Bandeira Heliovânio T, Barbosa Catão T F, De Oliveira Regina A Campos, Aguiar José F, Nogueira Romildo A
Department of Statistic and Informatics, Federal Rural University of Pernambuco, R. Dom Manuel de Medeiros, s/n, Dois Irmãos, 52171-030 Recife, PE, Brazil.
Chaos. 2008 Sep;18(3):033136. doi: 10.1063/1.2944980.
Ion channels are pores formed by proteins and responsible for carrying ion fluxes through cellular membranes. The ion channels can assume conformational states thereby controlling ion flow. Physically, the conformational transitions from one state to another are associated with energy barriers between them and are dependent on stimulus, such as, electrical field, ligands, second messengers, etc. Several models have been proposed to describe the kinetics of ion channels. The classical Markovian model assumes that a future transition is independent of the time that the ion channel stayed in a previous state. Others models as the fractal and the chaotic assume that the rate of transitions between the states depend on the time that the ionic channel stayed in a previous state. For the calcium activated potassium channels of Leydig cells the R/S Hurst analysis has indicated that the channels are long-term correlated with a Hurst coefficient H around 0.7, showing a persistent memory in this kinetic. Here, we applied the RS analysis to the opening and closing dwell time series obtained from simulated data from a chaotic model proposed by L. Liebovitch and T. Tóth [J. Theor. Biol. 148, 243 (1991)] and we show that this chaotic model or any model that treats the set of channel openings and closings as independent events is inadequate to describe the long-term correlation (memory) already described for the experimental data.
离子通道是由蛋白质形成的孔道，负责携带离子通量穿过细胞膜。离子通道可以呈现构象状态，从而控制离子流动。从物理角度来看，从一种状态到另一种状态的构象转变与它们之间的能量屏障相关，并取决于刺激因素，如电场、配体、第二信使等。已经提出了几种模型来描述离子通道的动力学。经典的马尔可夫模型假设未来的转变与离子通道在前一个状态停留的时间无关。其他模型，如分形模型和混沌模型，则假设状态之间的转变速率取决于离子通道在前一个状态停留的时间。对于睾丸间质细胞的钙激活钾通道，R/S赫斯特分析表明这些通道具有长期相关性，赫斯特系数H约为0.7，在这种动力学中表现出持续记忆。在这里，我们将R/S分析应用于从L. Liebovitch和T. Tóth [《理论生物学杂志》148, 243 (1991)]提出的混沌模型的模拟数据中获得的开放和关闭驻留时间序列，我们表明这种混沌模型或任何将通道开放和关闭集合视为独立事件的模型都不足以描述已经在实验数据中描述的长期相关性（记忆）。
