Dynamical estimation of neuron and network properties II: Path integral Monte Carlo methods.

Department of Physics, University of California, 9500 Gilman Drive, San Diego, La Jolla, CA 92093-0402, USA.
Biological Cybernetics (Impact Factor: 1.93). 04/2012; 106(3):155-67. DOI: 10.1007/s00422-012-0487-5
Source: PubMed

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.


Available from: C Daniel Meliza, Nov 11, 2014
1 Follower
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: We investigate the dynamics of a conductance-based neuron model coupled to a model of intracellular calcium uptake and release by the endoplasmic reticulum. The intracellular calcium dynamics occur on a time scale that is orders of magnitude slower than voltage spiking behavior. Coupling these mechanisms sets the stage for the appearance of chaotic dynamics, which we observe within certain ranges of model parameter values. We then explore the question of whether one can, using observed voltage data alone, estimate the states and parameters of the voltage plus calcium (V+Ca) dynamics model. We find the answer is negative. Indeed, we show that voltage plus another observed quantity must be known to allow the estimation to be accurate. We show that observing both the voltage time course V(t) and the intracellular Ca time course will permit accurate estimation, and from the estimated model state, accurate prediction after observations are completed. This sets the stage for how one will be able to use a more detailed model of V+Ca dynamics in neuron activity in the analysis of experimental data on individual neurons as well as functional networks in which the nodes (neurons) have these biophysical properties.
    Physical Review E 06/2014; 89(6-1):062714. DOI:10.1103/PhysRevE.89.062714 · 2.33 Impact Factor
  • [Show abstract] [Hide abstract]
    ABSTRACT: Recent results demonstrate techniques for fully quantitative, statistical inference of the dynamics of individual neurons under the Hodgkin-Huxley framework of voltage-gated conductances. Using a variational approximation, this approach has been successfully applied to simulated data from model neurons. Here, we use this method to analyze a population of real neurons recorded in a slice preparation of the zebra finch forebrain nucleus HVC. Our results demonstrate that using only 1,500 ms of voltage recorded while injecting a complex current waveform, we can estimate the values of 12 state variables and 72 parameters in a dynamical model, such that the model accurately predicts the responses of the neuron to novel injected currents. A less complex model produced consistently worse predictions, indicating that the additional currents contribute significantly to the dynamics of these neurons. Preliminary results indicate some differences in the channel complement of the models for different classes of HVC neurons, which accords with expectations from the biology. Whereas the model for each cell is incomplete (representing only the somatic compartment, and likely to be missing classes of channels that the real neurons possess), our approach opens the possibility to investigate in modeling the plausibility of additional classes of channels the cell might possess, thus improving the models over time. These results provide an important foundational basis for building biologically realistic network models, such as the one in HVC that contributes to the process of song production and developmental vocal learning in songbirds.
    Biological Cybernetics 06/2014; 108(4). DOI:10.1007/s00422-014-0615-5 · 1.93 Impact Factor
  • [Show abstract] [Hide abstract]
    ABSTRACT: Estimating the behavior of a network of neurons requires accurate models of the individual neurons along with accurate characterizations of the connections among them. Whereas for a single cell, measurements of the intracellular voltage are technically feasible and sufficient to characterize a useful model of its behavior, making sufficient numbers of simultaneous intracellular measurements to characterize even small networks is infeasible. This paper builds on prior work on single neurons to explore whether knowledge of the time of spiking of neurons in a network, once the nodes (neurons) have been characterized biophysically, can provide enough information to usefully constrain the functional architecture of the network: the existence of synaptic links among neurons and their strength. Using standardized voltage and synaptic gating variable waveforms associated with a spike, we demonstrate that the functional architecture of a small network of model neurons can be established.
    Biological Cybernetics 04/2014; 108(3). DOI:10.1007/s00422-014-0601-y · 1.93 Impact Factor