Data Assimilation Methods for Neuronal State and Parameter Estimation

Abstract

This tutorial illustrates the use of data assimilation algorithms to estimate unobserved variables and unknown parameters of conductance-based neuronal models. Modern data assimilation (DA) techniques are widely used in climate science and weather prediction, but have only recently begun to be applied in neuroscience. The two main classes of DA techniques are sequential methods and variational methods. We provide computer code implementing basic versions of a method from each class, the Unscented Kalman Filter and 4D-Var, and demonstrate how to use these algorithms to infer several parameters of the Morris–Lecar model from a single voltage trace. Depending on parameters, the Morris–Lecar model exhibits qualitatively different types of neuronal excitability due to changes in the underlying bifurcation structure. We show that when presented with voltage traces from each of the various excitability regimes, the DA methods can identify parameter sets that produce the correct bifurcation structure even with initial parameter guesses that correspond to a different excitability regime. This demonstrates the ability of DA techniques to perform nonlinear state and parameter estimation and introduces the geometric structure of inferred models as a novel qualitative measure of estimation success. We conclude by discussing extensions of these DA algorithms that have appeared in the neuroscience literature.Electronic Supplementary MaterialThe online version of this article (10.1186/s13408-018-0066-8) contains supplementary material.

On Temporal Scale Separation in Coupled Data Assimilation with the Ensemble Kalman Filter

“…Examples include, but are not limited to, the attribution of climate change [25], neuro-(e.g. [32,40]) and life-sciences [30] or traffic management [43].…”

Spectral estimates for saddle point matrices arising in weak constraint four‐dimensional variational data assimilation

“…Data assimilation is used to produce initial conditions in numerical weather prediction (NWP), 1,2 as well as other areas, for example, flood forecasting, 3 research into atmospheric composition, 4 and neuroscience. 5 In operational applications, the process is made more challenging by the size of the system, for example, the numerical model may be operating on 10 8 state variables and 10 5 −10 6 observations may be incorporated. 6,7 Moreover, there is usually a constraint on the time that can be spent on calculations.…”

Cell Fate Forecasting: A Data-Assimilation Approach to Predict Epithelial-Mesenchymal Transition

“…Several studies by Hamilton and colleagues have applied data-assimilation approaches to predict dynamics of neural electrical activity, including determination of neural network connectivity ( 33 ) and reconstruction of intracellular ion concentrations ( 34 ) and of intracellular potential ( 35 ). Moye and Diekman apply two different classes of data-assimilation approaches to improve estimates of both neural cell state and model parameters for different types of bifurcation behavior ( 40 ). Ullah and Schiff applied Kalman filters to predict unobserved states in neurons and small neural networks ( 36 , 37 ).…”

“…Although data-assimilation approaches have been well utilized in weather forecasting and atmospheric science ( 28 , 29 , 30 , 31 ), there are relatively few applications in the biomedical sciences ( 32 , 33 , 34 , 35 , 36 , 37 , 38 , 39 , 40 , 41 , 42 ). In this study, we present a data-assimilation approach to reconstruct cell marker expression and predict the timing of the EMT-associated state transitions.…”