[Ca2+] oscillations in a model of energy-dependent Ca2+ uptake by the endoplasmic reticulum.

Active Ca2+ transport in living cells necessitates controlled supply of metabolic energy. Direct coupling between sarco/endoplasmic reticulum (ER) Ca2+ ATPases (SERCA) and intracellular energy-generation sites has been well established experimentally. On the basis of these experimental findings we propose a pump-driven model to investigate complex dynamic properties of a cell system. The model describes the pump process both by the Ca2+ ATPase itself and by a suitable description of the glycolysis. The associated set of differential equations shows a rich behavior, the solutions ranging from simple periodic oscillations to complex patterns such as bursting and spiking. Recent experimental results on calcium oscillations in Xenopus laevis oocytes and on dynamic patterns of intracellular Ca2+ concentrations in electrically non-excitable cells are well described by corresponding theoretical results derived within the proposed model. The simulation results are further compared to spontaneous [Ca2+] oscillations in primitive endodermal cells.

Higher-order probabilistic perceptrons as Bayesian inference engines.

An explicit structural connection is established between the Bayes optimal classifier operating on K binary input variables and a corresponding two-layer perceptron having normalized output activities and couplings from input to output units of all orders up to K. With suitable modification of connection weights and biases, such a higher-order probabilistic perceptron should in principle be able to learn the statistics of the classification problem and match the a posteriori probabilities given by Bayes optimal inference. Specific training algorithms are developed that allow this goal to be approximated in a controlled variational sense. An application to the task of discriminating between stable and unstable nuclides in nuclear physics yields network models with predictive performance comparable to the best that has been achieved with conventional multilayer perceptrons containing only pairwise connections.