Simple Two-state Research Articles

Analyzing paramagnetic NMR data on target DNA search by proteins using a discrete-state kinetic model for translocation.

Before reaching their targets, sequence-specific DNA-binding proteins nonspecifically bind to DNA through electrostatic interactions and stochastically change their locations on DNA. Investigations into the dynamics of DNA-scanning by proteins are nontrivial due to the simultaneous presence of multiple translocation mechanisms and many sites for the protein to nonspecifically bind to DNA. Nuclear magnetic resonance (NMR) spectroscopy can provide information about the target DNA search processes at an atomic level. Paramagnetic relaxation enhancement (PRE) is particularly useful to study how the proteins scan DNA in the search process. Previously, relatively simple two-state or three-state exchange models were used to explain PRE data reflecting the target search process. In this work, using more realistic discrete-state stochastic kinetics models embedded into an NMR master equation, we analyzed the PRE data for the HoxD9 homeodomain interacting with DNA. The kinetic models that incorporate sliding, dissociation, association, and intersegment transfer can reproduce the PRE profiles observed at some different ionic strengths. The analysis confirms the previous interpretation of the PRE data and shows that the protein's probability distribution among nonspecific sites is nonuniform during the target DNA search process.

Allostery and protein plasticity: the keystones for bacterial signaling and regulation.

Bacteria sense intracellular and environmental signals using an array of proteins as antennas. The information is transmitted from such sensory modules to other protein domains that act as output effectors. Sensor and effector can be part of the same polypeptide or instead be separate diffusible proteins that interact specifically. The output effector modules regulate physiologic responses, allowing the cells to adapt to the varying conditions. These biological machineries are known as signal transduction systems (STSs). Despite the captivating architectural diversity exhibited by STS proteins, a universal feature is their allosteric regulation: signal binding at one site modifies the activity at a physically distant site. Allostery requires protein plasticity, precisely encoded within their 3D structures, and implicating programmed molecular motions. This review summarizes how STS proteins connect stimuli to specific responses by exploiting allostery and protein plasticity. Illustrative examples spanning a wide variety of protein folds will focus on one- and two-component systems (TCSs). The former encompass the entire transmission route within a single polypeptide, whereas TCSs have evolved as separate diffusible proteins that interact specifically, sometimes including additional intermediary proteins in the pathway. Irrespective of their structural diversity, STS proteins are able to modulate their own molecular motions, which can be relatively slow, rigid-body movements, all the way to fast fluctuations in the form of macromolecular flexibility, thus spanning a continuous protein dynamics spectrum. In sum, STSs rely on allostery to steer information transmission, going from simple two-state switching to rich multi-state conformational order/disorder transitions.

Possible Mechanism for Effects Caused by Exposure to Extremely Low Frequency Magnetic Fields

This paper introduces a possible mechanism to explain the changes in neurons following extremely low frequency magnetic fields (ELF-MFs). The model in this paper contains two parts: the physical part and the bio-trigger part. The first part is an electric current equation, which is a generalization of the Nernst–Plank equation with the exposure of ELF-MF, and the second bio-part is a phenomenological model, which is a simple two-state channel with two steady state open (O) state and closed state (C). The two parts are complementary. The first part is utilized to explain changes about synaptic plasticity following ELF-MF exposure at embryonic and postnatal age. The second part is used to simulate the process of three different types of neurons reported by previous papers. According to the results, the present model is feasible for the simulation process. The concept of ion mobility or permeability is emphasized in this paper in part I, and channel state transition probabilities are paid much attention to in part II. In this paper, the ion mobility or permeability is supposed to have close relationships with ion channel transition probabilities, which connects the two parts of the model together.

Information Theory and the IrisCode

Iris recognition has legendary resistance to false matches, and the tools of information theory can help to explain why. The concept of entropy is fundamental to understanding biometric collision avoidance. This paper analyses the bit sequences of IrisCodes computed both from real iris images and from synthetic white noise iris images, whose pixel values are random and uncorrelated. The capacity of the IrisCode as a channel is found to be 0.566 bits per bit encoded, of which 0.469 bits of entropy per bit is encoded from natural iris images. The difference between these two rates reflects the existence of anatomical correlations within a natural iris, and the remaining gap from one full bit of entropy per bit encoded reflects the correlations in both phase and amplitude introduced by the Gabor wavelets underlying the IrisCode. A simple two-state hidden Markov model is shown to emulate exactly the statistics of bit sequences generated both from natural and white noise iris images, including their imposter distributions, and may be useful for generating large synthetic IrisCode databases.

Novel space-time trellis codes for free-space optical communications using transmit laser selection.

In this paper, the deployment of novel space-time trellis codes (STTCs) with transmit laser selection (TLS) for free-space optical (FSO) communication systems using intensity modulation and direct detection (IM/DD) over atmospheric turbulence and misalignment fading channels is presented. Combining TLS and STTC with rate 1 bit/(s · Hz), a new code design criterion based on the use of the largest order statistics is here proposed for multiple-input/single-output (MISO) FSO systems in order to improve the diversity order gain by properly chosing the transmit lasers out of the available L lasers. Based on a pairwise error probability (PEP) analysis, closed-form asymptotic bit error-rate (BER) expressions in the range from low to high signal-to-noise ratio (SNR) are derived when the irradiance of the transmitted optical beam is susceptible to moderate-to-strong turbulence conditions, following a gamma-gamma (GG) distribution, and pointing error effects, following a misalignment fading model where the effect of beam width, detector size and jitter variance is considered. Obtained results show diversity orders of 2L and 3L when simple two-state and four-state STTCs are considered, respectively. Simulation results are further demonstrated to confirm the analytical results.

Informational and Causal Architecture of Discrete-Time Renewal Processes

Renewal processes are broadly used to model stochastic behavior consisting of isolated events separated by periods of quiescence, whose durations are specified by a given probability law. Here, we identify the minimal sufficient statistic for their prediction (the set of causal states), calculate the historical memory capacity required to store those states (statistical complexity), delineate what information is predictable (excess entropy), and decompose the entropy of a single measurement into that shared with the past, future, or both. The causal state equivalence relation defines a new subclass of renewal processes with a finite number of causal states despite having an unbounded interevent count distribution. We use the resulting formulae to analyze the output of the parametrized Simple Nonunifilar Source, generated by a simple two-state hidden Markov model, but with an infinite-state machine presentation. All in all, the results lay the groundwork for analyzing more complex processes with infinite statistical complexity and infinite excess entropy.

Effects of configuration mixing in heavy-ion elastic scattering

A theoretical study of the influence of configuration mixing on elastic scattering cross section is performed for the system 16O + 27Al at 100 MeV. A simple twostate model space, including the 27Al 5/2+ ground and 5/2+ excited state at 2.73 MeV, is used in the coupled channel equations. The results indicate that even a weak degree of mixing is able to sizeably affect the elastic cross section, determining mainly a damping of Fraunhofer oscillations, as observed in the experiments.

The H/D-Exchange Kinetics of the Escherichia coli Co-Chaperonin GroES Studied by 2D NMR and DMSO-Quenched Exchange Methods

We studied hydrogen/deuterium-exchange reactions of peptide amide protons of GroES using two different techniques: (1) two-dimensional 1H–15N transverse-optimized NMR spectroscopy and (2) the dimethylsulfoxide-quenched hydrogen-exchange method combined with conventional 1H–15N heteronuclear single quantum coherence spectroscopy. By using these techniques together with direct heteronuclear single quantum coherence experiments, we quantitatively evaluated the exchange rates for 33 out of the 94 peptide amide protons of GroES and their protection factors, and for the remaining 61 residues, we obtained the lower limits of the exchange rates. The protection factors of the most highly protected amide protons were on the order of 106–107, and the values were comparable in magnitude to those observed in typical small globular proteins, but the number of the highly protected amide protons with a protection factor larger than 106 was only 10, significantly smaller than the numbers reported for the small globular proteins, indicating that significant portions of free heptameric GroES are flexible and natively unfolded. The highly protected amino acid residues with a protection factor larger than 105 were mainly located in three β-strands that form the hydrophobic core of GroES, while the residues in a mobile loop (residues 17–34) were not highly protected. The protection factors of the most highly protected amide protons were orders of magnitude larger than the value expected from the equilibrium unfolding parameters previously reported, strongly suggesting that the equilibrium unfolding of GroES is more complicated than a simple two-state or three-state mechanism and may involve more than a single intermediate.

Triaspartate: A Model System for Conformationally Flexible DDD Motifs in Proteins

Understanding the interactions that govern turn formation in the unfolded state of proteins is necessary for a complete picture of the role that these turns play in both normal protein folding and functionally relevant yet disordered linear motifs. It is still unclear, however, whether short peptides can adopt stable turn structures in aqueous environments in the absence of any nonlocal interactions. To explore the effect that nearest-neighbor interactions and the local peptide environment have on the turn-forming capability of individual amino acid residues in short peptides, we combined vibrational (IR, Raman, and VCD), UV-CD, and (1)H NMR spectroscopies in order to probe the conformational ensemble of the central aspartic acid residue of the triaspartate peptide (DDD). The study was motivated by the recently discovered turn propensities of aspartic acid in GDG (Hagarman; et al. Chem.-Eur. J. 2011, 17, 6789). We investigated the DDD peptide under both acidic and neutral conditions in order to elucidate the effect that side-chain protonation has on the conformational propensity of the central aspartic acid residue. Amide I' profiles were analyzed in terms of two-dimensional Gaussian distributions representing conformational subdistributions in Ramachandran space. Interestingly, our results show that while the protonated form of the DDD peptide samples various turn-like conformations similar to GDG, deprotonation of the peptide eliminates this propensity for turns, causing the fully ionized peptide to exclusively sample pPII and β-strand-like structures. To further explore the factors stabilizing these more extended conformations in fully ionized DDD, we analyzed the temperature dependence of both the UV-CD spectrum and the (3)J(H(N),H(α)) coupling constants of the two amide protons (N- and C-terminal) in terms of a simple two-state (pPII-β) thermodynamic model. Thus, we were able to obtain the enthalpic and entropic differences between the pPII and β-strand conformations of the central and C-terminal residue. For the central residue, we obtained ΔH(3) = -12.0 kJ/mol and ΔS(3) = -73.8 J/mol·K, resulting in a much larger room-temperature Gibbs free energy of 10.0 kJ/mol, which effectively locks the C-terminal in a β-like conformation. A comparison of the temperature dependence of the chemical shifts reveals that there is indeed some type of protection of the amide protons from solvent in ionized DDD. This finding and several other lines of evidence suggest that both conformations of ionized DDD are stabilized by hydrogen bonding between the carboxylate groups of the central and C-terminal residue and the respective amide protons. These hydrogen bonds can be expected to be eliminated by side-chain protonation and substituted by hydrogen bonds between the N-terminal amide proton and the C-terminal carbonyl group as well as between the central aspartate side chain and the N-terminal amide proton. Hence, our results are indicative of a pH-induced switch in hydrogen-bonding patterns of aspartic acid motifs.

Testing Predictions of a Simple Two-State Model of Thin Filament Regulation: Inhibitors that can Activate Thin Filament Motility

Striated muscle is activated by calcium binding and further activated when myosin heads strongly bind the regulated thin filament (RTF). Several intermediate states of the myosin-RTF binding pathway continue to be debated, however for an accurate mesoscopic kinetic model it is imperative to define only stable chemical states without inclusion of transient intermediate structures. Our novel simplified model of thin filament regulation (SMoR) is a streamlined, two-state system with calcium- and myosin-dependent binding rates. This minimalist model is consistent with both the Hill and the McKilloop and Geeves models. It is easily incorporated into larger scale models of skeletal and cardiac mechanics and provides a simple analytical expression with powerful predictive value for accurate hypothesis testing. SMoR predicts amrinone, an inhibitor of ADP release, will increase calcium sensitivity; sucrose, an inhibitor of myosin attachment, will decrease calcium sensitivity as a result of modulations of attachment and detachment kinetics, respectively. Our experimental data shows pCa50 shifts from a standard value of 5.65 to 6.44 with 4mM amrinone; and to 5.14 with 180mM sucrose. Our model predicts that altering both attachment and detachment kinetics will have compensatory effects, allowing calcium sensitivity to be “rescued”. Complex modulations of myosin kinetics were tested experimentally with 4mM amrinone which was rescued with low myosin density and 120mM sucrose to restore the pCa50 to 5.64 and 5.66 respectively. SMoR predicts that decreasing the ADP release rate at low calcium can increase actin-sliding velocities. Consistent with the prediction, we show amrinone increase actin-sliding velocities at sub-activating calcium concentrations. The ability to make complex predictions from fundamental principles has yet to be shown by any other model. SMoR is an accessible and accurate alternative to more complex models of regulation.

Experimental Exploration of the Mulliken−Hush Relationship for Intramolecular Electron Transfer Reactions

The Mulliken-Hush (M-H) relationship provides the critical link between optical and thermal electron transfer processes, and yet very little direct experimental support for its applicability has been provided. Dicyanovinylazaadamantane (DCVA) represents a simple two-state (neutral/charge-transfer) intramolecular electron transfer system that exhibits charge-transfer absorption and emission spectra that are readily measurable in solvents with a wide range of polarities. In this regard it represents an ideal model system for studying the factors that control both optical charge separation (absorption) and recombination (emission) processes in solution. Here we explore the applicability of the M-H relation to quantitative descriptions of the optical charge-transfer processes in DCVA. For DCVA, the measured radiative rate constants exhibit a linear dependence on transition energy, and transition dipole moments exhibit an inverse dependence on transition energy, consistent with the M-H relationship.

An effective description of a periodic one-dimensional hopping model

In this research, methods of reducing a general periodic one-dimensional hopping model to a one- or two-state model, which keeps the basic properties of the original process, are discussed. This reduction also implies that, to some extent, many processes can be well described by simple two-state or even one-state models.

Rapid Collapse into a Molten Globule Is Followed by Simple Two-State Kinetics in the Folding of Lysozyme from Bacteriophage λ

Stopped-flow fluorescence and circular dichroism spectroscopy have been used in combination with quenched-flow hydrogen exchange labeling, monitored by two-dimensional NMR and electrospray ionization mass spectrometry, to investigate the folding kinetics of lysozyme from bacteriophage λ (λ lysozyme) at pH 5.6, 20 °C. The first step in the folding of λ lysozyme occurs very rapidly (τ < 1 ms) after refolding is initiated and involves both hydrophobic collapse and formation of a high content of secondary structure but only weak protection from (1)H/(2)H exchange and no fixed tertiary structure organization. This early folding step is reflected in the dead-time events observed in the far-UV CD and ANS fluorescence experiments. Following accumulation of this kinetic molten globule species, the secondary structural elements are stabilized and the majority (ca. 88%) of refolding molecules acquire native-like properties in a highly cooperative two-state process, with τ = 0.15 ± 0.03 s. This is accompanied by the acquisition of substantial native-like protection from hydrogen exchange. A double-mixing experiment and the absence of a denaturant effect reveal that slow (τ = 5 ± 1 s) folding of the remaining (ca. 12%) molecules is rate limited by the cis/trans isomerization of prolines that are trans in the folded enzyme. In addition, native state hydrogen exchange and classical denaturant unfolding experiments have been used to characterize the thermodynamic properties of the enzyme. In good agreement with previous crystallographic evidence, our results show that λ lysozyme is a highly dynamic protein, with relatively low conformational stability (ΔG°(N-U) = 25 ± 2 kJ·mol(-1)).

Synergistic Activation of Phospholipase C-β3 by Gαq and Gβγ Describes a Simple Two-State Coincidence Detector

Receptors that couple to G(i) and G(q) often interact synergistically in cells to elicit cytosolic Ca(2+) transients that are several-fold higher than the sum of those driven by each receptor alone. Such synergism is commonly assumed to be complex, requiring regulatory interaction between components, multiple pathways, or multiple states of the target protein. We show that cellular G(i)-G(q) synergism derives from direct supra-additive stimulation of phospholipase C-beta3 (PLC-beta3) by G protein subunits Gbetagamma and Galpha(q), the relevant components of the G(i) and G(q) signaling pathways. No additional pathway or proteins are required. Synergism is quantitatively explained by the classical and simple two-state (inactive<-->active) allosteric mechanism. We show generally that synergistic activation of a two-state enzyme reflects enhanced conversion to the active state when both ligands are bound, not merely the enhancement of ligand affinity predicted by positive cooperativity. The two-state mechanism also explains why synergism is unique to PLC-beta3 among the four PLC-beta isoforms and, in general, why one enzyme may respond synergistically to two activators while another does not. Expression of synergism demands that an enzyme display low basal activity in the absence of ligand and becomes significant only when basal activity is </= 0.1% of maximal. Synergism can be explained by a simple and general mechanism, and such a mechanism sets parameters for its occurrence. Any two-state enzyme is predicted to respond synergistically to multiple activating ligands if, but only if, its basal activity is strongly suppressed.

Merger Arbitrage Risk Model

A traditional VaR approach is not suitable to assess the risk that merger arbitrage funds carry in their portfolios. We propose a simple two-state or three-state model that captures the risk characteristics of the deals in which merger arbitrage funds invest.This model has been tested on a set of mergers and acquisitions between large US public companies in 2005.

Heterogeneity in dynamic discrete choice models

Summary We consider dynamic discrete choice models with heterogeneity in both the levels parameter and the state dependence parameter. We first present an empirical analysis that motivates the theoretical analysis which follows. The theoretical analysis considers a simple two-state, first-order Markov chain model without covariates in which both transition probabilities are heterogeneous. Using such a model we are able to derive exact small sample results for bias and mean squared error (MSE). We discuss the maximum likelihood approach and derive two novel estimators. The first is a bias corrected version of the Maximum Likelihood Estimator (MLE) although the second, which we term MIMSE, minimizes the integrated mean square error. The MIMSE estimator is always well defined, has a closed-form expression and inherits the desirable large sample properties of the MLE. Our main finding is that in almost all short panel contexts the MIMSE significantly outperforms the other two estimators in terms of MSE. A final section extends the MIMSE estimator to allow for exogenous covariates.

Gerade-ungerade symmetry breaking in HD: Bound states supported by the I′Πg1 outer potential well

Gerade-ungerade symmetry breaking in HD for the bound states supported by the shallow outer I' (1)Pi(g) potential is studied theoretically. By clarifying the asymptotic behavior of the relevant nonadiabatic couplings among the stats correlating to the n=2 dissociation limit, simple two-state (for f-parity) and three-state (for e-parity) approximations are formulated. They reproduce binding energies in very good agreement with recent spectroscopic measurements. Comparisons with the calculations based on a single model potential are presented and the dependence of the results on the used ab initio Born-Oppenheimer (clamped nuclei) potentials is discussed.

Premicellar Aggregation of Amphiphilic Molecules

We revisit the problem of amphiphilic aggregation using a simple two-state (monomer-aggregate) thermodynamic model, which allows the study of metastable aggregates of variable size. A sequence of well separated concentrations emerge: c(1), where a metastable aggregated state appears; c(2), above which an appreciable amount of metastable aggregates forms; and c(3), where the aggregated state becomes stable. Of these, c(3) is shown to correspond to the critical micelle concentration (cmc) as commonly measured in macroscopic experiments. Thus, appreciable premicellar aggregation is predicted in the concentration range between c(2) and c(3). We show that, so long as the micelles are not too large, the extent of premicellar aggregation is much larger than that expected from mere finite-size effects. It stems from the variability of the micelle size and the small free energy difference between the metastable state, containing monomers and aggregates, and the pure monomeric one. The aggregate size is found to weakly change with concentration below and above the cmc. The existence of premicellar aggregates and their concentration-insensitive size are in agreement with a recent experiment.

Protein Folding Mechanisms Studied by Time-Resolved Electrospray Mass Spectrometry

Mass spectrometry (MS) owes its remarkable rise as a bioanalytical tool to the development of two “soft” ionization techniques: matrix-assisted laser desorption/ ionization (MALDI) (1,2) and electrospray ionization (ESI) (3). The salient feature of soft ionization is that a wide range of analytes, from small metabolites to very large biomolecular systems, can be transferred intact into the gas phase, thus making them amenable to mass spectrometric analysis. For MALDI-MS, the sample is embedded into a crystalline matrix prior to analysis. For ESI, in contrast, ionization is initiated directly from the liquid phase by spraying analyte solution from the tip of an electrically charged capillary. The small droplets formed by the ESI emitter undergo rapid evaporation and fi ssion, ultimately releasing the analyte as multiply protonated (or deprotonated) species (4).

MR-FQ: A Fair Scheduling Algorithm for Wireless Networks with Variable Transmission Rates

Wireless networks are characterized by bursty and location-dependent errors. Although many fair scheduling algorithms have been proposed to address these issues, most of them assume a simple two-state channel model, where a channel can be either good or bad. In fact, the situation is not so pessimistic because different modulation techniques can be used to adapt to different channel conditions. Multirate transmission is a common technique for wireless networks now a days. This leads to a dilemma: should fairness be built based on the amount of time that a user utilizes the medium or the amount of services that a user receives? In this work, the authors propose a multirate wireless fair queueing (MR-FQ) algorithm that allows a flow to transmit at different rates according to its channel condition and lagging degree. MR-FQ takes both time and service fairness into account. They demonstrate that MR-FQ can guarantee fairness and bounded delays for packet flows by mathematical modeling and analyses. Besides, simulation results show that MR-FQ can also increase the overall system throughput compared to other scheduling methods.