Article Information

• PDF (1275 kb)

PubMed

• Articles by M.W. Levine

Related Articles

• Kramers’ Diffusion Theory Applied to Gating Kinetics of Volt...

  Kramers’ Diffusion Theory Applied to Gating Kinetics of Voltage-Dependent Ion Channels Biophysical Journal, Volume 76, Issue 2, 1 February 1999, Pages 782-803 Daniel Sigg, Hong Qian and Francisco Bezanilla Abstract Kramers’ diffusion theory of reaction rates in the condensed phase is considered as an alternative to the traditional discrete-state Markov (DSM) model in describing ion channel gating current kinetics. Diffusion theory can be expected to be particularly relevant in describing high-frequency (>100kHz) events in channel activation. The generalized voltage sensor of a voltage-dependent ion channel is treated as a Brownian motion particle undergoing spatial diffusion along a one-dimensional energy landscape. Two classes of energy landscapes are considered. The first class contains large barriers, which give rise to gating currents with two distinct time scales: the usual low-frequency decay, which can modeled with a DSM scheme, and a high-frequency component arising from intrastate relaxation. Large depolarizations reduce potential barriers to such a degree that activation rates are diffusion limited, causing the two time scales to merge. Landscapes of the second class are either featureless or contain barriers that are small compared to these are termed “drift landscapes.” These landscapes require a larger friction coefficient to generate slow gating kinetics. The high-frequency component that appears with barrier models is not present in pure drift motion. The presence of a high-frequency component can be tested experimentally with large-bandwidth recordings of gating currents. Topics such as frequency domain analysis, spatial dependence of the friction coefficient, methods for determining the adequacy of a DSM model, and the development of physical models of gating are explored. Abstract | Full Text | PDF (297 kb)

• Nonlinear sequence-dependent structure of nigral dopamine ne...

  Nonlinear sequence-dependent structure of nigral dopamine neuron interspike interval firing patterns Biophysical Journal, Volume 69, Issue 1, 1 July 1995, Pages 128-137 R.E. Hoffman, W.X. Shi and B.S. Bunney Abstract Firing patterns of 15 dopamine neurons in the rat substantia nigra were studied. These cells alternated between two firing modes, single-spike and bursting, which interwove to produce irregular, aperiodic interspike interval (ISI) patterns. When examined by linear autocorrelation analysis, these patterns appeared to reflect a primarily stochastic or random process. However, dynamical analysis revealed that the sequential behavior of a majority of these cells expressed "higher-dimensional" nonlinear deterministic structure. Dimensionality refers to the number of degrees of freedom or complexity of a time series. Bursting was statistically associated with some aspects of nonlinear ISI sequence dependence. Controlling for the effects of nonstationarity substantially increased overall predictability of ISI sequences. We hypothesize that the nonlinear deterministic structure of ISI firing patterns reflects the neuron's response to coordinated synaptic inputs emerging from neural circuit interactions. Abstract | PDF (1198 kb)

• Applying Hidden Markov Models to the Analysis of Single Ion ...

  Applying Hidden Markov Models to the Analysis of Single Ion Channel Activity Biophysical Journal, Volume 82, Issue 4, 1 April 2002, Pages 1930-1942 L. Venkataramanan and F.J. Sigworth Abstract Hidden Markov models have recently been used to model single ion channel currents as recorded with the patch clamp technique from cell membranes. The estimation of hidden Markov models parameters using the forward-backward and Baum-Welch algorithms can be performed at signal to noise ratios that are too low for conventional single channel kinetic analysis; however, the application of these algorithms relies on the assumptions that the background noise be white and that the underlying state transitions occur at discrete times. To address these issues, we present an “-noise” algorithm that accounts for correlated background noise and the randomness of sampling relative to transitions. We also discuss three issues that arise in the practical application of the algorithm in analyzing single channel data. First, we describe a digital inverse filter that removes the effects of the analog antialiasing filter and yields a sharp frequency roll-off. This enhances the performance while reducing the computational intensity of the algorithm. Second, the data may be contaminated with baseline drifts or deterministic interferences such as 60-Hz pickup. We propose an extension of previous results to consider baseline drift. Finally, we describe the extension of the algorithm to multiple data sets. Abstract | Full Text | PDF (188 kb)

• …more

Abstract

The intervals between successive action potentials (impulses, or "spikes") produced the maintained firing of a neuron (ISIs) are often treated as if they were independent on each other; that is, an impulse train is considered as a stationary renewal process. If this is so, the variability of the mean rate of firing impulses in a sequence of temporal windows should be predictable from the distribution of ISIs. This was found not to be the case for the maintained firing of retinal ganglion cells in goldfish. Although some evident nonstationarity sometimes resulted in greater variability of the observed rate distributions than those predicted (for relatively long temporal windows), as a general rule the observed rate distributions were considerable less dispersed than would be predicted by sampling of the ISI distributions. This was taken as evidence of long-term serial dependency between successive ISIs; however, two standard test for dependency (autocorrelations and serial correlograms failed to to reveal structure of sufficiently long duration to account for the effect noted.