force between the two strands due to the negative charges on the fluorine and oxygen atoms. Throughout all simulations, we observe that backbone hydrogen bonds are very sensitive to the perturbations and are easily broken. In contrast, the hydrophobic core survives most perturbations. In the decisive test of fluorination, the fluorinated peptide remains folded under our simulation conditions (5 ns, 278 K). Hydrophobic interactions keep the peptide folded, even with a repulsive force between the beta-strands. Thus, our results strongly support a side-chain centric view for protein folding.

Amino Acid Sequence↗

Solution structure of hyaluronic acid oligomers by experimental and theoretical NMR, and molecular dynamics simulation.

The conformational properties of hyaluronic acid (HA) oligomers in aqueous solution were investigated by combining high-resolution NMR experimental results, theoretical simulation of NMR two-dimensional (2D) spectra by Complete Relaxation Matrix Analysis (CORMA), and molecular dynamics calculations. New experimental findings recorded for the tetra- and hexasaccharides enabled the stiffness of the HA and its viscoelastic properties to be interpreted. In particular, rotating frame nuclear Overhauser effect spectroscopy spectra provided new information about the arrangement of the glycosidic linkage. From (13)C NMR relaxation the rotational correlation time (tau(c)) were determined. The tau(c) were employed in the calculation of geometrical constraints, by using the MARDIGRAS algorithm. Restrained simulated annealing and 1 ns of unrestrained molecular dynamic simulations were performed on the hexasaccharide in a box of 1215 water molecules. The beta(1 --> 3) and beta(1 --> 4) glycosidic links were found to be rigid. The lack of rotational degree of freedom is due to direct and/or water-mediated interresidue hydrogen bonding. Both single or tandem water bridges were found between carboxylate group and N-acetil group. The carboxylate group of glucuronic acid is not involved in a direct link with the amide group of N-acetyl glucosamine and this facilitated bonding between the residue and the water molecules.

Biopolymers↗

Rotational motion in liquid water is anisotropic: a nuclear magnetic resonance and molecular dynamics simulation study.

Experimental NMR measurements of the deuterium and (17)O T(1) relaxation times in deuterium-enriched liquid water have been performed from 275 to 350 K. These relaxation times can yield rotational correlation times of appropriate molecule-fixed unit vectors if the quadrupole coupling constants and asymmetry parameters are known. We determine the latter from ab initio studies of water clusters and experimental chemical shift measurements. We find that the rotational correlation time for the OD bond vector in D(2)(16)O varies from 5.8 ps at 275 K to 0.86 ps at 350 K, and that the rotational correlation time for the out-of-plane vector of dilute D(2)(17)O in D(2)(16)O varies from 4.4 ps at 275 K to 0.64 ps at 350 K. These results indicate that the rotational motion of water is anisotropic. Molecular dynamics simulations of liquid water are in good agreement with these experiments at the higher temperatures, but the simulation results are considerably faster than experiment at the lower temperatures.

Journal Article↗

Molecular dynamics simulation of truncated bovine adrenodoxin.

The 128 amino acid long soluble protein adrenodoxin (Adx) is a typical member of the ferredoxin protein family that are electron carrier proteins with an iron-sulfur cofactor. Adx carries electrons from adrenodoxin reductase (AdR) to cytochrome P450s. Its binding modes to these proteins were previously characterized by site-directed mutagenesis, by X-ray crystallography for the complex Adx:AdR, and by NMR. However, no clear evidence has been provided for the driving force that promotes Adx detachment from AdR upon reduction. Here, we characterized the conformational dynamics of unbound Adx in the oxidized and reduced forms using 2-20 ns long molecular dynamics simulations. The most noticeable difference between both forms is the enhanced flexibility of the loop (47-51) surrounding the iron-sulfur cluster in the reduced form. Together with several structural displacements at the binding interface, this increased flexibility may be the key factor promoting unbinding of reduced Adx from AdR. This points to an intrinsic property of reduced Adx that drives dissociation.

Adrenodoxin↗