Stochastic models for cell kinetics

A survey is given of branching process type methods in cell kinetics. Some results are given that allow circadian rhythm and do not require complete independence between cells. Some more classical results on balanced exponential growth are given and some comments are made on flow microfluorometry.     

Random variation and concentration effects in PCR

Even though the efficiency of the polymerase chain reaction (PCR) reaction decreases, analyses are made in terms of Galton-Watson processes, or simple deterministic models with constant replication probability (efficiency). Recently, Schnell and Mendoza have suggested that the form of the efficiency, can be derived from enzyme kinetics. This results in the sequence of molecules numbers forming a stochastic process with the properties of a branching process with population size dependence, which is supercritical, but has a mean reproduction number that approaches one. Such processes display ultimate linear growth, after an initial exponential phase, as is the case in PCR. It is also shown that the resulting stochastic process for a large Michaelis-Menten constant behaves like the deterministic sequence x(n) arising by iterations of the function f(x)=x+x/(1+x).     

What can be observed in real time PCR and when does it show?

Journal of Mathematical Biology - Real time, or quantitative, PCR typically starts from a very low concentration of initial DNA strands. During iterations the numbers increase, first essentially by...     

Longitudinal Analysis of Tick Densities and Borrelia, Anaplasma, and Ehrlichia Infections of Ixodes ricinus Ticks in Different Habitat Areas in The Netherlands

From 2000 to 2004, ticks were collected by dragging a blanket in four habitat areas in The Netherlands: dunes, heather, forest, and a city park. Tick densities were calculated, and infection with Borrelia burgdorferi and Anaplasma and Ehrlichia species was investigated by reverse line blot analysis. The lowest tick density was observed in the heather area (1 to 8/100 m²). In the oak forest and city park, the tick densities ranged from 26 to 45/100 m². The highest tick density was found in the dune area (139 to 551/100 m²). The infection rates varied significantly for the four study areas and years, ranging from 0.8 to 11. 5% for Borrelia spp. and 1 to 16% for Ehrlichia or Anaplasma (Ehrlichia/Anaplasma) spp. Borrelia infection rates were highest in the dunes, followed by the forest, the city park, and heather area. In contrast, Ehrlichia/Anaplasma was found most often in the forest and less often in the city park. The following Borrelia species were found: Borrelia sensu lato strains not identified to the species level (2.5%), B. afzelii (2.5%), B. valaisiana (0.9%), B. burgdorferi sensu stricto (0.13%), and B. garinii (0.13%). For Ehrlichia/Anaplasma species, Ehrlichia and Anaplasma spp. not identified to the species level (2.5%), Anaplasma schotti variant (3.5%), Anaplasma phagocytophilum variant (0.3%), and Ehrlichia canis (0.19%) were found. E. canis is reported for the first time in ticks in The Netherlands in this study. Borrelia lusitaniae, Ehrlichia chaffeensis, and the human granylocytic anaplasmosis agent were not detected. About 1.6% of the ticks were infected with both Borrelia and Ehrlichia/Anaplasma, which was higher than the frequency predicted from the individual infection rates, suggesting hosts with multiple infections or a possible selective advantage of coinfection.     

Coalescent approximation for structured populations in a stationary random environment

We establish convergence to the Kingman coalescent for the genealogy of a geographically-or otherwise-structured version of the Wright-Fisher population model with fast migration. The new feature is that migration probabilities may change in a random fashion. This brings a novel formula for the coalescent effective population size (EPS). We call it a quenched EPS to emphasize the key feature of our model — random environment. The quenched EPS is compared with an annealed (mean-field) EPS which describes the case of constant migration probabilities obtained by averaging the random migration probabilities over possible environments.     

Stochasticity in the adaptive dynamics of evolution: the bare bones

First a population model with one single type of individuals is considered. Individuals reproduce asexually by splitting into two, with a population-size-dependent probability. Population extinction, growth and persistence are studied. Subsequently the results are extended to such a population with two competing morphs and are applied to a simple model, where morphs arise through mutation. The movement in the trait space of a monomorphic population and its possible branching into polymorphism are discussed. This is a first report. It purports to display the basic conceptual structure of a simple exact probabilistic formulation of adaptive dynamics.     

Analysing hierarchy in the organization of biological and physical systems

A structured approach is discussed for analysing hierarchy in the organization of biological and physical systems. The need for a structured approach follows from the observation that many hierarchies in the literature apply conflicting hierarchy rules and include ill-defined systems. As an alternative, we suggest a framework that is based on the following analytical steps: determination of the succession stage of the universe, identification of a specific system as part of the universe, specification of external influences on a system's creation and analysis of a system's internal organization. At the end, the paper discusses practical implications of the proposed method for the analysis of system organization and hierarchy in biology, ecology and physics.     

Longitudinal analysis of tick densities and Borrelia, Anaplasma, and Ehrlichia infections of Ixodes ricinus ticks in different habitat areas in The Netherlands

From 2000 to 2004, ticks were collected by dragging a blanket in four habitat areas in The Netherlands: dunes, heather, forest, and a city park. Tick densities were calculated, and infection with Borrelia burgdorferi and Anaplasma and Ehrlichia species was investigated by reverse line blot analysis. The lowest tick density was observed in the heather area (1 to 8/100 m2). In the oak forest and city park, the tick densities ranged from 26 to 45/100 m2. The highest tick density was found in the dune area (139 to 551/100 m2). The infection rates varied significantly for the four study areas and years, ranging from 0.8 to 11. 5% for Borrelia spp. and 1 to 16% for Ehrlichia or Anaplasma (Ehrlichia/Anaplasma) spp. Borrelia infection rates were highest in the dunes, followed by the forest, the city park, and heather area. In contrast, Ehrlichia/Anaplasma was found most often in the forest and less often in the city park. The following Borrelia species were found: Borrelia sensu lato strains not identified to the species level (2.5%), B. afzelii (2.5%), B. valaisiana (0.9%), B. burgdorferi sensu stricto (0.13%), and B. garinii (0.13%). For Ehrlichia/Anaplasma species, Ehrlichia and Anaplasma spp. not identified to the species level (2.5%), Anaplasma schotti variant (3.5%), Anaplasma phagocytophilum variant (0.3%), and Ehrlichia canis (0.19%) were found. E. canis is reported for the first time in ticks in The Netherlands in this study. Borrelia lusitaniae, Ehrlichia chaffeensis, and the human granylocytic anaplasmosis agent were not detected. About 1.6% of the ticks were infected with both Borrelia and Ehrlichia/Anaplasma, which was higher than the frequency predicted from the individual infection rates, suggesting hosts with multiple infections or a possible selective advantage of coinfection.