Choice of the Right Supporting Electrolyte in Electrochemical Reductions: A Principal Component Analysis.

We present an analysis of a set of molecular, electrical, and electronic properties for a large number of the cations of quaternary ammonium salts usually employed as supporting electrolytes in cathodic reduction reactions. The goal of the present study is to define a measure for the quality of a supporting electrolyte in terms of the yield of the reaction considered. We performed a principal component analysis using the normalized values of the properties in order to lower the number of relevant reaction coordinates and find that the integral variance of 13 properties can well be represented by three principal components. The yield of the electrochemical hydrodimerization of acrylonitrile employing different quaternary ammonium salts as supporting electrolytes was determined in a series of experiments. We found only a very weak correlation between the yield and the values of the properties but a strong correlation between the yield and the values of the most important principal component. Very similar results are obtained for two further existing systematic experimental studies of the impact of the supporting electrolyte on the yield of cathodic reductions. For all three example reactions, a supervised regression using the two most important principal components as variables yields excellent values for the coefficients of determination. For comparison, we also applied our methodology to sets of purely structure-based features that are usually employed in cheminformatics and obtained results of almost similar quality. We therefore conjecture that our methodology in combination with a small number of experiments can be used to predict the yield of a given cathodic reduction on the basis of the properties of the supporting electrolyte.

Supramolecular Packing Drives Morphological Transitions of Charged Surfactant Micelles.

The shape and size of self-assembled structures upon local organization of their molecular building blocks are hard to predict in the presence of long-range interactions. Combining small-angle X-ray/neutron scattering data, theoretical modelling, and computer simulations, sodium dodecyl sulfate (SDS), over a broad range of concentrations and ionic strengths, was investigated. Computer simulations indicate that micellar shape changes are associated with different binding of the counterions. By employing a toy model based on point charges on a surface, and comparing it to experiments and simulations, it is demonstrated that the observed morphological changes are caused by symmetry breaking of the irreducible building blocks, with the formation of transient surfactant dimers mediated by the counterions that promote the stabilization of cylindrical instead of spherical micelles. The present model is of general applicability and can be extended to all systems controlled by the presence of mobile charges.

Temperature dependent mechanical unfolding of calixarene nanocapsules studied by molecular dynamics simulations.

Using atomistic molecular dynamics simulations, we study the temperature dependence of the mechanical unfolding of a model supramolecular complex, a dimer of interlocked calixarene capsules. This system shows reversible transitions between two conformations that are stabilized by different networks of hydrogen bonds. We study the forced dissociation and formation of these networks as a function of temperature and find a strong impact of the nonequilibrium conditions imposed by pulling the system mechanically. The kinetics of the transition between the two conformations is ideally suited to investigate the range of validity of the stochastic models employed in the analysis of force dependent kinetic rates obtained from experimental or simulation data. These models usually assume activated dynamics for the relevant transitions, and therefore, the analytical expressions for the kinetic rates are of an Arrhenius form. A study of the temperature- and force-dependent kinetics by simulation allows an analysis of the transition rates without any model assumption. We find that the temperature dependence of the rates is well described by an Arrhenius law for each value of the force. This enables us to determine the activation free energy and the bare kinetic rate as a function of force independent of each other. In accord with the common model assumptions, we find that the activation free energy decreases with increasing force. The force dependence of the bare rates is compatible with the results of model calculations in the low force regime, and deviations are observed at high forces.

Intramolecular structural parameters are key modulators of the gel-liquid transition in coarse grained simulations of DPPC and DOPC lipid bilayers.

The capability of coarse-grained models based on the MARTINI mapping to reproduce the gel-liquid phase transition in saturated and unsaturated model lipids was investigated. We found that the model is able to reproduce a lower critical temperature for 1,2-dioleoyl-sn-glycero-3-phosphocholine (DOPC) with respect to 1,2-dipalmitoyl-sn-glycero-3-phosphocholine (DPPC). Nonetheless, the appearance of a gel phase for DOPC is strictly dependent on the intramolecular parameters chosen to model its molecular structure. In particular, we show that the bending angle at the coarse-grained bead corresponding to the unsaturated carbon-carbon bond acts as an order parameter determining the temperature of the phase transition. Structural analysis of the molecular dynamics simulations runs evidences that in the gel phase, the packing of the lipophilic tails of DOPC assume a different conformation than in the liquid phase. In the latter phase, the DOPC geometry resembles that of the relaxed free molecule. DPPC:DOPC mixtures show a single phase transition temperature, indicating that the observation of a phase separation between the two lipids requires the simulation of systems with sizes much larger than the ones used here.

Structural Origin of Metal Specificity in Isatin Hydrolase from Labrenzia aggregata Investigated by Computer Simulations.

We performed quantum-chemical calculations, ab initio molecular dynamics, hybrid quantum mechanics/molecular mechanics (QM/MM) and enhanced sampling metadynamics simulations to investigate the origin of metal specificity in isatin hydrolase from Labrenzia aggregata. The peculiar octahedral binding geometry of the Mn2+ ion in the Michaelis complex includes both the isatin substrate and the catalytic water within the first coordination shell of the cation. Our calculations show that the same arrangement of the ligands cannot be efficiently achieved in the presence of other small divalent metal cations such as Zn2+ or Cu2+ . On the contrary, bulkier alkaline-earth cations such as Mg2+ , which allow octahedral coordination, are not able to activate the catalytic water into the stronger OH- nucleophile required to attack the stable N-aryl-amide moiety of isatin.

Dynamic coarse-graining fills the gap between atomistic simulations and experimental investigations of mechanical unfolding.

We present a dynamic coarse-graining technique that allows one to simulate the mechanical unfolding of biomolecules or molecular complexes on experimentally relevant time scales. It is based on Markov state models (MSMs), which we construct from molecular dynamics simulations using the pulling coordinate as an order parameter. We obtain a sequence of MSMs as a function of the discretized pulling coordinate, and the pulling process is modeled by switching among the MSMs according to the protocol applied to unfold the complex. This way we cover seven orders of magnitude in pulling speed. In the region of rapid pulling, we additionally perform steered molecular dynamics simulations and find excellent agreement between the results of the fully atomistic and the dynamically coarse-grained simulations. Our technique allows the determination of the rates of mechanical unfolding in a dynamical range from approximately 10-8/ns to 1/ns thus reaching experimentally accessible time regimes without abandoning atomistic resolution.

Force probe simulations of a reversibly rebinding system: Impact of pulling device stiffness.

We present a detailed study of the parameter dependence of force probe molecular dynamics (FPMD) simulations. Using a well studied calix[4]arene catenane dimer as a model system, we systematically vary the pulling velocity and the stiffness of the applied external potential. This allows us to investigate how the results of pulling simulations operating in the constant velocity mode (force-ramp mode) depend on the details of the simulation setup. The system studied has the further advantage of showing reversible rebinding meaning that we can monitor the opening and the rebinding transition. Many models designed to extract kinetic information from rupture force distributions work in the limit of soft springs and all quantities are found to depend solely on the so-called loading rate, the product of spring stiffness and pulling velocity. This approximation is known to break down when stiff springs are used, a situation often encountered in molecular simulations. We find that while some quantities only depend on the loading rate, others show an explicit dependence on the spring constant used in the FPMD simulation. In particular, the force versus extension curves show an almost stiffness independent rupture force but the force jump after the rupture transition does depend roughly linearly on the value of the stiffness. The kinetic rates determined from the rupture force distributions show a dependence on the stiffness that can be understood in terms of the corresponding dependence of the characteristic forces alone. These dependencies can be understood qualitatively in terms of a harmonic model for the molecular free energy landscape. It appears that the pulling velocities employed are so large that the crossover from activated dynamics to diffusive dynamics takes place on the time scale of our simulations. We determine the effective distance of the free energy minima of the closed and the open configurations of the system from the barrier via an analysis of the hydrogen-bond network with results in accord with earlier simulations. We find that the system is quite brittle in the force regime monitored in the sense that the barrier is located near to the closed state.

Force probe simulations using a hybrid scheme with virtual sites.

Hybrid simulations, in which a part of the system is treated with atomistic resolution and the remainder is represented on a coarse-grained level, allow for fast sampling while using the accuracy of atomistic force fields. We apply a hybrid scheme to study the mechanical unfolding and refolding of a molecular complex using force probe molecular dynamics (FPMD) simulations. The degrees of freedom of the solvent molecules are treated in a coarse-grained manner while atomistic resolution is retained for the solute. The coupling between the solvent and the solute is provided using virtual sites. We test two different common coarse-graining procedures, the iterative Boltzmann inversion method and the force matching procedure, and find that both methodologies give similar results. The results of the FPMD simulations are compared to all-atom simulations of the same system and we find that differences between these simulations and the ones using the hybrid scheme are in a similar range as the differences obtained when using different atomistic force fields. Thus, a hybrid scheme yields qualitatively correct results in the strong non-equilibrium situation the system is experiencing in FPMD simulations.

Mechanical unfolding pathway of a model ß-peptide foldamer.

Foldamers constructed from oligomers of ß-peptides form stable secondary helix structures already for small chain lengths, which makes them ideal candidates for the investigation of the (un)folding of polypeptides. Here, the results of molecular simulations of the mechanical unfolding of a ß-heptapeptide in methanol solvent revealing the detailed unfolding pathway are reported. The unfolding process is shown to proceed via a stable intermediate even for such a small system. This result is arrived at performing non-equilibrium force ramp simulations employing different pulling velocities and also using standard calculations of the potential of mean force, i.e., the free energy as a function of the helix elongation. It is thus demonstrated that even with the rather large pulling velocities employed in the force ramp simulations relevant information about the equilibrium kinetics can be obtained. The smallness of the system allows a detailed analysis of the unfolding pathway, which is characterized by an opening of the terminal loops followed by the unfolding of the center. This sequence is in accord with the configurational preferences of the system that also are responsible for the stability of the 314-helix. From an analysis of the distributions of rupture forces and the force spectra, the kinetic rates for both transitions were determined and common models were used to extract geometric quantities describing the free energy landscape of the system.

Statistics of reversible transitions in two-state trajectories in force-ramp spectroscopy.

A possible way to extract information about the reversible dissociation of a molecular adhesion bond from force fluctuations observed in force ramp experiments is discussed. For small loading rates the system undergoes a limited number of unbinding and rebinding transitions observable in the so-called force versus extension (FE) curves. The statistics of these transient fluctuations can be utilized to estimate the parameters for the rebinding rate. This is relevant in the experimentally important situation where the direct observation of the reversed FE-curves is hampered, e.g., due to the presence of soft linkers. I generalize the stochastic theory of the kinetics in two-state models to the case of time-dependent kinetic rates and compute the relevant distributions of characteristic forces. While for irreversible systems there is an intrinsic relation between the rupture force distribution and the population of the free-energy well of the bound state, the situation is slightly more complex if reversible systems are considered. For a two-state model, a "stationary" rupture force distribution that is proportional to the population can be defined and allows to consistently discuss quantities averaged over the transient fluctuations. While irreversible systems are best analyzed in the soft spring limit of small pulling device stiffness and large loading rates, here I argue to use the stiffness of the pulling device as a control parameter in addition to the loading rate.

The temperature dependence of vibronic lineshapes: linear electron-phonon coupling.

We calculate the effect of a linear electron-phonon coupling on vibronic transitions of dye molecules of arbitrary complexity. With the assumption of known vibronic frequencies (for instance from quantum-chemical calculations), we give expressions for the absorption or emission lineshapes in a second-order cumulant expansion. We show that the results coincide with those obtained from generalized Redfield theory if one uses the time-local version of the theory and applies the secular approximation. Furthermore, the theory allows to go beyond the Huang-Rhys approximation and can be used to incorporate Dushinsky effects in the treatment of the temperature dependence of optical spectra. We consider both, a pure electron-phonon coupling independent of the molecular vibrations and a coupling bilinear in the molecular vibrational modes and the phonon coordinates. We discuss the behavior of the vibronic density of states for various models for the spectral density representing the coupling of the vibronic system to the harmonic bath. We recover some of the results that have been derived earlier for the spin-boson model and we show that the behavior of the spectral density at low frequencies determines the dominant features of the spectra. In case of the bilinear coupling between the molecular vibrations and the phonons we give analytical expressions for different spectral densities. The spectra are reminiscent of those obtained from the well known Brownian oscillator model and one finds a zero-phonon line and phonon-side bands located at vibrational frequencies of the dye. The intensity of the phonon-side bands diminishes with increasing vibrational frequencies and with decreasing coupling strength (Huang-Rhys factor). It vanishes completely in the Markovian limit where only a Lorentzian zero-phonon line is observed.

Oxidative two-state photoreactivity of a manganese(IV) complex using near-infrared light.

Highly reducing or oxidizing photocatalysts are a fundamental challenge in photochemistry. Only a few transition metal complexes with Earth-abundant metal ions have so far advanced to excited state oxidants. All these photocatalysts require high-energy light for excitation, and their oxidizing power has not been fully exploited due to energy dissipation before reaching the photoactive state. Here we demonstrate that the complex [Mn(dgpy)2]4+, based on Earth-abundant manganese and the tridentate 2,6-diguanidylpyridine ligand (dgpy), evolves to a luminescent doublet ligand-to-metal charge transfer (2LMCT) excited state (1,435 nm, 0.86 eV) with a lifetime of 1.6 ns after excitation with low-energy near-infrared light. This 2LMCT state oxidizes naphthalene to its radical cation. Substrates with extremely high oxidation potentials up to 2.4 V enable the [Mn(dgpy)2]4+ photoreduction via a high-energy quartet 4LMCT excited state with a lifetime of 0.78 ps, proceeding via static quenching by the solvent. This process minimizes free energy losses and harnesses the full photooxidizing power, and thus allows oxidation of nitriles and benzene using Earth-abundant elements and low-energy light.

Higher-order correlation functions and nonlinear response functions in a gaussian trap model.

The four-time correlation function of a general dynamical variable obeying gaussian statistics is calculated for the trap model with a gaussian density of states. It is argued that for energy-independent variables this function is reminiscent of the four-time functions that have been discussed earlier in the interpretation of the results of four-dimensional NMR experiments on supercooled liquids. Using an approximative relation between the four-time correlation function and the cubic response function the nonlinear susceptibility is calculated and the results are compared with the corresponding ones resulting from an exact calculation. It is found that the results of the approximation change the qualitative behavior of the modulus of the susceptibility. Whereas in the exact calculation a peak is found in the modulus in most cases, depending on temperature and the additional model parameters no such peak occurs in the approximation. This difference has its origin mainly in an incorrect estimate of the static response. The results are discussed in relation to recent experimental findings.

Nonlinear response theory for Markov processes. IV. The asymmetric double-well potential model revisited.

The dielectric response of noninteracting dipoles is discussed in the framework of the classical model of stochastic reorientations in an asymmetric double-well potential (ADWP). In the nonlinear regime, this model exhibits some pecularities in the static response. We find that the saturation behavior of the symmetric double-well potential model does not follow the Langevin function and only in the linear regime are the standard results recovered. If a finite asymmetry is assumed, then the nonlinear susceptibilities are found to change the sign at a number of characteristic temperatures that depend on the magnitude of the asymmetry, as has been observed earlier for the third-order and fifth-order responses. If the kinetics of the barrier crossing in the ADWP model is described as a two-state model, then we can give analytical expressions for the values of the characteristic temperatures. The results for the response obtained from a (numerical) solution of the Fokker-Planck equation for the Brownian motion in a model ADWP behaves very similarly to the two-state model for high barriers. For small barriers no clear-cut timescale separation between the barrier crossing process and the intrawell relaxation exists and the model exhibits a number of timescales. In this case, the frequency-dependent linear susceptibility at low temperatures is dominated by the fast intrawell transitions and at higher temperatures by the barrier crossing kinetics. We find that for nonlinear susceptibilities the latter process appears to be more important and the intrawell transitions play only a role at the lowest temperatures.

Force probe simulations using an adaptive resolution scheme.

Molecular simulations of the forced unfolding and refolding of biomolecules or molecular complexes allow to gain important kinetic, structural and thermodynamic information about the folding process and the underlying energy landscape. In force probe molecular dynamics (FPMD) simulations, one pulls one end of the molecule with a constant velocity in order to induce the relevant conformational transitions. Since the extended configuration of the system has to fit into the simulation box together with the solvent such simulations are very time consuming. Here, we apply a hybrid scheme in which the solute is treated with atomistic resolution and the solvent molecules far away from the solute are described in a coarse-grained manner. We use the adaptive resolution scheme (AdResS) that has very successfully been applied to various examples of equilibrium simulations. We perform FPMD simulations using AdResS on a well studied system, a dimer formed from mechanically interlocked calixarene capsules. The results of the multiscale simulations are compared to all-atom simulations of the identical system and we observe that the size of the region in which atomistic resolution is required depends on the pulling velocity, i.e. the particular non-equilibrium situation. For large pulling velocities a larger all atom region is required. Our results show that multiscale simulations can be applied also in the strong non-equilibrium situations that the system experiences in FPMD simulations.

Force-clamp spectroscopy of reversible bond breakage.

We consider reversible breaking of adhesion bonds or folding of proteins under the influence of a constant external force. We discuss the statistical properties of the unbinding/rebinding events and analyze their mean number and their variance in the framework of simple kinetic models. In the calculations, we explicitly exploit the analogy to single molecule fluorescence and particularly between unbinding/rebinding and photon emission events. Whereas for two-state behavior Poisson or sub-Poisson statistics of the events is found, we show that for more general kinetic schemes also super-Poisson statistics can occur. Temporal fluctuations of the transition rates, a hallmark for the presence of dynamic disorder, should become experimentally accessible via the determination of the second moment of the event-number distribution.

Mechanical and Structural Tuning of Reversible Hydrogen Bonding in Interlocked Calixarene Nanocapsules.

We present force probe molecular dynamics simulations of dimers of interlocked calixarene nanocapsules and study the impact of structural details and solvent properties on the mechanical unfolding pathways. The system consists of two calixarene "cups" that form a catenane structure via interlocked aliphatic loops of tunable length. The dimer shows reversible rebinding, and the kinetics of the system can be understood in terms of a two-state model for shorter loops (≤14 CH2 units) and a three-state model for longer loops (≥15 CH2 units). The various conformational states of the dimer are stabilized by networks of hydrogen bonds, the mechanical susceptibility of which can be altered by changing the polarity and proticity of the solvent. The variation of the loop length and the solvent properties in combination with changes in the pulling protocol allows to tune the reversibility of the conformational transitions.

Dynamic force spectroscopy: Analysis of reversible bond-breaking dynamics.

The problem of diffusive bond dissociation in a double well potential under application of an external force is scrutinized. We compute the probability distribution of rupture forces and present a detailed discussion of the influence of finite rebinding probabilities on the dynamic force spectrum. In particular, we focus on barrier crossing upon extension, i.e., under linearly increased load, and upon relaxation starting from completely separated bonds. For large loading rates the rupture force and the rejoining force depend on the loading rate in the expected manner determined by the shape of the potential. For small loading rates the mean forces obtained from pull and relax modes approach each other as the system reaches equilibrium. We investigate the dependence of the rupture force distributions and mean rupture forces on external parameters such as cantilever stiffness and influence of a soft linker. We find that depending on the implementation of a soft linker the equilibrium rupture force is either unaffected by the presence of the linker or changes in a predictable way with the linker compliance. Additionally, we show that it is possible to extract the equilibrium constant of the on and off rates from the determination of the equilibrium rupture forces.

A fundamental catalytic difference between zinc and manganese dependent enzymes revealed in a bacterial isatin hydrolase.

The catalytic mechanism of the cyclic amidohydrolase isatin hydrolase depends on a catalytically active manganese in the substrate-binding pocket. The Mn2+ ion is bound by a motif also present in other metal dependent hydrolases like the bacterial kynurenine formamidase. The crystal structures of the isatin hydrolases from Labrenzia aggregata and Ralstonia solanacearum combined with activity assays allow for the identification of key determinants specific for the reaction mechanism. Active site residues central to the hydrolytic mechanism include a novel catalytic triad Asp-His-His supported by structural comparison and hybrid quantum mechanics/classical mechanics simulations. A hydrolytic mechanism for a Mn2+ dependent amidohydrolases that disfavour Zn2+ as the primary catalytically active site metal proposed here is supported by these likely cases of convergent evolution. The work illustrates a fundamental difference in the substrate-binding mode between Mn2+ dependent isatin hydrolase like enzymes in comparison with the vast number of Zn2+ dependent enzymes.

Hybrid Particle-Field Molecular Dynamics Simulations of Charged Amphiphiles in an Aqueous Environment.

We develop and test specific coarse-grained models for charged amphiphilic systems such as palmitoyloleoylphosphatidylglycerol (POPG) lipid bilayer and sodium dodecyl sulfate (SDS) surfactant in an aqueous environment, to verify the ability of the hybrid particle-field method to provide a realistic description of polyelectrolytes. According to the hybrid approach, the intramolecular interactions are treated by a standard molecular Hamiltonian, and the nonelectrostatic intermolecular forces are described by density fields. Electrostatics is introduced as an additional external field obtained by a modified particle-mesh Ewald procedure, as recently proposed [Zhu et al. Phys. Chem. Chem. Phys. 2016 , 18 , 9799 ]. Our results show that, upon proper calibration of key parameters, electrostatic forces can be correctly reproduced. Molecular dynamics simulations indicate that the methodology is robust with respect to the choice of the relative dielectric constant, yielding the same correct qualitative behavior for a broad range of values. In particular, our methodology reproduces well the organization of the POPG bilayer, as well as the SDS concentration-dependent change in the morphology of the micelles from spherical to microtubular aggregates. The inclusion of explicit electrostatics with good accuracy and low computational cost paves the way for a significant extension of the hybrid particle-field method to biological systems, where the polyelectrolyte component plays a fundamental role for both structural and dynamical molecular properties.