Two-state Model Research Articles

A Closed-Form Expression for Analysis of Dark State Exchange Saturation Transfer (DEST) NMR Experiments.

Closed-form expressions for the analysis of Dark state Exchange Saturation Transfer (DEST) NMR experiments, a powerful experimental tool for characterizing exchange processes involving the interaction of NMR visible species with very high molecular weight partners, is presented. Essentially identical exchange and relaxation parameters are derived from the analytical and numerical best fits of the DEST profiles obtained for a protein construct derived from huntingtin exon-1, comprising the N-terminal amphiphilic sequence followed by a seven-residue glutamine repeat, httNTQ7, in the presence of small (SUV) and large (LUV) unilamellar lipid vesicles. The use of analytical expressions significantly speeds up the fitting of experimental DEST profiles to a two-state exchange model and simplifies the analysis of the DEST effects.

Qubit analog with polariton superfluid in an annular trap.

We report on the experimental realization and characterization of a qubit analog with semiconductor exciton-polaritons. In our system, a polaritonic condensate is confined by a spatially patterned pump laser in an annular trap that supports energy-degenerate vortex states of the polariton superfluid. Using temporal interference measurements, we observe coherent oscillations between a pair of counter-circulating vortex states coupled by elastic scattering of polaritons off the laser-imprinted potential. The qubit basis states correspond to the symmetric and antisymmetric superpositions of the two vortex states. By engineering the potential, we tune the coupling and coherent oscillations between the two circulating current states, control the energies of the qubit basis states, and initialize the qubit in the desired state. The dynamics of the system is accurately reproduced by our theoretical two-state model, and we discuss potential avenues to implement quantum gates and algorithms with polaritonic qubits analogous to quantum computation with standard qubits.

Universal Health Coverage of Opioid Agonist Treatment in Norway: An Equity-Adjusted Economic Evaluation.

Detailed information on the efficiency of health services targeting opioid use disorder (OUD) and treatment with opioid agonist treatment (OAT) is sparse. Many countries, including Norway, are still falling short of universal health coverage (UHC) of OAT. This study aims to evaluate the incremental lifetime costs and effects of treating OUD with OAT as compared to no OAT in Norway and scaling up the treatment to a universal coverage level using equity-adjusted health economic evaluations. We conducted cost-utility and budget impact analyses and constructed a two-state Markov model to compare the lifetime costs and outcomes among patients with OUD with and without OAT. Model inputs were derived from routine health information systems and the literature, with costs reported in 2023 Norwegian Kroner (NOK). The analyses were conducted from a Norwegian extended health-service and societal perspectives, with a lifetime time horizon. Quality-adjusted life years (QALYs) was the metric of health benefits. Outcomes were reported as incremental cost-effectiveness ratios (ICERs). The willingness-to-pay (WTP) threshold was equity-adjusted according to the future prognostic healthy life year loss method in Norway (severity of disease criterion), which is sensitive to the size of future undiscounted healthy life year loss due to the affected conditions. The WTP threshold is NOK 825,000 per QALY gained in Norwegian policy for conditions with undiscounted future QALY loss > 20. Uncertainty in the parameters and robustness of the results were assessed with one-way and probabilistic sensitivity analyses and scenario analyses. The mean results from probabilistic sensitivity analysis estimated that OAT was associated with 3.03 additional discounted QALYs gain and incremental lifetime discounted cost of NOK 1.45 million, leading to an ICER of NOK 479,099 per QALY gained when compared with not providing OAT, with the extended health-service perspective. From a societal perspective, OAT was cost-saving, i.e. OAT produced greater health benefits while resulting in lower overall societal costs compared to no OAT. The mean undiscounted future health loss was estimated to be 21.34 QALYs for the Norwegian patient group with OUD. A total 5-year budget increase of NOK 1.208 billion was estimated if OAT was going to be scaled up from the current coverage level of 70% to UHC. Compared with the current coverage, 100% coverage of OAT was associated with an additional lifetime cost of NOK 4.332 billion but also an additional 6760 QALYs gained. Our analysis suggests that OAT is cost-effective in Norway and has the potential to be cost-saving from a societal perspective. Therefore, Norwegian policy should consider scaling up treatment to extend the coverage of OAT.

Within Thermal Scales: The Kinetic and Energetic Pull of Chemical Entropy.

Biological systems are fundamentally containers of thermally fluctuating atoms that through unknown mechanisms are structurally layered across many thermal scales from atoms to amino acids to primary, secondary, and tertiary structures to functional proteins to functional macromolecular assemblies and up. Understanding how the irreversible kinetics (i.e., the arrow of time) of biological systems emerge from the equilibrium kinetics of constituent structures defined on smaller thermal scales is central to describing biological function. Muscle's irreversible power stroke - with its mechanochemistry defined on both the thermal scale of muscle and the thermal scale of myosin motors - provides a clear solution to this problem. Individual myosin motors function as reversible force-generating switches induced by actin binding and gated by the release of inorganic phosphate, P i . As shown in a companion article, when N individual switches thermally scale up to an ensemble of N switches in muscle, the entropy of a binary system of switches is created. We have shown in muscle that a change in state of this binary system of switches entropically drives actin-myosin binding (the switch) and muscle's irreversible power stroke, and that this simple two-state model accurately accounts for most key aspects of muscle contraction. Extending this observation beyond muscle, here I show that the chemical kinetics of an ensemble of N molecules differs fundamentally from a conventional chemical analysis of N individual molecules, describing irreversible chemical reactions as being pulled into the future by the a priori defined entropy of a binary system rather than being pushed forward by the physical occupancy of chemical states (e.g., mass action).

Molecular Dynamics Unveils Multiple-Site Binding of Inhibitors with Reduced Activity on the Surface of Dihydrofolate Reductase.

The sensitivity to protein inhibitors is altered by modifications or protein mutations, as represented by drug resistance. The mode of stable drug binding to the protein pocket has been experimentally clarified. However, the nature of the binding of inhibitors with reduced sensitivity remains unclear at the atomic level. In this study, we analyzed the thermodynamics and kinetics of inhibitor binding to the surface of wild-type and mutant dihydrofolate reductase (DHFR) using molecular dynamics simulations combined with Markov state modeling. A strong inhibitor of methotrexate (MTX) showed a preference for the active site of wild-type DHFR with minimal binding to unrelated (secondary) sites. Deletion of a side-chain fragment in MTX largely destabilized the active site-bound state, with clear evidence of binding to secondary sites. Similarly, the F31V mutation in DHFR diminished the specificity of MTX binding to the active site. These results reveal the presence of multiple-bound states whose stabilities are comparable to or higher than those of the unbound state, suggesting that a reduction in the binding affinity for the active site significantly elevates the fractions of these states. This study presents a theoretical model that more accurately interprets the altered drug sensitivity than the traditional two-state model.

Two-state free-volume model for anomalous dynamics in supercooled water macromolecules undergoing liquid–liquid phase transition

Modelling anomalous dynamics of complex liquid water is a huge challenge due to its various condensed molecular structures and the associated liquid–liquid phase transitions (LLPTs). In this study, we considered, for the first time, the influences of free volume and entropy on LLPTs for both low-density liquid (LDL) and high-density liquid (HDL) waters. Firstly, we proposed a two-state free-volume model and combined with the Adam-Gibbs models to investigate the dynamic equilibria with free diffusion coefficient, viscosity, glass transition temperature and the anomalous dynamics in the two-state water. Free-energy equation was then developed to explore the constitutive relationships of free volume, entropy and anomalously dynamic behaviors. Finally, analytical results of the proposed two-state free-volume model were compared with the experimental data of two-state water reported in literature, and good agreements between them were demonstrated. This study offers a new physical insight into free volume for the anomalous dynamics and LLPTs in the two-state water.

Carbon Taxation and Electricity Price Dynamics: Empirical Evidence from the Australian Market

AbstractIn this paper, we study the change of Australian electricity price dynamics that was observed before, during and after the two-year period in which a Carbon Pricing Mechanism was in force. We fit a two-states Markov Switching Model, representing a high- and a low-volatility state of the world. To avoid the interference due to periodic patterns, a deseasonalization process accounting for short- and long-term seasonality is carried out prior to the study of volatility. Estimation results highlight that, during the period when the carbon tax applies, the volatility level is lower for both the states of the world. Furthermore, the persistence in the low-volatility state is increased in the presence of the carbon tax. This conclusion is particularly relevant for macroeconomic and investment considerations because the increased uncertainty in electricity prices can significantly influence firms’ investment decisions and shape inflation expectations.

End-to-end synaptic molecular communication with astrocytic feedback and generic three-state receptors

This paper investigates the mutual information of synaptic molecular communications using a realistic end-to-end synaptic model. In particular, we have considered the influence of astrocytes on neural signaling within the synaptic molecular communication. We have evaluated the average mutual information of the resultant tripartite synapse while considering realistic synaptic geometry that accounts for neurotransmitter reflections from the pre-synaptic and post-synaptic boundaries. The clearance of neurotransmitters from the synapse through diffusion and re-absorption by pre-synaptic terminal is also considered in the simulated model. Moreover, we have used a generic three-state model for postsynaptic receptors to include desensitization state of the receptors. The presented simulation results depict the effects of different pre-synaptic and post-synaptic parameters on the information transfer for a tripartite synaptic channel with three-state receptor model, which is more realistic than the commonly-used bipartite synaptic channel with the two-state receptor model.

Mpsqd: A matrix product state based Python package to simulate closed and open system quantum dynamics.

We introduce a Python package based on matrix product states (MPS) to simulate both the time-dependent Schrödinger equation (TDSE) and the hierarchical equations of motion (HEOM). The wave function in the TDSE or the reduced density operator/auxiliary density operators in the HEOM are represented using MPS. A matrix product operator (MPO) is then constructed to represent the Hamiltonian in the TDSE or the generalized Liouvillian in the HEOM. The fourth-order Runge-Kutta method and the time-dependent variational principle are used to propagate the MPS. Several examples, including the nonadiabatic interconversion dynamics of the pyrazine molecule, excitation energy transfer dynamics in molecular aggregates and photosynthetic light-harvesting complexes, the spin-boson model, a laser driven two-state model, the Holstein model, and charge transport in the Anderson impurity model, are presented to demonstrate the capability of the package.

Effect of Market-Wide Investor Sentiment on South African Government Bond Indices of Varying Maturities under Changing Market Conditions

The excess levels of investor participation coupled with irrational behaviour in the South African bond market causes excess volatility, which in turn exposes investors to losses. Consequently, the study aims to examine the effect of market-wide investor sentiment on government bond index returns of varying maturities under changing market conditions. This study constructs a new market-wide investor sentiment index for South Africa and uses the two-state Markov regime-switching model for the sample period 2007/03 to 2024/01. The findings illustrate that the effect investor sentiment has on government bond indices returns of varying maturities is regime-specific and time-varying. For instance, the 1–3-year government index return and the over-12-year government bond index were negatively affected by investor sentiment in a bull market condition and not in a bear market condition. Moreover, the bullish market condition prevailed among the returns of selected government bond indices of varying maturities. The findings suggest that the government bond market is adaptive, as proposed by AMH, and contains alternating efficiencies. The study contributes to the emerging market literature, which is limited. That being said, it uses market-wide investor sentiment as a tool to make pronunciations on asset selection, portfolio formulation, and portfolio diversification, which assists in limiting investor losses. Moreover, the findings of the study contribute to settling the debate surrounding the efficiency of bond markets and the effect between market-wide sentiment and bond index returns in South Africa. That being said, it is nonlinear, which is a better modelled using nonlinear models and alternates with market conditions, making the government bond market adaptive.

A Third Generation Calphad Description of Pure Lithium.

This study, based on the analysis of existing experimental data, presents a third generation Calphad description of lithium, covering all temperature ranges, using nonlinear least squares in Matlab. We have expanded the SGTE database's description of lithium phases (face-centered cube, body-centered cube, liquid) down to 0 K with reasonable accuracy, taking into account the significant effort required to reconstruct the database for each element. During the evaluation process, it was determined that the low-temperature phase of lithium is fcc. The heat capacity of crystalline Li was accurately described using the extended Debye model. The third generation Calphad description of lithium utilized the two-state model and the extended Einstein model, leading to improved agreement with experimental data compared to previous assessments.

Cellular automaton model for the analysis of design and plan of bus station in the mixed traffic environment

With the quick development of Connected Autonomous Vehicles (CAVs), CAVs would gradually become an important part of urban traffic. Hence, the impacts of CAVs on urban traffic should be further explored. This study aims to analyze the mixed traffic comprising CAVs and human-driven vehicles (HDVs) in different urban scenarios in which different bus station types (i.e., roadside and bay bus stations) and capacities are considered. To do this analysis, this study proposes a cellular automaton model which simulates car following behaviours of vehicles using a two-state safe speed model, and designs specific modeling rules for lane-changing behaviours and vehicle behaviours near bus stations with consideration of the differences between CAVs and HDVs. The analysis results indicate that the impacts of various bus station types and capacities on the mixed traffic flow vary with traffic volumes, while increasing the CAV penetration rate can reduce the traffic congestion caused by bus stop-and-go. Furthermore, the study explores the optimal number of bus routes for different types of bus stations in different urban traffic scenarios, and several possible policy implications have been given according to the analysis results.

Understanding molecular geometric phase effects with exact effective force: case study of a model system

In this work, molecular geometric phase effects are studied using the idea of exact factorization (EF) (Abediet al2010Phys. Rev. Lett.105123002) and exact effective force (Liet al2022Phys. Rev. Lett.128113001). In particular, we performed dynamics simulations for a two-state vibronic coupling model, and interpreted the results in three different perspectives: the Born-Huang expansion, the exact time-dependent potential energy surface (TDPES) and the exact effective force. We find that (i) at particular moment, while the vanishing nuclear density that occurs periodically in space is conventionally attributed to destructive interference of the nuclear wave packet owing to the geometric phase, such phenomenon can be equally well interpreted through the energy perspective, as manifested in the exact TDPES in the EF scheme; (ii) when combined with trajectory-based classical dynamics, the exact effective force obtained through EF qualitatively reproduces the correct nuclear density, while the adiabatic force gives the wrong density, particularly in the interference region. Our results suggest that the exact effective force is a potential starting point for making approximations and improving trajectory-based computational methods towards an accurate description of geometric phase effects.

Modeling relaxation experiments with a mechanistic model of gene expression

BackgroundIn the present work, we aimed at modeling a relaxation experiment which consists in selecting a subfraction of a cell population and observing the speed at which the entire initial distribution for a given marker is reconstituted.MethodsFor this we first proposed a modification of a previously published mechanistic two-state model of gene expression to which we added a state-dependent proliferation term. This results in a system of two partial differential equations. Under the assumption of a linear dependence of the proliferation rate with respect to the marker level, we could derive the asymptotic profile of the solutions of this model.ResultsIn order to confront our model with experimental data, we generated a relaxation experiment of the CD34 antigen on the surface of TF1-BA cells, starting either from the highest or the lowest CD34 expression levels. We observed in both cases that after approximately 25 days the distribution of CD34 returns to its initial stationary state. Numerical simulations, based on parameter values estimated from the dataset, have shown that the model solutions closely align with the experimental data from the relaxation experiments.ConclusionAltogether our results strongly support the notion that cells should be seen and modeled as probabilistic dynamical systems.

Metformin-Induced Invertase Unfolding: Enzyme Kinetics and Activity Regulation.

The effects of metformin on invertase activity and its inhibition on sucrose digestion were studied. The rapid unfolding kinetics of invertases, followed a two-state model with an inactive intermediate formation. The dynamic interaction between metformin and invertase caused the secondary structure of the enzyme to become less β-sheet, more α-helix, and random coiling oriented, which weakened the binding force between enzyme and its substrate. Metformin acted as a chaotrope and disrupted the hydrogen bonds of water, which facilitated the unfolding of invertase. However, some sugar alcohols, which promoted the H-bond formation of water, could repair the secondary structure of metformin-denatured invertase and therefore regulate the enzyme activity. This research enriches our understanding of the mechanism of enzyme unfolding induced by guanidine compounds. Moreover, because metformin and sugar substitutes are of concern to diabetes, this research also provides useful information for understanding the activity of the digestive enzyme that coexists with metformin and sugar alcohols.

Analysis of the dynamics of transition from non-colonization to colonization and Staphylococcus aureus bacteremia in hemodialysis patients using Markov models.

Background Hemodialysis patients are frequently colonized by Staphylococcus aureus, leading to severe infections with high mortality rates. However, little is known about transition from non-colonization to colonization or bacteremia over time. The aim was to analyze the behavior of S. aureus colonization, identifying the probability of transition from non-colonized to colonized state or bacteremia, and the influence of some covariates. Methods The study was conducted in a dialysis unit associated with a high complexity hospital in Medellín between October 2017 and October 2019. An initial measurement was taken to evaluate S. aureus colonization, and follow-up measurements were performed 2 and 6 months later. Bacteremia evolution was monitored for 12 months. A two-state recurrent continuous-time Markov model was constructed to model transition dynamics from non-colonization to S. aureus colonization in hemodialysis patients. Subsequently, the model was applied to a third state of bacteremia. Results Of 178 patients on hemodialysis, 30.3% were colonized by S. aureus. Transition intensity from non-colonization to colonization was three times higher (0.21; CI: 0.14-0.29) than from colonization to non-colonization (0.07; CI: 0.05-0.11). The colonization risk increased in patients with previous infections (HR: 2.28; CI: 0.78-6.68), hospitalization (HR: 1.29; CI: 0.56-2.99) and antibiotics consumption (HR: 1.17; CI: 0.53-2.58). Mean non-colonized state duration was 10.9 months, while in the colonized state was 5.2 months. In the 3-state model, it was found that patients colonized were more likely to develop S. aureus infection (13.9%). Conclusion A more likely transition from non-colonization to colonization was found, which increases with factors such as previous infection. In addition, the development of bacteremia was more likely in colonized than in non-colonized patients. These results underline the importance of surveillance and proper management of S. aureus colonization to prevent serious complications, such as bacteremia, and improve prognosis in this vulnerable population.

A constrained price-based demand response framework employing utility functions in three-state Overlapping Generation and Gift and Bequest based model in distribution system

Demand response provides an opportunity for consumers to play a significant role in the operation of the electric grid by reducing or shifting their electricity usage during peak periods in response to time-based rates or other forms of financial incentives. These programs are important as they have the potential to help electricity providers save money through reductions in peak demand and the ability to defer construction of new power plants and power delivery systems specifically, those reserved for use during peak times. For the successful application of DR in day-to-day life, DR models are necessary to be implemented. Many of the existing DR models primarily focus on the formulation of after-DR demand based on price elasticity. Though these models are devoid of basic humans’ micro-economic behavior, which is an essential part of a DR stakeholder. Considering these shortcomings of the existing DR literature, this paper envisages formulating DR models based on the foundation of basic humans’ manifestations of demand flexibility, willingness, load recovery, and altruistic behavior. Hence, this paper proposes two price-based DR models known as the three-state Overlapping Generation (OLG) model and the Gift and Bequest (G&B) based DR model. These models are based on customers’ microeconomic behaviors and are suitable for representing load recovery with minimal parameters. Both three-state OLG and G&B-based DR models are examined on IEEE 33-bus and 118-bus distribution systems and are compared with the existing price-elasticity model (PEM) and two-state OLG-based DR model.

Understanding Nonlinear Optical Phenomena in N-Pyrimidinyl Stilbazolium Crystals via a Self-Consistent Electrostatic Embedding - DFT Approach.

Density functional theory (DFT) and time-dependent density functional theory (TD-DFT) have been used to investigate the nonlinear optical (NLO) properties of phenolic N-pyrimidinyl stilbazolium cationic chromophore in its corresponding noncentrosymmetric crystals. Such a cationic chromophore, the OPR (4-(4-hydroxystyryl)-1-(pyrimidin-2-yl)pyridinium), consists of a strong electron donor, the 4-hydroxyphenyl group, and a strong electron acceptor, the N-pyrimidinylpyridinium group based on two electron-withdrawing groups. The in-crystal NLO properties were determined by applying a supermolecule approach in combination with an iterative electrostatic scheme, in which the surrounding molecules of a unit cell are represented by point charges. With CAM-B3LYP, our absolute estimates for the largest diagonal component of the second-order nonlinear susceptibility tensor of OPR-based crystals range from 64.00 to 80.34 pm/V in the static regime and from 162.09 to 175.52 pm/V at 1907 nm. These values are significant when compared to those of benchmark stilbazolium-based crystals. Furthermore, the third-order susceptibility, which is related to the nonlinear optical process of the intensity-dependent refractive index, is also significant compared to the results for other organic crystals, such as chalcone derivatives. With TD-CAM-B3LYP, the two-state model effectively explains the similarity in the first hyperpolarizability values in the crystalline phase. This similarity arises from the combination of the oscillator strength and the charge transfer of the crucial transition. Therefore, phenolic organic salt crystals show great promise for various nonlinear optical applications.

Suppressed electric quadrupole collectivity in 49Ti

Single-step Coulomb excitation of 46,48,49,50Ti is presented. A complete set of E2 matrix elements for the quintuplet of states in 49Ti, centred on the 2+ core excitation, was measured for the first time. A total of nine E2 matrix elements are reported, four of which were previously unknown. 2249Ti27 shows a 20% quenching in electric quadrupole transition strength as compared to its semi-magic 2250Ti28 neighbour. This 20% quenching, while empirically unprecedented, can be explained with a remarkably simple two-state mixing model, which is also consistent with other ground-state properties such as the magnetic dipole moment and electric quadrupole moment. A connection to nucleon transfer data and the quenching of single-particle strength is also demonstrated. The simplicity of the 49Ti-50Ti pair (i.e., approximate single-j0f7/2 valence space and isolation of yrast states from non-yrast states) provides a unique opportunity to disentangle otherwise competing effects in the ground-state properties of atomic nuclei, the emergence of collectivity, and the role of proton-neutron interactions.

Tradeoffs in the design of RNA thermometers

The synthesis of RNA thermometers is aimed at achieving temperature responses with desired thresholds and sensitivities. Although previous works have generated thermometers with a variety of thresholds and sensitivities as well as guidelines for design, possible constraints in the achievable thresholds and sensitivities remain unclear. We addressed this issue using a two-state model and its variants, as well as melt profiles generated from thermodynamic computations. In the two-state model, we found that the threshold was inversely proportional to the sensitivity, in the case of a fixed energy difference between the two states. Notably, this constraint could persist in variations of the two-state model with sequentially unfolding states and branched parallel pathways. Furthermore, the melt profiles generated from a library of thermometers exhibited a similar constraint. These results should inform the design of RNA thermometers as well as other responses that are mediated in a similar fashion.