Abstract
Conductance-based compartment modeling requires tuning of many parameters to fit the neuron model to target electrophysiological data. Automated parameter optimization via evolutionary algorithms (EAs) is a common approach to accomplish this task, using error functions to quantify differences between model and target. We present a three-stage EA optimization protocol for tuning ion channel conductances and kinetics in a generic neuron model with minimal manual intervention. We use the technique of Latin hypercube sampling in a new way, to choose weights for error functions automatically so that each function influences the parameter search to a similar degree. This protocol requires no specialized physiological data collection and is applicable to commonly-collected current clamp data and either single- or multi-objective optimization. We applied the protocol to two representative pyramidal neurons from layer 3 of the prefrontal cortex of rhesus monkeys, in which action potential firing rates are significantly higher in aged compared to young animals. Using an idealized dendritic topology and models with either 4 or 8 ion channels (10 or 23 free parameters respectively), we produced populations of parameter combinations fitting the target datasets in less than 80 hours of optimization each. Passive parameter differences between young and aged models were consistent with our prior results using simpler models and hand tuning. We analyzed parameter values among fits to a single neuron to facilitate refinement of the underlying model, and across fits to multiple neurons to show how our protocol will lead to predictions of parameter differences with aging in these neurons.










Similar content being viewed by others
References
Abouzeid, A., & Kath, W.L. (2014). Fully automated multi-objective fitting of morphologically realistic hippocampal CA1 pyramidal cell models. In 2014 Neuroscience meeting planner, (Vol. 372 p. 14).
Achard, P., & De Schutter, E. (2006). Complex parameter landscape for a complex neuron model. PLoS Computational Biology, 2(7), e94.
Achard, P., & De Schutter, E. (2008). Calcium, synaptic plasticity and intrinsic homeostasis in purkinje neuron models. Frontiers in computational neuroscience 2 (December) 8.
Achard, P., Van Geit, W., & LeMasson, G. (2010). Parameter searching. In De Schutter, E (Ed.) Computational Modeling Methods for Neuroscientists Press, MIT, Cambridge, MA, 2 (pp. 31–60).
Ahern, C.A., Payandeh, J., Bosmans, F., & Chanda, B. (2016). The hitchhiker’s guide to the voltage-gated sodium channel galaxy. Journal of General Physiology, 147(1), 1–24.
Almog, M., & Korngreen, A. (2014). A quantitative description of dendritic conductances and its application to dendritic excitation in layer 5 pyramidal neurons. Journal of Neuroscience, 34(1), 182–196.
Amatrudo, J.M., Weaver, C.M., Crimins, J.L., Hof, P.R., Rosene, D.L., & Luebke, J.I. (2012). Influence of highly distinctive structural properties on the excitability of pyramidal neurons in monkey visual and prefrontal cortices. Journal of Neuroscience, 32(40), 13,644–13,660.
Amendola, J., Woodhouse, A., Marin-Eauclaire, M.F., & Goaillard, J.M. (2012). Ca 2+/cAMP-Sensitive covariation of I A and I H voltage dependences tunes rebound firing in dopaminergic neurons. Journal of Neuroscience, 32(6), 2166–2181.
Bahl, A., Stemmler, M.B., Herz, A.V.M., & Roth, A. (2012). Automated optimization of a reduced layer 5 pyramidal cell model based on experimental data. Journal of Neuroscience Methods, 210(1), 22–34.
Brookings, T., Goeritz, M.L., & Marder, E. (2014). Automatic parameter estimation of multicompartmental neuron models via minimization of trace error with control adjustment. Journal of Neurophysiology, 112, 2332–2348.
Buhry, L., Pace, M., & Saïghi, S. (2012). Global parameter estimation of an Hodgkin-Huxley formalism using membrane voltage recordings: Application to neuro-mimetic analog integrated circuits. Neurocomputing, 81, 75–85.
Burke, R.E. (2000). Comparison of alternative designs for reducing complex neurons to equivalent cables. Journal of Computational Neuroscience, 9(1), 31–47.
Bush, P.C., & Sejnowski, T.J. (1993). Reduced compartmental models of neocortical pyramidal cells. Journal of Neuroscience Methods, 46(2), 159–166.
Carnevale, N.T., & Hines, M.L. (2006). The NEURON book. Cambridge: Cambridge University Press.
Chang, Y.M., Rosene, D.L., Killiany, R.J., La, Mangiamele, & Luebke, J.I. (2005). Increased action potential firing rates of layer 2/3 pyramidal cells in the prefrontal cortex are significantly related to cognitive performance in aged monkeys. Cerebral Cortex, 15(4), 409–418.
Coskren, P.J., Luebke, J.I., Kabaso, D., Wearne, S.L., Yadav, A., Rumbell, T., Hof, P.R., & Weaver, C.M. (2015). Functional consequences of age-related morphologic changes to pyramidal neurons of the rhesus monkey prefrontal cortex. Journal of Computational Neuroscience, 38(2), 263–283.
Destexhe, A. (2001). Simplified models of neocortical pyramidal cells preserving somatodendritic voltage attenuation. Neurocomputing, 38-40, 167–173.
Druckmann, S., Banitt, Y., Gidon, A., Schürmann, F., Markram, H., & Segev, I. (2007). A novel multiple objective optimization framework for constraining conductance-based neuron models by experimental data. Frontiers in Neuroscience, 1(1), 7–18.
Druckmann, S., Berger, T.K., Hill, S., Schürmann, F., Markram, H., & Segev, I. (2008). Evaluating automated parameter constraining procedures of neuron models by experimental and surrogate data. Biological Cybernetics, 99(4-5), 371–379.
Druckmann, S., Berger, T.K., Schürmann, F., Hill, S., Markram, H., & Segev, I. (2011). Effective stimuli for constructing reliable neuron models. PLoS Computational Biology, 7(8), e1002,133.
Eiben, A.E., & Smith, J.E. (2003). Introduction to Evolutionary Computing, 1st. Berlin: Springer.
Friedrich, P., Vella, M., Gulyás, A.I., Freund, T.F., & Káli, S. (2014). A flexible, interactive software tool for fitting the parameters of neuronal models. Frontiers in Neuroinformatics, 8(63), 1–19.
Gilman, J.P., Medalla, M., & Luebke, J.I. (2016). Area-specific features of pyramidal neurons - a comparative study in mouse and rhesus monkey. Cerebral Cortex in Press.
Goldman, M.S., Golowasch, J., Marder, E., & Abbott, L.F. (2001). Global structure, robustness, and modulation of neuronal models. Journal of Neuroscience, 21(14), 5229–5238.
Günay, C., Edgerton, J.R., & Jaeger, D. (2008). Channel density distributions explain spiking variability in the globus pallidus: a combined physiology and computer simulation database approach. Journal of Neuroscience, 28(30), 7476–7491.
Handl, J., Kell, D.B., & Knowles, J. (2007). Multiobjective optimization in bioinformatics and computational biology. IEEE/ACM Transactions on Computational Biology and Bioinformatics, 4(2), 279–291.
Hay, E., Hill, S., Schürmann, F., Markram, H., & Segev, I. (2011). Models of neocortical layer 5b pyramidal cells capturing a wide range of dendritic and perisomatic active properties. PLoS Computational Biology, 7(7), e1002,107.
Hay, E., Schürmann, F., Markram, H., & Segev, I. (2013). Preserving axosomatic spiking features despite diverse dendritic morphology. Journal of Neurophysiology, 109(12), 2972–2981.
Hendrickson, E.B., Edgerton, J.R., & Jaeger, D. (2011). The capabilities and limitations of conductance-based compartmental neuron models with reduced branched or unbranched morphologies and active dendrites. Journal of Computational Neuroscience, 30(2), 301–321.
Hendrickson, E.B., Edgerton, J.R., & Jaeger, D. (2011). The use of automated parameter searches to improve ion channel kinetics for neural modeling. Journal of Computational Neuroscience, 31(2), 329–346.
Hollander, M., Wolfe, D.A., & Chicken, E. (2014). Nonparametric statistical methods, 3rd. Hoboken: John Wiley and Sons.
Huys, Q.J.M., & Paninski, L. (2009). Smoothing of, and parameter estimation from, noisy biophysical recordings. PLoS Computational Biology, 5(5), e1000,379.
Huys, Q.J.M., Ahrens, M.B., & Paninski, L. (2006). Efficient estimation of detailed single-neuron models. Journal of Neurophysiology, 96(2), 872–890.
Jan, L.Y., & Jan, Y.N. (2012). Voltage-gated potassium channels and the diversity of electrical signalling. Journal of Physiology, 590, 2591–2599.
Johnson, M.E., Moore, L.M., & Ylvisaker, D. (1990). Minimax and maximin distance designs. Journal of Statistical Planning and Inference, 26(2), 131–148.
Jolliffe, I.T. (2002). Principal Component Analysis, 2nd edn. Springer.
Kabaso, D., Coskren, P.J., Henry, B.I., Hof, P.R., & Wearne, S.L. (2009). The electrotonic structure of pyramidal neurons contributing to prefrontal cortical circuits in macaque monkeys is significantly altered in aging. Cerebral Cortex, 19(10), 2248–2268.
Keren, N., Peled, N., & Korngreen, A. (2005). Constraining compartmental models using multiple voltage recordings and genetic algorithms. Journal of Neurophysiology, 94(6), 3730–3742.
Kostuk, M., Toth, B.A., Meliza, C.D., Margoliash, D., & Abarbanel, H.D.I. (2012). Dynamical estimation of neuron and network properties II: Path integral Monte Carlo methods. Biological Cybernetics, 106(3), 155–167.
LeMasson, G., & Maex, R. (2001). Introduction to equation solving and parameter fitting. In De Schutter, E (Ed.) Computational neuroscience: realistic modeling for experimentalists (pp. 1–21). London: CRC Press.
Loeppky, J.L., Sacks, J., & Welch, W.J. (2009). Choosing the sample size of a computer experiment: A practical guide. Technometrics, 51(4), 366–376.
Malik, A., Shim, K., Prinz, A.A., & Smolinski, T.G. (2013). Multi-objective evolutionary algorithms for analysis of conductance correlations involved in recovery of bursting after neuromodulator deprivation in lobster stomatogastric neuron models. BMC Neuroscience, 14(Suppl 1), P370.
Marder, E., & Goaillard, J.M. (2006). Variability, compensation and homeostasis in neuron and network function. Nature Reviews Neuroscience, 7(July), 563–574.
Martina, M., & Jonas, P. (1997). Functional differences in Na+ channel gating between fast-spiking interneurones and principal neurones of rat hippocampus. Journal of Physiology, 505(3), 593–603.
Meliza, C.D., Kostuk, M., Huang, H., Nogaret, A., Margoliash, D., & Abarbanel, H.D.I. (2014). Estimating parameters and predicting membrane voltages with conductance-based neuron models. Biological Cybernetics, 108, 495–516.
Mensi, S., Naud, R., Pozzorini, C., Avermann, M., Petersen, C.C.H., & Gerstner, W. (2012). Parameter extraction and classification of three cortical neuron types reveals two distinct adaptation mechanisms. Journal of Neurophysiology, 107(6), 1756–1775.
Mezura-Montes, E., Reyes-Sierra, M., & Coello Coello, C.A. (2008). Multi-objective optimization using differential evolution: a survey of the state-of-the-art. In Chakraborty, U (Ed.) Advances in differential evolution (pp. 173–196). Berlin: Springer.
Morris, M.D., & Mitchell, T.J. (1995). Exploratory designs for computational experiments. Journal of Statistical Planning and Inference, 43(3), 381–402.
O’Leary, T., WA, H., Franci, A., & Marder, E. (2014). Cell types, network homeostasis, and pathological compensation from a biologically plausible ion channel expression model. Neuron, 82(4), 809–821.
Pospischil, M., Toledo-Rodriguez, M., Monier, C., Piwkowska, Z., Bal, T., Frégnac, Y., Markram, H., & Destexhe, A. (2008). Minimal Hodgkin-Huxley type models for different classes of cortical and thalamic neurons. Biological Cybernetics, 99(4-5), 427–441.
Price, K.V. (2008). Eliminating drift bias from the differential evoluation algorithm. In Chakraborty, U K (Ed.) Advances in differential evolution, 1st edn, springer-verlag, berlin heidelberg, chap, (Vol. 2 pp. 33–88).
Price, K.V., Storn, R.M., & Lampinen, J.A. (2005). Differential Evolution. Berlin: Springer.
Prinz, A.A., Billimoria, C.P., & Marder, E. (2003). Alternative to hand-tuning conductance-based models: construction and analysis of databases of model neurons. Journal of Neurophysiology, 90, 3998–4015.
Rodriguez, A., Ehlenberger, D.B., Dickstein, D.L., Hof, P.R., & Wearne, S.L. (2008). Automated three-dimensional detection and shape classification of dendritic spines from fluorescence microscopy images. PloS One, 3(4), e1997.
Rodriguez, A., Ehlenberger, D.B., Hof, P.R., & Wearne, S.L. (2009). Three-dimensional neuron tracing by voxel scooping. Journal of Neuroscience Methods, 184(1), 169–175.
Schulz, D.J., Goaillard, J.M., & Marder, E. (2006). Variable channel expression in identified single and electrically coupled neurons in different animals. Nature Neuroscience, 9(3), 356–362.
Sekulić, V., Lawrence, J.J., & Skinner, F.K. (2014). Using multi-compartment ensemble modeling as an investigative tool of spatially distributed biophysical balances: application to hippocampal Oriens-Lacunosum/Moleculare (o-LM) cells. PLoS One, 9(10), e106,567.
Sivagnanam, S., Majumdar, A., Yoshimoto, K., Astakhov, V., Bandrowski, A., Martone, M., & Carnevale, N.T. (2013). Introducing the neuroscience gateway. In CEUR Workshop proceedings, (Vol. 993 p. 7).
Smolinski, T.G., & Prinz, A.A. (2009). Computational Intelligence in modeling of biological neurons: a case study of an invertebrate pacemaker neuron. Proceedings of the International Joint Conference on Neural Networks 2964–2970.
Swensen, A.M., & Bean, B.P. (2005). Robustness of burst firing in dissociated purkinje neurons with acute or long-term reductions in sodium conductance. Journal of Neuroscience, 25(14), 3509–3520.
Tobin, A.E., Van Hooser, S.D., & Calabrese, R.L. (2006). Creation and reduction of a morphologically detailed model of a leech heart interneuron. Journal of Neurophysiology, 96(4), 2107–2120.
Toth, B.A., Kostuk, M., Meliza, C.D., Margoliash, D., & Abarbanel, H.D.I. (2011). Dynamical estimation of neuron and network properties i: variational methods. Biological Cybernetics, 105(3-4), 217–237.
Traub, R.D., Jefferys, J.G., Miles, R., Whittington, M.A., & Tóth, K. (1994). A branching dendritic model of a rodent CA3 pyramidal neurone. Journal of Physiology, 481(1), 79–95.
Traub, R.D., Buhl, E.H., Gloveli, T., & Whittington, M.A. (2003). Fast rhythmic bursting can be induced in layer 2/3 cortical neurons by enhancing persistent Na+ conductance or by blocking BK channels. Journal of neurophysiology, 89(2), 909–921.
Van Geit, W., Achard, P., & De Schutter, E. (2007). Neurofitter: A parameter tuning package for a wide range of electrophysiological neuron models. Frontiers in Neuroinformatics, 1(1), 1–18.
Van Geit, W., De Schutter, E., & Achard, P. (2008). Automated neuron model optimization techniques: A review. Biological Cybernetics, 99, 241–251.
Vanier, M.C., & Bower, J.M. (1999). A comparative survey of automated parameter-search methods for compartmental neuron models. Journal of Computational Neuroscience, 7(2), 149– 171.
Weaver, C.M., & Wearne, S.L. (2006). The role of action potential shape and parameter constraints in optimization of compartment models. Neurocomputing, 69(10-12), 1053–1057.
Weaver, C.M., & Wearne, S.L. (2008). Neuronal firing sensitivity to morphologic and active membrane parameters. PLoS Computational Biology, 4(1), e11.
Yadav, A., Weaver, C.M., Gao, Y.Z., Luebke, J.I., & Wearne, S.L. (2008). Why are pyramidal cell firing rates increased with aging, and what can we do about it? BMC Neuroscience, 9(Suppl 1), P51.
Yadav, A., Weaver, C.M., Gao, Y.Z., Luebke, J.I., & Hof, P.R. (2010). Age-related morphologic changes alter robustness of neuronal function. BMC Neuroscience, 11(Suppl 1), P140.
Zielinski, K., & Laur, R. (2008). Stopping criteria for differential evolution in constrained single-objective optimization. In Chakraborty, U K (Ed.) Advances in Differential Evolution, (Vol. 4 pp. 111–138). Berlin: Springer.
Acknowledgments
Special thanks to Amit Majumdar, Subha Sivagnanam, Kenneth Yoshimoto and Ted Carnevale for development of the Neuroscience Gateway project, providing us with the HPC resource access required for this work. This work was supported by the National Institutes of Health (grant numbers P01 AG000001, R01 AG025062 and R01 AG035071).
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interests
The authors declare that they have no conflict of interest.
Additional information
Communicated by: Action Editor: Erik De Schutter
This work was supported by the National Institutes of Health (grant numbers P01 AG000001, R01 AG025062 and R01 AG035071).
Electronic supplementary material
Below is the link to the electronic supplementary material.
Rights and permissions
About this article
Cite this article
Rumbell, T.H., Draguljić, D., Yadav, A. et al. Automated evolutionary optimization of ion channel conductances and kinetics in models of young and aged rhesus monkey pyramidal neurons. J Comput Neurosci 41, 65–90 (2016). https://doi.org/10.1007/s10827-016-0605-9
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10827-016-0605-9