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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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).
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).
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).
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).
Edelman, G.M. & Gally, J.A. Degeneracy and complexity in biological systems. Proc. Natl. Acad. Sci. USA 98, 13763–13768 (2001).
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).
Demarque, M. & Spitzer, N.C. Activity-dependent expression of Lmx1b regulates specification of serotonergic neurons modulating swimming behavior. Neuron 67, 321–334 (2010).
Marder, E. & Calabrese, R.L. Principles of rhythmic motor pattern generation. Physiol. Rev. 76, 687–717 (1996).
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).
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).
Goldman, M.S., Golowasch, J., Marder, E. & Abbott, L.F. Global structure, robustness, and modulation of neuronal models. J. Neurosci. 21, 5229–5238 (2001).
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).
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).
Khorkova, O. & Golowasch, J. Neuromodulators, not activity, control coordinated expression of ionic currents. J. Neurosci. 27, 8709–8718 (2007).
MacLean, J.N. et al. Activity-independent coregulation of IA and Ih in rhythmically active neurons. J. Neurophysiol. 94, 3601–3617 (2005).
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).
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).
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).
Hagiwara, S. & Oomura, Y. The critical depolarization for the spike in the squid giant axon. Jpn. J. Physiol. 8, 234–245 (1958).
Prinz, A.A., Bucher, D. & Marder, E. Similar network activity from disparate circuit parameters. Nat. Neurosci. 7, 1345–1352 (2004).
Marder, E. & Goaillard, J.M. Variability, compensation and homeostasis in neuron and network function. Nat. Rev. Neurosci. 7, 563–574 (2006).
Hudson, A.E. & Prinz, A.A. Conductance ratios and cellular identity. PLOS Comput. Biol. 6, e1000838 (2010).
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).
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).
Sobie, E.A. Parameter sensitivity analysis in electrophysiological models using multivariable regression. Biophys. J. 96, 1264–1274 (2009).
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).
Taylor, A.L., Goaillard, J.M. & Marder, E. How multiple conductances determine electrophysiological properties in a multicompartment model. J. Neurosci. 29, 5573–5586 (2009).
Olypher, A.V. & Calabrese, R.L. Using constraints on neuronal activity to reveal compensatory changes in neuronal parameters. J. Neurophysiol. 98, 3749–3758 (2007).
Olypher, A.V. & Prinz, A.A. Geometry and dynamics of activity-dependent homeostatic regulation in neurons. J. Comput. Neurosci. 28, 361–374 (2010).
Grashow, R., Brookings, T. & Marder, E. Compensation for variable intrinsic neuronal excitability by circuit-synaptic interactions. J. Neurosci. 30, 9145–9156 (2010).
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).
MacLean, J.N., Zhang, Y., Johnson, B.R. & Harris-Warrick, R.M. Activity-independent homeostasis in rhythmically active neurons. Neuron 37, 109–120 (2003).
LeMasson, G., Marder, E. & Abbott, L.F. Activity-dependent regulation of conductances in model neurons. Science 259, 1915–1917 (1993).
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).
Turrigiano, G.G. The self-tuning neuron: synaptic scaling of excitatory synapses. Cell 135, 422–435 (2008).
Davis, G.W. Homeostatic Control of Neural Activity: From Phenomenology to Molecular Design. Annu. Rev. Neurosci. 29, 307–323 (2006).
Maffei, A. & Fontanini, A. Network homeostasis: a matter of coordination. Curr. Opin. Neurobiol. 19, 168–173 (2009).
Grashow, R., Brookings, T. & Marder, E. Reliable neuromodulation from circuits with variable underlying structure. Proc. Natl. Acad. Sci. USA 106, 11742–11746 (2009).
Tang, L. et al. Precise Temperature Compensation of Phase in a Rhythmic Motor Pattern. PLoS Biol. 8, e1000469 (2010).
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).
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).
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).
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).
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).
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).
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).
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).
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).
Robert, C.P. & Casella, G. Monte Carlo Statistical Methods (Springer-Verlag, New York, 2004).
Padmanabhan, K. & Urban, N.N. Intrinsic biophysical diversity decorrelates neuronal firing while increasing information content. Nat. Neurosci. 13, 1276–1282 (2010).
This work was supported by US National Institutes of Health grants NS17813 and MH46742, and by the James D. McDonnell Foundation.
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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