Desynchronization of systems of coupled Hindmarsh-Rose oscillators

It is widely assumed that neural activity related to synchronous rhythms of large portions of neurons in specific locations of the brain is responsible for the pathology manifested in patients' uncontrolled tremor and other similar diseases. To model such systems Hindmarsh-Rose (HR) oscillators are considered as appropriate as they mimic the qualitative behaviour of neuronal firing. Here we consider a large number of identical HR-oscillators interacting through the mean field created by the corresponding components of all oscillators. Introducing additional coupling by feedback of Pyragas type, proportional to the difference between the current value of the mean-field and its value some time in the past, Rosenblum and Pikovsky (Phys. Rev. E 70, 041904, 2004) demonstrated that the desirable desynchronization could be achieved with appropriate set of parameters for the system. Following our experience with stabilization of unstable steady states in dynamical systems, we show that by introducing a variable delay, desynchronization is obtainable for much wider range of parameters and that at the same time it becomes more pronounced.Comment: 5 pages, 2 figures, RevTe

Mechanisms for the Intracellular Manipulation of Organelles by Conventional Electroporation

Conventional electroporation (EP) changes both the conductance and molecular permeability of the plasma membrane (PM) of cells and is a standard method for delivering both biologically active and probe molecules of a wide range of sizes into cells. However, the underlying mechanisms at the molecular and cellular levels remain controversial. Here we introduce a mathematical cell model that contains representative organelles (nucleus, endoplasmic reticulum, mitochondria) and includes a dynamic EP model, which describes formation, expansion, contraction, and destruction for the plasma and all organelle membranes. We show that conventional EP provides transient electrical pathways into the cell, sufficient to create significant intracellular fields. This emerging intracellular electrical field is a secondary effect due to EP and can cause transmembrane voltages at the organelles, which are large enough and long enough to gate organelle channels, and even sufficient, at some field strengths, for the poration of organelle membranes. This suggests an alternative to nanosecond pulsed electric fields for intracellular manipulations.National Science Foundation (U.S.) (NSF Graduate Research Fellowship)National Institutes of Health (U.S.) (grant No. R01-GM63857)Aegis Industries, Inc