Walter M. Yamada

Time course of transmitter release calculated from simulations of a calcium diffusion model.

A three-dimensional presynaptic calcium diffusion model developed to account for characteristics of transmitter release was modified to provide for binding of calcium to a receptor and subsequent triggering of exocytosis. When low affinity (20 microM) and rapid kinetics were assumed for the calcium receptor triggering exocytosis, and stimulus parameters were selected to match those of experiments, the simulations predicted a virtual invariance of the time course of transmitter release to paired stimulation, stimulation with pulses of different amplitude, and stimulation in different calcium solutions. The large temperature sensitivity of experimental release time course was explained by a temperature sensitivity of the models final rate limiting exocytotic process. Inclusion of calcium tail currents and a saturable buffer with finite binding kinetics resulted in high peak calcium transients near release sites, exceeding 100 microM. Models with a single class of calcium binding site to the secretory trigger molecule failed to produce sufficient synaptic facilitation under this condition. When at least one calcium ion binds to a different site having higher affinity and slow kinetics, facilitation again reaches levels similar to those seen experimentally. It is possible that the neurosecretory trigger molecule reacts with calcium at more than one class of binding site.

Accurate detection of outliers and subpopulations with Pmetrics, a nonparametric and parametric pharmacometric modeling and simulation package for R.

Introduction: Nonparametric population modeling algorithms have a theoretical superiority over parametric methods to detect pharmacokinetic and pharmacodynamic subgroups and outliers within a study population. Methods: The authors created “Pmetrics,” a new Windows and Unix R software package that updates the older MM-USCPACK software for nonparametric and parametric population modeling and simulation of pharmacokinetic and pharmacodynamic systems. The parametric iterative 2-stage Bayesian and the nonparametric adaptive grid (NPAG) approaches in Pmetrics were used to fit a simulated population with bimodal elimination (Kel) and unimodal volume of distribution (Vd), plus an extreme outlier, for a 1-compartment model of an intravenous drug. Results: The true means (SD) for Kel and Vd in the population sample were 0.19 (0.17) and 102 (22.3), respectively. Those found by NPAG were 0.19 (0.16) and 104 (22.6). The iterative 2-stage Bayesian estimated them to be 0.18 (0.16) and 104 (24.4). However, given the bimodality of Kel, no subject had a value near the mean for the population. Only NPAG was able to accurately detect the bimodal distribution for Kel and to find the outlier in both the population model and in the Bayesian posterior parameter estimates. Conclusions: Built on over 3 decades of work, Pmetrics adopts a robust, reliable, and mature nonparametric approach to population modeling, which was better than the parametric method at discovering true pharmacokinetic subgroups and an outlier.

Two general methods for population pharmacokinetic modeling: non-parametric adaptive grid and non-parametric Bayesian

Population pharmacokinetic (PK) modeling methods can be statistically classified as either parametric or nonparametric (NP). Each classification can be divided into maximum likelihood (ML) or Bayesian (B) approaches. In this paper we discuss the nonparametric case using both maximum likelihood and Bayesian approaches. We present two nonparametric methods for estimating the unknown joint population distribution of model parameter values in a pharmacokinetic/pharmacodynamic (PK/PD) dataset. The first method is the NP Adaptive Grid (NPAG). The second is the NP Bayesian (NPB) algorithm with a stick-breaking process to construct a Dirichlet prior. Our objective is to compare the performance of these two methods using a simulated PK/PD dataset. Our results showed excellent performance of NPAG and NPB in a realistically simulated PK study. This simulation allowed us to have benchmarks in the form of the true population parameters to compare with the estimates produced by the two methods, while incorporating challenges like unbalanced sample times and sample numbers as well as the ability to include the covariate of patient weight. We conclude that both NPML and NPB can be used in realistic PK/PD population analysis problems. The advantages of one versus the other are discussed in the paper. NPAG and NPB are implemented in R and freely available for download within the Pmetrics package from www.lapk.org.

Predicting the temporal responses of non-phase-locking bullfrog auditory units to complex acoustic waveforms

Axons from the basilar papilla of the American bullfrog (Rana catesbeiana) do not phase lock to stimuli within an octave of their best frequencies. Nevertheless, they show consistent temporal patterns of instantaneous spike rate (as reflected in peristimulus time histograms) in response to repeated stimuli in that frequency range. We show that the second-order Wiener kernels for these axons, derived from the cross-correlation of continuous (non-repeating), broad-band noise stimulus with the spike train produced in response to that stimulus, can predict with considerable precision the temporal pattern of instantaneous spike rate in response to a novel, complex acoustic waveform (a repeated, 100-ms segment of noise, band-limited to cover the single octaves above and below best frequency). Furthermore, we show that most of this predictive power is retained when the second-order Wiener kernel is reduced to the highest-ranking pair of singular vectors derived from singular-value decomposition, that the retained pair of vectors corresponds to a single auditory filter followed by an envelope-detection process, and that the auditory filter itself predicts the characteristic frequency (CF) of the axon and the shape of the frequency-threshold tuning curve in the vicinity of CF.

Tuning and timing in the gerbil ear: Wiener-kernel analysis

Information about the tuning and timing of excitation in cochlear axons with low-characteristic frequency (CF) is embodied in the first-order Wiener kernel, or reverse correlation function. For high-CF axons, the highest-ranking eigenvector (or singular vector) of the second-order Wiener kernel often can serve as a surrogate for the first-order kernel, providing the same information. For mid-CF axons, the two functions are essentially identical. In this paper we apply these tools to gerbil cochlear-nerve axons with CFs ranging from 700 Hz to 14 kHz. Eigen or singular-value decomposition of the second-order Wiener kernel allows us to separate excitatory and suppressive effects, and to determine precisely the timing of the latter.

Tuning and timing of excitation and inhibition in primary auditory nerve fibers

Information about the tuning and timing of excitation, adaptation and suppression in an auditory primary afferent axon can be obtained from the second-order Wiener kernel. Through the process of singular-value decomposition, this information can be extracted from the kernel and displayed graphically in separate two-dimensional images for excitation and inhibition(1). For low- to mid-frequency units, the images typically include checkerboard patterns. For all units they may include patterns of parallel diagonal lines. The former represent non-linearities in the phase-locked (ac) response of the unit; the latter reflect non-linear envelope-following (dc) responses. Examples of detailed interpretation are presented for three amphibian-papillar units from the American bullfrog. The second-order Wiener kernel itself is derived from second-order reverse correlation between spikes and a continuous, non-repeating, broad-band white-noise stimulus.

Essential roles of noise in neural coding and in studies of neural coding.

We present examples of results from our studies of auditory primary afferent nerve fibers and populations of such fibers in the frog and gerbil. We take advantage of the natural dithering effect of internal noise, where it is sufficient, to construct highly predictive descriptive models (based on the Wiener series with kernels derived from white-noise analysis). Where the internal noise is insufficient, we enhance dithering by applying external acoustic noise together with our stimuli. Using acoustic noise as a background sound, orthogonal to the stimulus waveform, we show that under some circumstances such background sound can enhance the ability of individual fibers and populations of fibers to encode the stimulus waveform.

Speaker recognition using dynamic synapse based neural networks with wavelet processing

Two problems in the field of speaker recognition are noise robustness and low interspeaker variability. This project involved the design of a system that is capable of speaker verification on a closed set of speakers using a wavelet processing technique that allows for a speaker‐dependent feature set extraction. Verification is accomplished using a dynamic synapse‐based neural network with noise‐resistance properties that is trained using a genetic algorithm technique. Using these techniques, the system was able to perform speaker verification without being adversely affected by normal levels of noise, and perform verification despite low variability between speakers.

Nonparametric population modeling and Bayesian analysis

We read with great interest the article by Premaud et al., in your ournal [1], The nonparametric (NP) population modeling approach stimated the model parameter values and predicted the observed ycophenolic acid concentrations more precisely than the paraetric method did. We expect this because the NP method makes, s the authors say, no assumptions about the shape of the model arameter distributions, as parametric methods do. We would like o respectfully offer the comments below in the hope that they will e well taken by a group we respect very highly.

Real Time Coding of Complex Sounds in the Auditory Nerve

ABSTRACT All of an organisms knowledge about the acoustic world is coded in the spike trains of its auditory nerve fibers. Several fundamental aspects of this internal representation are not well understood: How much information is carried by the auditory nerve and how efficient is the coding of information? What is the role of nonlinearities in the coding of complex, natural stimuli? Is the code structured to make subsequent computation simple? We have recently developed methods for decoding neural spike trains in real time to estimate continuous input stimuli. Here we extend this approach to non-phase locked cells, for which we reconstruct the stimulus envelope. These methods allow us to quantify the performance of the auditory neural code in single afferent fibers and to begin to address the issues listed above. In particular, we measure the information transfer rate in a spike train directly as the information we gain about the auditory stimulus by observing the spikes. Comparing the experimental information rate with an upper bound to the rate determined by the statistics of the spike trains results in a direct measure of the efficiency of the coding process. In a single cell in the bullfrog auditory system we measure information rates as high as 160 baud (∼3 bits/spike) and coding efficiencies greater than 50%.