A formula for thermal stability (Tm) prediction of PNA/DNA duplexes

An empirical formula for thermal stability (T m) prediction of PNA/DNA duplexes has been derived. The model is based on the T m as calculated for the corresponding DNA/DNA duplex employing a nearest neighbour approach, by including terms for the pyrimidine content and length of the PNA to take into account the increased thermostability of PNA/DNA hybrids and the asymmetry of the PNA-DNA heteroduplex. The predictive power of the T m prediction formula was challenged with an independent data set not used for model building. The T m of >90% of the sequences was predicted within 5 K; 98% of the predicted T ms differ by not more than 10 K from the experimentally determined T m.

Critical level and detection limit: performance measures for PCR-based assays

In clinical diagnostic work, sensitivity and specificity are key assay features. In this note we introduce two clinically relevant statistical assay performance measures, the critical level (CL), and the detection limit (DL) for the PCR-based assay. To allow for easy access to these characteristics a Windows-based program has been developed. The application of CL and DL by means of examples is described.

The population dynamics of acquired immunity to helminth infection: experimental and natural transmission

Recently we described a mathematical model of the role of acquired immunity in host-helminth interactions. The model gives a good quantitative description of the results of experiments involving the nematode Heligmosomoides polygyrus in laboratory mice. Here we apply the model to the results of two further laboratory studies of the same parasite-host interaction: (i) the repeated experimental infection of a genetically heterogeneous host population, and (ii) the natural transmission of the parasite within mouse populations under different dietary conditions. Numerical simulation again reveals good quantitative agreement between the model predictions and laboratory data. Finally, the model is extended to give a preliminary description of the dynamics of helminth-host interactions of medical and ecological significance in the real world.

The population dynamics of acquired immunity to helminth infection

Based on experimental evidence we develop and exploit a mathematical model to describe the role of acquired immunity in host-helminth interactions. We show that the model gives a quantitative description of the population dynamics in a laboratory situation involving a host immunological response. We make practical predictions based on these results.

On the dynamics of a simple biochemical control circuit

The quantitative dynamics of a biochemical control circuit that regulates enzyme or protein synthesis by end-product feedback is analyzed. We first study a simplified repressible system, which is known to exhibit either a steady state or an oscillatory solution. By showing the analogy of this n-dimensional system with a time-delay equation for a single variable the mechanism of the self-sustained oscillations becomes transparent. In a more sophisticated system we will find as well either steady state or oscillatory solutions. We determine the role of the parameters with respect to stability and frequency. The most general case will be treated by means of the concept of Lyapunov exponents.

Pattern formation in morphogenesis. Analytical treatment of the Gierer-Meinhardt model on a sphere

We first treat the Gierer-Meinhardt equations by linear stability analysis to determine the critical parameter, at which the homogeneous distributions of activator and inhibitor concentrations become unstable. We find two types of instabilities: one leading to spatial pattern formation and another one leading to temporal oscillations. We consider the case where two instabilities are present. Using the method of generalized Ginzburg-Landau equations introduced earlier we then analyze the nonlinear equations. As we are mainly interested in spatial pattern formation on a sphere we consider the problem under an appropriate constraint. Combining the two occurring solutions we find patterns well-known in biology, such as a gradient system and temporal oscillations.