Estimating parameters and predicting membrane voltages with conductance-based neuron models

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.

Using waveform information in nonlinear data assimilation

“…As in practical geophysical dynamics (for example, numerical weather prediction) sparse measurements of the network behavior under selected forcing is to be expected. One strategy [11] for understanding the underlying physical properties of such problems is to analyze carefully the properties of the nodes; namely, the specific oscillators such as the ones we have covered here, and then use the same approach to analyze the nature and strengths of the couplings among the oscillators at the nodes to complete a model for the network as a whole.…”

“…To test or validate a model requires an accurate estimate of its fixed parameters and its unobserved state variables, which then must be used to predict the outcome of new measurements when the same system is subjected to forces different from those that were used to construct the estimate. This enterprise of incorporating information from measured data into the properties of a predictive model is known as data assimilation in geophysical sciences and is practiced in a wide spectrum of scientific inquiries, including numerical weather prediction [1], systems biology [2,3], biomedical engineering [4], chemical engineering [5], biochemistry [6], coastal and estuarine modeling [7,8], cardiac dynamics [9], and nervous system networks [10,11], among many others.…”

Computational models in the age of large datasets

“…First, the models are typically nonlinear, so the relation between the parameters and the output can be complicated and many-valued. Averages of measured parameters can give rise to non-observed behavior [26] and models can be exquisitely sensitive to measured parameters [27,28,29,30]. The value of averaging as a means of combating experimental noise might thus be obviated by the possibility that the average values are not valid parameter combinations themselves.…”

“…Second, biological systems have degenerate pathways and components, meaning that properties and functions of structurally distinct components overlap. While this confers robustness to the systems themselves, it means that models can be remarkably insensitive to many combinations of parameters [5**,21,22,23,27,29,30,31]. This ‘sloppy’ property of biological systems is well-documented in systems biology [8**] and neuroscientists may benefit from a wider appreciation of the tribulations and successes of model building in this sister field [32].…”

“…Alternative strategies for fitting data, including evolutionary algorithms [52,53] and dynamic state estimation [29] have also been developed to exploit multiple, time-series measurements. In spite of the sophistication of current data analysis techniques and the increasing richness and quality of data, any model that is constrained by data is only as sound as the necessary assumptions upon which it rests: even incorrect models can fit the data.…”