Recolonisation by diffusion can generate increasing rates of spread

Diffusion is one of the most frequently used assumptions to explain dispersal. Diffusion models and in particular reaction-diffusion equations usually lead to solutions moving at constant speeds, too slow compared to observations. As early as 1899, Reid had found that the rate of spread of tree species migrating to northern environments at the beginning of the Holocene was too fast to be explained by diffusive dispersal. Rapid spreading is generally explained using long distance dispersal events, modelled through integro-differential equations (IDEs) with exponentially unbounded (EU) kernels, i.e. decaying slower than any exponential. We show here that classical reaction-diffusion models of the Fisher-Kolmogorov-Petrovsky-Piskunov type can produce patterns of colonisation very similar to those of IDEs, if the initial population is EU at the beginning of the considered colonisation event. Many similarities between reaction-diffusion models with EU initial data and IDEs with EU kernels are found; in particular comparable accelerating rates of spread and flattening of the solutions. There was previously no systematic mathematical theory for such reaction-diffusion models with EU initial data. Yet, EU initial data can easily be understood as consequences of colonisation-retraction events and lead to fast spreading and accelerating rates of spread without the long distance hypothesis.     

Characterization of the calcium paradox in the isolated perfused frog heart: enzymatic,ionic, contractile and electrophysiological studies

Summary The effect of perfusion temperature and duration of calcium deprivation on the occurrence of the calcium paradox was studied in the isolated frog heart. Loss of electrical and mechanical activity, ion fluxes, creatine kinase and protein release were used to define cell damage. Perfusion was performed at 22, 27, 32, and 37°C, and calcium deprivation lasted 10, 20, 30, or 40 min. At 22°C and 27°C even a prolonged calcium-free perfusion failed to induce a calcium paradox. After 30 min of calcium-free perfusion at 37°C ventricular activity ceased and a major contraction occurred followed by an increase in resting tension. During the 15-min re-perfusion period the release of creatine kinase was 158.24±2.49 IU·g dry wt^-1, and the total amount of protein lost was 70.37±0.73 mg·g dry wt^–1, while lower perfusion temperatures resulted in a decreased loss of protein and creatine kinase. Ion fluxes in the perfusion effluent indicate that during re-perfusion a massive calcium influx accompanied by a potassium and a magnesium efflux, and an apparent sodium efflux, occur at a perfusion temperature of 37°C after 30 min of calcium deprivation. The results suggest that the basic principles and damaging effects of calcium overloading are common to both mammalian and frog hearts.     

Prevention by 7-oxo-prostacyclin of the calcium paradox in rat heart: Role of the sarcolemmal (Na,K)-ATPase

It is demonstrated a fast and significant depression in the sarcolemmal (Na,K)-ATPase activity that occurs as early as 25 sec after the onset of Ca²⁺ depletion, and participates in the development of Ca²⁺-paradox in the rat heart. Pretreatment of the animals with 7-oxo-prostacyclin (PG12) 24–48 h prior to the experiment prevented fairly the Ca²⁺-depletion-induced depression in (Na,K)ATPase activity and the accompanying structural and functional damage to the heart and sarcolemma during Ca²⁺-depletion as well as the development of Ca²⁺-paradox during the subsequent Ca²⁺-repletion. Pretreatment with PGI, was chosen intentionally because previous experiments revealed, that in its late effect the drug is acting via stabilizing the membranes due induction of high activity of (Na,K)-ATPase that has increased affinity to ATP. From results obtained the following may be concluded: If during the phase of Ca²⁺-deprivation, the capability of heart sarcolemma to maintain sodium extrusion remains preserved, the expected aggravation of Ca²⁺-overload injury to Ca²⁺-paradox that would develop during Ca²⁺-repletion, may be definitely prevented. Sufficiently preserved (Na,K)-ATPase activity, hand in hand with stabilized sarcolemmal structure, may prevent an accumulation of sodium beneath the sarcolemma and consequently also an overexcessive entry of Ca²⁺ into the myocytes.