Membrane time constant as a tool to assess cell degeneration

Abstract

Changes in neuronal surface area may be monitored by measuring the plasma membrane capacitance [8]. Membrane time constant ( τ m) is given by the product of the membrane resistance ( r m) and membrane capacitance ( c m), τ m= r m c m. Thus, when membrane resistance is kept constant at a steady state (resting), membrane time constant can reflect the size of neuronal surface area. Membrane time constant is the time for the potential to fall from the resting to a fraction (1−1/e), or 63%, of its final value in the charging curve during the application of a small negative current pulse [9]. Negative voltage shift from the resting potential hardly activates any voltage-dependent ion channel, resulting in nominal changes in cell membrane resistance. Although elaborated methods for mathematical models and simulations are available for the electrophysiological assessment of neuron geometry in order to estimate subthreshold potential attenuation during the propagation of synaptically mediated electrical signals [1, 4, 10], they involve a number of critical assumptions for the convenience to each model, and some of these assumptions are unlikely to be valid [7]. With these restrictive assumptions, very little can be determined about the electrotonic structure of a neuron beyond the measurement of neuronal membrane resistance and membrane time constant. Alternatively, numerous tracers are available to visualize morphologies of neurons intracellularly and extracellularly. These anatomical methods provide direct and quantitative evidence for neuron geometry; however, they involve tissue processing and a series of chemical reactions, some of which are time- and effort-demanding. The purpose of the present paper is to show that membrane time constant can be effectively used as a tool to assess diminution in cell surface area without involving extensive mathematical theories and/or neuroanatomical techniques. This approach is particularly effective in electrotonically compact cells such as hippocampal neurons [1]. Recent development in the technique of the whole-cell patch clamp recording in the slice preparation yielded longer time constant with better resolution due to the absence of the leak conductance associated with microelectrode impalement [10]. Indeed, when membrane time constant was measured with the whole-cell patch clamp recording technique, it successfully detected the reduction in dendritic arbors (dendritic degeneration) in dentate granule cells in the pilocarpine model of chronic epilepsy, and this finding is supported by the neuroanatomical evidence that was obtained from the same specimen samples [6]. Membrane time constant is an easy-to-measure “passive membrane property” and can be used as a reliable probe by itself for detecting dendritic degeneration, or as a tool for decision-making in introducing neuroanatomical technique in combination with slice neurophysiology.