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# 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

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

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**ABSTRACT:**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 [Formula: see text] 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.Biological Cybernetics 10/2011; 105(3-4):217-37. DOI:10.1007/s00422-011-0459-1 · 1.93 Impact Factor -
##### Article: Dynamical estimation of neuron and network properties III: network analysis using neuron spike times

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**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 - [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