High frequency difraction by a soft circular disc. I the plane wave at normal incidence

The far scattered field off the axis of symmetry of the disc is found for a high frequency, harmonic, normally incident, plane wave. The method used is due to Jones and involves the solution of a singular integral equation of the first kind for the field on the disc. This integral equation can be converted into an integral equation of the second kind which is of particular value at high frequencies. In the present work the known function in the equation is written in the form of a contour integral. A suitable change of unknown function then produces extensive cancellation and yields a single function fundamental to the problem. The detailed calculations of the far field give terms which are believed to be new. In executing these calculations some interesting relationships between the terms involved are demonstrated

Random intermittent search and the tug-of-war model of motor-driven transport

We formulate the tug-of-war model of microtubule cargo transport by multiple molecular motors as an intermittent random search for a hidden target. A motor-complex consisting of multiple molecular motors with opposing directional preference is modeled using a discrete Markov process. The motors randomly pull each other off of the microtubule so that the state of the motor-complex is determined by the number of bound motors. The tug-of-war model prescribes the state transition rates and corresponding cargo velocities in terms of experimentally measured physical parameters. We add space to the resulting Chapman-Kolmogorov (CK) equation so that we can consider delivery of the cargo to a hidden target somewhere on the microtubule track. Using a quasi-steady state (QSS) reduction technique we calculate analytical approximations of the mean first passage time (MFPT) to find the target. We show that there exists an optimal adenosine triphosphate (ATP)concentration that minimizes the MFPT for two different cases: (i) the motor complex is composed of equal numbers of kinesin motors bound to two different microtubules (symmetric tug-of-war model), and (ii) the motor complex is composed of different numbers of kinesin and dynein motors bound to a single microtubule(asymmetric tug-of-war model)

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 $N$ 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 $n$ successive particles can find the target and deliver its cargo. Assuming that the rate of target detection scales as $1/N$, we show that there exists a well--defined mean field limit $N\rightarrow \infty$, 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 $\lambda(t)$ 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 $n$ particles in terms of the waiting time density $f_n(t)$. The latter is determined by the integrated Poisson rate $\mu(t)=\int_0^t\lambda(s)ds$, 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 $N$. We thus determine how the mean first passage time (MFPT) for filling the target depends on $N$ and $n$

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 mechanisms—intended to improve the chances of capturing the target—are 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 tau—a microtubule-associated protein involved in Alzheimer’s disease—coating 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

Metastability in a stochastic neural network modeled as a velocity jump Markov process

One of the major challenges in neuroscience is to determine how noise that is present at the molecular and cellular levels affects dynamics and information processing at the macroscopic level of synaptically coupled neuronal populations. Often noise is incorprated into deterministic network models using extrinsic noise sources. An alternative approach is to assume that noise arises intrinsically as a collective population effect, which has led to a master equation formulation of stochastic neural networks. In this paper we extend the master equation formulation by introducing a stochastic model of neural population dynamics in the form of a velocity jump Markov process. The latter has the advantage of keeping track of synaptic processing as well as spiking activity, and reduces to the neural master equation in a particular limit. The population synaptic variables evolve according to piecewise deterministic dynamics, which depends on population spiking activity. The latter is characterised by a set of discrete stochastic variables evolving according to a jump Markov process, with transition rates that depend on the synaptic variables. We consider the particular problem of rare transitions between metastable states of a network operating in a bistable regime in the deterministic limit. Assuming that the synaptic dynamics is much slower than the transitions between discrete spiking states, we use a WKB approximation and singular perturbation theory to determine the mean first passage time to cross the separatrix between the two metastable states. Such an analysis can also be applied to other velocity jump Markov processes, including stochastic voltage-gated ion channels and stochastic gene networks

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 self–organization of subcellular structures

Quasi-steady state reduction of molecular motor-based models of directed intermittent search

We present a quasi–steady state reduction of a linear reaction–hyperbolic master equation describing the directed intermittent search for a hidden target by a motor–driven particle moving on a one–dimensional 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 motor–driven transport of vesicular cargo to synaptic targets located on the axon or dendrites of a neuron. The reduced model is described by a scalar Fokker–Planck (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 λ of the random search. The quasi–steady state reduction determines V, D and λ in terms of the various biophysical parameters of the underlying motor transport model. We first apply our analysis to a simple 3–state model and show that our quasi–steady 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 “tug-of-war,” and use this to explore how ATP concentration might regulate the delivery of cargo to synaptic targets

Living on the margin: Assessing the economic impacts of Landcare in the Philippine uplands

In the Philippines, about 38 per cent of the population resides in rural areas where poverty remains a significant problem. In 2006, 47 per cent of all households in Bohol Province fell below the national poverty line, with the percentage even higher in upland communities. These households often exist in marginal landscapes that are under significant pressure from ongoing resource degradation and rising input costs. This paper first explores whether the adoption of Landcare practices in a highly degraded landscape has resulted in improved livelihood outcomes for upland farming families in Bohol. Second, it analyses the potential for the piecemeal adoption of these measures to deliver tangible benefits at the watershed scale. Finally, using a BCA approach, these outcomes are compared to the costs of the research and extension projects that have helped achieve them.Landcare, Philippines, livelihoods, poverty, watershed, ACIAR,

Metabolic and functional consequences of cytosolic 5′-nucleotidase-IA overexpression in neonatal rat cardiomyocytes

Adenosine exerts a spectrum of energy-preserving actions on the heart negative chronotropic effects. The pathways leading to adenosine formation have remained controversial. In particular, although cytosolic 5′-nucleotidases can catalyze adenosine formation in cardiomyocytes, their contribution to the actions of adenosine has not been documented previously. We recently cloned two closely related AMP-preferring cytosolic 5′-nucleotidases (cN-IA and -IB); the A form predominates in the heart. In this study, we overexpressed pigeon cN-IA in neonatal rat cardiomyocytes using an adenovirus. cN-IA overexpression increased adenosine formation and release into the medium caused by simulated hypoxia and by isoproterenol in the absence and presence of inhibitors of adenosine metabolism. Adenosine release was not affected by an ecto-5′-nucleotidase inhibitor, α,β-methylene-ADP, but was affected by a nucleoside transporter, dipyridamole. The positive chronotropic effect of isoproterenol (130 ±3 vs. 100 ±4 beats/min) was inhibited (107 ±3 vs. 94 ±3 beats/min) in cells overexpressing cN-IA, and this was reversed by the addition of the adenosine receptor antagonist 8-(p-sulfophenyl)theophilline (120 ± 3 vs. 90 ± 4 beats/min). Our results demonstrate that overexpressed cN-IA can be sufficiently active in cardiomyocytes to generate physiologically effective concentrations of adenosine at its receptors.Fil: Sala-Newby, Graciela B.. University of Bristol; Reino UnidoFil: Freeman, Nicola V. E.. University of Bristol; Reino UnidoFil: Curto, Maria de Los Angeles. University of Bristol; Reino Unido. Consejo Nacional de Investigaciones Científicas y Técnicas. Instituto de Investigaciones en Ingeniería Genética y Biología Molecular "Dr. Héctor N. Torres"; ArgentinaFil: Newby, Andrew C.. University of Bristol; Reino Unid