A jump-growth model for predator-prey dynamics: derivation and application to marine ecosystems

This paper investigates the dynamics of biomass in a marine ecosystem. A stochastic process is defined in which organisms undergo jumps in body size as they catch and eat smaller organisms. Using a systematic expansion of the master equation, we derive a deterministic equation for the macroscopic dynamics, which we call the deterministic jump-growth equation, and a linear Fokker-Planck equation for the stochastic fluctuations. The McKendrick--von Foerster equation, used in previous studies, is shown to be a first-order approximation, appropriate in equilibrium systems where predators are much larger than their prey. The model has a power-law steady state consistent with the approximate constancy of mass density in logarithmic intervals of body mass often observed in marine ecosystems. The behaviours of the stochastic process, the deterministic jump-growth equation and the McKendrick--von Foerster equation are compared using numerical methods. The numerical analysis shows two classes of attractors: steady states and travelling waves.Comment: 27 pages, 4 figures. Final version as published. Only minor change

An autonomous chemically fuelled small-molecule motor

Molecular machines are among the most complex of all functional molecules and lie at the heart of nearly every biological process. A number of synthetic small-molecule machines have been developed, including molecular muscles, synthesizers, pumps, walkers, transporters and light-driven and electrically driven rotary motors. However, although biological molecular motors are powered by chemical gradients or the hydrolysis of adenosine triphosphate (ATP), so far there are no synthetic small-molecule motors that can operate autonomously using chemical energy (that is, the components move with net directionality as long as a chemical fuel is present). Here we describe a system in which a small molecular ring (macrocycle) is continuously transported directionally around a cyclic molecular track when powered by irreversible reactions of a chemical fuel, 9-fluorenylmethoxycarbonyl chloride. Key to the design is that the rate of reaction of this fuel with reactive sites on the cyclic track is faster when the macrocycle is far from the reactive site than when it is near to it. We find that a bulky pyridine-based catalyst promotes carbonate-forming reactions that ratchet the displacement of the macrocycle away from the reactive sites on the track. Under reaction conditions where both attachment and cleavage of the 9-fluorenylmethoxycarbonyl groups occur through different processes, and the cleavage reaction occurs at a rate independent of macrocycle location, net directional rotation of the molecular motor continues for as long as unreacted fuel remains. We anticipate that autonomous chemically fuelled molecular motors will find application as engines in molecular nanotechnology.</p

Dose Effects of Oxaliplatin on Persistent and Transient Na+ Conductances and the Development of Neurotoxicity

BACKGROUND: Oxaliplatin, a platinum-based chemotherapy utilised in the treatment of colorectal cancer, produces two forms of neurotoxicity--acute sensorimotor neuropathic symptoms and a dose-limiting chronic sensory neuropathy. Given that a Na(+) channelopathy has been proposed as the mechanism underlying acute oxaliplatin-induced neuropathy, the present study aimed to determine specific mechanisms of Na(+) channel dysfunction. METHODOLOGY/PRINCIPAL FINDINGS: Specifically the function of transient and persistent Na(+) currents were followed during treatment and were investigated in relation to oxaliplatin dose level. Eighteen patients were assessed before and after a single oxaliplatin infusion with motor and sensory axonal excitability studies performed on the median nerve at the wrist. While refractoriness (associated with Na(+) channel inactivation) was significantly altered post-oxaliplatin infusion in both motor (Pre: 31.7±6.4%; Post: 68.8±14.5%; P≤.001) and sensory axons (Pre: 31.4±5.4%; Post: 21.4±5.5%; P<.05), strength-duration time constant (marker of persistent Na(+) conductances) was not significantly altered post-infusion (Motor Pre: 0.395±0.01 ms; Post: 0.394±0.02 ms; NS; Sensory Pre:0.544±0.03 ms; Post: 0.535±0.05 ms; NS). However, changes in strength-duration time constant were significantly correlated with changes in refractoriness in motor and sensory axons (Motor correlation coefficient = -.65; P<.05; Sensory correlation coefficient = .67; P<.05). CONCLUSIONS/SIGNIFICANCE: It is concluded that the predominant effect of acute oxaliplatin exposure in human motor and sensory axons is mediated through changes in transient rather than persistent Na(+) conductances. These findings are likely to have implications for the design and trial of neuroprotective strategies

Sheldon Spectrum and the Plankton Paradox: Two Sides of the Same Coin : A trait-based plankton size-spectrum model

The Sheldon spectrum describes a remarkable regularity in aquatic ecosystems: the biomass density as a function of logarithmic body mass is approximately constant over many orders of magnitude. While size-spectrum models have explained this phenomenon for assemblages of multicellular organisms, this paper introduces a species-resolved size-spectrum model to explain the phenomenon in unicellular plankton. A Sheldon spectrum spanning the cell-size range of unicellular plankton necessarily consists of a large number of coexisting species covering a wide range of characteristic sizes. The coexistence of many phytoplankton species feeding on a small number of resources is known as the Paradox of the Plankton. Our model resolves the paradox by showing that coexistence is facilitated by the allometric scaling of four physiological rates. Two of the allometries have empirical support, the remaining two emerge from predator-prey interactions exactly when the abundances follow a Sheldon spectrum. Our plankton model is a scale-invariant trait-based size-spectrum model: it describes the abundance of phyto- and zooplankton cells as a function of both size and species trait (the maximal size before cell division). It incorporates growth due to resource consumption and predation on smaller cells, death due to predation, and a flexible cell division process. We give analytic solutions at steady state for both the within-species size distributions and the relative abundances across species

Drilling constraints on lithospheric accretion and evolution at Atlantis Massif, Mid-Atlantic Ridge 30°N

Author Posting. © American Geophysical Union, 2011. This article is posted here by permission of American Geophysical Union for personal use, not for redistribution. The definitive version was published in Journal of Geophysical Research 116 (2011): B07103, doi:10.1029/2010JB007931.Expeditions 304 and 305 of the Integrated Ocean Drilling Program cored and logged a 1.4 km section of the domal core of Atlantis Massif. Postdrilling research results summarized here constrain the structure and lithology of the Central Dome of this oceanic core complex. The dominantly gabbroic sequence recovered contrasts with predrilling predictions; application of the ground truth in subsequent geophysical processing has produced self-consistent models for the Central Dome. The presence of many thin interfingered petrologic units indicates that the intrusions forming the domal core were emplaced over a minimum of 100–220 kyr, and not as a single magma pulse. Isotopic and mineralogical alteration is intense in the upper 100 m but decreases in intensity with depth. Below 800 m, alteration is restricted to narrow zones surrounding faults, veins, igneous contacts, and to an interval of locally intense serpentinization in olivine-rich troctolite. Hydration of the lithosphere occurred over the complete range of temperature conditions from granulite to zeolite facies, but was predominantly in the amphibolite and greenschist range. Deformation of the sequence was remarkably localized, despite paleomagnetic indications that the dome has undergone at least 45° rotation, presumably during unroofing via detachment faulting. Both the deformation pattern and the lithology contrast with what is known from seafloor studies on the adjacent Southern Ridge of the massif. There, the detachment capping the domal core deformed a 100 m thick zone and serpentinized peridotite comprises ∼70% of recovered samples. We develop a working model of the evolution of Atlantis Massif over the past 2 Myr, outlining several stages that could explain the observed similarities and differences between the Central Dome and the Southern Ridge