A state-mutating genetic algorithm to design ion-channel models
Edited by Nancy J. Kopell, Boston University, Boston, MA, and approved July 21, 2009
Abstract
Realistic computational models of single neurons require component ion channels that reproduce experimental findings. Here, a topology-mutating genetic algorithm that searches for the best state diagram and transition-rate parameters to model macroscopic ion-channel behavior is described. Important features of the algorithm include a topology-altering strategy, automatic satisfaction of equilibrium constraints (microscopic reversibility), and multiple-protocol fitting using sequential goal programming rather than explicit weighting. Application of this genetic algorithm to design a sodium-channel model exhibiting both fast and prolonged inactivation yields a six-state model that produces realistic activity-dependent attenuation of action-potential backpropagation in current-clamp simulations of a CA1 pyramidal neuron.
Acknowledgments.
We thank A. Korngreen for helpful discussions concerning genetic algorithms. This work was supported by National Institutes of Health Grant NS-046064.
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References
1
AL Hodgkin, AF Huxley, A quantitative description of membrane current and its application to conduction and excitation in nerve. J Physiol 117, 500–544 (1952).
2
B Sakmann, E Neher Single-Channel Recording (Plenum Press, New York, 1995).
3
D Colquhoun, AG Hawkes, Relaxation and fluctuations of membrane currents that flow through drug-operated channels. Proc R Soc London Ser B 199, 231–262 (1977).
4
D Colquhoun, AG Hawkes, The principles of the stochastic interpretation of ion channel mechanisms. In Single-Channel Recording, eds B Sakmann, E Neher (Plenum Press, 2nd Ed), pp. 397–479 (1995).
5
R Horn, K Lange, Estimating kinetic constants from single channel data. Biophys J 43, 207–223 (1983).
6
S Klein, J Timmer, J Honerkamp, Analysis of multichannel patch clamp recordings by hidden Markov models. Biometrics 53, 870–884 (1997).
7
F Qin, A Auerbach, F Sachs, A direct optimization approach to hidden Markov modeling for single channel kinetics. Biophys J 79, 1915–1927 (2000).
8
J Patlak, Molecular kinetics of voltage-dependent Na+ channels. Physiol Rev 71, 1047–1080 (1991).
9
FJ Sigworth, J Zhou, Ion channels. Analysis of nonstationary single-channel currents. Methods Enzymol 207, 746–762 (1992).
10
A Destexhe, J Huguenard, Which formalism to use for modeling voltage-dependent conductances. In Computational Neuroscience: Realistic Modeling for Experimentalists, ed E De Schutter (CRC Press, Boca Raton, FL), pp. 129–158 (2001).
11
D Colquhoun, AG Hawkes, On the stochastic properties of single ion channels. Proc R Soc London Ser B 211, 205–235 (1981).
12
CC Kuo, BP Bean, Na+ channels must deactivate to recover from inactivation. Neuron 12, 819–829 (1994).
13
LA Irvine, MS Jafri, RL Winslow, Cardiac sodium channel Markov model with temperature dependence and recovery from inactivation. Biophys J 76, 1868–1885 (1999).
14
G Baranauskas, M Martina, Sodium currents activate without a Hodgkin and Huxley-type delay in central mammalian neurons. J Neurosci 26, 671–684 (2006).
15
M Gurkiewicz, A Korngreen, A numerical approach to ion channel modelling using whole-cell voltage-clamp recordings and a genetic algorithm. PLOS Comput Biol 3, e169 (2007).
16
T Mickus, H Jung, N Spruston, Properties of slow, cumulative sodium channel inactivation in rat hippocampal CA1 pyramidal neurons. Biophys J 76, 846–860 (1999).
17
CA Vandenberg, F Bezanilla, A sodium channel gating model based on single channel, macroscopic ionic, and gating currents in the squid giant axon. Biophys J 60, 1511–1533 (1991).
18
LS Milescu, G Akk, F Sachs, Maximum likelihood estimation of ion channel kinetics from macroscopic currents. Biophys J 88, 2494–2515 (2005).
19
JR Koza Genetic Programming: On the Programming of Computers by Means of Natural Selection Complex Adaptive Systems (MIT Press, Cambridge, MA, 1992).
20
FP Boynton, Detailed Balance + Microscopic Reversibility. J Chem Phys 40, 3124 (1964).
21
D Colquhoun, KA Dowsland, M Beato, AJ Plested, How to impose microscopic reversibility in complex reaction mechanisms. Biophys J 86, 3510–3518 (2004).
22
JP Ignizio Goal Programming and Extensions (Lexington Books, Lexington, MA, 1976).
23
B Rudy, Slow inactivation of the sodium conductance in squid giant axons. Pronase resistance. J Physiol 283, 1–21 (1978).
24
IA Fleidervish, A Friedman, MJ Gutnick, Slow inactivation of Na+ current and slow cumulative spike adaptation in mouse and guinea-pig neocortical neurones in slices. J Physiol 493, 83–97 (1996).
25
HY Jung, T Mickus, N Spruston, Prolonged sodium channel inactivation contributes to dendritic action potential attenuation in hippocampal pyramidal neurons. J Neurosci 17, 6639–6646 (1997).
26
N Spruston, Y Schiller, G Stuart, B Sakmann, Activity-dependent action potential invasion and calcium influx into hippocampal CA1 dendrites. Science 268, 297–300 (1995).
27
NL Golding, WL Kath, N Spruston, Dichotomy of action-potential backpropagation in CA1 pyramidal neuron dendrites. J Neurophysiol 86, 2998–3010 (2001).
28
DC Cooper, S Chung, N Spruston, Output-mode transitions are controlled by prolonged inactivation of sodium channels in pyramidal neurons of subiculum. PLOS Biol 3, e175 (2005).
29
NL Golding, N Spruston, Dendritic spikes are variable triggers of axonal action potentials in hippocampal CA1 pyramidal neurons. Neuron 21, 1189–1200 (1998).
30
S Remy, J Csicsvari, H Beck, Activity-dependent control of neuronal output by local and global dendritic spike attenuation. Neuron 61, 906–916 (2009).
31
M Martina, P Jonas, Functional differences in Na+ channel gating between fast-spiking interneurones and principal neurones of rat hippocampus. J Physiol 505, 593–603 (1997).
32
NL Golding, TJ Mickus, Y Katz, WL Kath, N Spruston, Factors mediating powerful voltage attenuation along CA1 pyramidal neuron dendrites. J Physiol 568, 69–82 (2005).
33
JC Callaway, WN Ross, Frequency-dependent propagation of sodium action potentials in dendrites of hippocampal CA1 pyramidal neurons. J Neurophysiol 74, 1395–403 (1995).
34
CM Colbert, JC Magee, DA Hoffman, D Johnston, Slow recovery from inactivation of Na+ channels underlies the activity-dependent attenuation of dendritic action potentials in hippocampal CA1 pyramidal neurons. J Neurosci 17, 6512–6521 (1997).
35
E Perozo, F Bezanilla, Phosphorylation affects voltage gating of the delayed rectifier K+ channel by electrostatic interactions. Neuron 5, 685–90 (1990).
36
S Marom, LF Abbott, Modeling state-dependent inactivation of membrane currents. Biophys J 67, 515–20 (1994).
37
RC Cannon, G D'Alessandro, The ion channel inverse problem: Neuroinformatics meets biophysics. PLoS Comput Biol 2, e91 (2006).
38
M Migliore, Modeling the attenuation and failure of action potentials in the dendrites of hippocampal neurons. Biophys J 71, 2394–403 (1996).
39
PJ Olver, C Shakiban Applied Linear Algebra (Prentice Hall, Upper Saddle River, NJ, 2006).
40
K Gatermann, B Huber, A family of sparse polynomial systems arising in chemical reaction systems. J Symb Comp 33, 275–305 (2002).
41
B Hille Ion Channels of Excitable Membranes (Sinauer, Sunderland, MA, 2001).
42
RL Haupt, SE Haupt Practical Genetic Algorithms (Wiley, New York, 1998).
43
ML Hines, NT Carnevale, The NEURON simulation environment. Neural Comput 9, 1179–1209 (1997).
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Cover image: Pictured is an open polyp of the reef coral Stylophora pistillata. The sensitivity of corals and other symbiotic reef-dwelling organisms to environmental change is currently poorly understood. A. A. Venn et al. use live-cell imaging of intracellular pH to provide insight into the delicate relationship between corals and their intracellular symbionts and the processes of photosynthesis and calcification. See the article by Venn et al. on pages 16574–16579. Photo by E. Tambutté.
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© 2009.
Submission history
Received: April 5, 2009
Published online: September 29, 2009
Published in issue: September 29, 2009
Acknowledgments
We thank A. Korngreen for helpful discussions concerning genetic algorithms. This work was supported by National Institutes of Health Grant NS-046064.
Notes
This article is a PNAS Direct Submission.
This article contains supporting information online at www.pnas.org/cgi/content/full/0807786105/DCSupplemental.
*
This formulation is the transpose of standard notation (3); this is done so that the incidence matrices in the graph-theoretic formulation to follow can be used in their standard forms.
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Competing Interests
The authors declare no conflict of interest.
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