Estimation of neuron parameters from imperfect observations

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.
Author summary The accurate estimation of neuronal parameters inaccessible to experiment is essential to our understanding of intracellular dynamics and to predicting the behaviour of biocircuits. However, 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. The imprecise knowledge of model and data introduces uncertainty in the parameter field. Our work describes a regularization method that arrives at the optimal parameter solution with a probability of 94%. The uncertainty on parameter estimates is further reduced with the help of an adaptive sampling method that maximises the duration of the assimilation window while keeping the size of the problem constant. Our work shows that the true configuration of a neuronal system may be inferred from time series observations provided external stimuli are calibrated to drive the system over its entire dynamic range.