Allosteric Control of Gating Mechanisms Revisited: The Large Conductance Ca(2+)-Activated K(+) Channel

Large-conductance Ca(2+)-activated K(+) channels (BK) play a fundamental role in modulating membrane potential in many cell types. The gating of BK channels and its modulation by Ca(2+) and voltage has been the subject of intensive research over almost three decades, yielding several of the most complicated kinetic mechanisms ever proposed. A large number of open and closed states disposed, respectively, in two planes, named tiers, characterize these mechanisms. Transitions between states in the same plane are cooperative and modulated by Ca(2+). Transitions across planes are highly concerted and voltage-dependent. Here we reexamine the validity of the two-tiered hypothesis by restricting attention to the modulation by Ca(2+). Large single channel data sets at five Ca(2+) concentrations were simultaneously analyzed from a Bayesian perspective by using hidden Markov models and Markov-chain Monte Carlo stochastic integration techniques. Our results support a dramatic reduction in model complexity, favoring a simple mechanism derived from the Monod-Wyman-Changeux allosteric model for homotetramers, able to explain the Ca(2+) modulation of the gating process. This model differs from the standard Monod-Wyman-Changeux scheme in that one distinguishes when two Ca(2+) ions are bound to adjacent or diagonal subunits of the tetramer.

Bayesian online algorithms for learning in discrete Hidden Markov Models

We propose and analyze two different Bayesian online algorithms for learning in discrete Hidden Markov Models and compare their performance with the already known Baldi-Chauvin Algorithm. Using the Kullback-Leibler divergence as a measure of generalization we draw learning curves in simplified situations for these algorithms and compare their performances.

Multiclass Hammersley-Aldous-Diaconis process and multiclass-customer queues

In the Hammersley-Aldous-Diaconis process, infinitely many particles sit in R and at most one particle is allowed at each position. A particle at x, whose nearest neighbor to the right is at y, jumps at rate y - x to a position uniformly distributed in the interval (x, y). The basic coupling between trajectories with different initial configuration induces a process with different classes of particles. We show that the invariant measures for the two-class process can be obtained as follows. First, a stationary M/M/1 queue is constructed as a function of two homogeneous Poisson processes, the arrivals with rate, and the (attempted) services with rate rho > lambda Then put first class particles at the instants of departures (effective services) and second class particles at the instants of unused services. The procedure is generalized for the n-class case by using n - 1 queues in tandem with n - 1 priority types of customers. A multi-line process is introduced; it consists of a coupling (different from Liggett's basic coupling), having as invariant measure the product of Poisson processes. The definition of the multi-line process involves the dual points of the space-time Poisson process used in the graphical construction of the reversed process. The coupled process is a transformation of the multi-line process and its invariant measure is the transformation described above of the product measure.

Plasma Kallikrein and Angiotensin I-converting enzyme N- and C-terminal domain activities are modulated by the insertion/deletion polymorphism

Angiotensin I-converting enzyme (ACE) is recognized as one of the main effector molecules involved in blood pressure regulation. In the last few years some polymorphisms of ACE such as the insertion/deletion (I/D) polymorphism have been described, but their physiologic relevance is poorly understood. In addition, few studies investigated if the specific activity of ACE domain is related to the I/D polymorphism and if it can affect other systems. The aim of this study was to establish a biochemical and functional characterization of the I/D polymorphism and correlate this with the corresponding ACE activity. For this purpose, 119 male brazilian army recruits were genotyped and their ACE plasma activities evaluated from the C- and N-terminal catalytic domains using fluorescence resonance energy transfer (FRET) peptides, specific for the C-domain (Abz-LFK(Dnp)OH), N-domain (Abz-SDK(Dnp)P-OH) and both C- and N-domains (Abz-FRK(Dnp)P-OH). Plasma kallikrein activity was measured using Z-Phe-Arg-AMC as substrate and inhibited by selective plasma kallikrein inhibitor (PKSI). Some physiological parameters previously described related to the I/D polymorphism such as handgrip strength, blood pressure, heart rate and BMI were also evaluated. The genotype distribution was II n = 27, ID n = 64 and DD n = 28. Total plasma ACE activity of both domains in II individuals was significantly lower in comparison to ID and DD. This pattern was also observed for C- and N-domain activities. Difference between ID and DD subjects was observed only with the N-domain specific substrate. Blood pressure, heart rate, handgrip strength and BMI were similar among the genotypes. This polymorphism also affected the plasma kallikrein activity and DD group presents high activity level. Thus, our data demonstrate that the I/D ACE polymorphism affects differently both ACE domains without effects on handgrip strength. Moreover, this polymorphism influences the kallikrein-kinin system of normotensive individuals. (C) 2009 Elsevier Ltd. All rights reserved.

Relationship Between Cortisol Levels and Memory Performance may be Modulated by the Presence or Absence of Cognitive Impairment: Evidence from Healthy Elderly, Mild Cognitive Impairment and Alzheimer`s Disease Subjects

An inverted U-shape function between cortisol levels and memory performance has been reported in studies on both young animals and humans. Yet little is known about this relationship in normal aging or in older subjects with cognitive impairment. This issue is particularly significant since increased levels of cortisol have been reported in Alzheimer`s disease (AD). The present study examined the association between cortisol levels and visual memory performance in healthy subjects as well as in individuals presenting mild cognitive impairment (MCI) or AD. Salivary cortisol was measured in 40 healthy elderly subjects, 31 individuals with amnestic MCI, and 40 subjects with mild probable AD. Memory performance was evaluated using the Brief Cognitive Screening Battery. Higher cortisol levels were associated with better memory performance in healthy elderly (p = 0.005), while higher cortisol levels were correlated with poorer memory performance in MCI subjects (p = 0.011). No correlation between cortisol and memory was found in the AD group (p > 0.05). These results suggest that the relationship between cortisol levels and memory performance in the aging process could vary according to the presence or absence of cognitive impairment.

Phase-Locked Loop design applied to frequency-modulated atomic force microscope

The atomic force microscope (AFM) introduced the surface investigation with true atomic resolution. In the frequency modulation technique (FM-AFM) both the amplitude and the frequency of oscillation of the micro-cantilever must be kept constant even in the presence of tip-surface interaction forces. For that reason, the proper design of the Phase-Locked Loop (PLL) used in FM-AFM is vital to system performance. Here, the mathematical model of the FM-AFM control system is derived considering high order PLL In addition a method to design stable third-order Phase-Locked Loops is presented. (C) 2010 Elsevier B.V. All rights reserved.

The Policy Iteration Algorithm for Average Continuous Control of Piecewise Deterministic Markov Processes

The main goal of this paper is to apply the so-called policy iteration algorithm (PIA) for the long run average continuous control problem of piecewise deterministic Markov processes (PDMP`s) taking values in a general Borel space and with compact action space depending on the state variable. In order to do that we first derive some important properties for a pseudo-Poisson equation associated to the problem. In the sequence it is shown that the convergence of the PIA to a solution satisfying the optimality equation holds under some classical hypotheses and that this optimal solution yields to an optimal control strategy for the average control problem for the continuous-time PDMP in a feedback form.

THE VANISHING DISCOUNT APPROACH FOR THE AVERAGE CONTINUOUS CONTROL OF PIECEWISE DETERMINISTIC MARKOV PROCESSES

This work is concerned with the existence of an optimal control strategy for the long-run average continuous control problem of piecewise-deterministic Markov processes (PDMPs). In Costa and Dufour (2008), sufficient conditions were derived to ensure the existence of an optimal control by using the vanishing discount approach. These conditions were mainly expressed in terms of the relative difference of the alpha-discount value functions. The main goal of this paper is to derive tractable conditions directly related to the primitive data of the PDMP to ensure the existence of an optimal control. The present work can be seen as a continuation of the results derived in Costa and Dufour (2008). Our main assumptions are written in terms of some integro-differential inequalities related to the so-called expected growth condition, and geometric convergence of the post-jump location kernel associated to the PDMP. An example based on the capacity expansion problem is presented, illustrating the possible applications of the results developed in the paper.

On the Filtering Problem for Continuous-Time Markov Jump Linear Systems with no Observation of the Markov Chain

We consider in this paper the optimal stationary dynamic linear filtering problem for continuous-time linear systems subject to Markovian jumps in the parameters (LSMJP) and additive noise (Wiener process). It is assumed that only an output of the system is available and therefore the values of the jump parameter are not accessible. It is a well known fact that in this setting the optimal nonlinear filter is infinite dimensional, which makes the linear filtering a natural numerically, treatable choice. The goal is to design a dynamic linear filter such that the closed loop system is mean square stable and minimizes the stationary expected value of the mean square estimation error. It is shown that an explicit analytical solution to this optimal filtering problem is obtained from the stationary solution associated to a certain Riccati equation. It is also shown that the problem can be formulated using a linear matrix inequalities (LMI) approach, which can be extended to consider convex polytopic uncertainties on the parameters of the possible modes of operation of the system and on the transition rate matrix of the Markov process. As far as the authors are aware of this is the first time that this stationary filtering problem (exact and robust versions) for LSMJP with no knowledge of the Markov jump parameters is considered in the literature. Finally, we illustrate the results with an example.

Singular Perturbation for the Discounted Continuous Control of Piecewise Deterministic Markov Processes

This paper deals with the expected discounted continuous control of piecewise deterministic Markov processes (PDMP`s) using a singular perturbation approach for dealing with rapidly oscillating parameters. The state space of the PDMP is written as the product of a finite set and a subset of the Euclidean space a""e (n) . The discrete part of the state, called the regime, characterizes the mode of operation of the physical system under consideration, and is supposed to have a fast (associated to a small parameter epsilon > 0) and a slow behavior. By using a similar approach as developed in Yin and Zhang (Continuous-Time Markov Chains and Applications: A Singular Perturbation Approach, Applications of Mathematics, vol. 37, Springer, New York, 1998, Chaps. 1 and 3) the idea in this paper is to reduce the number of regimes by considering an averaged model in which the regimes within the same class are aggregated through the quasi-stationary distribution so that the different states in this class are replaced by a single one. The main goal is to show that the value function of the control problem for the system driven by the perturbed Markov chain converges to the value function of this limit control problem as epsilon goes to zero. This convergence is obtained by, roughly speaking, showing that the infimum and supremum limits of the value functions satisfy two optimality inequalities as epsilon goes to zero. This enables us to show the result by invoking a uniqueness argument, without needing any kind of Lipschitz continuity condition.

Generalized Coupled Algebraic Riccati Equations for Discrete-time Markov Jump with Multiplicative Noise Systems

In this paper we consider the existence of the maximal and mean square stabilizing solutions for a set of generalized coupled algebraic Riccati equations (GCARE for short) associated to the infinite-horizon stochastic optimal control problem of discrete-time Markov jump with multiplicative noise linear systems. The weighting matrices of the state and control for the quadratic part are allowed to be indefinite. We present a sufficient condition, based only on some positive semi-definite and kernel restrictions on some matrices, under which there exists the maximal solution and a necessary and sufficient condition under which there exists the mean square stabilizing solution fir the GCARE. We also present a solution for the discounted and long run average cost problems when the performance criterion is assumed be composed by a linear combination of an indefinite quadratic part and a linear part in the state and control variables. The paper is concluded with a numerical example for pension fund with regime switching.

Linear minimum mean square filter for discrete-time linear systems with Markov jumps and multiplicative noises

In this paper we obtain the linear minimum mean square estimator (LMMSE) for discrete-time linear systems subject to state and measurement multiplicative noises and Markov jumps on the parameters. It is assumed that the Markov chain is not available. By using geometric arguments we obtain a Kalman type filter conveniently implementable in a recurrence form. The stationary case is also studied and a proof for the convergence of the error covariance matrix of the LMMSE to a stationary value under the assumption of mean square stability of the system and ergodicity of the associated Markov chain is obtained. It is shown that there exists a unique positive semi-definite solution for the stationary Riccati-like filter equation and, moreover, this solution is the limit of the error covariance matrix of the LMMSE. The advantage of this scheme is that it is very easy to implement and all calculations can be performed offline. (c) 2011 Elsevier Ltd. All rights reserved.

A generalized multi-period mean-variance portfolio optimization with Markov switching parameters

In this paper, we deal with a generalized multi-period mean-variance portfolio selection problem with market parameters Subject to Markov random regime switchings. Problems of this kind have been recently considered in the literature for control over bankruptcy, for cases in which there are no jumps in market parameters (see [Zhu, S. S., Li, D., & Wang, S. Y. (2004). Risk control over bankruptcy in dynamic portfolio selection: A generalized mean variance formulation. IEEE Transactions on Automatic Control, 49, 447-457]). We present necessary and Sufficient conditions for obtaining an optimal control policy for this Markovian generalized multi-period meal-variance problem, based on a set of interconnected Riccati difference equations, and oil a set of other recursive equations. Some closed formulas are also derived for two special cases, extending some previous results in the literature. We apply the results to a numerical example with real data for Fisk control over bankruptcy Ill a dynamic portfolio selection problem with Markov jumps selection problem. (C) 2008 Elsevier Ltd. All rights reserved.

Fluorescent indication that nitric oxide formation in NTS neurons is modulated by glutamate and GABA

Nitric oxide (NO) in NTS plays an important role in regulating autonomic function to the cardiovascular system. Using the fluorescent dye DAF-2 DA, we evaluated the NO concentration in NTS. Brainstem slices of rats were loaded with DAF-2 DA, washed, fixed in paraformaldehyde and examined under fluorescent light. In different experimental groups, NTS slices were pre-incubated with 1 mM L-NAME (a non-selective NOS inhibitor), 1 MM D-NAME (an inactive enantiomere of L-NAME), 1 mM kynurenic acid (a nonselective ionotropic receptors antagonist) or 20 mu M bicuculline (a selective GABA(A) receptors antagonist) before and during DAF-2 DA loading. Images were acquired using a confocal microscope and the intensity of fluorescence was quantified in three antero-posterior NTS regions. In addition, slices previously loaded with DAF-2 DA were incubated with NeuN or GFAP antibody. A semi-quantitative analysis of the fluorescence intensity showed that the basal NO concentration was similar in all antero-posterior aspects of the NTS (rostral intermediate, 15.5 +/- 0.8 AU: caudal intermediate, 13.2 +/- 1.4 AU; caudal commissural, 13.8 +/- 1.4 AU, n = 10). In addition, the inhibition of NOS and the antagonism of glutamatergic receptors decreased the NO fluorescence in the NTS. On the other hand, D-NAME did not affect the NO fluorescence and the antagonism of GABAA receptors increased the NO fluorescence in the NTS. It is important to note that the fluorescence for NO was detected mainly in neurons. These data show that the fluorescence observed after NTS loading with DAF-2 DA is a result of NO present in the NTS and support the concept that NTS neurons have basal NO production which is modulated by L-glutamate and GABA. (C) 2009 Elsevier Inc. All rights reserved.

A numerical study of large sparse matrix exponentials arising in Markov chains

Krylov subspace techniques have been shown to yield robust methods for the numerical computation of large sparse matrix exponentials and especially the transient solutions of Markov Chains. The attractiveness of these methods results from the fact that they allow us to compute the action of a matrix exponential operator on an operand vector without having to compute, explicitly, the matrix exponential in isolation. In this paper we compare a Krylov-based method with some of the current approaches used for computing transient solutions of Markov chains. After a brief synthesis of the features of the methods used, wide-ranging numerical comparisons are performed on a power challenge array supercomputer on three different models. (C) 1999 Elsevier Science B.V. All rights reserved.AMS Classification: 65F99; 65L05; 65U05.