scholarly journals Spatiotemporal relationships defining the adaptive gating of the bacterial mechanosensitive channel MscS

2017 ◽  
Author(s):  
Uğur Çetiner ◽  
Sergei Sukharev
Keyword(s):  
Resting State ◽  
Continuous Time ◽  
Mechanosensitive Channel ◽  
Transition Rates ◽  
Osmotic Permeability ◽  
Adaptive Desensitization ◽  
Low Threshold ◽  
Analytic Expression ◽  
Environmental Fitness ◽  
Small Conductance

AbstractAdaptive desensitization and inactivation are common properties of most ion channels and receptors. The mechanosensitive channel of small conductance MscS, which serves as a low-threshold osmolyte release valve in most bacteria, is unusual because it slowly inactivates not from the open, but from the resting state under moderate tensions. The manifestation of this mechanism is the channel’s ability to discriminate the rate of tension application, i.e., to ignore slow tension ramps but fully respond to abruptly applied stimuli. In this work, we present a reconstruction of the landscape for tension-dependent MscS transitions based on patch current kinetics recorded under specially designed pressure protocols. The data are analyzed with a three-state continuous time Markov model of gating, where the tension-dependent transition rates are governed by Arrhenius-type relations. The analysis provides assignments to the intrinsic opening, closing, inactivation, and recovery rates as well as their tension dependencies. These parameters, which define the spatial (areal) distances between the energy wells and the positions of barriers, describe the tension-dependent distribution of the channel population between the three states and quantitatively predict the experimentally observed dynamic pulse and ramp responses. Our solution also provides an analytic expression for the area of the inactivated state in terms of two experimentally accessible parameters: the tension at which inactivation probability is maximized, γ*, and the midpoint tension for activation, γ0.5. The analysis initially performed on Escherichia coli MscS shows its applicability to the previously uncharacterized MscS homolog from Pseudomonas aeruginosa. MscS inactivation minimizes metabolic losses during osmotic permeability response and thus contributes to the environmental fitness of bacteria.

scholarly journals Denumerable state continuous time Markov decision processes with unbounded cost and transition rates under average criterion

2002 ◽  
Vol 43 (4) ◽  
pp. 541-557 ◽  
Author(s):  
Xianping Guo ◽  
Weiping Zhu
Keyword(s):  
Markov Decision Processes ◽  
Continuous Time ◽  
Decision Processes ◽  
Transition Rates ◽  
Birth And Death Processes ◽  
Optimality Equation ◽  
Average Criterion ◽  
Markov Decision ◽  
Unbounded Cost ◽  
Queue Model

AbstractIn this paper, we consider denumerable state continuous time Markov decision processes with (possibly unbounded) transition and cost rates under average criterion. We present a set of conditions and prove the existence of both average cost optimal stationary policies and a solution of the average optimality equation under the conditions. The results in this paper are applied to an admission control queue model and controlled birth and death processes.

On the relationship between µ-invariant measures and quasi-stationary distributions for continuous-time Markov chains

1993 ◽  
Vol 25 (01) ◽  
pp. 82-102
Author(s):  
M. G. Nair ◽  
P. K. Pollett
Keyword(s):  
Invariant Measure ◽  
Stationary Distribution ◽  
Continuous Time ◽  
Sufficient Condition ◽  
Transition Rates ◽  
Necessary And Sufficient Condition ◽  
Absorbing State ◽  
Necessary And Sufficient ◽  
Forward Equations ◽  
Quasi Stationary Distribution

In a recent paper, van Doorn (1991) explained how quasi-stationary distributions for an absorbing birth-death process could be determined from the transition rates of the process, thus generalizing earlier work of Cavender (1978). In this paper we shall show that many of van Doorn's results can be extended to deal with an arbitrary continuous-time Markov chain over a countable state space, consisting of an irreducible class, C, and an absorbing state, 0, which is accessible from C. Some of our results are extensions of theorems proved for honest chains in Pollett and Vere-Jones (1992). In Section 3 we prove that a probability distribution on C is a quasi-stationary distribution if and only if it is a µ-invariant measure for the transition function, P. We shall also show that if m is a quasi-stationary distribution for P, then a necessary and sufficient condition for m to be µ-invariant for Q is that P satisfies the Kolmogorov forward equations over C. When the remaining forward equations hold, the quasi-stationary distribution must satisfy a set of ‘residual equations' involving the transition rates into the absorbing state. The residual equations allow us to determine the value of µ for which the quasi-stationary distribution is µ-invariant for P. We also prove some more general results giving bounds on the values of µ for which a convergent measure can be a µ-subinvariant and then µ-invariant measure for P. The remainder of the paper is devoted to the question of when a convergent µ-subinvariant measure, m, for Q is a quasi-stationary distribution. Section 4 establishes a necessary and sufficient condition for m to be a quasi-stationary distribution for the minimal chain. In Section 5 we consider ‘single-exit' chains. We derive a necessary and sufficient condition for there to exist a process for which m is a quasi-stationary distribution. Under this condition all such processes can be specified explicitly through their resolvents. The results proved here allow us to conclude that the bounds for µ obtained in Section 3 are, in fact, tight. Finally, in Section 6, we illustrate our results by way of two examples: regular birth-death processes and a pure-birth process with absorption.

Dynamic performance evaluation of multi – state systems under non – homogeneous continuous time Markov process degradation using lifetimes in terms of order statistics

2017 ◽  
Vol 231 (3) ◽  
pp. 255-264 ◽  
Author(s):  
Funda Iscioglu
Keyword(s):  
Markov Process ◽  
Order Statistics ◽  
Continuous Time ◽  
Dynamic Performance ◽  
Real Life ◽  
State Change ◽  
Transition Rates ◽  
Lifetime Analysis ◽  
Complete Failure ◽  
Effect Of Age

In multi-state modelling a system and its components have a range of performance levels from perfect functioning to complete failure. Such a modelling is more flexible to understand the behaviour of mechanical systems. To evaluate a system’s dynamic performance, lifetime analysis of a multi-state system has been considered in many research articles. The order statistics related analysis for the lifetime properties of multi-state k-out-of-n systems have recently been studied in the literature in case of homogeneous continuous time Markov process assumption. In this paper, we develop the reliability measures for multi-state k-out-of-n systems by assuming a non-homogeneous continuous time Markov process for the components which provides time dependent transition rates between states of the components. Therefore, we capture the effect of age on the state change of the components in the analysis which is typical of many systems and more practical to use in real life applications.

The effects of focal stimulation in nucleus raphe magnus and periaqueductal gray on intracellularly recorded neurons in spinal laminae I and II

1986 ◽  
Vol 56 (3) ◽  
pp. 555-571 ◽  
Author(s):  
A. R. Light ◽  
E. J. Casale ◽  
D. M. Menetrey
Keyword(s):  
Brain Stem ◽  
Periaqueductal Gray ◽  
The Other ◽  
Descending Pathways ◽  
Nucleus Raphe Magnus ◽  
Raphe Magnus ◽  
Low Threshold ◽  
Conductance Increase ◽  
Small Conductance ◽  
Postsynaptic Mechanism

Single neurons in spinal laminae I and II of cats were recorded intracellularly while stimulating in nucleus raphe magnus (NRM) and periaqueductal gray (PAG) with monopolar tungsten microelectrodes. Brain stem stimulation inhibited about one-half of the nociceptive-specific neurons, whereas the other half was unaffected. Brain stem stimulation inhibited about one-half of the multireceptive neurons, but the other half was excited and then inhibited. Brain stem stimulation inhibited about one-third of the low-threshold neurons, one-half was excited then inhibited, and one-fifth showed no effect. In all classes of neurons, the inhibition was produced by an inhibitory postsynaptic potential (IPSP) that began with a latency of approximately 25 ms and lasted approximately 400 ms following a single stimulus. The IPSP occurred with a small conductance increase and was reversed by hyperpolarizing currents applied to the cell. These data indicate that NRM and PAG modulated laminae I and II neurons via a postsynaptic mechanism. The conduction velocity of this descending pathway was calculated to range from 6.1 to 66.6 m/s with an average of 13.8 m/s. These data also indicate heterogeneity in the pathway, since some neurons were inhibited, whereas other neurons were excited then inhibited by descending stimulation. Finally, these data indicate specificity in these descending pathways since nearly one-half of neurons that had low-threshold inputs were excited by brain stem stimulation, whereas nearly all nociceptive-specific neurons were either inhibited or unaffected.

scholarly journals Defining the Role of the Tension Sensor in the Mechanosensitive Channel of Small Conductance

2011 ◽  
Vol 101 (2) ◽  
pp. 345-352 ◽  
Author(s):  
Hannah R. Malcolm ◽  
Yoon-Young Heo ◽  
Donald E. Elmore ◽  
Joshua A. Maurer
Keyword(s):  
Mechanosensitive Channel ◽  
Tension Sensor ◽  
Small Conductance

scholarly journals H∞ Synchronization of Semi-Markovian Jump Neural Networks with Randomly Occurring Time-Varying Delays

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-16 ◽  
Author(s):  
Mengping Xing ◽  
Hao Shen ◽  
Zhen Wang
Keyword(s):  
Neural Networks ◽  
Continuous Time ◽  
Lyapunov Stability Theory ◽  
Schur Complement ◽  
Jensen Inequality ◽  
Time Varying ◽  
Transition Rates ◽  
Markovian Jump ◽  
Synchronization Problem ◽  
Markovian Jump Neural Networks

Based on the Lyapunov stability theory, this paper mainly investigates the H∞ synchronization problem for semi-Markovian jump neural networks (semi-MJNNs) with randomly occurring time-varying delays (TVDs). The continuous-time semi-MJNNs, where the transition rates are dependent on sojourn time, are introduced to make the issue under our consideration more general. One of the main characteristics of our work is the handling of TVDs. In addition to using the improved Jensen inequality and the reciprocal convexity lemma to deal with the integral inequality, we also employ Schur complement and the projection lemma to achieve the decoupling between the square term of TVDs. Finally, we verify the validity and feasibility of our method by a couple of simulation examples.

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