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Quantifying relative contributions to voltage noise increase
In the manuscript, we calculate the relative contribution of impedance and current noise to voltage noise changes between experimental conditions. These comparisons are performed in the LF range (see Fig. 5D, Fig.8D). We rely on the identity EMBED Equation.DSMT4 ADDIN EN.CITE Diba2004100101550976124432004Oct 27Intrinsic noise in cultured hippocampal neurons: experiment and modeling9723-33Sloan-Swartz Center for Theoretical Neurobiology, California Institute of Technology, Pasadena, California 91125, USA. diba@klab.caltech.eduDiba, K.Lester, H. A.Koch, C.J Neuroscihttp://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&dopt=Citation&list_uids=15509761(Diba et al., 2004), generalizing to EMBED Equation.DSMT4 . Because in our data voltage spectra and impedance curves are constant in the LF range, the integral form collapses to EMBED Equation.DSMT4 (where EMBED Equation.DSMT4 corresponds to the input resistance). The ratio of voltage noise power between two experimental conditions (1) and (2) is given by EMBED Equation.DSMT4 . Taking the logarithm of both sides, we define EMBED Equation.DSMT4 . The relative contribution of impedance change is EMBED Equation.DSMT4 , while the relative contribution of current noise is EMBED Equation.DSMT4 . This measure of relative contribution in the LF range is invariant to units, and identical results are attained if variance is replaced by noise amplitude and impedance squared by impedance. The relative contributions may assume negative values and values > 1.
The above measure of relative contribution assumes that noise increase is interpreted in the multiplicative sense. It is possible to get a measure of relative contribution using an additive interpretation of noise increase, using the identity:
EMBED Equation.DSMT4 . Because power in different frequency bins is uncorrelated, one can take the integral of the above equation to obtain:
EMBED Equation.DSMT4
Jacobson et al., Supplementary Material
We denote:
EMBED Equation.DSMT4
This implies EMBED Equation.DSMT4 . We define the relative contribution of impedance as EMBED Equation.DSMT4 and the relative contribution of current as EMBED Equation.DSMT4 . While this measure is not used in the manuscript, it can also be calculated using only voltage and impedance measurements, by using the identity EMBED Equation.DSMT4 ADDIN EN.CITE Diba2004100101550976124432004Oct 27Intrinsic noise in cultured hippocampal neurons: experiment and modeling9723-33Sloan-Swartz Center for Theoretical Neurobiology, California Institute of Technology, Pasadena, California 91125, USA. diba@klab.caltech.eduDiba, K.Lester, H. A.Koch, C.J Neuroscihttp://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&dopt=Citation&list_uids=15509761(Diba et al., 2004). This measure is not restricted to frequency bands in which impedance and voltage noise are constant.
The relative contributions of impedance reported in the paper are based on the first, multiplicative form. Using this measure, impedance increase was shown to account for 70% of the voltage noise amplitude increase with depolarisation (in the multiplicative sense). Using the additive relative contribution measure, EMBED Equation.DSMT4 changes were responsible for 75% of the noise power increase with depolarisation. Thus, in our preparation, the two measures do not differ significantly.
References to the Supplementary Material:
ADDIN EN.REFLIST Diba, K., Lester, H. A. & Koch, C. (2004). Intrinsic noise in cultured hippocampal neurons: experiment and modeling. J Neurosci 24, 9723-9733.
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