Nevertheless, in all cases the magnetic helicity of the cloud structures seen at NEAR is the same as at Wind. The radial speeds of the shock and ICME leading edge as they cross Wind and the time delays of those events, for which we have some assurance that they also arrived at NEAR, indicate that the ICMEs decelerate measurably as they travel near 1 AU.
We present a method for using measurements of membrane voltage in individual neurons to estimate the parameters and states of the voltage-gated ion channels underlying the dynamics of the neuron’s behavior. Short injections of a complex time-varying current provide sufficient data to determine the reversal potentials, maximal conductances, and kinetic parameters of a diverse range of channels, representing tens of unknown parameters and many gating variables in a model of the neuron’s behavior. These estimates are used to predict the response of the model at times beyond the observation window. This method of extends to the general problem of determining model parameters and unobserved state variables from a sparse set of observations, and may be applicable to networks of neurons. We describe an exact formulation of the tasks in nonlinear data assimilation when one has noisy data, errors in the models, and incomplete information about the state of the system when observations commence. This is a high dimensional integral along the path of the model state through the observation window. In this article, a stationary path approximation to this integral, using a variational method, is described and tested employing data generated using neuronal models comprising several common channels with Hodgkin–Huxley dynamics. These numerical experiments reveal a number of practical considerations in designing stimulus currents and in determining model consistency. The tools explored here are computationally efficient and have paths to parallelization that should allow large individual neuron and network problems to be addressed.
Hodgkin-Huxley (HH) models of neuronal membrane dynamics consist of a set of nonlinear differential equations that describe the time-varying conductance of various ion channels. Using observations of voltage alone we show how to estimate the unknown parameters and unobserved state variables of an HH model in the expected circumstance that the measurements are noisy, the model has errors, and the state of the neuron is not known when observations commence. The joint probability distribution of the observed membrane voltage and the unobserved state variables and parameters of these models is a path integral through the model state space. The solution to this integral allows estimation of the parameters and thus a characterization of many biological properties of interest, including channel complement and density, that give rise to a neuron's electrophysiological behavior. This paper describes a method for directly evaluating the path integral using a Monte Carlo numerical approach. This provides estimates not only of the expected values of model parameters but also of their posterior uncertainty. Using test data simulated from neuronal models comprising several common channels, we show that short (<50 ms) intracellular recordings from neurons stimulated with a complex time-varying current yield accurate and precise estimates of the model parameters as well as accurate predictions of the future behavior of the neuron. We also show that this method is robust to errors in model specification, supporting model development for biological preparations in which the channel expression and other biophysical properties of the neurons are not fully known.
Neuroscientists often propose detailed computational models to probe the properties of their studied neural systems. With the advent of neuromorphic engineering, there * emre@ini.phys.ethz.ch † btoth@physics.ucsd.edu 1 is an increasing number of hardware electronic analogs of biological neural systems being proposed as well. However, for both biological and hardware systems, it is often difficult to estimate the parameters of the model such that they are meaningful to the studied experimental system, especially when these models involve a large number of states and parameters which cannot be simultaneously measured. We have developed a procedure to solve this problem in the context of interacting neural populations using a recently developed Dynamic State and Parameter Estimation (DSPE) technique.This technique uses synchronization as a tool for dynamically coupling experimentally measured data to its corresponding model to determine its parameters and internal state variables. While in its conventional use, the experimental data is obtained from the biological neural system, and the model is simulated in software, here we show that this technique is also efficient in validating proposed network models for neuromorphic spike-based Very Large Scale Integration (VLSI) chips, and that it is able to systematically extract network parameters such as synaptic weights, time constants and other variables which are not accessible by direct observation. Our results suggest that this method can become a very useful tool for model-based identification and configuration of neuromorphic multi-chip VLSI systems.
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