A simple parametric method for reducing sample sizes in gut passage time trials

Seed dispersal is now regularly analyzed using spatially explicit models, relying in part on frugivore gut passage times to produce model outputs. In determining species-specific gut passage times, there is a trade-off in sample size between minimizing collection effort and maintaining statistical reliability. Here we demonstrate that a two-parameter lognormal parametric distribution reliably fits empirical gut passage time distributions and is easily parameterized using relatively small data sets of approximately 30 defecations. We suggest this approach as a statistically reliable substitute for larger empirical gut passage data sets in seed dispersal modeling, and also as a way of using published gut passage data sets to parameterize new models.

Sedimentary Metal Bioavailability Determined By the Digestive Constraints of Marine Deposit Feeders: Gut Retention Time and Dissolved Amino Acids

Contaminant metals bound to sediments are subject to considerable solubilization during passage of the sediments through the digestive systems of deposit feeders. We examined the kinetics of this process, using digestive fluids extracted from deposit feeders Arenicola marina and Parastichopus californicus and then incubated with contaminated sediments. Kinetics are complex, with solubilization followed occasionally by readsorption onto the sediment. In general, solubilization kinetics are biphasic, with an initial rapid step followed by a slower reaction. For many sediment-organism combinations, the reaction will not reach a steady state or equilibrium within the gut retention time (GRT) of the organisms, suggesting that metal bioavailability in sediments is a time-dependent parameter. Experiments with commercial protein solutions mimic the kinetic patterns observed with digestive fluids, which corroborates our previous study that complexation by dissolved amino acids (AA) in digestive fluids leads to metal solubilization (Chen & Mayer 1998b; Environ Sci Technol 32:770-778). The relative importance of the fast and slow reactions appears to depend on the ratio of ligands in gut fluids to the amount of bound metal in sediments. High ligand to solid metal ratios result in more metals released in fast reactions and thus higher lability of sedimentary metals. Multiple extractions of a sediment with digestive fluid of A. marina confirm the potential importance of incomplete reactions within a single deposit-feeding event, and make clear that bioavailability to a single animal is Likely different from that to a community of organisms. The complex kinetic patterns lead to the counterintuitive prediction that toxification of digestive enzymes by solubilized metals will occur more readily in species that dissolve less metals.

A lower bound to the survival probability and an approximate first passage time distribution for Markovian and non-Markovian dynamics in phase space

We derive a very general expression of the survival probability and the first passage time distribution for a particle executing Brownian motion in full phase space with an absorbing boundary condition at a point in the position space, which is valid irrespective of the statistical nature of the dynamics. The expression, together with the Jensen's inequality, naturally leads to a lower bound to the actual survival probability and an approximate first passage time distribution. These are expressed in terms of the position-position, velocity-velocity, and position-velocity variances. Knowledge of these variances enables one to compute a lower bound to the survival probability and consequently the first passage distribution function. As examples, we compute these for a Gaussian Markovian process and, in the case of non-Markovian process, with an exponentially decaying friction kernel and also with a power law friction kernel. Our analysis shows that the survival probability decays exponentially at the long time irrespective of the nature of the dynamics with an exponent equal to the transition state rate constant.

Mean first passage time approach to the problem of optimal barrier subdivision for Kramer's escape rate

We consider the effect of subdividing the potential barrier along the reaction coordinate on Kramer's escape rate for a model potential, Using the known supersymmetric potential approach, we show the existence of an optimal number of subdivisions that maximizes the rate, We cast the problem as a mean first passage time problem of a biased random walker and obtain equivalent results, We briefly summarize the results of our investigation on the increase in the escape rate by placing a blow-torch in the unstable part of one of the potential wells. (C) 1999 Elsevier Science B.V. All rights reserved.

1D Tight-Binding Models Render Quantum First Passage Time ``Speakable''

The calculation of First Passage Time (moreover, even its probability density in time) has so far been generally viewed as an ill-posed problem in the domain of quantum mechanics. The reasons can be summarily seen in the fact that the quantum probabilities in general do not satisfy the Kolmogorov sum rule: the probabilities for entering and non-entering of Feynman paths into a given region of space-time do not in general add up to unity, much owing to the interference of alternative paths. In the present work, it is pointed out that a special case exists (within quantum framework), in which, by design, there exists one and only one available path (i.e., door-way) to mediate the (first) passage -no alternative path to interfere with. Further, it is identified that a popular family of quantum systems - namely the 1d tight binding Hamiltonian systems - falls under this special category. For these model quantum systems, the first passage time distributions are obtained analytically by suitably applying a method originally devised for classical (stochastic) mechanics (by Schroedinger in 1915). This result is interesting especially given the fact that the tight binding models are extensively used in describing everyday phenomena in condense matter physics.

First-passage time of Duffing oscillator under combined harmonic and white-noise excitations

The first-passage time of Duffing oscillator under combined harmonic and white-noise excitations is studied. The equation of motion of the system is first reduced to a set of averaged Ito stochastic differential equations by using the stochastic averaging method. Then, a backward Kolmogorov equation governing the conditional reliability function and a set of generalized Pontryagin equations governing the conditional moments of first-passage time are established. Finally, the conditional reliability function, and the conditional probability density and moments of first-passage time are obtained by solving the backward Kolmogorov equation and generalized Pontryagin equations with suitable initial and boundary conditions. Numerical results for two resonant cases with several sets of parameter values are obtained and the analytical results are verified by using those from digital simulation.

First-passage time distribution and non-Markovian diffusion dynamics of protein folding

We study the kinetics of protein folding via statistical energy landscape theory. We concentrate on the local-connectivity case, where the configurational changes can only occur among neighboring states, with the folding progress described in terms of an order parameter given by the fraction of native conformations. The non-Markovian diffusion dynamics is analyzed in detail and an expression for the mean first-passage time (MFPT) from non-native unfolded states to native folded state is obtained. It was found that the MFPT has a V-shaped dependence on the temperature. We also find that the MFPT is shortened as one increases the gap between the energy of the native and average non-native folded states relative to the fluctuations of the energy landscape. The second- and higher-order moments are studied to infer the first-passage time distribution. At high temperature, the distribution becomes close to a Poisson distribution, while at low temperatures the distribution becomes a Levy-type distribution with power-law tails, indicating a nonself-averaging intermittent behavior of folding dynamics. We note the likely relevance of this result to single-molecule dynamics experiments, where a power law (Levy) distribution of the relaxation time of the underlined protein energy landscape is observed.

Diffusion dynamics, moments, and distribution of first-passage time on the protein-folding energy landscape, with applications to single molecules

We study the dynamics of protein folding via statistical energy-landscape theory. In particular, we concentrate on the local-connectivity case with the folding progress described by the fraction of native conformations. We found that the first passage-time (FPT) distribution undergoes a dynamic transition at a temperature below which the FPT distribution develops a power-law tail, a signature of the intermittent nonexponential kinetic phenomena for the folding dynamics. Possible applications to single-molecule dynamics experiments are discussed.

Temperature dependence of the distribution of the first passage time: Results from discontinuous molecular dynamics simulations of an all-atom model of the second beta-hairpin fragment of protein G

More than 22 000 folding kinetic simulations were performed to study the temperature dependence of the distribution of first passage time (FPT) for the folding of an all-atom Go-like model of the second beta-hairpin fragment of protein G. We find that the mean FPT (MFPT) for folding has a U (or V)-shaped dependence on the temperature with a minimum at a characteristic optimal folding temperature T-opt*. The optimal folding temperature T-opt* is located between the thermodynamic folding transition temperature and the solidification temperature based on the Lindemann criterion for the solid. Both the T-opt* and the MFPT decrease when the energy bias gap against nonnative contacts increases. The high-order moments are nearly constant when the temperature is higher than T-opt* and start to diverge when the temperature is lower than T-opt*. The distribution of FPT is close to a log-normal-like distribution at T* greater than or equal to T-opt*. At even lower temperatures, the distribution starts to develop long power-law-like tails, indicating the non-self-averaging intermittent behavior of the folding dynamics. It is demonstrated that the distribution of FPT can also be calculated reliably from the derivative of the fraction not folded (or fraction folded), a measurable quantity by routine ensemble-averaged experimental techniques at dilute protein concentrations.

Digestion of copepod eggs by larval turbot Scophthalmus maximus and egg viability following gut passage

Between 20.5 and 93.6 % of the subitaneous eggs of 6 species of egg-carrying copepods passed undigested through the digestive tracts of larval and early postlarval turbot Scophthalmus maximus. Viability of the eggs of Eurytemora affinis, E. velox and Euterpina acutifrons remained high on egestion (67.0 to 91.7 %), Pseudocalanus elongatus and Oncaea venusta eggs had low viability (1.1 to 1.5 %), while all Corycaeus anglicus eggs were rendered inviable. The indigestibility of the eggs denies the turbot larvae a potentially valuable food resource, while retention of high egg viability in certain species reduces the effect of predation.

Impact of gut passage and mucus secretion by the earthworm Lumbricus terrestris on mobility and speciation of arsenic in contaminated soil

Earthworms inhabiting arsenic contaminated soils may accelerate the leaching of As into surface and ground waters. We carried out three experiments to determine the impact of passage of As contaminated soil (1150 mgAs kg−1) through the gut of the earthworm Lumbricus terrestris on the mobility and speciation of As and the effects of earthworm mucus on As mobility. The concentration of water soluble As in soil increased (from 1.6 to 18 mg kg−1) after passage through the earthworm gut. Casts that were aged for 56 days still contained more than nine times greater water soluble As than bulk earthworm inhabited soil. Changes were due to increases in As(V) mobility, with no change in As(III). Dilute mucus extracts reduced As mobility through the formation of As-amino acid-iron oxide ternary complexes. More concentrated mucus extracts increased As mobility. These changes, together with those due to the passage through the gut, were due to increases in pH, phosphate and soluble organic carbon. The mobilisation of As from contaminated soils in the environment by cast production and mucus secretion may allow for accelerated leaching or uptake into biota which is underestimated when bulk soil samples are analysed and the influence of soil biota ignored.

First passages in bounded domains: When is the mean first passage time meaningful?

We study the first passage statistics to adsorbing boundaries of a Brownian motion in bounded two-dimensional domains of different shapes and configurations of the adsorbing and reflecting boundaries. From extensive numerical analysis we obtain the probability P(ω) distribution of the random variable ω=τ1/(τ1+τ2), which is a measure for how similar the first passage times τ1 and τ2 are of two independent realizations of a Brownian walk starting at the same location. We construct a chart for each domain, determining whether P(ω) represents a unimodal, bell-shaped form, or a bimodal, M-shaped behavior. While in the former case the mean first passage time (MFPT) is a valid characteristic of the first passage behavior, in the latter case it is an insufficient measure for the process. Strikingly we find a distinct turnover between the two modes of P(ω), characteristic for the domain shape and the respective location of absorbing and reflective boundaries. Our results demonstrate that large fluctuations of the first passage times may occur frequently in two-dimensional domains, rendering quite vague the general use of the MFPT as a robust measure of the actual behavior even in bounded domains, in which all moments of the first passage distribution exist.