2,874 research outputs found
A perturbation analysis of spontaneous action potential initiation by stochastic ion channels
A stochastic interpretation of spontaneous action potential initiation is developed for the Morris- Lecar equations. Initiation of a spontaneous action potential can be interpreted as the escape from one of the wells of a double well potential, and we develop an asymptotic approximation of the mean exit time using a recently-developed quasi-stationary perturbation method. Using the fact that the activating ionic channelās random openings and closings are fast relative to other processes, we derive an accurate estimate for the mean time to fire an action potential (MFT), which is valid for a below-threshold applied current. Previous studies have found that for above-threshold applied current, where there is only a single stable fixed point, a diffusion approximation can be used. We also explore why different diffusion approximation techniques fail to estimate the MFT
Filling of a Poisson trap by a population of random intermittent searchers
We extend the continuum theory of random intermittent search processes to the case of independent searchers looking to deliver cargo to a single hidden target located somewhere on a semi--infinite track. Each searcher randomly switches between a stationary state and either a leftward or rightward constant velocity state. We assume that all of the particles start at one end of the track and realize sample trajectories independently generated from the same underlying stochastic process. The hidden target is treated as a partially absorbing trap in which a particle can only detect the target and deliver its cargo if it is stationary and within range of the target; the particle is removed from the system after delivering its cargo. As a further generalization of previous models, we assume that up to successive particles can find the target and deliver its cargo. Assuming that the rate of target detection scales as , we show that there exists a well--defined mean field limit , in which the stochastic model reduces to a deterministic system of linear reaction--hyperbolic equations for the concentrations of particles in each of the internal states. These equations decouple from the stochastic process associated with filling the target with cargo. The latter can be modeled as a Poisson process in which the time--dependent rate of filling depends on the concentration of stationary particles within the target domain. Hence, we refer to the target as a Poisson trap. We analyze the efficiency of filling the Poisson trap with particles in terms of the waiting time density . The latter is determined by the integrated Poisson rate , which in turn depends on the solution to the reaction-hyperbolic equations. We obtain an approximate solution for the particle concentrations by reducing the system of reaction-hyperbolic equations to a scalar advection--diffusion equation using a quasi-steady-state analysis. We compare our analytical results for the mean--field model with Monte-Carlo simulations for finite . We thus determine how the mean first passage time (MFPT) for filling the target depends on and
Local synaptic signaling enhances the stochastic transport of\ud motor-driven cargo in neurons
The tug-of-war model of motor-driven cargo transport is formulated as an intermittent trapping process. An immobile trap, representing the cellular machinery that sequesters a motor-driven cargo for eventual use, is located somewhere within a microtubule track. A particle representing a motor-driven cargo that moves randomly with a forward bias is introduced at the beginning of the track. The particle switches randomly between a fast moving phase and a slow moving phase. When in the slow moving phase, the particle can be captured by the trap. To account for the possibility the particle avoids the trap, an absorbing boundary is placed at the end of the track. Two local signaling mechanismsāintended to improve the chances of capturing the targetāare considered by allowing the trap to affect the tug-of-war parameters within a small region around itself. The first is based on a localized adenosine triphosphate (ATP) concentration gradient surrounding a synapse, and the second is based on a concentration of tauāa microtubule-associated protein involved in Alzheimerās diseaseācoating the microtubule near the synapse. It is shown that both mechanisms can lead to dramatic improvements in the capture probability, with a minimal increase in the mean capture time. The analysis also shows that tau can cause a cargo to undergo random oscillations, which could explain some experimental observations
Stochastic models of intracellular transport
The interior of a living cell is a crowded, heterogenuous, fluctuating environment. Hence, a major challenge in modeling intracellular transport is to analyze stochastic processes within complex environments. Broadly speaking, there are two basic mechanisms for intracellular transport: passive diffusion and motor-driven active transport. Diffusive transport can be formulated in terms of the motion of an over-damped Brownian particle. On the other hand, active transport requires chemical energy, usually in the form of ATP hydrolysis, and can be direction specific, allowing biomolecules to be transported long distances; this is particularly important in neurons due to their complex geometry. In this review we present a wide range of analytical methods and models of intracellular transport. In the case of diffusive transport, we consider narrow escape problems, diffusion to a small target, confined and single-file diffusion, homogenization theory, and fractional diffusion. In the case of active transport, we consider Brownian ratchets, random walk models, exclusion processes, random intermittent search processes, quasi-steady-state reduction methods, and mean field approximations. Applications include receptor trafficking, axonal transport, membrane diffusion, nuclear transport, protein-DNA interactions, virus trafficking, and the selfāorganization of subcellular structures
Quasi-steady state reduction of molecular motor-based models of directed intermittent search
We present a quasiāsteady state reduction of a linear reactionāhyperbolic master equation describing the directed intermittent search for a hidden target by a motorādriven particle moving on a oneādimensional filament track. The particle is injected at one end of the track and randomly switches between stationary search phases and mobile, non-search phases that are biased in the anterograde direction. There is a finite possibility that the particle fails to find the target due to an absorbing boundary at the other end of the track. Such a scenario is exemplified by the motorādriven transport of vesicular cargo to synaptic targets located on the axon or dendrites of a neuron. The reduced model is described by a scalar FokkerāPlanck (FP) equation, which has an additional inhomogeneous decay term that takes into account absorption by the target. The FP equation is used to compute the probability of finding the hidden target (hitting probability) and the corresponding conditional mean first passage time (MFPT) in terms of the effective drift velocity V , diffusivity D and target absorption rate Ī» of the random search. The quasiāsteady state reduction determines V, D and Ī» in terms of the various biophysical parameters of the underlying motor transport model. We first apply our analysis to a simple 3āstate model and show that our quasiāsteady state reduction yields results that are in excellent agreement with Monte Carlo simulations of the full system under physiologically reasonable conditions. We then consider a more complex multiple motor model of bidirectional transport, in which opposing motors compete in a ātug-of-war,ā and use this to explore how ATP concentration might regulate the delivery of cargo to synaptic targets
Effects of demographic noise on the synchronization of a metapopulation in a fluctuating environment
We use the theory of noise-induced phase synchronization to analyze the effects of demographic noise on the synchronization of a metapopulation of predator-prey systems within a fluctuating environment (Moran effect). Treating each local predatorāprey population as a stochastic urn model, we derive a Langevin equation for the stochastic dynamics of the metapopulation. Assuming each local population acts as a limit cycle oscillator in the deterministic limit, we use phase reduction and averaging methods to derive the steady state probability density for pairwise phase differences between oscillators, which is then used to determine the degree of synchronization of\ud
the metapopulation
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Advantages of open source processes for reliability: clarifying the issues
Isolating intrinsic noise sources in a stochastic genetic switch
The stochastic mutual repressor model is analysed using perturbation methods. This simple model of a gene circuit consists of two genes and three promotor states. Either of the two protein products can dimerize, forming a repressor molecule that binds to the promotor of the other gene. When the repressor is bound to a promotor, the corresponding gene is not transcribed and no protein is produced. Either one of the promotors can be repressed at any given time or both can be unrepressed, leaving three possible promotor states. This model is analysed in its bistable regime in which the deterministic limit exhibits two stable fixed points and an unstable saddle, and the case of small noise is considered. On small time scales, the stochastic process fluctuates near one of the stable fixed points, and on large time scales, a metastable transition can occur, where fluctuations drive the system past the unstable saddle to the other stable fixed point. To explore how different intrinsic noise sources affect these transitions, fluctuations in protein production and degradation are eliminated, leaving fluctuations in the promotor state as the only source of noise in the system. Perturbation methods are then used to compute the stability landscape and the distribution of transition times, or first exit time density. To understand how protein noise affects the system, small magnitude fluctuations are added back into the process, and the stability landscape is compared to that of the process without protein noise. It is found that significant differences in the random process emerge in the presence of protein noise
Assessing the Risk of Crew Injury Due to Dynamic Loads During Spaceflight
No abstract availabl
Estimating urban flood risk - uncertainty in design criteria
The design of urban stormwater infrastructure is generally performed assuming that climate is static. For engineering practitioners, stormwater infrastructure is designed using a peak flow method, such as the Rational Method as outlined in the Australian Rainfall and Runoff (AR&R) guidelines and estimates of design rainfall intensities. Changes to Australian rainfall intensity design criteria have been made through updated releases of the AR&R77, AR&R87 and the recent 2013 AR&R Intensity Frequency Distributions (IFDs). The primary focus of this study is to compare the three IFD sets from 51 locations Australia wide. Since the release of the AR&R77 IFDs, the duration and number of locations for rainfall data has increased and techniques for data analysis have changed. Updated terminology coinciding with the 2013 IFD release has also resulted in a practical change to the design rainfall. For example, infrastructure that is designed for a 1: 5 year ARI correlates with an 18.13 % AEP, however for practical purposes, hydraulic guidelines have been updated with the more intuitive 20 % AEP. The evaluation of design rainfall variation across Australia has indicated that the changes are dependent upon location, recurrence interval and rainfall duration. The changes to design rainfall IFDs are due to the application of differing data analysis techniques, the length and number of data sets and the change in terminology from ARI to AEP. Such changes mean that developed infrastructure has been designed to a range of different design criteria indicating the likely inadequacy of earlier developments to the current estimates of flood risk. In many cases, the under-design of infrastructure is greater than the expected impact of increased rainfall intensity under climate change scenarios
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