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Dynamical Models and Explanation in Neuroscience

Published online by Cambridge University Press:  01 January 2022

Lauren N. Ross
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Abstract

Kaplan and Craver claim that all explanations in neuroscience appeal to mechanisms. They extend this view to the use of mathematical models in neuroscience and propose a constraint such models must meet in order to be explanatory. I analyze a mathematical model used to provide explanations in dynamical systems neuroscience and indicate how this explanation cannot be accommodated by the mechanist framework. I argue that this explanation is well characterized by Batterman’s account of minimal model explanations and that it demonstrates how relationships between explanatory models in neuroscience and the systems they represent is more complex than has been appreciated.

Type
Research Article
Information
Philosophy of Science , Volume 82 , Issue 1 , January 2015 , pp. 32 - 54
Copyright
Copyright © The Philosophy of Science Association

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Footnotes

†

I would like to thank Robert Batterman, G. Bard Ermentrout, Mazviita Chirimuuta, Edouard Machery, Michael Miller, and James Woodward for helpful discussions and comments on earlier drafts of this article. I would also like to thank three anonymous reviewers for helpful feedback and suggestions.

References

Abbott, L. F. 1994. “Single Neuron Dynamics: An Introduction.” In Neural Modeling and Neural Networks, ed. Ventriglia, F., 57–78. New York: Pergamon.CrossRefGoogle Scholar
Batterman, R. 2000. “A ‘Modern’ (= Victorian?) Attitude towards Scientific Understanding.” Monist 83:228–57.CrossRefGoogle Scholar
Batterman, R. 2001. The Devil in the Details: Asymptotic Reasoning in Explanation, Reduction, and Emergence. New York: Oxford University Press.CrossRefGoogle Scholar
Batterman, R. 2002. “Asymptotics and the Role of Minimal Models.” British Journal for the Philosophy of Science 53 (1): 21–38.CrossRefGoogle Scholar
Batterman, R. 2010. “On the Explanatory Role of Mathematics in Empirical Science.” British Journal for the Philosophy of Science 61 (1): 1–25.CrossRefGoogle Scholar
Batterman, R., and Rice, C.. 2014. “Minimal Model Explanations.” Philosophy of Science 81 (3): 349–76.CrossRefGoogle Scholar
Bean, B. P. 2007. “The Action Potential in Mammalian Central Neurons.” Nature Reviews Neuroscience 8 (6): 451–65.CrossRefGoogle ScholarPubMed
Bechtel, W., and Richardson, R. C.. 2010. Discovering Complexity: Decomposition and Localization as Strategies in Scientific Research. 2nd ed. Princeton, NJ: Princeton University Press.CrossRefGoogle Scholar
Börgers, C., Epstein, S., and Kopell, N. J.. 2008. “Gamma Oscillations Mediate Stimulus Competition and Attentional Selection in a Cortical Network Model.” Proceedings of the National Academy of Sciences 105 (46): 18023–28.CrossRefGoogle Scholar
Cauli, B., Audinat, E., Lambolez, B., Angulo, M. C., Ropert, N., Tsuzuki, K., Hestrin, S., and Rossier, J.. 1997. “Molecular and Physiological Diversity of Cortical Nonpyramidal Cells.” Journal of Neuroscience 17 (10): 3894–3906.CrossRefGoogle ScholarPubMed
Chirimuuta, M. 2013. “Minimal Models and Canonical Neural Computations: The Distinctness of Computational Explanation in Neuroscience.” Synthese 191 (2): 127–53.Google Scholar
Connor, J. A. 1975. “Neural Repetitive Firing: A Comparative Study of Membrane Properties of Crustacean Walking Leg Axons.” Journal of Neurophysiology 38 (4): 922–32.CrossRefGoogle ScholarPubMed
Craver, C. F. 2006. “When Mechanistic Models Explain.” Synthese 153 (3): 355–76.CrossRefGoogle Scholar
Craver, C. F. 2008. “Physical Law and Mechanistic Explanation in the Hodgkin and Huxley Model of the Action Potential.” Philosophy of Science 75 (5): 1022–33.CrossRefGoogle Scholar
Doi, S., and Kumagai, S.. 2001. “Nonlinear Dynamics of Small-Scale Biophysical Neural Networks.” In Biophysical Neural Networks: Foundations of Integrative Neuroscience, ed. Poznanski, R. R., 261–302. Larchmont, NY: Liebert.Google Scholar
Ermentrout, B., Rubin, J., and Osan, R.. 2002. “Regular Traveling Waves in a One-Dimensional Network of Theta Neurons.” SIAM Journal on Applied Mathematics 62 (4): 1197–1221.CrossRefGoogle Scholar
Ermentrout, G. B., and Terman, D. H.. 2010. Mathematical Foundations of Neuroscience. Interdisciplinary Applied Mathematics 35. New York: Springer.CrossRefGoogle Scholar
Fitzhugh, R. 1960. “Thresholds and Plateaus in the Hodgkin-Huxley Nerve Equations.” Journal of General Physiology 43 (5): 867–96.Google ScholarPubMed
Fitzhugh, R. 1961. “Impulses and Physiological States in Theoretical Models of Nerve Membrane.” Biophysical Journal 1 (6): 445–66.CrossRefGoogle ScholarPubMed
Fowler, A. C. 2007. Mathematical Models in the Applied Sciences. Cambridge: Cambridge University Press.Google Scholar
Glennan, S. S. 1996. “Mechanisms and the Nature of Causation.” Erkenntnis 44 (1): 49–71.CrossRefGoogle Scholar
Goldenfeld, N., Martin, O., and Oono, Y.. 1989. “Intermediate Asymptotics and Renormalization Group Theory.” Scientific Computing 4:1–19.Google Scholar
Gutkin, B. S., and Ermentrout, B. G.. 1998. “Dynamics of Membrane Excitability Determine Interspike Interval Variability: A Link between Spike Generation Mechanisms and Cortical Spike Train Statistics.” Neural Computation 10 (5): 1047–65.CrossRefGoogle ScholarPubMed
Hodgkin, A. L. 1948. “The Local Electric Changes Associated with Repetitive Action in Non-medullated Axon.” Journal of Physiology 107:165–81.CrossRefGoogle ScholarPubMed
Hoppensteadt, F. C., and Izhikevich, E. M.. 1997. Weakly Connected Neural Networks. New York: Springer.CrossRefGoogle Scholar
Izhikevich, E. M. 2004. “Which Model to Use for Cortical Spiking Neurons?” IEEE Transactions on Neural Networks 15 (5): 1063–70.CrossRefGoogle ScholarPubMed
Izhikevich, E. M. 2007. Dynamical Systems in Neuroscience. Cambridge, MA: MIT Press.Google Scholar
Jia, B., Gu, H.-G., and Li, Y.-Y.. 2011. “Coherence-Resonance-Induced Neuronal Firing Near a Saddle-Node and Homoclinic Bifurcation Corresponding to Type-I Excitability.” Chinese Physics Letters 28 (9): 090507.CrossRefGoogle Scholar
Kaplan, D. M. 2011. “Explanation and Description in Computational Neuroscience.” Synthese 183 (3): 339–73.CrossRefGoogle Scholar
Kaplan, D. M., and Craver, C. F.. 2011. “The Explanatory Force of Dynamical and Mathematical Models in Neuroscience: A Mechanistic Perspective.” Philosophy of Science 78 (4): 601–27.CrossRefGoogle Scholar
Machamer, P., Darden, L., and Craver, C. F.. 2000. “Thinking about Mechanisms.” Philosophy of Science 67:1–25.CrossRefGoogle Scholar
Nagumo, J., Arimoto, S., and Yoshizawa, S.. 1962. “An Active Pulse Transmission Line Simulating Nerve Axon.” Proceedings of the Institute of Radio Engineers 50 (10): 2061–70.Google Scholar
Rinzel, J., and Ermentrout, G. B.. 1998. “Analysis of Neural Excitability and Oscillations.” In Methods in Neuronal Modelling: From Synapses to Networks, 2nd ed., ed. Koch, C. and Segev, I., 251–92. Cambridge, MA: MIT Press.Google Scholar
Silberstein, M., and Chemero, A.. 2008. “Replacing Scholasticism with Science.” Philosophy of Science 75 (1): 1–27.Google Scholar
Silberstein, M., and Chemero, A. 2013. “Constraints on Localization and Decomposition as Explanatory Strategies in the Biological Sciences.” Philosophy of Science 80 (5): 958–70.CrossRefGoogle Scholar
Stepp, N., Chemero, A., and Turvey, M. T.. 2011. “Philosophy for the Rest of Cognitive Science.” Topics in Cognitive Science 3 (2): 425–37.CrossRefGoogle ScholarPubMed
Tateno, T. 2004. “Threshold Firing Frequency-Current Relationships of Neurons in Rat Somatosensory Cortex: Type 1 and Type 2 Dynamics.” Journal of Neurophysiology 92 (4): 2283–94.CrossRefGoogle ScholarPubMed
Vacher, H., Mohapatra, D. P., and Trimmer, J. S.. 2008. “Localization and Targeting of Voltage-Dependent Ion Channels in Mammalian Central Neurons.” Physiological Reviews 88 (4): 1407–47.CrossRefGoogle ScholarPubMed
Woodward, J. 2002. “What Is a Mechanism? A Counterfactual Account.” Philosophy of Science 69 (Proceedings): S366–S377.CrossRefGoogle Scholar
Woodward, J. 2003. Making Things Happen: A Theory of Causal Explanation. New York: Oxford University Press.Google Scholar