Interconversion Of States Research Articles

Exploring Biased Probability Using Loaded Dice: An Active Learning Exercise with Analogy to Entropic and Energetic Determinants of Equilibria in Chemical Systems

The equilibrium position of a chemical system is based on two distinct considerations, namely, the entropy and enthalpy differences between the states. Loaded dice provide a physical system for exploring the probability of observing different interconverting states on the basis of two distinct factors: the number of sides of the die (entropy) and the asymmetric distribution of mass in the die (gravitational potential energy). Although potential energy analogies such as pushing a rock up a hill have often been used for teaching differences in energy in chemistry, and dice have likewise often been used to explain entropy, such analogies can be unsatisfactory when entropic and enthalpic considerations favor different states. We present an activity that allows students to explore how potential energy and entropy together contribute to observed probability and then draw parallels to chemical systems. Students collect statistics for observed rolls of loaded dice, rationalize the different patterns as distinct states, and determine the difference in entropy between the states. These observations are then related to chemical reactions and to the definition of entropy. The effect of varying the loaded mass within the dice is related to the role enthalpy plays in determining equilibrium. This analogy and associated active learning exercises are applicable to a wide variety of college chemistry and physics courses; provide a hands-on approach to introducing concepts such as probability, entropy, and energy differences; and can be used to draw parallels to chemical reactions, enthalpy, and Gibbs free energy.

Triplet Sensitization by Lead Halide Perovskite Thin Films for Efficient Solid-State Photon Upconversion at Subsolar Fluxes

Summary We investigate the rubrene triplet sensitization by perovskite thin films based on methylammonium formamidinium lead triiodide (MAFA) of varying thicknesses. The power-law dependence of both the MAFA photoluminescence (PL) intensity and upconverted emission is tracked as a function of the incident power density. Bimolecular triplet-triplet annihilation (TTA) exhibits a unique power-law dependence with a slope change from quadratic-to-linear at the threshold Ith. The underlying MAFA PL power-law dependence dictates the power law of the upconverted PL: (1) below Ith, the slope of the upconverted PL is twice the value of the MAFA PL; (2) above Ith, it follows the same power law as the underlying recombination of mobile electrons and holes in the MAFA films. We find that the Ith shifts to subsolar incident laser powers when increasing the MAFA thickness above 30 nm. For the thickest MAFA film of 380 nm we find an upconversion threshold of Ith = 7.1 mW/cm2.

The quantum thermodynamic force responsible for quantum state transformation and the flow and backflow of information

Why do quantum evolutions occur and why do they stop at certain points? In classical thermodynamics affinity was introduced to predict in which direction an irreversible process proceeds. In this paper the quantum mechanical counterpart of the classical affinity is found. It is shown that the quantum version of affinity can predict in which direction a process evolves. A new version of the second law of thermodynamics is derived through quantum affinity for energy-incoherent state interconversion under thermal operations. we will also see that the quantum affinity can be a good candidate to be responsible, as a force, for driving the flow and backflow of information in Markovian and non-Markovian evolutions. Finally we show that the rate of quantum coherence can be interpreted as the pure quantum mechanical contribution of the total thermodynamic force and flow. Thus it is seen that, from a thermodynamic point of view, any interaction from the outside with the system or any measurement on the system may be represented by a quantum affinity.

Spin-dependent charge state interconversion of nitrogen vacancy centers in nanodiamonds

The nitrogen vacancy (NV) center in diamond is the most widely studied color center in diamond for its wide range of applications in both physics and biology. The negatively charged state ${\mathrm{NV}}^{\ensuremath{-}}$ is often favored for its better spin-optical properties, whereas the presence of the neutral charge state ${\mathrm{NV}}^{0}$ is often minimized or neglected by using a single optimized excitation wavelength. In many cases, the use of additional laser wavelengths has an important impact on the NV optical properties and can lead to a dramatically quenched fluorescence. Through measurements of the photophysics of the NV center we show in this work that this quenching mechanism is mediated by charge state interconversion providing additional channels for nonradiative decay. Our results show that this mechanism is also sensitive to the spin state of the ${\mathrm{NV}}^{\ensuremath{-}}$. A better understanding of this physical mechanism will help mitigate the spin and charge state depolarization effects that are detrimental for quantum technology applications.

Radical pair intersystem crossing: Quantum dynamics or incoherent kinetics?

Magnetic field effects on radical pair reactions arise due to the interplay of coherent electron spin dynamics and spin relaxation effects, a rigorous treatment of which requires the solution of the Liouville-von Neumann equation. However, it is often found that simple incoherent kinetic models of the radical pair singlet-triplet intersystem crossing provide an acceptable description of experimental measurements. In this paper, we outline the theoretical basis for this incoherent kinetic description, elucidating its connection to exact quantum mechanics. We show, in particular, how the finite lifetime of the radical pair spin states, as well as any additional spin-state dephasing, leads to incoherent intersystem crossing. We arrive at simple expressions for the radical pair spin state interconversion rates to which the functional form proposed recently by Steiner et al. [J. Phys. Chem. C 122, 11701 (2018)] can be regarded as an approximation. We also test the kinetic master equation against exact quantum dynamical simulations for a model radical pair and for a series of PTZ•+-Phn-PDI•- molecular wires.

Cell Reprogramming in Tumorigenesis and Its Therapeutic Implications for Breast Cancer.

Breast cancer is the most common malignancy in women worldwide and can be categorized into several subtypes according to histopathological parameters or genomic signatures. Such heterogeneity of breast cancer can arise from the reactivation of mammary stem cells in situ during tumorigenesis. Moreover, different breast cancer subtypes exhibit varieties of cancer incidence, therapeutic response, and patient prognosis, suggesting that a specific therapeutic protocol is required for each breast cancer subtype. Recent studies using molecular and cellular assays identified a link between specific genetic/epigenetic alterations and distinct cells of origin of breast cancer subtypes. These alterations include oncogenes, tumor suppressor genes, and cell-lineage determinants, which can induce cell reprogramming (dedifferentiation and transdifferentiation) among two lineage-committed mammary epithelial cells, namely basal and luminal cells. The interconversion of cell states through cell reprogramming into the intermediates of mammary stem cells can give rise to heterogeneous breast cancers that complicate effective therapies of breast cancer. A better understanding of mechanisms underlying cell reprogramming in breast cancer can help in not only elucidating tumorigenesis but also developing therapeutics for breast cancer. This review introduces recent findings on cancer gene-mediated cell reprogramming in breast cancer and discusses the therapeutic potential of targeting cell reprogramming.

Distinct regulation of sigma‐1 receptor multimerization by its agonists and antagonists

Since its initial proposal four decades ago, extensive studies have shown that the sigma‐1 receptor (σ1R) interacts with and modulates the activity of multiple proteins with important functions. Recent crystal structures of σ1R as a homo‐trimer differ from a dimer‐tetramer model postulated by early work. Further it is not clear whether ligand binding regulates σ1R multimerization. Here I conducted mutational analyses and examined ligands' effects on σ1R oligomerization using novel non‐denaturing gels. In transfected cells σ1R exhibited as monomer, dimer, and mainly as high‐order multimers. Agonists ((+)pentazocine, (+)SKF10,047, DTG, PRE‐084) decreased, whereas antagonists (BD1008, BD1047, BD1063, haloperidol, NE‐100, progesterone) increased σ1R multimers, suggesting that agonists and antagonists differentially affect the stability of σ1R multimers. Mutations at key residues lining the trimerization interface abolished multimerization but preserved dimerization. Intriguingly, deletion of the transmembrane domain (TM) reduced σ1R to monomer. These results demonstrate that multiple domains play crucial roles in coordinating high‐order quaternary organization of σ1R, which may comprise interconvertible oligomeric states in a dynamic equilibrium. σ1R multimers exhibited high‐affinity and high‐capacity [3H](+)pentazocine binding, whereas monomers lacked binding. In competition binding the antagonist haloperidol appeared to show an apparent 10‐fold higher potency in wild‐type σ1R than in mutants with only dimers, which might explain why haloperidol binding increased σ1R multimers. Further, a σ1R mutant (E102Q) implicated in early‐onset amyotrophic lateral sclerosis exhibited as dimer only, suggesting that dysregulation of σ1R quaternary structure impairs its physiological function. Further exploration of ligand‐regulated σ1R multimerization may provide novel approaches to modulate the function of σ1R and its interacting proteins.Support or Funding InformationButler University Faculty Startup FundThis abstract is from the Experimental Biology 2019 Meeting. There is no full text article associated with this abstract published in The FASEB Journal.

On the classification of two-qubit group orbits and the use of coarse-grained 'shape' as a superselection property

Recently a complete set of entropic conditions has been derived for the interconversion structure of states under quantum operations that respect a specified symmetry action, however the core structure of these conditions is still only partially understood. Here we develop a coarse-grained description with the aim of shedding light on both the structure and the complexity of this general problem. Specifically, we consider the degree to which one can associate a basic `shape' property to a quantum state or channel that captures coarse-grained data either for state interconversion or for the use of a state within a simulation protocol. We provide a complete solution for the two-qubit case under the rotation group, give analysis for the more general case and discuss possible extensions of the approach.

Decomposing NMR Ensemble with the Assistance of Single Molecule FRET

Proteins are inherently dynamic, and the dynamics allow the protein to fulfill specific functions. NMR is exquisitely sensitive to protein dynamics. In particular, paramagnetic relaxation enhancement (PRE) has an <r−6> distance dependence, and has been used to visualize sparsely populated protein conformation(s). However, owing to the averaging of NMR signals over many different copies of protein molecules, it can be difficult to resolve the constituting conformational states that contribute to the observables. Single molecule techniques, on the other hand, can be used to visualize the fluctuation of a single protein molecule over time. Here I will present how the characterization of protein ensemble structures can be made easier and more accurate with the incorporation of single molecule FRET data. The relative populations of the inter-converting conformational states can be obtained from single-molecule measurement, and detailed structural information can be characterized by NMR and other biophysical techniques. Moreover, the calculated ensemble structures of the protein can be verified by the distance information from single molecule FRET. Using both bulk and single-molecule techniques, we have resolved and visualized the ensemble structures of polyubiquitin and other multi-domain/subunit proteins. We envision that such an integrative approach will play an increasingly important role in characterizing the dynamics of biological macromolecules.

Chemical Exchange.

The phenomenon of chemical or conformational exchange in NMR spectroscopy has enabled detailed characterization of time-dependent aspects of biomolecular function, including folding, molecular recognition, allostery, and catalysis, on timescales from microsecond to second. Importantly, NMR methods based on a variety of spin relaxation parameters have been developed that provide quantitative information on interconversion kinetics, thermodynamic properties, and structural features of molecular states populated to a fraction of a percent at equilibrium and otherwise unobservable by other NMR approaches. The ongoing development of more sophisticated experimental techniques and the necessity to apply these methods to larger and more complex molecular systems engenders a corresponding need for theoretical advances describing such techniques and facilitating data analysis in applications. This review surveys current aspects of the theory of chemical exchange, as utilized in ZZ-exchange; Hahn and Carr-Purcell-Meiboom-Gill (CPMG) spin-echo; and R1ρ, chemical exchange saturation transfer (CEST), and dark state saturation transfer (DEST) spin-locking experiments. The review emphasizes theoretical results for kinetic topologies with more than two interconverting states, both to obtain compact analytical forms suitable for data analysis and to establish conditions for distinguishability between alternative kinetic schemes.

Spectroelectrochemical studies of the redox active tris[4-(triazol-1-yl)phenyl]amine linker and redox state manipulation of Mn(ii)/Cu(ii) coordination frameworks.

This work describes the successful incorporation of a redox active linker, tris(4-(1H-1,2,4-triazol-1-yl)phenyl)amine (TTPA) into Mn(ii)/Cu(ii) based coordination frameworks. Solution state in situ spectroelectrochemistry of EPR and UV/Vis/NIR of the TTPA ligand were measured to gain a deeper understanding of the charge delocalization of the triphenylamine backbone. The assignments of the absorption bands for the radical cations in UV/Vis/NIR spectroelectrochemistry were supported by DFT calculations. For Mn(ii)/Cu(ii) based coordination frameworks, solid state electrochemical and in situ spectroelectrochemical methods were applied to elucidate the accessible redox states and the optical properties of the frameworks. The findings provide a basic comprehension of the interconversion of different redox states and how an electroactive framework can be potentially used in applications of electrochromic and optical devices.

Beyond the thermodynamic limit: finite-size corrections to state interconversion rates

Thermodynamics is traditionally constrained to the study of macroscopic systems whose energy fluctuations are negligible compared to their average energy. Here, we push beyond this thermodynamic limit by developing a mathematical framework to rigorously address the problem of thermodynamic transformations of finite-size systems. More formally, we analyse state interconversion under thermal operations and between arbitrary energy-incoherent states. We find precise relations between the optimal rate at which interconversion can take place and the desired infidelity of the final state when the system size is sufficiently large. These so-called second-order asymptotics provide a bridge between the extreme cases of single-shot thermodynamics and the asymptotic limit of infinitely large systems. We illustrate the utility of our results with several examples. We first show how thermodynamic cycles are affected by irreversibility due to finite-size effects. We then provide a precise expression for the gap between the distillable work and work of formation that opens away from the thermodynamic limit. Finally, we explain how the performance of a heat engine gets affected when one of the heat baths it operates between is finite. We find that while perfect work cannot generally be extracted at Carnot efficiency, there are conditions under which these finite-size effects vanish. In deriving our results we also clarify relations between different notions of approximate majorisation.

Monte Carlo Diffusion-Enhanced Photon Inference: Distance Distributions and Conformational Dynamics in Single-Molecule FRET.

Single-molecule Förster resonance energy transfer (smFRET) is utilized to study the structure and dynamics of many biomolecules, such as proteins, DNA, and their various complexes. The structural assessment is based on the well-known Förster relationship between the measured efficiency of energy transfer between a donor (D) and an acceptor (A) dye and the distance between them. Classical smFRET analysis methods called photon distribution analysis (PDA) take into account photon shot-noise, D-A distance distribution, and, more recently, interconversion between states in order to extract accurate distance information. It is known that rapid D-A distance fluctuations on the order of the D lifetime (or shorter) can increase the measured mean FRET efficiency and thus decrease the estimated D-A distance. Nonetheless, this effect has been so far neglected in smFRET experiments, potentially leading to biases in estimated distances. Here we introduce a PDA approach dubbed Monte Carlo diffusion-enhanced photon inference (MC-DEPI). MC-DEPI recolor detected photons of smFRET experiments taking into account dynamics of D-A distance fluctuations, multiple interconverting states, and photoblinking. Using this approach, we show how different underlying conditions may yield identical FRET histograms and how the additional information from fluorescence decays helps in distinguishing between the different conditions. We also introduce a machine learning fitting approach for retrieving the D-A distance distribution, decoupled from the above-mentioned effects. We show that distance interpretation of smFRET experiments of even the simplest dsDNA is nontrivial and requires decoupling the effects of rapid D-A distance fluctuations on FRET in order to avoid systematic biases in the estimation of the D-A distance distribution.

Redox control and autoxidation of class 1, 2 and 3 phytoglobins from Arabidopsis thaliana

Despite a recent increase in interest towards phytoglobins and their importance in plants, much is still unknown regarding their biochemical/biophysical properties and physiological roles. The present study presents data on three recombinant Arabidopsis phytoglobins in terms of their UV-vis and Raman spectroscopic characteristics, redox state control, redox potentials and autoxidation rates. The latter are strongly influenced by pH for all three hemoglobins – (with a fundamental involvement of the distal histidine), as well as by added anion concentrations – suggesting either a process dominated by nucleophilic displacement of superoxide for AtHb2 or an inhibitory effect for AtHb1 and AtHb3. Reducing agents, such as ascorbate and glutathione, are found to either enhance– (presumably via direct electron transfer or via allosteric regulation) or prevent autoxidation. HbFe3+ reduction was possible in the presence of high (presumably not physiologically relevant) concentrations of NADH, glutathione and ascorbate, with differing behaviors for the three globins. The iron coordination sphere is found to affect the autoxidation, redox state interconversion and redox potentials in these three phytoglobins.

Epigenetic and Transcriptomic Profiling of Mammary Gland Development and Tumor Models Disclose Regulators of Cell State Plasticity

Cell state reprogramming during tumor progression complicates accurate diagnosis, compromises therapeutic effectiveness, and fuels metastatic dissemination. We used chromatin accessibility assays and transcriptional profiling during mammary development as an agnostic approach to identify factors that mediate cancer cell state interconversions. We show that fetal and adult basal cells share epigenetic features consistent with multi-lineage differentiation potential. We find that DNA-binding motifs for SOX transcription factors are enriched in chromatin that is accessible in stem/progenitor cells and inaccessible in differentiated cells. In both mouse and human tumors, SOX10 expression correlates with stem/progenitor identity, dedifferentiation, and invasive characteristics. Strikingly, we demonstrate that SOX10 binds to genes that regulate neural crest cell identity, and that SOX10-positive tumor cells exhibit neural crest cell features.

Photophysical Behavior of mNeonGreen, an Evolutionarily Distant Green Fluorescent Protein

Fluorescent proteins (FPs) feature complex photophysical behavior that must be considered when studying the dynamics of fusion proteins in model systems and live cells. In this work, we characterize mNeonGreen (mNG), a recently introduced FP from the bilaterian Branchiostoma lanceolatum, in comparison to the well-known hydrozoan variants enhanced green fluorescent protein (EGFP) and Aequorea coerulescens GFP by steady-state spectroscopy and fluorescence correlation spectroscopy in solutions of different pH. Blind spectral unmixing of sets of absorption spectra reveals three interconverting electronic states of mNG: a nonfluorescent protonated state, a bright state showing bell-shaped pH dependence, and a similarly bright state dominating at high pH. The gradual population of the acidic form by external protonation is reflected by increased flickering at low pH in fluorescence correlation spectroscopy measurements, albeit with much slower flicker rates and lower amplitudes as compared to Aequorea GFPs. In addition, increased flickering of mNG indicates a second deprotonation step above pH 10 leading to a slight decrease in fluorescence. Thus, mNG is distinguished from Aequorea GFPs by a two-step protonation response with opposite effects that reflects a chemically distinct chromophore environment. Despite the more complex pH dependence, mNG represents a superior FP under a broad range of conditions.

Translational control of the undifferentiated phenotype in ER‑positive breast tumor cells: Cytoplasmic localization of ERα and impact of IRES inhibition.

Using a series of potential biomarkers relevant to mechanisms of protein synthesis, we observed that estrogen receptor (ER)-positive breast tumor cells exist in two distinct yet interconvertible phenotypic states (of roughly equal proportion) which differ in the degree of differentiation and use of IRES-mediated translation. Nascently translated IGF1R in the cytoplasm positively correlated with IRES activity and the undifferentiated phenotype, while epitope accessibility of RACK1, an integral component of the 40S ribosomal subunit, aligned with the more differentiated IRES-off state. When deprived of soluble growth factors, the entire tumor cell population shifted to the undifferentiated phenotype in which IRES-mediated translation was active, facilitating survival under these adverse microenvironmental conditions. However, if IRES-mediated translation was inhibited, the cells instead were forced to transition uniformly to the more differentiated state. Notably, cytoplasmic localization of estrogen receptor α (ERα/ESR1) precisely mirrored the pattern observed with nascent IGF1R, correlating with the undifferentiated IRES-active phenotype. Inhibition of IRES-mediated translation resulted in both a shift in ERα to the nucleus (consistent with differentiation) and a marked decrease in ERα abundance (consistent with the inhibition of ERα synthesis via its IRES). Although breast tumor cells tolerated forced differentiation without extensive loss of their viability, their reproductive capacity was severely compromised. In addition, CDK1 was decreased, connexin 43 eliminated and Myc translation altered as a consequence of IRES inhibition. Isolated or low-density ER-positive breast tumor cells were particularly vulnerable to IRES inhibition, losing the ability to generate viable cohesive colonies, or undergoing massive cell death. Collectively, these results provide further evidence for the integral relationship between IRES-mediated translation and the undifferentiated phenotype and demonstrate how therapeutic manipulation of this specialized mode of protein synthesis may be used to limit the phenotypic plasticity and incapacitate or eliminate these otherwise highly resilient breast tumor cells.

Two distinct conformational states define the interaction of human RAD51‐ATP with single‐stranded DNA

An essential mechanism for repairing DNA double‐strand breaks is homologous recombination (HR). One of its core catalysts is human RAD51 (hRAD51), which assembles as a helical nucleoprotein filament on single‐stranded DNA, promoting DNA‐strand exchange. Here, we study the interaction of hRAD51 with single‐stranded DNA using a single‐molecule approach. We show that ATP‐bound hRAD51 filaments can exist in two different states with different contour lengths and with a free‐energy difference of ~4 kBT per hRAD51 monomer. Upon ATP hydrolysis, the filaments convert into a disassembly‐competent ADP‐bound configuration. In agreement with the single‐molecule analysis, we demonstrate the presence of two distinct protomer interfaces in the crystal structure of a hRAD51‐ATP filament, providing a structural basis for the two conformational states of the filament. Together, our findings provide evidence that hRAD51‐ATP filaments can exist in two interconvertible conformational states, which might be functionally relevant for DNA homology recognition and strand exchange.

Identification of GPCR Transition Pathways using Go Models

One caveat of standard all-atom molecular dynamics (MD) simulations is that they are resource-intensive, particularly when inspecting state transition pathways. To date, the timescales involved in processes such as G protein-coupled receptor (GPCR) activation make it largely impossible to study them using standard all-atom MD under equilibrium conditions. Indeed, the nature of their activation/deactivation pathway(s) is not yet fully characterized. To overcome this issue, our group previously showed that simpler structure-based (Go-like) potentials could be used to study GPCR state transitions, yielding results in qualitative agreement with those obtained from standard all-atom simulations but with negligible computational cost. These potentials are energetically smooth by design with few non-native traps and a single global energy minimum corresponding to the end-point of the transition of interest. In the case of rhodopsin, a prototypical GPCR, two distinct but reproducible pathways were observed to be populated during activation and deactivation. While it is possible that a separation of pathways is mechanistically required for function, it could also be the result of simulating state transitions occurring in two separate energy surfaces out of equilibrium (one for activation and one for deactivation). To address this potential source of error, we implemented a strategy for modeling Go-like energy landscapes with multiple energy minima at all-heavy atom resolution. This approach allows the study of state interconversion in equilibrium and extensive sampling, still at a low computational cost. Moreover, it can also be used for quick hypothesis testing, to characterize the effects of different ligands, model point mutations, study substate fluctuations and guide all-atom simulations by quickly generating reasonable reaction coordinates. As long as the end states are known, this strategy can be extrapolated to almost any biomolecular system in a straight forward manner, complementing current standard all-atom MD approaches.

Probing Conformational Exchange in Weakly Interacting, Slowly Exchanging Protein Systems via Off-Resonance R1ρ Experiments: Application to Studies of Protein Phase Separation.

R1ρ relaxation dispersion experiments are increasingly used in studies of protein dynamics on the micro- to millisecond time scale. Traditional R1ρ relaxation dispersion approaches are typically predicated on changes in chemical shifts between corresponding probe spins, ΔωGE, in the interconverting states. Here, we present a new application of off-resonance 15N R1ρ relaxation dispersion that enables the quantification of slow exchange processes even in the limit where ΔωGE = 0 so long as the spins in the exchanging states have different intrinsic transverse relaxation rates (ΔR2 = R2,E - R2,G ≠ 0). In this limit, the dispersion profiles become inverted relative to those measured in the case where ΔωGE ≠ 0, ΔR2 = 0. The theoretical background to understand this effect is presented, along with a simplified exchange matrix that is valid in the limits that are germane here. An application to the study of the dynamics of the germ granule protein Ddx4 in a highly concentrated phase-separated state is described. Notably, exchange-based dispersion profiles can be obtained despite the fact that ΔωGE ≈ 0 and ΔR2 is small, ∼20-30 s-1. Our results are consistent with the formation of a significantly populated excited conformational state that displays increased contacts between adjacent protein molecules relative to the major conformer in solution, leading to a decrease in overall motion of the protein backbone. A complete set of exchange parameters is obtained from analysis of a single set of 15N off-resonance R1ρ measurements recorded at a single static magnetic field and with a single spin-lock radio frequency field strength. This new approach holds promise for studies of weakly interacting systems, especially those involving intrinsically disordered proteins that form phase-separated organelles, where little change to chemical shifts between interconverting states would be expected, but where finite ΔR2 values are observed.