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Automatic Construction of Predictive Neuron Models through Large Scale Assimilation of Electrophysiological Data

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ABSTRACT

We report on the construction of neuron models by assimilating electrophysiological data with large-scale constrained nonlinear optimization. The method implements interior point line parameter search to determine parameters from the responses to intracellular current injections of zebra finch HVC neurons. We incorporated these parameters into a nine ionic channel conductance model to obtain completed models which we then use to predict the state of the neuron under arbitrary current stimulation. Each model was validated by successfully predicting the dynamics of the membrane potential induced by 20–50 different current protocols. The dispersion of parameters extracted from different assimilation windows was studied. Differences in constraints from current protocols, stochastic variability in neuron output, and noise behave as a residual temperature which broadens the global minimum of the objective function to an ellipsoid domain whose principal axes follow an exponentially decaying distribution. The maximum likelihood expectation of extracted parameters was found to provide an excellent approximation of the global minimum and yields highly consistent kinetics for both neurons studied. Large scale assimilation absorbs the intrinsic variability of electrophysiological data over wide assimilation windows. It builds models in an automatic manner treating all data as equal quantities and requiring minimal additional insight.

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Assimilation-prediction method.The injected current waveform  and resultant time series membrane voltage  of the epoch to assimilate (Epoch 0) are input into the nonlinear optimization filter (IPOPT). These provide the equality constraints. The user specifies the inequality constraints by choosing the upper and lower boundaries of the parameter search intervals, pL and pU. IPOPT outputs the state variables x*(t) solution of the minimization problem at each point of the assimilation window, together with the parameter solutions p*. The extracted parameters p* are inserted in the model equations to construct the completed model. The state of the neuron xpredict(t) is predicted by integrating the current protocol  forward from initial conditions x*(0) using a fifth order, adaptive step size, Runge-Kutta solver (RK5). The model is validated by comparing the predicted membrane voltage  with the voltage  recorded in Epoch e.
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f1: Assimilation-prediction method.The injected current waveform and resultant time series membrane voltage of the epoch to assimilate (Epoch 0) are input into the nonlinear optimization filter (IPOPT). These provide the equality constraints. The user specifies the inequality constraints by choosing the upper and lower boundaries of the parameter search intervals, pL and pU. IPOPT outputs the state variables x*(t) solution of the minimization problem at each point of the assimilation window, together with the parameter solutions p*. The extracted parameters p* are inserted in the model equations to construct the completed model. The state of the neuron xpredict(t) is predicted by integrating the current protocol forward from initial conditions x*(0) using a fifth order, adaptive step size, Runge-Kutta solver (RK5). The model is validated by comparing the predicted membrane voltage with the voltage recorded in Epoch e.

Mentions: The assimilated neuron models were primarily validated by testing their ability to predict multiple epochs implementing a wide range of current protocols (see methods). To this end, we constructed the fully automated assimilation-prediction procedure depicted in Fig. 1. In the first stage, the inputs of IPOPT are the electrophysiological recordings and , i = 0, 1 … N chosen to assimilate data from Epoch 0, and the boundaries of the parameter search intervals, pL and pU. IPOPT outputs the state vector that minimizes the objective function at each point of the assimilation window x*(ti), i = 0, 1 … N and the parameter vector solution p*. In the second stage, the p* were inserted into the model equations Eqs 6, 7, 8, 9 to obtain the completed model. This model was then used to predict the state of this neuron by forward integrating the experimental current protocol of another epoch . By default, the initial conditions x(0) at the start of integration were obtained from data assimilation (see below). Although the system of equations in Eq. 2 is not believed to be chaotic, the multiplicity of recovery times arising from 9 ion channels induces system stiffness and reduces tolerance to integration error. It was therefore necessary to implement forward integration using adaptive step size fifth order Runge-Kutta (RK5) to achieve the required level of accuracy38.


Automatic Construction of Predictive Neuron Models through Large Scale Assimilation of Electrophysiological Data
Assimilation-prediction method.The injected current waveform  and resultant time series membrane voltage  of the epoch to assimilate (Epoch 0) are input into the nonlinear optimization filter (IPOPT). These provide the equality constraints. The user specifies the inequality constraints by choosing the upper and lower boundaries of the parameter search intervals, pL and pU. IPOPT outputs the state variables x*(t) solution of the minimization problem at each point of the assimilation window, together with the parameter solutions p*. The extracted parameters p* are inserted in the model equations to construct the completed model. The state of the neuron xpredict(t) is predicted by integrating the current protocol  forward from initial conditions x*(0) using a fifth order, adaptive step size, Runge-Kutta solver (RK5). The model is validated by comparing the predicted membrane voltage  with the voltage  recorded in Epoch e.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC5015021&req=5

f1: Assimilation-prediction method.The injected current waveform and resultant time series membrane voltage of the epoch to assimilate (Epoch 0) are input into the nonlinear optimization filter (IPOPT). These provide the equality constraints. The user specifies the inequality constraints by choosing the upper and lower boundaries of the parameter search intervals, pL and pU. IPOPT outputs the state variables x*(t) solution of the minimization problem at each point of the assimilation window, together with the parameter solutions p*. The extracted parameters p* are inserted in the model equations to construct the completed model. The state of the neuron xpredict(t) is predicted by integrating the current protocol forward from initial conditions x*(0) using a fifth order, adaptive step size, Runge-Kutta solver (RK5). The model is validated by comparing the predicted membrane voltage with the voltage recorded in Epoch e.
Mentions: The assimilated neuron models were primarily validated by testing their ability to predict multiple epochs implementing a wide range of current protocols (see methods). To this end, we constructed the fully automated assimilation-prediction procedure depicted in Fig. 1. In the first stage, the inputs of IPOPT are the electrophysiological recordings and , i = 0, 1 … N chosen to assimilate data from Epoch 0, and the boundaries of the parameter search intervals, pL and pU. IPOPT outputs the state vector that minimizes the objective function at each point of the assimilation window x*(ti), i = 0, 1 … N and the parameter vector solution p*. In the second stage, the p* were inserted into the model equations Eqs 6, 7, 8, 9 to obtain the completed model. This model was then used to predict the state of this neuron by forward integrating the experimental current protocol of another epoch . By default, the initial conditions x(0) at the start of integration were obtained from data assimilation (see below). Although the system of equations in Eq. 2 is not believed to be chaotic, the multiplicity of recovery times arising from 9 ion channels induces system stiffness and reduces tolerance to integration error. It was therefore necessary to implement forward integration using adaptive step size fifth order Runge-Kutta (RK5) to achieve the required level of accuracy38.

View Article: PubMed Central - PubMed

ABSTRACT

We report on the construction of neuron models by assimilating electrophysiological data with large-scale constrained nonlinear optimization. The method implements interior point line parameter search to determine parameters from the responses to intracellular current injections of zebra finch HVC neurons. We incorporated these parameters into a nine ionic channel conductance model to obtain completed models which we then use to predict the state of the neuron under arbitrary current stimulation. Each model was validated by successfully predicting the dynamics of the membrane potential induced by 20–50 different current protocols. The dispersion of parameters extracted from different assimilation windows was studied. Differences in constraints from current protocols, stochastic variability in neuron output, and noise behave as a residual temperature which broadens the global minimum of the objective function to an ellipsoid domain whose principal axes follow an exponentially decaying distribution. The maximum likelihood expectation of extracted parameters was found to provide an excellent approximation of the global minimum and yields highly consistent kinetics for both neurons studied. Large scale assimilation absorbs the intrinsic variability of electrophysiological data over wide assimilation windows. It builds models in an automatic manner treating all data as equal quantities and requiring minimal additional insight.

No MeSH data available.


Related in: MedlinePlus