Abstract
The estimation of parameters controlling the electrical properties of biological neurons is essential to determine their complement of ion channels and to understand the function of biological circuits. By synchronizing conductance models to time series observations of the membrane voltage, one may construct models capable of predicting neuronal dynamics. However, identifying the actual set of parameters of biological ion channels remains a formidable theoretical challenge. Here, we present a regularization method that improves convergence towards this optimal solution when data are noisy and the model is unknown. Our method relies on the existence of an offset in parameter space arising from the interplay between model nonlinearity and experimental error. By tuning this offset, we induce saddle-node bifurcations from sub-optimal to optimal solutions. This regularization method increases the probability of finding the optimal set of parameters from 67% to 94.3%. We also reduce parameter correlations by implementing adaptive sampling and stimulation protocols compatible with parameter identifiability requirements. Our results show that the optimal model parameters may be inferred from imperfect observations provided the conditions of observability and identifiability are fulfilled.
Highlights
Data assimilation is increasingly important in quantitative biology to infer unmeasurable microscopic quantities from the observation of macroscopic variables
The accurate estimation of neuronal parameters inaccessible to experiment is essential to our understanding of intracellular dynamics and to predicting the behaviour of biocircuits. This program is met with challenges including our lack of knowledge of the precise equations of biological neurons, their highly nonlinear response to stimulation and error introduced by the measurement apparatus
Our work describes a regularization method that arrives at the optimal parameter solution with a probability of 94%
Summary
Data assimilation is increasingly important in quantitative biology to infer unmeasurable microscopic quantities from the observation of macroscopic variables. It has successfully obtained quantitative neuron models by synchronizing model equations to membrane voltage oscillations [1–3] and inferred the connectivity of neuron populations from electroencephalographic recordings of brain activity [4, 5]. A different, yet related problem, is that, under ordinary conditions, biocircuits may exhibit functional overlap [8, 9], redundancies [10] and compensation [11]. This further increases the need to determine whether experimental protocols exist which can yield actual biocircuit parameters. We briefly review the theoretical challenges of estimating parameters with inverse methods before summarizing our solutions
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