Hurst Analysis Applied to the Study of Single Calcium-activated Potassium Channel Kinetics

Chaotic model and memory in single calcium-activated potassium channel kinetics

“…The conductance observed in this record is in accordance with the characteristic conductance of the calcium-activated potassium channel in cells of Leydig, equal to 265 pS. 13 Table I shows the values of Hurst coefficients for eleven experimental recordings of calcium activated potassium channels. The average value for the coefficient of Hurst is equal to H E = 0.7077Ϯ 0.0522 for the experimental data ͑n =11͒.…”

“…However, it is interesting to note the excellent adjustment of the curve of distribution of probabilities derived from the two states Markovian model to the experimental data. Therefore, Markovian models with two, three, four, or eleven states 5,6,13,18 can describe the kinetic process of the ion channels in an adequate way without any physical meaning with regard to the dynamic process of the transitions between the open and closed states of the BK channel.…”

“…5,6,13,18 Kochetkov and co-workers 3 also showed the presence of memory in calcium-activated potassium channel in cells Vero of the kidney and that Markovians models are inadequate to describe the memory found in the kinetics of these channels. Markovianv models may even describe very well the distributions of times of permanence of the channel in the open and closed states, but they are inefficient to describe the long-term correlation for the opening and closing times in the calcium-activated potassium channels.…”

“…Another interesting aspect is that the coefficient of Hurst does not vary with the voltage applied through the channel. 13 Although the kinetics of the channel varies with changes in membrane potentials, the dynamics of the process remains invariable, suggesting that memory is an intrinsic property of the system. This means that memory appears to be a property of the internal dynamics of the channel protein, which is completely different from saying that memory arises from a specific kinetic process.…”

Transfer of calibration between hand and foot: Functional equivalence and fractal fluctuations

“…The power-law growth of fluctuations is evidence of long-range temporal correlations (Scafetta & Grigolini, 2002;Viswanathan et al, 1996;Zanette, 1997). Temporally fractal scaling can be found in neuromuscular fluctuations from the coarser grain, such as posture (Duarte & Zatsiorsky, 2001) and gait (Hausdorff et al, 1997), to a finer grain, such as breathing (Govindan, Wilson, Murphy, Russel, & Lowery, 2007), heartbeats (Peng, Havlin, Stanley, & Goldberger, 1995), and finger tapping (Lemoine, Torre, & Delignières, 2006), to even finer grains, such as electric current in muscle (Gitter & Czerniecki, 1995), neurotransmitter exocytosis (Lowen, Cash, Poo, & Teich, 1997), ion-channel kinetics (Varanda, Liebovitch, Figueiroa, & Nogueira, 2000), and interspike intervals in neuron firing (Das, Gebber, Barman, & Lewis, 2003)-even independently of spinal influences (Orer, Das, Barman, & Gebber, 2003). Temporally fractal scaling is a signature of memory throughout the neuromuscular apparatus available for dynamic touch.…”