Adaptive targeting of chaotic response in periodically stimulated neural systems

Reliability of unstable periodic orbit based control strategies in biological systems

Presence of recurrent and statistically significant unstable periodic orbits (UPOs) in time series obtained from biological systems is now routinely used as evidence for low dimensional chaos. Extracting accurate dynamical information from the detected UPO trajectories is vital for successful control strategies that either aim to stabilize the system near the fixed point or steer the system away from the periodic orbits. A hybrid UPO detection method from return maps that combines topological recurrence criterion, matrix fit algorithm, and stringent criterion for fixed point location gives accurate and statistically significant UPOs even in the presence of significant noise. Geometry of the return map, frequency of UPOs visiting the same trajectory, length of the data set, strength of the noise, and degree of nonstationarity affect the efficacy of the proposed method. Results suggest that establishing determinism from unambiguous UPO detection is often possible in short data sets with significant noise, but derived dynamical properties are rarely accurate and adequate for controlling the dynamics around these UPOs. A repeat chaos control experiment on epileptic hippocampal slices through more stringent control strategy and adaptive UPO tracking is reinterpreted in this context through simulation of similar control experiments on an analogous but stochastic computer model of epileptic brain slices. Reproduction of equivalent results suggests that far more stringent criteria are needed for linking apparent success of control in such experiments with possible determinism in the underlying dynamics.

Extreme sensitivity of gene expression in human SH-SY5Y neurocytes to ultra-low doses of Gelsemium sempervirens

Background

Gelsemium sempervirens L. (Gelsemium s.) is a traditional medicinal plant, employed as an anxiolytic at ultra-low doses and animal models recently confirmed this activity. However the mechanisms by which it might operate on the nervous system are largely unknown. This work investigates the gene expression of a human neurocyte cell line treated with increasing dilutions of Gelsemium s. extract.

Methods

Starting from the crude extract, six 100 × (centesimal, c) dilutions of Gelsemium s. (2c, 3c, 4c, 5c, 9c and 30c) were prepared according to the French homeopathic pharmacopoeia. Human SH-SY5Y neuroblastoma cells were exposed for 24 h to test dilutions, and their transcriptome compared by microarray to that of cells treated with control vehicle solutions.

Results

Exposure to the Gelsemium s. 2c dilution (the highest dose employed, corresponding to a gelsemine concentration of 6.5 × 10^-9 M) significantly changed the expression of 56 genes, of which 49 were down-regulated and 7 were overexpressed. Several of the down-regulated genes belonged to G-protein coupled receptor signaling pathways, calcium homeostasis, inflammatory response and neuropeptide receptors. Fisher exact test, applied to the group of 49 genes down-regulated by Gelsemium s. 2c, showed that the direction of effects was significantly maintained across the treatment with high homeopathic dilutions, even though the size of the differences was distributed in a small range.

Conclusions

The study shows that Gelsemium s., a medicinal plant used in traditional remedies and homeopathy, modulates a series of genes involved in neuronal function. A small, but statistically significant, response was detected even to very low doses/high dilutions (up to 30c), indicating that the human neurocyte genome is extremely sensitive to this regulation.

Pinning control of threshold coupled chaotic neuronal maps

Chaotic neuronal maps are studied with threshold activated coupling at selected pinning sites with increasing pinning density. A transition from spatiotemporal chaos to a fixed spatial profile with synchronized temporal cycles is observed. There is an optimal fraction of sites where it is necessary to apply the control algorithm in order to effectively suppress chaotic dynamics.