Journal of Computational Neuroscience

, Volume 41, Issue 1, pp 65–90 | Cite as

Automated evolutionary optimization of ion channel conductances and kinetics in models of young and aged rhesus monkey pyramidal neurons

  • Timothy H. Rumbell
  • Danel Draguljić
  • Aniruddha Yadav
  • Patrick R. Hof
  • Jennifer I. Luebke
  • Christina M. WeaverEmail author


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.


Neuron model Pyramidal neurons Rhesus monkey Prefrontal cortex Evolutionary algorithms Parameter optimization 



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).

Compliance with Ethical Standards

Conflict of interests

The authors declare that they have no conflict of interest.

Supplementary material

10827_2016_605_MOESM1_ESM.pdf (1.4 mb)
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  1. 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).Google Scholar
  2. Achard, P., & De Schutter, E. (2006). Complex parameter landscape for a complex neuron model. PLoS Computational Biology, 2(7), e94.CrossRefPubMedPubMedCentralGoogle Scholar
  3. Achard, P., & De Schutter, E. (2008). Calcium, synaptic plasticity and intrinsic homeostasis in purkinje neuron models. Frontiers in computational neuroscience 2 (December) 8.Google Scholar
  4. 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).Google Scholar
  5. 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.CrossRefPubMedGoogle Scholar
  6. 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.CrossRefPubMedGoogle Scholar
  7. 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.CrossRefGoogle Scholar
  8. 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.CrossRefPubMedGoogle Scholar
  9. 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.CrossRefPubMedGoogle Scholar
  10. 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.CrossRefPubMedPubMedCentralGoogle Scholar
  11. 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.CrossRefGoogle Scholar
  12. Burke, R.E. (2000). Comparison of alternative designs for reducing complex neurons to equivalent cables. Journal of Computational Neuroscience, 9(1), 31–47.CrossRefPubMedGoogle Scholar
  13. Bush, P.C., & Sejnowski, T.J. (1993). Reduced compartmental models of neocortical pyramidal cells. Journal of Neuroscience Methods, 46(2), 159–166.CrossRefPubMedGoogle Scholar
  14. Carnevale, N.T., & Hines, M.L. (2006). The NEURON book. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
  15. 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.CrossRefPubMedGoogle Scholar
  16. 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.CrossRefPubMedGoogle Scholar
  17. Destexhe, A. (2001). Simplified models of neocortical pyramidal cells preserving somatodendritic voltage attenuation. Neurocomputing, 38-40, 167–173.CrossRefGoogle Scholar
  18. 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.CrossRefPubMedPubMedCentralGoogle Scholar
  19. 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.CrossRefPubMedGoogle Scholar
  20. 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.CrossRefGoogle Scholar
  21. Eiben, A.E., & Smith, J.E. (2003). Introduction to Evolutionary Computing, 1st. Berlin: Springer.CrossRefGoogle Scholar
  22. 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.Google Scholar
  23. 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.Google Scholar
  24. 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.PubMedGoogle Scholar
  25. 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.CrossRefPubMedGoogle Scholar
  26. 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.CrossRefPubMedGoogle Scholar
  27. 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.CrossRefGoogle Scholar
  28. Hay, E., Schürmann, F., Markram, H., & Segev, I. (2013). Preserving axosomatic spiking features despite diverse dendritic morphology. Journal of Neurophysiology, 109(12), 2972–2981.CrossRefPubMedGoogle Scholar
  29. 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.CrossRefPubMedGoogle Scholar
  30. 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.CrossRefPubMedGoogle Scholar
  31. Hollander, M., Wolfe, D.A., & Chicken, E. (2014). Nonparametric statistical methods, 3rd. Hoboken: John Wiley and Sons.Google Scholar
  32. Huys, Q.J.M., & Paninski, L. (2009). Smoothing of, and parameter estimation from, noisy biophysical recordings. PLoS Computational Biology, 5(5), e1000,379.CrossRefGoogle Scholar
  33. Huys, Q.J.M., Ahrens, M.B., & Paninski, L. (2006). Efficient estimation of detailed single-neuron models. Journal of Neurophysiology, 96(2), 872–890.CrossRefPubMedGoogle Scholar
  34. Jan, L.Y., & Jan, Y.N. (2012). Voltage-gated potassium channels and the diversity of electrical signalling. Journal of Physiology, 590, 2591–2599.CrossRefPubMedPubMedCentralGoogle Scholar
  35. Johnson, M.E., Moore, L.M., & Ylvisaker, D. (1990). Minimax and maximin distance designs. Journal of Statistical Planning and Inference, 26(2), 131–148.CrossRefGoogle Scholar
  36. Jolliffe, I.T. (2002). Principal Component Analysis, 2nd edn. Springer.Google Scholar
  37. 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.CrossRefPubMedPubMedCentralGoogle Scholar
  38. Keren, N., Peled, N., & Korngreen, A. (2005). Constraining compartmental models using multiple voltage recordings and genetic algorithms. Journal of Neurophysiology, 94(6), 3730–3742.CrossRefPubMedGoogle Scholar
  39. 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.CrossRefPubMedGoogle Scholar
  40. 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.Google Scholar
  41. 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.CrossRefGoogle Scholar
  42. 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.CrossRefPubMedCentralGoogle Scholar
  43. Marder, E., & Goaillard, J.M. (2006). Variability, compensation and homeostasis in neuron and network function. Nature Reviews Neuroscience, 7(July), 563–574.CrossRefPubMedGoogle Scholar
  44. 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.CrossRefPubMedPubMedCentralGoogle Scholar
  45. 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.CrossRefPubMedGoogle Scholar
  46. 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.CrossRefPubMedGoogle Scholar
  47. 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.Google Scholar
  48. Morris, M.D., & Mitchell, T.J. (1995). Exploratory designs for computational experiments. Journal of Statistical Planning and Inference, 43(3), 381–402.CrossRefGoogle Scholar
  49. 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.CrossRefPubMedPubMedCentralGoogle Scholar
  50. 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.CrossRefPubMedGoogle Scholar
  51. 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).Google Scholar
  52. Price, K.V., Storn, R.M., & Lampinen, J.A. (2005). Differential Evolution. Berlin: Springer.Google Scholar
  53. 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.CrossRefPubMedGoogle Scholar
  54. 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.CrossRefPubMedPubMedCentralGoogle Scholar
  55. 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.CrossRefPubMedPubMedCentralGoogle Scholar
  56. 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.CrossRefPubMedGoogle Scholar
  57. 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.CrossRefGoogle Scholar
  58. 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).Google Scholar
  59. 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.Google Scholar
  60. 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.CrossRefPubMedGoogle Scholar
  61. 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.CrossRefPubMedPubMedCentralGoogle Scholar
  62. 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.CrossRefPubMedGoogle Scholar
  63. 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.CrossRefPubMedPubMedCentralGoogle Scholar
  64. 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.CrossRefPubMedGoogle Scholar
  65. 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.PubMedPubMedCentralGoogle Scholar
  66. Van Geit, W., De Schutter, E., & Achard, P. (2008). Automated neuron model optimization techniques: A review. Biological Cybernetics, 99, 241–251.CrossRefPubMedGoogle Scholar
  67. 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.CrossRefPubMedGoogle Scholar
  68. 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.CrossRefGoogle Scholar
  69. Weaver, C.M., & Wearne, S.L. (2008). Neuronal firing sensitivity to morphologic and active membrane parameters. PLoS Computational Biology, 4(1), e11.CrossRefPubMedPubMedCentralGoogle Scholar
  70. 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.CrossRefGoogle Scholar
  71. 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.CrossRefPubMedCentralGoogle Scholar
  72. 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.Google Scholar

Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  • Timothy H. Rumbell
    • 1
    • 4
  • Danel Draguljić
    • 2
  • Aniruddha Yadav
    • 1
    • 5
  • Patrick R. Hof
    • 1
  • Jennifer I. Luebke
    • 3
  • Christina M. Weaver
    • 2
    Email author
  1. 1.Fishberg Department of Neuroscience and Friedman Brain InstituteIcahn School of Medicine at Mount SinaiNew YorkUSA
  2. 2.Department of MathematicsFranklin and Marshall CollegeLancasterUSA
  3. 3.Department of Anatomy and NeurobiologyBoston University School of MedicineBostonUSA
  4. 4.Computational Biology Center, IBM ResearchThomas J. Watson Research CenterYorktown HeightsUSA
  5. 5.Gauge Data Solutions Pvt LtdNoidaIndia

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