Dynamical estimation of neuron and network properties II: Path integral Monte Carlo methods.
ABSTRACT 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.
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ABSTRACT: Biophysically detailed models of single cells are difficult to fit to real data. Recent advances in imaging techniques allow simultaneous access to various intracellular variables, and these data can be used to significantly facilitate the modelling task. These data, however, are noisy, and current approaches to building biophysically detailed models are not designed to deal with this. We extend previous techniques to take the noisy nature of the measurements into account. Sequential Monte Carlo ("particle filtering") methods, in combination with a detailed biophysical description of a cell, are used for principled, model-based smoothing of noisy recording data. We also provide an alternative formulation of smoothing where the neural nonlinearities are estimated in a non-parametric manner. Biophysically important parameters of detailed models (such as channel densities, intercompartmental conductances, input resistances, and observation noise) are inferred automatically from noisy data via expectation-maximization. Overall, we find that model-based smoothing is a powerful, robust technique for smoothing of noisy biophysical data and for inference of biophysical parameters in the face of recording noise.PLoS Computational Biology 06/2009; 5(5):e1000379. · 4.87 Impact Factor
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ABSTRACT: 1. The physiological and functional features of time-dependent anomalous rectification activated by hyperpolarization and the current which underlies it, Ih, were examined in guinea-pig and cat thalamocortical relay neurones using in vitro intracellular recording techniques in thalamic slices. 2. Hyperpolarization of the membrane from rest with a constant-current pulse resulted in time-dependent rectification, expressed as a depolarizing sag of the membrane potential back towards rest. Under voltage clamp conditions, hyperpolarizing steps to membrane potentials negative to approximately -60 mV were associated with the activation of a slow inward current, Ih, which showed no inactivation with time. 3. The activation curve of the conductance underlying Ih was obtained through analysis of tail currents and ranged from -60 to -90 mV, with half-activation occurring at -75 mV. The time course of activation of Ih was well fitted by a single-exponential function and was strongly voltage dependent, with time constants ranging from greater than 1-2 s at threshold to an average of 229 ms at -95 mV. The time course of de-activation was also described by a single-exponential function, was voltage dependent, and the time constant ranged from an average of 1000 ms at -80 mV to 347 ms at -55 mV. 4. Raising [K+]o from 2.5 to 7.5 mM enhanced, while decreasing [Na+]o from 153 to 26 mM reduced, the amplitude of Ih. In addition, reduction of [Na+]o slowed the rate of Ih activation. These results indicate that Ih is carried by both Na+ and K+ ions, which is consistent with the extrapolated reversal potential of -43 mV. Replacement of Cl- in the bathing medium with isethionate shifted the chloride equilibrium potential positive by approximately 30-70 mV, evoked an inward shift of the holding current at -50 mV, and resulted in a marked reduction of instantaneous currents as well as Ih, suggesting a non-specific blocking action of impermeable anions. 5. Local (2-10 mM in micropipette) or bath (1-2 mM) applications of Cs+ abolished Ih over the whole voltage range tested (-60 to -110 mV), with no consistent effects on instantaneous currents. Barium (1 mM, local; 0.3-0.5 mM, bath) evoked a steady inward current, reduced the amplitude of instantaneous currents, and had only weak suppressive effects on Ih. 6. Block of Ih with local application of Cs+ resulted in a hyperpolarization of the membrane from the resting level, a decrease in apparent membrane conductance, and a block of the slow after-hyperpolarization that appears upon termination of depolarizing membrane responses, indicating that Ih contributes substantially to the resting and active membrane properties of thalamocortical relay neurones.(ABSTRACT TRUNCATED AT 400 WORDS)The Journal of Physiology 01/1991; 431:291-318. · 4.38 Impact Factor
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ABSTRACT: We present a novel framework for automatically constraining parameters of compartmental models of neurons, given a large set of experimentally measured responses of these neurons. In experiments, intrinsic noise gives rise to a large variability (e.g., in firing pattern) in the voltage responses to repetitions of the exact same input. Thus, the common approach of fitting models by attempting to perfectly replicate, point by point, a single chosen trace out of the spectrum of variable responses does not seem to do justice to the data. In addition, finding a single error function that faithfully characterizes the distance between two spiking traces is not a trivial pursuit. To address these issues, one can adopt a multiple objective optimization approach that allows the use of several error functions jointly. When more than one error function is available, the comparison between experimental voltage traces and model response can be performed on the basis of individual features of interest (e.g., spike rate, spike width). Each feature can be compared between model and experimental mean, in units of its experimental variability, thereby incorporating into the fitting this variability. We demonstrate the success of this approach, when used in conjunction with genetic algorithm optimization, in generating an excellent fit between model behavior and the firing pattern of two distinct electrical classes of cortical interneurons, accommodating and fast-spiking. We argue that the multiple, diverse models generated by this method could serve as the building blocks for the realistic simulation of large neuronal networks.Frontiers in Neuroscience 12/2007; 1(1):7-18.