Multi-state Dynamics Research Articles

Single-molecule FRET studies of HIV TAR-DNA hairpin unfolding dynamics.

We directly measure the dynamics of the HIV trans-activation response (TAR)–DNA hairpin with multiple loops using single-molecule Förster resonance energy transfer (smFRET) methods. Multiple FRET states are identified that correspond to intermediate melting states of the hairpin. The stability of each intermediate state is calculated from the smFRET data. The results indicate that hairpin unfolding obeys a “fraying and peeling” mechanism, and evidence for the collapse of the ends of the hairpin during folding is observed. These results suggest a possible biological function for hairpin loops serving as additional fraying centers to increase unfolding rates in otherwise stable systems. The experimental and analytical approaches developed in this article provide useful tools for studying the mechanism of multistate DNA hairpin dynamics and of other general systems with multiple parallel pathways of chemical reactions.

Stochastic models of transcription: From single molecules to single cells

Genes in prokaryotic and eukaryotic cells are typically regulated by complex promoters containing multiple binding sites for a variety of transcription factors leading to a specific functional dependence between regulatory inputs and transcriptional outputs. With increasing regularity, the transcriptional outputs from different promoters are being measured in quantitative detail in single-cell experiments thus providing the impetus for the development of quantitative models of transcription. We describe recent progress in developing models of transcriptional regulation that incorporate, to different degrees, the complexity of multi-state promoter dynamics, and its effect on the transcriptional outputs of single cells. The goal of these models is to predict the statistical properties of transcriptional outputs and characterize their variability in time and across a population of cells, as a function of the input concentrations of transcription factors. The interplay between mathematical models of different regulatory mechanisms and quantitative biophysical experiments holds the promise of elucidating the molecular-scale mechanisms of transcriptional regulation in cells, from bacteria to higher eukaryotes.

Theory of the energy transfer efficiency and fluorescence lifetime distribution in single-molecule FRET

In single-molecule FRET experiments with pulsed lasers, not only the colors of the photons but also the fluorescence lifetimes can be monitored. Although these quantities appear to be random, they are modulated by conformational dynamics. In order to extract information about such dynamics, we develop the theory of the joint distribution of FRET efficiencies and fluorescence lifetimes determined from bins (or bursts) of photons. Our starting point is a rigorous formal expression for the distribution of the numbers of donor and acceptor photons and donor lifetimes in a bin that treats the influence of conformational dynamics on all timescales. This formula leads to an analytic result for a two-state system interconverting on a timescale slower than the interphoton time and to an efficient simulation algorithm for multistate dynamics. The shape of the joint distribution contains more information about conformational dynamics than the FRET efficiency histogram alone. In favorable cases, the connectivity of the underlying conformational states can be determined directly by simple inspection of the projection of the joint distribution on the efficiency-lifetime plane.

Exploration of Multi-State Conformational Dynamics and Underlying Global Functional Landscape of Maltose Binding Protein

An increasing number of biological machines have been revealed to have more than two macroscopic states. Quantifying the underlying multiple-basin functional landscape is essential for understanding their functions. However, the present models seem to be insufficient to describe such multiple-state systems. To meet this challenge, we have developed a coarse grained triple-basin structure-based model with implicit ligand. Based on our model, the constructed functional landscape is sufficiently sampled by the brute-force molecular dynamics simulation. We explored maltose-binding protein (MBP) which undergoes large-scale domain motion between open, apo-closed (partially closed) and holo-closed (fully closed) states responding to ligand binding. We revealed an underlying mechanism whereby major induced fit and minor population shift pathways co-exist by quantitative flux analysis. We found that the hinge regions play an important role in the functional dynamics as well as that increases in its flexibility promote population shifts. This finding provides a theoretical explanation of the mechanistic discrepancies in PBP protein family. We also found a functional “backtracking” behavior that favors conformational change. We further explored the underlying folding landscape in response to ligand binding. Consistent with earlier experimental findings, the presence of ligand increases the cooperativity and stability of MBP. This work provides the first study to explore the folding dynamics and functional dynamics under the same theoretical framework using our triple-basin functional model.

Optimized control of multistate quantum systems by composite pulse sequences

We introduce a technique for derivation of high-fidelity composite pulse sequences for two types of multistate quantum systems: systems with the SU(2) and Morris-Shore dynamic symmetries. For the former type, we use the Majorana decomposition to reduce the dynamics to an effective two-state system, which allows us to find the propagator analytically and use the pool of available composite pulses for two-state systems. For the latter type of multistate systems, we use the Morris-Shore decomposition, which reduces the multistate dynamics to a set of two-state systems. We present examples which demonstrate that the multistate composite sequences open a variety of possibilities for coherent control of quantum systems with multiple states.

Excitation transport through Rydberg dressing

We show how to create long-range interactions between alkali atoms in different hyperfine ground states, with the goal of coherent quantum transport. The scheme uses off-resonant dressing with atomic Rydberg states. We demonstrate coherent migration of electronic excitation through dressed dipole–dipole interaction by full solutions of models with four essential states per atom and give the structure of the spectrum of dressed states for a dimer. In addition, we present an effective (perturbative) Hamiltonian for the ground-state manifold and show that it correctly describes the full multi-state dynamics. We discuss excitation transport in detail for a chain of five atoms. In the presented scheme, the actual population in the Rydberg state is kept small. Dressing offers many advantages over the direct use of Rydberg levels: it reduces ionization probabilities and provides an additional tuning parameter for lifetimes and interaction strengths.

Enhancement of Proton Conductance by Mutations of the Selectivity Filter of Aquaporin-1

Prevention of cation permeation in wild-type aquaporin-1 (AQP1) is believed to be associated with the Asn-Pro-Ala (NPA) region and the aromatic/arginine selectivity filter (SF) domain. Previous work has suggested that the NPA region helps to impede proton permeation due to the protein backbone collective macrodipoles that create an environment favoring a directionally discontinuous channel hydrogen-bonded water chain and a large electrostatic barrier. The SF domain contributes to the proton permeation barrier by a spatial restriction mechanism and direct electrostatic interactions. To further explore these various effects, the free-energy barriers and the maximum cation conductance for the permeation of various cations through the AQP1-R195V and AQP1-R195S mutants are predicted computationally. The cations studied included the hydrated excess proton that utilizes the Grotthuss shuttling mechanism, a model “classical” charge localized hydronium cation that exhibits no Grotthuss shuttling, and a sodium cation. The hydrated excess proton was simulated using a specialized multi-state molecular dynamics method including a proper physical treatment of the proton shuttling and charge defect delocalization. Both AQP1 mutants exhibit a surprising cooperative effect leading to a reduction in the free-energy barrier for proton permeation around the NPA region due to altered water configurations in the SF region, with AQP1-R195S having a higher conductance than AQP1-R195V. The theoretical predictions are experimentally confirmed in wild-type AQP1 and the mutants expressed in Xenopus oocytes. The combined results suggest that the SF domain is a specialized structure that has evolved to impede proton permeation in aquaporins.

Multi-state multi-mode nuclear dynamics on three isomers of C6H4F+2 using parallelized TDDVR approach

We have performed molecular dynamics on the three isomers of the difluorobenzene radical cation (C(6)H(4)F(2)(+)) after excitation from the ground state to a specific higher electronically excited state by using our recently implemented parallelized Time-Dependent Discrete Variable Representation (TDDVR) methodology. A five-state eleven-mode realistic model Hamiltonian for o-C(6)H(4)F(2)(+) and two separate five-state ten-mode Hamiltonians for m- and p-isomer of the same radical cation are considered, where those five electronic states are interconnected through several conical intersections in the vicinity of the Franck-Condon (FC) region and thus the dynamics for each case become complex. The photoelectron, mass analyzed threshold ionization spectra and population profiles obtained by using our TDDVR approach show reasonably good agreement with the results obtained by multiconfiguration time dependent Hartree (MCTDH) method. It is worthwhile to mention that the parallelized TDDVR algorithm reduces the computation time by more than an order of magnitude compared to its serial analog and, therefore, such approach appears to be a good compromise between accuracy and speed for a large molecular system.

Defining Condensed Phase Reactive Force Fields from ab Initio Molecular Dynamics Simulations: The Case of the Hydrated Excess Proton.

In this report, a general methodology is presented for the parametrization of a reactive force field using data from a condensed phase ab initio molecular dynamics (AIMD) simulation. This algorithm allows for the creation of an empirical reactive force field that accurately reproduces the underlying ab initio reactive surface while providing the ability to achieve long-time statistical sampling for large systems not possible with AIMD alone. In this work, a model for the hydrated excess proton is constructed where the hydronium cation and proton hopping portions of the model are statistically force-matched to the results of Car-Parrinello Molecular Dynamics (CPMD) simulations. The flexible nature of the algorithm also allows for the use of the more accurate classical simple point-charge flexible water (SPC/Fw) model to describe the water-water interactions while utilizing the ab initio data to create an overall multistate molecular dynamics (MS-MD) reactive model of the hydrated excess proton in water. The resulting empirical model for the system qualitatively reproduces thermodynamic and dynamic properties calculated from the ab initio simulation while being in good agreement with experimental results and previously developed multistate empirical valence bond (MS-EVB) models. The present methodology, therefore, bridges the AIMD technique with the MS-MD modeling of reactive events, while incorporating key strengths of both.

Sola schola et sanitate: human capital as the root cause and priority for international development?

This paper summarizes new scientific evidence supporting the hypothesis that among the many factors contributing to international development, the combination of education and health stands out as a root cause on which other dimensions of development depend. Much of this recent analysis is based on new reconstructions and projections of populations by age, sex and four levels of educational attainment for more than 120 countries using the demographic method of multi-state population dynamics. It also refers to a series of systems analytical population-development-environment case studies that comprehensively assess the role of population and education factors relative to other factors in the struggle for sustainable development. The paper also claims that most concerns about the consequences of population trends are in fact concerns about human capital, and that only by adding the 'quality' dimension of education to the traditionally narrow focus on size and age structure can some of the long-standing population controversies be resolved.

Investigating Hydroxide Anion Interfacial Activity by Classical and Multistate Empirical Valence Bond Molecular Dynamics Simulations

Molecular dynamics simulations were carried out to understand the propensity of the hydroxide anion for the air-water interface. Two classes of molecular models were used, a classical polarizable model and a polarizable multistate empirical valence bond (MS-EVB) potential. The latter model was parametrized to reproduce the structures of small hydroxide-water clusters based on proton reaction coordinates. Furthermore, nuclear quantum effects were introduced into the MS-EVB model implicitly by refitting its potential energy function to account for them. The final MS-EVB model showed reasonable agreement with experiment and ab initio molecular dynamics simulations for dynamical and structural properties. The free-energy profiles for both the classical and MS-EVB models were mapped out across the air-water interface, and the classical model gave a higher free energy at the interface with respect to bulk. However, the MS-EVB model gave little free-energy difference between when the hydroxide anion was in the bulk and when it was present at the air-water interface with its oxygen fully solvated and its hydrogen pointing toward the vapor. When the hydroxide oxygen started to desolvate, the free energy increased dramatically, suggesting that the hydroxide anion can be found in the interfacial region.

The multistate multimode vibronic dynamics of benzene radical cation with a realistic model Hamiltonian using a parallelized algorithm of the quantumclassical approach

We demonstrate the workability of a parallelized algorithm of the time-dependent discrete variable representation (TDDVR) method to explore the detailed dynamical aspects of vibronic interaction in two three-state model Hamiltonians (X (2)E(1g), B (2)E(2g), C (2)A(2u) and B (2)E(2g), D (2)E(1u), E (2)B(2u)) of benzene radical cation along with a preliminary investigation on its five electronic states (X (2)E(1g), B (2)E(2g), C (2)A(2u), D (2)E(1u), and E(2)B(2u)). Since those electronic states are interconnected through a series of conical intersections, we have used six and nine vibronically important modes for the three- and five-state Hamiltonians, respectively, in order to perform the quantum dynamics on such system. The population profiles calculated by using our TDDVR approach show reasonably good agreement with the results obtained by exact quantum mechanical (multiconfiguration time-dependent Hartree) method, whereas the corresponding (calculated) photoabsorption spectra originating from various electronic states agree well with the experimental ones. It is important to note that the parallelized algorithm of our TDDVR approach reduces the computation cost by more than an order of magnitude compared to its serial analog. The TDDVR approach appears to be a good compromise between accuracy and speed for such large molecular system, where quantum mechanical description is needed in a restricted region.

Photodynamics in Complex Environments: Ab Initio Multiple Spawning Quantum Mechanical/Molecular Mechanical Dynamics

Our picture of reactions on electronically excited states has evolved considerably in recent years, due to advances in our understanding of points of degeneracy between different electronic states, termed "conical intersections" (CIs). CIs serve as funnels for population transfer between different electronic states, and play a central role in ultrafast photochemistry. Because most practical photochemistry occurs in solution and protein environments, it is important to understand the role complex environments play in directing excited-state dynamics generally, as well as specific environmental effects on CI geometries and energies. In order to model such effects, we employ the full multiple spawning (FMS) method for multistate quantum dynamics, together with hybrid quantum mechanical/molecular mechanical (QM/MM) potential energy surfaces using both semiempirical and ab initio QM methods. In this article, we present an overview of these methods, and a comparison of the excited-state dynamics of several biological chromophores in solvent and protein environments. Aqueous solvation increases the rate of quenching to the ground state for both the photoactive yellow protein (PYP) and green fluorescent protein (GFP) chromophores, apparently by energetic stabilization of their respective CIs. In contrast, solvation in methanol retards the quenching process of the retinal protonated Schiff base (RPSB), the rhodopsin chromophore. Protein environments serve to direct the excited-state dynamics, leading to higher quantum yields and enhanced reaction selectivity.

The trigger sequence in the GCN4 leucine zipper: α-helical propensity and multistate dynamics of folding and dimerization

We investigate the importance of the trigger sequence in the folding and dimerization of the GCN4 leucine zipper. We examine the role of the enhanced propensity of the amino acids in the trigger sequence to form an alpha-helix. Using computer simulations, we calculate heat capacities, free energy profiles, and the probability for successful dimerization as a function of the strength of the alpha-helical propensity of the trigger sequence. Our results elucidate the experimentally observed importance of the trigger sequence for dimerization and why it is not necessary for the trigger to have a specific "consensus" sequence of amino acids. We also find that a stronger trigger sequence not only increases the probability for dimerization but also changes the dimerization dynamics by introducing multiple intermediate states.

Multistate vibronic interactions in difluorobenzene radical cations. II. Quantum dynamical simulations

The multistate vibronic dynamics in the X-D electronic states of all three difluorobenzene radical cations are investigated theoretically by an ab initio quantum dynamical approach. The vibronic coupling scheme and the ab initio values of the system parameters are adopted from Paper I [S. Faraji and H. Koppel, J. Chem. Phys. 129, 074310 (2008)]. Extensive calculations by wave-packet propagation have been performed with the aid of the multiconfiguration time-dependent Hartree method. Five coupled electronic potential energy surfaces and 10 (11 in the case of the orthoisomer) vibrational degrees of freedom have been included in these calculations. The nonadiabatic interactions lead to the restructuring of the photoelectron spectral envelopes. Ultrafast internal conversion processes within the electronic manifolds in question demonstrate the strength of the nonadiabatic coupling effects and complement the analogous findings for the electronic spectra. The internal conversion dynamics is characterized by a stepwise transfer of the electronic population to the lowest electronic state on a time scale of femtoseconds to picoseconds. A difference between the three isomers is found to be related to the weaker interaction between the sets of X-A and B-C-D states (with high-energy conical intersections) in the meta isomer, as compared to the other isomers. The implications of these findings for the qualitative understanding of the fluorescence dynamics of fluorinated benzene radical cations are discussed.

Molecular simulation of multistate peptide dynamics: A comparison between microsecond timescale sampling and multiple shorter trajectories

Molecular dynamics simulations of the RN24 peptide, which includes a diverse set of structurally heterogeneous states, are carried out in explicit solvent. Two approaches are employed and compared directly under identical simulation conditions. Specifically, we examine sampling by two individual long trajectories (microsecond timescale) and many shorter (MS) uncoupled trajectories. Statistical analysis of the structural properties indicates a qualitative agreement between these approaches. Microsecond timescale sampling gives large uncertainties on most structural metrics, while the shorter timescale of MS simulations results in slight structural memory for beta-structure starting states. Additionally, MS sampling detects numerous transitions on a relatively short timescale that are not observed in microsecond sampling, while long simulations allow for detection of a few transitions on significantly longer timescales. A correlation between the complex free energy landscape and the kinetics of the equilibrium is highlighted by principal component analysis on both simulation sets. This report highlights the increased precision of the MS approach when studying the kinetics of complex conformational change, while revealing the complementary insight and qualitative agreement offered by far fewer individual simulations on significantly longer timescales.

Rotational Dynamics of Phospholamban Determined by Multifrequency Electron Paramagnetic Resonance

We have used multifrequency electron paramagnetic resonance to define the multistate structural dynamics of an integral membrane protein, phospholamban (PLB), in a lipid bilayer. PLB is a key regulator of cardiac calcium transport, and its function requires transitions between distinct states of intramolecular dynamics. Monomeric PLB was synthesized with the TOAC spin label at positions 11 (in the cytoplasmic domain) and 46 (in the transmembrane domain) and reconstituted into lipid bilayers. Unlike other protein spin labels, TOAC reports directly the motion of the peptide backbone, so quantitative analysis of its dynamics is worthwhile. Electron paramagnetic resonance spectra at 9.4 GHz (X-band) and 94 GHz (W-band) were analyzed in terms of anisotropic rotational diffusion of the two domains. Motion of the transmembrane domain is highly restricted, while the cytoplasmic domain exhibits two distinct conformations, a major one with moderately restricted nanosecond dynamics ( T) and another with nearly unrestricted subnanosecond motion ( R). The global analysis of spectra at two frequencies yielded values for the rotational correlation times and order parameters that were much more precisely determined than at either frequency alone. Multifrequency EPR is a powerful approach for analysis of complex rotational dynamics of proteins.

Multistate multimode vibronic dynamics: Entanglement of electronic and vibrational degrees of freedom in the benzene radical cation

An earlier theoretical treatment of multimode and multistate vibronic coupling in the benzene radical cation [Koppel et al., J. Chem. Phys. 117, 2657 (2002)] is extended to investigate also the behavior of the nuclear degrees of freedom and to include additional electronic states. The five lowest doublet electronic states are considered which have been shown earlier to be all interconnected through a series of conical intersections of their potential-energy surfaces. In the most extensive calculations, they are all included simultaneously in the quantum dynamical calculations performed, which represent a system of unprecedented complexity treated in this way. The results are compared with various reduced-dimensionality treatments (i.e., employing reduced vibrational and electronic function spaces). The different temporal behavior of the various electronic populations is emphasized and traced to the different locations of the various seams of conical intersections: due to the coherent oscillations of the time-dependent wave packet this leads to an oscillatory behavior in some cases and to monotonous behavior in others. A seemingly irreversible behavior of the system dynamics in this strictly microscopic treatment is confirmed. The importance of this benchmark system to highlight complex, entangled multimode, and multistate vibronic dynamics is pointed out.

Multi-mode–multi-state quantum dynamics of key five-membered heterocycles: spectroscopy and ultrafast internal conversion

The multi-mode and multi-state vibronic interactions in the heterocyclic molecules furan, pyrrole, thiophene and their radical cations are investigated theoretically, employing a linear vibronic coupling scheme. The underlying system parameters are determined from large-scale ab initio computations. Previous time-independent dynamical calculations on the radical cations are extended by wave-packet propagations (using the MCTDH method) confirming the strong nonadiabatic coupling effects. For the singlet excited states of furan and thiophene quantum dynamical calculations are presented which go beyond the two-state approximation frequently applied in the literature. The characteristic spectral structures are well reproduced, especially in the case of furan. The implications of these results on the photochemical reaction dynamics of these species are discussed.

Multistate vibronic interactions in the benzene radical cation. II. Quantum dynamical simulations

The multistate vibronic dynamics in the X̃ 2E1g-Ẽ 2B2u electronic states of the benzene radical cation is investigated theoretically by an ab initio quantum-dynamical approach. The vibronic coupling scheme and the ab initio values of the system parameters are adopted from the previous Paper I. Vibronic line spectra are obtained with the Lanczos procedure. Extensive calculations on wave-packet propagation have been performed with the aid of the multiconfiguration time-dependent Hartree method. Up to five coupled electronic potential energy surfaces and 13 vibrational degrees of freedom have been included in these calculations. As a result, the impact of a third electronic state (X̃ or B̃) on a strongly coupled manifold (B̃-C̃ or D̃-Ẽ states) is quantitatively assessed. It leads to a restructuring of the spectral envelope which is stronger for the B̃-D̃-Ẽ than for the X̃-B̃-C̃ system. The internal conversion dynamics is characterized by a stepwise transfer of electronic population to the lowest electronic state on a time scale of ∼100 fs, if the system is prepared initially on the highest potential energy surface. Companion calculations have also been performed for the case when the system is prepared in the intermediate state at t=0; they show a branching of the electronic populations. These are all novel findings which are discussed in terms of a series of conical intersections between the various potential energy surfaces. The importance of such multistate vibronic interactions for the photophysics and photochemistry of medium-sized systems is pointed out.