White noise approach for estimating the passive electrical properties of neurons

W. N. Wright, B. L. Bardakjian, T. A. Valiante, J. L. Perez-Velazquez and P. L. Carlen Department of Electrical and Computer Engineering, University of Toronto, Ontario, Canada. 1. The passive electrical properties of whole cell patched dentate granule cells were studied with the use of zero-mean Gaussian white noise current stimuli. Transmembrane voltage responses were used to compute the first-order Wiener kernels describing the current-voltage relationship at the soma for six cells. Frequency domain optimization techniques using a gradient method for function minimization were then employed to identify the optimal electrical parameter values. Low-power white noise stimuli are presented as a favorable alternative to the use of short-pulse current inputs for investigating neuronal passive electrical properties. 2. The optimization results demonstrated that the lumped resistive and capacitive properties of the recording electrode must be included in the analytic input impedance expression to optimally fit the measured cellular responses. The addition of the electrode resistance (Re) and capacitance (Ce) to the original parameters (somatic conductance, somatic capacitance, axial resistance, dendritic conductance, and dendritic capacitance) results in a seven-parameter model. The mean Ce value from the six cells was 5.4 +/- 0.3 (SE) pF, whereas Re following formation of the patch was found to be 20 +/- 2 M omega. 3. The six dentate granule cells were found to have an input resistance of 600 +/- 20 M omega and a dendritic to somatic conductance ratio of 6.3 +/- 1.1. The electronic length of the equivalent dendritic cylinder was found to be 0.42 +/- 0.03. The membrane time constant in the soma was found to be 13 +/- 3 ms, whereas the membrane time constant of the dendrites was 58 +/- 5 ms. Incorporation of morphological estimations led to the following distributed electrical parameters: somatic membrane resistance = 25 +/- 4 k omega cm2, somatic membrane capacitance = 0.48 +/- 0.05 microF/cm2, Ri (input resistance) = 72 +/- 5 omega cm, dendritic membrane resistance = 59 +/- 4 k omega cm2, and dendritic membrane capacitance = 0.97 +/- 0.06 microF/cm2. On the basis of capacitive measurements, the ratio of dendritic surface area to somatic surface area was found to be 34 +/- 2. 4. For comparative purposes, hyperpolarizing short pulses were also injected into each cell. The short-pulse input impedance measurements were found to underestimate the input resistance o