Stability of membrane bound reactions

We present a novel approach to the dynamics of reactions of diffusing chemical species with species fixed in space e.g. by binding to a membrane. The non-diffusing reaction partners are clustered in areas with a diameter smaller than the diffusion length of the diffusing partner. The activated fraction of the fixed species determines the size of an active sub-region of the cluster. Linear stability analysis reveals that diffusion is one of the ma jor determinants of the stability of the dynamics. We illustrate the model concept with Ca²⁺ dynamics in living cells, which has release channels as fixed reaction partners. Our results suggest that spatial and temporal structures in intracellular Ca²⁺ dynamics are caused by fluctuations due to the small number of channels per cluster.

Exploration of the dendritic cell algorithm with the duration calculus

As one of the newest members in Articial Immune Systems (AIS), the Dendritic Cell Algorithm (DCA) has been applied to a range of problems. These applications mainly belong to the eld of anomaly detection. However, real-time detection, a new challenge to anomaly detection, requires improvement on the real-time capability of the DCA. To assess such capability, formal methods in the research of real-time systems can be employed. The ndings of the assessment can provide guideline for the future development of the algorithm. Therefore, in this paper we use an interval logic based method, named the Duration Calcu- lus (DC), to specify a simplied single-cell model of the DCA. Based on the DC specications with further induction, we nd that each individual cell in the DCA can perform its function as a detector in real-time. Since the DCA can be seen as many such cells operating in parallel, it is potentially capable of performing real-time detection. However, the analysis process of the standard DCA constricts its real-time capability. As a result, we conclude that the analysis process of the standard DCA should be replaced by a real-time analysis component, which can perform periodic analysis for the purpose of real-time detection.