Two-state Processes Research Articles

Signal Fluctuations and the Information Transmission Rates in Binary Communication Channels.

In the nervous system, information is conveyed by sequence of action potentials, called spikes-trains. As MacKay and McCulloch suggested, spike-trains can be represented as bits sequences coming from Information Sources (). Previously, we studied relations between spikes’ Information Transmission Rates and their correlations, and frequencies. Now, I concentrate on the problem of how spikes fluctuations affect . The are typically modeled as stationary stochastic processes, which I consider here as two-state Markov processes. As a spike-trains’ fluctuation measure, I assume the standard deviation , which measures the average fluctuation of spikes around the average spike frequency. I found that the character of and signal fluctuations relation strongly depends on the parameter s being a sum of transitions probabilities from a no spike state to spike state. The estimate of the Information Transmission Rate was found by expressions depending on the values of signal fluctuations and parameter s. It turned out that for smaller , the quotient has a maximum and can tend to zero depending on transition probabilities, while for , the is separated from 0. Additionally, it was also shown that quotient by variance behaves in a completely different way. Similar behavior was observed when classical Shannon entropy terms in the Markov entropy formula are replaced by their approximation with polynomials. My results suggest that in a noisier environment , to get appropriate reliability and efficiency of transmission, with higher tendency of transition from the no spike to spike state should be applied. Such selection of appropriate parameters plays an important role in designing learning mechanisms to obtain networks with higher performance.

NmrLineGuru: Standalone and User-Friendly GUIs for Fast 1D NMR Lineshape Simulation and Analysis of Multi-State Equilibrium Binding Models

The ability of high-resolution NMR spectroscopy to readout the response of molecular interactions at multiple atomic sites presents a unique capability to define thermodynamic equilibrium constants and kinetic rate constants for complex, multiple-step biological interactions. Nonetheless, the extraction of the relevant equilibrium binding and rate constants requires the appropriate analysis of not only a readout that follows the equilibrium concentrations of typical binding titration curves, but also the lineshapes of NMR spectra. To best take advantage of NMR data for characterizing molecular interactions, we developed NmrLineGuru, a software tool with a user-friendly graphical user interface (GUI) to model two-state, three-state, and four-state binding processes. Application of NmrLineGuru is through stand-alone GUIs, with no dependency on other software and no scripted input. NMR spectra can be fitted or simulated starting with user-specified input parameters and a chosen kinetic model. The ability to both simulate and fit NMR spectra provides the user the opportunity to not only determine the binding parameters that best reproduce the measured NMR spectra for the selected kinetic model, but to also query the possibility that alternative models agree with the data. NmrLineGuru is shown to provide an accurate, quantitative analysis of complex molecular interactions.

Aging two-state process with Lévy walk and Brownian motion.

With the rich dynamics studies of single-state processes, the two-state processes are attracting more interest, since they are widely observed in complex system and have effective applications in diverse fields, such as foraging behavior of animals. This paper builds the theoretical foundation of the process with two states: Lévy walk and Brownian motion, having been proved to be an efficient intermittent search process. The sojourn time distributions in two states are both assumed to be heavy-tailed with exponents α_{±}∈(0,2). The dynamical behaviors of this two-state process are obtained through analyzing the ensemble-averaged and time-averaged mean-squared displacements (MSDs) in weak and strong aging cases. It is discovered that the magnitude relationship of α_{±} decides the fraction of two states for long times, playing a crucial role in these MSDs. According to the generic expressions of MSDs, some inherent characteristics of the two-state process are detected. The effects of the fraction on these observables are presented in detail for six different cases. The key of getting these results is to calculate the velocity correlation function of the two-state process, the techniques of which can be generalized to other multistate processes.

Influence of Calcium Ions on the Thermal Characteristics of α-amylase from Thermophilic Anoxybacillus sp. GXS-BL.

Background: α-Amylases are starch-degrading enzymes and used widely, the study on thermostability of α-amylase is a central requirement for its application in life science and biotech-nology.Objective:In this article, our motivation is to study how the effect of Ca2+ ions on the structure and thermal characterization of α-amylase (AGXA) from thermophilic Anoxybacillus sp.GXS-BL.Methods: α-Amylase activity was assayed with soluble starch as the substrate, and the amount of sugar released was determined by DNS method. For AGXA with calcium ions and without calcium ions, optimum temperature (Topt), half-inactivation temperature (T50) and thermal inactivation (half-life, t1/2) was evaluated. The thermal denaturation of the enzymes was determined by DSC and CD methods. 3D structure of AGXA was homology modeled with α-amylase (5A2A) as the template.Results:With calcium ions, the values of Topt, T50, t1/2, Tm and ΔH in AGXA were significantly high-er than those of AGXA without calcium ions, showing calcium ions had stabilizing effects on α-amylase structure with the increased temperature. Based on DSC measurements AGXA underwent thermal denaturation by adopting two-state irreversible unfolding processes. Based on the CD spectra, AGXA without calcium ions exhibited two transition states upon unfolding, including α-helical contents increasing, and the transition from α-helices to β-sheet structures, which was obviously dif-ferent in AGXA with Ca2+ ions, and up to 4 Ca2+ ions were located on the inter-domain or intra-domain regions according to the modeling structure.Conclusion: These results reveal that Ca2+ ions have pronounced influences on the thermostability of AGXA structure.

Exact and heuristic methods for personalized display advertising in virtual reality platforms

In this paper, motivated from a real problem faced by an online Virtual Reality (VR) platform provider, we study a personalized advertisement assignment problem. In this platform users log in/out and change their virtual locations. A number of advertisers are willing to pay for ad locations to reach these users. Every time a user visits a new location, the company displays one of the ads. At the end of a fixed time horizon, a reward is collected which depends on the number of ads of each advertiser displayed to different users. The objective is to assign ads dynamically to maximize the expected reward. The problem is studied in a framework where the behaviors of users are modeled with two-state continuous-time Markov processes. We describe two exact and four heuristic algorithms. We compare these algorithms and conduct a sensitivity analysis over problem and algorithm specific parameters. These are the main contributions of the current paper. Exact algorithms suffer from the curse of dimensionality, hence, heuristic methods might be considered instead in some cases. However, exact methods can also be used as part of heuristics since the experimental analysis demonstrates that they are robust for parameters that influence the computational requirements.

A mathematical model for personalized advertisement in virtual reality environments

We consider a personalized advertisement assignment problem faced by the manager of a virtual reality environment. In this online environment, users log in/out, and they spend time in different virtual locations while they are online. Every time a user visits a new virtual location, the site manager can show the ad of an advertiser. At the end of a fixed time horizon, the manager collects revenues from all of the advertisers, and the total revenue depends on the number of ads of different advertisers she displays to different users. In this setup, the objective of the manager is to find an optimal dynamic ad display policy in order to maximize her expected revenue. In the current paper, we formulate this problem as a continuous time stochastic optimization problem in which the actions of users are represented with two-state Markov processes and the manager makes display decisions at the transition times of these processes. To our best knowledge, no formal stochastic model and rigorous analysis has been given for this practical problem. Such a model and its analysis are the major contributions of this paper along with an optimal solution.

Radiative association of He(23P) with lithium cations

Formation of HeLi+ molecular ion by radiative association of metastable helium atoms with lithium ions is investigated on the triplet-Sigma manifold. Energy dependent cross-sections are calculated for He(23P) colliding with Li+ in the continuum of the c3Σ+ electronic state and undergoing radiative transition into one of the rotational-vibrational states of the lower electronic states a3Σ+,b3Σ+, or c3Σ+ of HeLi+. Evaluation of the cross-sections is based on the fully quantal approach taking into account all possible state-to-state transitions at thermal energies (spontaneous association) or at higher background temperatures (stimulated association). The corresponding rate coefficients are presented as functions of temperature. Calculations show that the rate coefficients for two-state processes c→a and c→b are several orders of magnitude larger than the rate coefficient for the c-state formation. The rate coefficient for the c→a radiative association reaches 10-15cm3s−1 at low temperatures. As expected stimulation of the radiative association by black-body background radiation has a noticeable effect only on the one-state c→c process.

Nonlinear Relationship Between Permanent and Transitory Components of Monetary Aggregates and the Economy

This paper uses several methods to study the interrelationship among Divisia monetary aggregates, prices, and income, allowing for nonstationary, nonlinearities, asymmetries, and time-varying relationships among the series. We propose a multivariate regime switching unobserved components model to obtain transitory and permanent components for each series, allowing for potential recurrent and structural changes in their dynamics. Each component follows distinct two-state Markov processes representing low or high phases. Since the lead-lag relationship between the phases can vary over time, rather than pre-imposing a structure to their linkages, the proposed flexible framework enables us to study their specific lead-lag relationship over each one of their cycles and over each U.S. recession in the last 40 years. The decomposition of the series into permanent and transitory components reveals striking results. First, we find a strong nonlinear association between the components of money and prices—all low phases of the transitory component of prices were preceded by tight transitory and permanent money phases. We also find that most recessions were preceded by tight money phases (its cyclical and permanent components) and high transitory price phases (with the exception of the 2001 and 2009-2010 recessions). In addition, all recessions were associated with a decrease in transitory and permanent income.

Nonlinear Relationship Between Permanent and Transitory Components of Monetary Aggregates and the Economy

This paper uses several methods to study the interrelationship among Divisia monetary aggregates, prices, and income; allowing for non-stationary, non-linearities, asymmetries, and time-varying relationships among the series. We propose a multivariate regime switching unobserved components model to obtain transitory and permanent components for each series, allowing for potential recurrent and structural changes in their dynamics. Each component follows distinct two-state Markov processes representing low or high phases. Since the lead-lag relationship between the phases can vary over time, rather than preimposing a structure to their linkages, the proposed flexible framework enables us to study their specific lead-lag relationship over each one of their cycles and over each U.S. recession in the last 40 years. The decomposition of the series into permanent and transitory components reveals striking results. First, we find a strong nonlinear association between the components of money and prices – all low phases of the transitory component of prices were preceded by tight transitory and permanent money phases. We also find that most recessions were preceded by tight money phases, (its cyclical and permanent components), and high transitory price phases, (with the exception of the 2001 and 2009-2010 recessions). In addition, all recessions were associated with a decrease in transitory and permanent income.

Slow, Reversible, Coupled Folding and Binding of the Spectrin Tetramerization Domain

Many intrinsically disordered proteins (IDPs) are significantly unstructured under physiological conditions. A number of these IDPs have been shown to undergo coupled folding and binding reactions whereby they can gain structure upon association with an appropriate partner protein. In general, these systems display weaker binding affinities than do systems with association between completely structured domains, with micromolar Kd values appearing typical. One such system is the association between α- and β-spectrin, where two partially structured, incomplete domains associate to form a fully structured, three-helix bundle, the spectrin tetramerization domain. Here, we use this model system to demonstrate a method for fitting association and dissociation kinetic traces where, using typical biophysical concentrations, the association reactions are expected to be highly reversible. We elucidate the unusually slow, two-state kinetics of spectrin assembly in solution. The advantages of studying kinetics in this regime include the potential for gaining equilibrium constants as well as rate constants, and for performing experiments with low protein concentrations. We suggest that this approach would be particularly appropriate for high-throughput mutational analysis of two-state reversible binding processes.

A comprehensive study of path-level performance evaluation and traffic aggregation for discrete-time tandem network

A simple and systematic path-level performance evaluation method mainly composed of a decomposition technique and a parameter-fitting algorithm is proposed in this paper. With comprehensive considerations, this method works for a discrete-time tandem network with input of two-state Markov-modulated Bernoulli processes (MMBPs), which have potential applications in computer and communication networks. Of course, this proposed method offers convenience of traffic aggregation and decomposition for multiple MMBPs. Furthermore, it can be easily extended to work for tree-type networks. To validate the proposed method, several experiments are conducted to demonstrate that the proposed method has good accuracy in terms of delay, delay variance, and packet loss probability. For further checking the effectiveness of this method, comparisons with some closely related methods in the literature are also made.

Structure and Dynamics of Molten Globular Intermediates Encountered during the Unfolding of Barstar

The modelling of the folding and unfolding reactions of small proteins as two-state processes has provided us wealth of information on the kinetics and thermodynamics of these processes and the stability and pathway of folding. Hidden in this misleading simplicity are various intermediate states including the molten globular (MG) forms. The nature of solvation of MG forms has acquired considerable importance in the context of identifying the forces that drive protein folding and unfolding reactions.In this work we monitored the solvent accessibility during the unfolding of barstar, a small single domain protein, by following the bimolecular quenching constant (kq) associated with dynamic fluorescence quenching of the single and buried tryptophan (Trp-53) by either acrylamide or potassium iodide. A pico-second time-domain fluorimeter capable of acquiring data every 200 ms of unfolding was used. Analysis of the time-dependence of kq showed the presence of an intermediate with solvent accessibility very similar to that of the unfolded (U) state. However, structural indicators such as steady-state fluorescence intensity and time-resolved anisotropy of Trp-53 and near UV-CD indicated the presence of another intermediate within ∼ 10 ms, the zero time associated with the initiation of unfolding. Taken together, our data is consistent with the following model for the process of unfolding. N a DMG a WMG a U, where DMG and WMG refer to ‘dry’ and ‘wet’ MG forms, respectively. The demonstration of the presence of a DMG has strong implications in dissecting the overall process of folding and unfolding into individual steps, apart from revealing the forces that lead to protein folding.

An improved method for measuring the stability of a three-state unfolding protein

In the current three-state protein unfolding model, the two transitions are considered to be independent and each transition is fitted to a two-state unfolding model. This three-state unfolding process is therefore composed of two sequential two-state unfolding processes. In this paper, a modified method is presented to determine the value of the unfolding free energy [δGtotal0(H2O)] for the three-state unfolding equilibrium of proteins. This method is demonstrated on the apoCopC protein mutant, Y79W-W83F-Cu, which unfolds via a three-state process. The value of ΔGtotal0(H2O) calculated using the modified method was found to be more accurate in determining ΔGtotal0(H2O) than the previously reported method.

Binding of Ca2+ and Zn2+ to factor IX/X-binding protein from venom of Agkistrodon halys Pallas: stabilization of the structure during GdnHCl-induced and thermally induced denaturation

Coagulation factor IX/coagulation factor X binding protein from the venom of Agkistrodon halys Pallas (AHP IX/X-bp) is a unique coagulation factor IX/coagulation factor X binding protein (IX/X-bp). Among all IX/X-bps identified, only AHP IX/X-bp is a Ca(2+)- and Zn(2+)-binding protein. The binding properties of Ca(2+) and Zn(2+) ions binding to apo-AHP IX/X-bp and their effects on the stability of the protein have been investigated by isothermal titration calorimetry, fluorescence spectroscopy, and differential scanning calorimetry. The results show that AHP IX/X-bp has two metal binding sites, one specific for Ca(2+) with lower affinity for Zn(2+) and one specific for Zn(2+) with lower affinity for Ca(2+). The bindings of Ca(2+) and Zn(2+) in the two sites are entropy- and enthalpy-driven. The binding affinity of AHP IX/X-bp for Zn(2+) is 1 order of magnitude higher than for Ca(2+) for either high-affinity binding or low-affinity binding, which accounts for the existence of one Zn(2+) in the purified AHP IX/X-bp. Guanidine hydrochloride (GdnHCl)-induced and thermally induced denaturations of Ca(2+)-Ca(2+)-AHP IX/X-bp, Zn(2+)-Zn(2+)-AHP IX/X-bp, and Ca(2+)-Zn(2+)-AHP IX/X-bp are all a two-state processes with no detectable intermediate state(s), indicating the Ca(2+)/Zn(2+)-induced tight packing of the protein. Ca(2+) and Zn(2+) increase the structural stability of AHP IX/X-bp against GdnHCl or thermal denaturation to a similar extent. Although Ca(2+) and Zn(2+) have no obvious effect on the secondary structure of AHP IX/X-bp, they induce different rearrangements in local conformation. The Zn(2+)-stabilized specific conformation of AHP IX/X-bp may be helpful to its recognition of the structure of coagulation factor IX. This work suggests that in vitro, Ca(2+) plays a structural rather than an active role in the anticoagulation of AHP IX/X-bp, whereas Zn(2+) plays both structural and active roles in the anticoagulation. In blood, Ca(2+) binds to AHP IX/X-bp and stabilizes its structure, whereas Zn(2+) cannot bind to AHP IX/X-bp owing to the low Zn(2+) concentration. AHP IX/X-bp prolongs the clotting time in vivo through its binding only with coagulation factor X/activated coagulation factor X.

On some solutions of Chapman-Kolmogorov equation for discrete-state Markov processes with continuous time

The nonlinear equation mentioned in the title is the basic one in the theory of Markov processes. In the case of a discrete-state process, its solution is given by the transition probability function. Usually, solving this equation amounts to solving a linear equation. In 1932, S. N. Bernstein posed the problem of direct determination of the solution. In 1961, such solutions were given in terms of bilinear series by O. V. Sarmanov for stationary continuous-state Markov processes. In 2007, several solutions were obtained by the author in terms of generalized bilinear series without placing Sarmanov’s restrictions. In this paper, our results are extended to discrete-state processes. Two solutions of the Chapman-Kolmogorov equation are derived by means of reducing it to some functional equation. The solutions are represented in the form of a bilinear sum and its generalizations, each term of the sum being proportional to the product of two orthogonal functions. The results obtained are illustrated by two-state processes, which exemplify the assertions derived in this paper. Another example is used to show that the Chapman-Kolmogorov equation has a solution which is devoid of probabilistic sense.

Relapse–remission and remission–relapse switches in rheumatoid arthritis patients were modeled by random effects

Objective To compare statistical models for the analysis of two-state disease processes. Study Design and Setting A two-armed randomized trial of patients with early rheumatoid arthritis (RA) treated by either combination therapy (sulfasazaline, methotrextate, prednisolone) or monotherapy (sulfasazaline). Disease activity (remission or relapse) was analyzed with the logistic regression model, the proportional hazards regression model, and the continuous-time Markov process model for panel data. The dependence among the switching times was studied by (1) including correlated normal random patient effects for the relapse–remission and remission–relapse switching probabilities; (2) assuming the population to be a mixture of patients responsive and nonresponsive to therapy; (3) including separate parameters for the first and subsequent relapse–remission switch; and (4) combining (1) and (3). The four approaches were compared using parametric bootstrap checks. Results The logistic regression model, the proportional hazards regression model, and the continuous-time Markov process model for panel data yielded similar combination therapy effects. The inclusion of random patient effects (approaches 1 and 4) gave the best fit to the observed disease activity pattern. Conclusion Models with correlated random effects can provide a satisfactory fit to two-state disease patterns.

Using iterations for finding the optimal virtual channel in telecommunication networks

We model telecommunication systems using two-state discrete Markov processes. Using the methods of dynamic programming we find the optimal virtual channel with minimal probability of a busy state. A simple example is also considered for the purpose of illustration.

On the Pathway of Forming Enzymatically Productive Ligand-Protein Complexes in Lactate Dehydrogenase

We have carried out a series of studies on the binding of a substrate mimic to the enzyme lactate dehydrogenase (LDH) using advanced kinetic approaches, which begin to provide a molecular picture of the dynamics of ligand binding for this protein. Binding proceeds via a binding-competent subpopulation of the nonligated form of the protein (the LDH/NADH binary complex) to form a protein-ligand encounter complex. The work here describes the collapse of the encounter complex to form the catalytically competent Michaelis complex. Isotope-edited static Fourier transform infrared studies on the bound oxamate protein complex reveal two kinds of oxamate environments: 1), a major populated structure wherein all significant hydrogen-bonding patterns are formed at the active site between protein and bound ligand necessary for the catalytically productive Michaelis complex and 2), a minor structure in a configuration of the active site that is unfavorable to carry out catalyzed chemistry. This latter structure likely simulates a dead-end complex in the reaction mixture. Temperature jump isotope-edited transient infrared studies on the binding of oxamate with LDH/NADH suggest that the evolution of the encounter complex between LDH/NADH and oxamate collapses via a branched reaction pathway to form the major and minor bound species. The production of the catalytically competent protein-substrate complex has strong similarities to kinetic pathways found in two-state protein folding processes. Once the encounter complex is formed between LDH/NADH and substrate, the ternary protein-ligand complex appears to “fold” to form a compact productive complex in an all or nothing like fashion with all the important molecular interactions coming together at the same time.

Controllability and Observability of the Photophysical System of Intermolecular Two-State Excited-State Processes

In this report, we focus on the consequences of controllability and observability on the number of distinct exponential terms in the fluorescence decay and on the identifiability analysis of the photophysical model of intermolecular two-state excited-state processes. Controllability and observability prove to be useful concepts in photophysics for exploring methodically the conditions under which intermolecular two-state excited-state processes lead to single-exponential fluorescence delta-response functions. A detailed discussion on the distinction of the possible origins of monoexponential fluorescence decays is presented. We also show that the similarity transformation approach to identifiability leads to erroneous conclusions concerning which model parameters can be identified if this photophysical system is not controllable or not observable. The results obtained for this relatively simple photophysical system can be extended in a systematic way to more complicated photophysical models.

Fluorescence anisotropy decay for intramolecular two-state excited-state processes with added quencher in the presence of rotational diffusion: An identifiability analysis

A deterministic identifiability analysis of kinetic models of a reversible intramolecular excited-state process involving species-dependent rotational Brownian diffusion is performed for spherical and cylindrically symmetric rotors. It is assumed that the axes of rotation do not change upon interconversion, and that the rate constants are independent of orientation. Use of three quencher concentrations allows the determination of two internally consistent sets of quenching rate constants, combinations of excited-state deactivation/exchange rate constants, individual rotational diffusion coefficients, relative orientations of transition moments, and restricted spectral information. Assignment of each set obtained to a particular species is not possible without additional prior information.