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dynamical state and parameter estimation example


This directory is a complete example of an analysis to estimate the parameters and state variables of a conductance-based neuron model using intracellular current clamp data. The code and data here were used in "Estimating Parameters and Predicting Membrane Voltages with Conductance-Based Neuron Models" by C Daniel Meliza, Mark Kostuk, Hao Huang, Alain Nogaret, Daniel Margoliash, and Henry D I Abarbanel, doi:10.1007/s00422-014-0615-5. The code is free for use under the terms described in the file LICENSE. The data are part of the public domain and free for use.

This file is a summary of the steps you need to run the analysis. For a more complete description of the algorithm, please consult Bryan Toth's dissertation, supplied here in the file tothdissertation0511.pdf.

Install prerequisites

Docker image

The quickest way to get started is to run the software using a pre-built Docker container. Assuming you have Docker installed, simply run docker run -it -v pwd:/app --rm dmeliza/dpse from this directory. Note that running the model can require a lot of memory, so be sure to allocate at least 16 GB to the container.

Manual build

You will need to have g++, IPOPT, Python, and sympy installed. This example has been tested with g++ 4.3, IPOPT 3.10.2, Python 2.7, and sympy 0.7.1. running on Debian 7.

All of the prerequisites are available through most OS package managers. We recommend Debian Linux or OS X. IPOPT requires some facility with the shell to install, but the instructions at are reliable if followed carefully. You need to install BLAS, LAPACK, and the MA57 solver at a minimum. Your mileage may vary with other solvers.

A Dockerfile is included for help in building the prerequisites in a container. You'll need to edit it to set the link to the HSL solvers (which you'll need to download from somewhere; they are only distributed by request). Run docker build -t dpse . to build from these instructions.

Specify the model

The model comprises a set of ordinary differential equations, which are specified in a file called equations.txt. This directory contains an example model with 12 state variables and 73 parameters. The file is commented. The model distributed here is the 9-current model described in the manuscript.

Generate the estimation code

Next, a python program (originally by Bryan Toth) converts the symbolic description of the model in equations.txt into C++ functions. Essentially this involves computing a lot of derivatives to get the Jacobian and Hessian. To run this step:

python model/

Expect this to take a long time, but you only need to run this when the equations.txt file changes. The makecode script expects to find equations.txt in the current directory.

Compile the estimation code

Successful completion of the previous step will result in generation of a number of C++ files and a Makefile. Run make to compile the code to a binary. The Makefile expects to find IPOPT using pkg-config. If you have problems you may need to edit the COIN_LDFLAGS and COIN_CFLAGS lines in the Makefile. You will also need a reasonably modern C++ compiler (e.g. gcc 4.3 or later). Older compilers may run out of memory when used with large models.

Run the estimation procedure

If the previous step completes successfully, you will have an executable called biohh1. At this point you can adjust the parameter guesses and bounds by editing specs.txt. This file is also commented. Changes to this file do not require a recompilation of the executable. Make sure it specifies the location of the input data files correctly, or you'll get a segmentation fault. You may also want to edit biohh1.opt to set tolerances and maximum number of iterations. Consult the IPOPT documentation for more information on the parameters in this file. To run the estimation:


This takes a long time, too. You will see some nice status updates as the estimates converge. At the end there will be two files you can inspect. param.dat has the parameter estimates; data.dat has the state variables.

Run forward predictions

The completed model can be used to predict forward in time by integrating with the estimated state and parameter values. The example specs.txt file uses 1500 ms for the assimilation, leaving quite a bit of data for prediction. Chris Knowlton's ipopt_predict script uses the equations.txt file and the output from IPOPT to generate forward predictions. To run the prediction for the rest of the data in the example:

python model/ -e equations.txt pred.dat 258334

The last commandline parameter specifies the number of time points to integrate forward after the end of the assimilation period.

Editing the model

To change the equations of motion, edit equations.txt. This file is commented, but the format is very sensitive to bookkeeping errors. It is critical that the nY,NP,nU,nI,nF line match the number of equations, parameters, control terms, forcing terms, and adjust functions exactly. To change parameter bounds or input file (i.e., the forcing current and voltage observations), edit specs.txt. It is also crucial that this file match the variable and parameter counts exactly. Any errors may result in segmentation faults. Sorry.

Additional data

The data subdirectory contains data for all three exemplar neurons from the manuscript. Each data collection epoch corresponds to two files, one ending in v.dat and the other ending in i.dat. The former file contains a single column of floating point numbers in ASCII format, which is the recorded voltage in mV, starting at time 0 and sampled at the rate specified in specs.txt (50 kHz). The latter file contains the injected current (in pA) sampled at the same times.

Three recording epochs are provided for each exemplar neuron. The epoch is given by the last number in the file name. The files used for data assimilation and prediction in the manuscript are as follows:

neuron assimilation cross-epoch prediction
N1 20120406_1_3_19 20120406_1_3_15
N2 20120424_1_1_21 20120424_1_1_15
N3 20120116_1_1_6 20120116_1_1_2

Currently the specs.txt file is set to run the analysis for N1. To analyze a different neuron, edit specs.txt and replace the names of the data files. Because the file names for the output of the biohh1 analysis are fixed, you may wish to copy specs.txt, equations.txt, the data files, and the executable to a new directory if you want to run a different analysis.

To generate cross-epoch predictions, you will need to take the parameter estimates from the estimation epochs and create a new specs.txt with those values fixed. Then run an estimation procedure on the first 100 ms or so of data from the new epoch to get updated state estimates for the new epoch, then predict forward as above.

The full dataset used in the manuscript is too large to include in this archive, but we are happy to make it available on request. Contact Dan Meliza (now in the University of Virginia Department of Psychology).


Example dynamical state and parameter estimation (From doi:10.1007/s00422-014-0615-5)




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