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Multiple models to capture the variability in biological neurons and networks

Abstract

How tightly tuned are the synaptic and intrinsic properties that give rise to neuron and circuit function? Experimental work shows that these properties vary considerably across identified neurons in different animals. Given this variability in experimental data, this review describes some of the complications of building computational models to aid in understanding how system dynamics arise from the interaction of system components. We argue that instead of trying to build a single model that captures the generic behavior of a neuron or circuit, it is beneficial to construct a population of models that captures the behavior of the population that provided the experimental data. Studying a population of models with different underlying structure and similar behaviors provides opportunities to discover unsuspected compensatory mechanisms that contribute to neuron and network function.

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Figure 1: The pyloric rhythm has a variable period but phase relationships are held invariant.
Figure 2: Example distributions of neuron parameters for neurons that all share a common behavior or set of behaviors.
Figure 3: Model LP neurons with similar behavior but substantially different parameters.
Figure 4: Tolerance and degeneracy.
Figure 5: Quantification of the effect of each model parameter on each model property for a population of LP models.

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References

  1. Hodgkin, A.L. & Huxley, A.F. A quantitative description of membrane current and its application to conduction and excitation in nerve. J. Physiol. (Lond.) 117, 500–544 (1952).

    Article  CAS  Google Scholar 

  2. Connor, J.A., Walter, D. & McKown, R. Neural repetitive firing: modifications of the Hodgkin-Huxley axon suggested by experimental results from crustacean axons. Biophys. J. 18, 81–102 (1977).

    Article  CAS  Google Scholar 

  3. Traub, R.D., Wong, R.K., Miles, R. & Michelson, H. A model of a CA3 hippocampal pyramidal neuron incorporating voltage-clamp data on intrinsic conductances. J. Neurophysiol. 66, 635–650 (1991).

    Article  CAS  Google Scholar 

  4. Jaeger, D., De Schutter, E. & Bower, J.M. The role of synaptic and voltage-gated currents in the control of Purkinje cell spiking: a modeling study. J. Neurosci. 17, 91–106 (1997).

    Article  CAS  Google Scholar 

  5. Edelman, G.M. & Gally, J.A. Degeneracy and complexity in biological systems. Proc. Natl. Acad. Sci. USA 98, 13763–13768 (2001).

    Article  CAS  Google Scholar 

  6. Korobkova, E., Emonet, T., Vilar, J.M., Shimizu, T.S. & Cluzel, P. From molecular noise to behavioural variability in a single bacterium. Nature 428, 574–578 (2004).

    Article  CAS  Google Scholar 

  7. Demarque, M. & Spitzer, N.C. Activity-dependent expression of Lmx1b regulates specification of serotonergic neurons modulating swimming behavior. Neuron 67, 321–334 (2010).

    Article  CAS  Google Scholar 

  8. Marder, E. & Calabrese, R.L. Principles of rhythmic motor pattern generation. Physiol. Rev. 76, 687–717 (1996).

    Article  CAS  Google Scholar 

  9. Bucher, D., Prinz, A.A. & Marder, E. Animal-to-animal variability in motor pattern production in adults and during growth. J. Neurosci. 25, 1611–1619 (2005).

    Article  CAS  Google Scholar 

  10. Goaillard, J.M., Taylor, A.L., Schulz, D.J. & Marder, E. Functional consequences of animal-to-animal variation in circuit parameters. Nat. Neurosci. 12, 1424–1430 (2009).

    Article  CAS  Google Scholar 

  11. Goldman, M.S., Golowasch, J., Marder, E. & Abbott, L.F. Global structure, robustness, and modulation of neuronal models. J. Neurosci. 21, 5229–5238 (2001).

    Article  CAS  Google Scholar 

  12. Schulz, D.J., Goaillard, J.M. & Marder, E. Variable channel expression in identified single and electrically coupled neurons in different animals. Nat. Neurosci. 9, 356–362 (2006).

    Article  CAS  Google Scholar 

  13. Schulz, D.J., Goaillard, J.M. & Marder, E.E. Quantitative expression profiling of identified neurons reveals cell-specific constraints on highly variable levels of gene expression. Proc. Natl. Acad. Sci. USA 104, 13187–13191 (2007).

    Article  Google Scholar 

  14. Khorkova, O. & Golowasch, J. Neuromodulators, not activity, control coordinated expression of ionic currents. J. Neurosci. 27, 8709–8718 (2007).

    Article  CAS  Google Scholar 

  15. MacLean, J.N. et al. Activity-independent coregulation of IA and Ih in rhythmically active neurons. J. Neurophysiol. 94, 3601–3617 (2005).

    Article  Google Scholar 

  16. Swensen, A.M. & Bean, B.P. Robustness of burst firing in dissociated Purkinje neurons with acute or long-term reductions in sodium conductance. J. Neurosci. 25, 3509–3520 (2005).

    Article  CAS  Google Scholar 

  17. Norris, B.J., Weaver, A.L., Wenning, A., Garcia, P.S. & Calabrese, R.L. A central pattern generator producing alternative outputs: pattern, strength, and dynamics of premotor synaptic input to leech heart motor neurons. J. Neurophysiol. 98, 2992–3005 (2007).

    Article  Google Scholar 

  18. Golowasch, J., Goldman, M.S., Abbott, L.F. & Marder, E. Failure of averaging in the construction of a conductance-based neuron model. J. Neurophysiol. 87, 1129–1131 (2002).

    Article  Google Scholar 

  19. Hagiwara, S. & Oomura, Y. The critical depolarization for the spike in the squid giant axon. Jpn. J. Physiol. 8, 234–245 (1958).

    Article  CAS  Google Scholar 

  20. Prinz, A.A., Bucher, D. & Marder, E. Similar network activity from disparate circuit parameters. Nat. Neurosci. 7, 1345–1352 (2004).

    Article  CAS  Google Scholar 

  21. Marder, E. & Goaillard, J.M. Variability, compensation and homeostasis in neuron and network function. Nat. Rev. Neurosci. 7, 563–574 (2006).

    Article  CAS  Google Scholar 

  22. Hudson, A.E. & Prinz, A.A. Conductance ratios and cellular identity. PLOS Comput. Biol. 6, e1000838 (2010).

    Article  Google Scholar 

  23. Beer, R.D., Chiel, H.J. & Gallagher, J.C. Evolution and analysis of model CPGs for walking: II. General principles and individual variability. J. Comput. Neurosci. 7, 119–147 (1999).

    Article  CAS  Google Scholar 

  24. Tobin, A.E. & Calabrese, R.L. Endogenous and half-center bursting in morphologically inspired models of leech heart interneurons. J. Neurophysiol. 96, 2089–2106 (2006).

    Article  Google Scholar 

  25. Sobie, E.A. Parameter sensitivity analysis in electrophysiological models using multivariable regression. Biophys. J. 96, 1264–1274 (2009).

    Article  CAS  Google Scholar 

  26. Prinz, A.A., Billimoria, C.P. & Marder, E. Alternative to hand-tuning conductance-based models: construction and analysis of databases of model neurons. J. Neurophysiol. 90, 3998–4015 (2003).

    Article  Google Scholar 

  27. Taylor, A.L., Goaillard, J.M. & Marder, E. How multiple conductances determine electrophysiological properties in a multicompartment model. J. Neurosci. 29, 5573–5586 (2009).

    Article  CAS  Google Scholar 

  28. Olypher, A.V. & Calabrese, R.L. Using constraints on neuronal activity to reveal compensatory changes in neuronal parameters. J. Neurophysiol. 98, 3749–3758 (2007).

    Article  Google Scholar 

  29. Olypher, A.V. & Prinz, A.A. Geometry and dynamics of activity-dependent homeostatic regulation in neurons. J. Comput. Neurosci. 28, 361–374 (2010).

    Article  Google Scholar 

  30. Grashow, R., Brookings, T. & Marder, E. Compensation for variable intrinsic neuronal excitability by circuit-synaptic interactions. J. Neurosci. 30, 9145–9156 (2010).

    Article  CAS  Google Scholar 

  31. Nerbonne, J.M., Gerber, B.R., Norris, A. & Burkhalter, A. Electrical remodelling maintains firing properties in cortical pyramidal neurons lacking KCND2-encoded A-type K+ currents. J. Physiol. (Lond.) 586, 1565–1579 (2008).

    Article  CAS  Google Scholar 

  32. MacLean, J.N., Zhang, Y., Johnson, B.R. & Harris-Warrick, R.M. Activity-independent homeostasis in rhythmically active neurons. Neuron 37, 109–120 (2003).

    Article  CAS  Google Scholar 

  33. LeMasson, G., Marder, E. & Abbott, L.F. Activity-dependent regulation of conductances in model neurons. Science 259, 1915–1917 (1993).

    Article  CAS  Google Scholar 

  34. Liu, Z., Golowasch, J., Marder, E. & Abbott, L.F. A model neuron with activity-dependent conductances regulated by multiple calcium sensors. J. Neurosci. 18, 2309–2320 (1998).

    Article  CAS  Google Scholar 

  35. Turrigiano, G.G. The self-tuning neuron: synaptic scaling of excitatory synapses. Cell 135, 422–435 (2008).

    Article  CAS  Google Scholar 

  36. Davis, G.W. Homeostatic Control of Neural Activity: From Phenomenology to Molecular Design. Annu. Rev. Neurosci. 29, 307–323 (2006).

    Article  CAS  Google Scholar 

  37. Maffei, A. & Fontanini, A. Network homeostasis: a matter of coordination. Curr. Opin. Neurobiol. 19, 168–173 (2009).

    Article  CAS  Google Scholar 

  38. Grashow, R., Brookings, T. & Marder, E. Reliable neuromodulation from circuits with variable underlying structure. Proc. Natl. Acad. Sci. USA 106, 11742–11746 (2009).

    Article  CAS  Google Scholar 

  39. Tang, L. et al. Precise Temperature Compensation of Phase in a Rhythmic Motor Pattern. PLoS Biol. 8, e1000469 (2010).

    Article  Google Scholar 

  40. Desai, N.J., Rutherford, L.C., Nelson, S.B. & Turrigiano, G.G. Activity-dependent regulation of intrinsic conductances in cortical neurons. Neurocomputing 26-27, 101–106 (1999).

    Article  Google Scholar 

  41. Guckenheimer, J., Gueron, S. & Harris-Warrick, R.M. Mapping the dynamics of a bursting neuron. Phil. Trans. R. Soc. Lond. B 341, 345–359 (1993).

    Article  CAS  Google Scholar 

  42. Butera, R.J. Jr. Rinzel, J. & Smith, J.C. Models of respiratory rhythm generation in the pre-Bötzinger complex. II. Populations of coupled pacemaker neurons. J. Neurophysiol. 82, 398–415 (1999).

    Article  Google Scholar 

  43. Jezzini, S.H., Hill, A.A., Kuzyk, P. & Calabrese, R.L. Detailed model of intersegmental coordination in the timing network of the leech heartbeat central pattern generator. J. Neurophysiol. 91, 958–977 (2004).

    Article  Google Scholar 

  44. Bhalla, U.S. & Bower, J.M. Exploring parameter space in detailed single neuron models: simulations of the mitral and granule cells of the olfactory bulb. J. Neurophysiol. 69, 1948–1965 (1993).

    Article  CAS  Google Scholar 

  45. Taylor, A.L., Hickey, T.J., Prinz, A.A. & Marder, E. Structure and visualization of high-dimensional conductance spaces. J. Neurophysiol. 96, 891–905 (2006).

    Article  Google Scholar 

  46. Hobbs, K.H. & Hooper, S.L. Using complicated, wide dynamic range driving to develop models of single neurons in single recording sessions. J. Neurophysiol. 99, 1871–1883 (2008).

    Article  Google Scholar 

  47. Vanier, M.C. & Bower, J.M. A comparative survey of automated parameter-search methods for compartmental neural models. J. Comput. Neurosci. 7, 149–171 (1999).

    Article  CAS  Google Scholar 

  48. Gunay, C., Edgerton, J.R. & Jaeger, D. Channel density distributions explain spiking variability in the globus pallidus: a combined physiology and computer simulation database approach. J. Neurosci. 28, 7476–7491 (2008).

    Article  CAS  Google Scholar 

  49. Robert, C.P. & Casella, G. Monte Carlo Statistical Methods (Springer-Verlag, New York, 2004).

  50. Padmanabhan, K. & Urban, N.N. Intrinsic biophysical diversity decorrelates neuronal firing while increasing information content. Nat. Neurosci. 13, 1276–1282 (2010).

    Article  CAS  Google Scholar 

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Acknowledgements

This work was supported by US National Institutes of Health grants NS17813 and MH46742, and by the James D. McDonnell Foundation.

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E.M. and A.L.T. wrote and edited the paper. A.L.T. made the figures, some of which are adapted versions of figures originally published elsewhere.

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Correspondence to Eve Marder.

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The authors declare no competing financial interests.

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Marder, E., Taylor, A. Multiple models to capture the variability in biological neurons and networks. Nat Neurosci 14, 133–138 (2011). https://doi.org/10.1038/nn.2735

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