Ion channels are fundamental molecules in the nervous system that catalyze the flux of ions across the cell membrane. There are mounting evidences suggesting that the kinetic properties of ion channels undergo activity-dependent changes in various pathophysiological conditions. Here such activity-dependent changes were studied in case of two different ion channels; the rat brain derived voltage-gated Na+ channel, rNav1.2 and the human background leak K+ channel, hTREK1 using the single channel patch-clamp technique. Our results on the voltage-gated Na+ channel (Chapter III) illustrated that sustained membrane depolarization, as seen in pathophysiological conditions like epilepsy, induced a defined non-linear variation in the unitary conductance, activation, inactivation and recovery kinetic properties of the channel. Signal processing tools attributed a pseudo-oscillatory nature to the non-linearity observed in the channel properties. Prolonged membrane depolarization also induced a “molecular memory” phenomenon, characterized by clustering of dwell time events and strong autocorrelation in the dwell time series. The persistence of such molecular memory was found to be dependent on the duration of depolarization. Similar plastic changes were observed in case of the hTREK1 channel in presence of saturating concentrations of agonist, trichloroethanol (TCE) (Chapter IV). TREK1 channel behaves similar to single enzyme molecules with a single binding site for the substrate K+ ion whereas TCE acts as an allosteric activator of the channel. We observed that with increasing concentration of TCE (10 M to 10 mM) the catalytic turnover rate exhibited progressive departure from monoexponential to multi-exponential distribution suggesting the presence of ‘dynamic disorder’ analogous to single enzyme molecules. In addition, we observed the induction of strong correlation in successive waiting times and flux intensities, exemplified by distinct mode switching between high and low flux activity, which implied the induction of memory in single ion channel. Our observation of such molecular memory in two different ion channels in different experimental conditions highlights the importance and generality of the phenomenon which is normally hidden under the ensemble behaviour of ion channels. In the final part of the work (chapter V) we observed strong negative cooperativity and half-of-sites saturation kinetics in the interaction of local anesthetic, lidocaine with hTREK1 channel. We also mapped the specific anesthetic binding site in the c-terminal domain of the channel. Further, single channel analysis and the heterodimer studies enabled us to propose a model for this interaction and provide a plausible paradigm for the inhibitory action of lidocaine on hTREK1.