Advertisement

Bulletin of Mathematical Biology

, Volume 75, Issue 11, pp 2208–2240 | Cite as

Computational Modeling of Channelrhodopsin-2 Photocurrent Characteristics in Relation to Neural Signaling

  • Roxana A. Stefanescu
  • R. G. Shivakeshavan
  • Pramod P. Khargonekar
  • Sachin S. TalathiEmail author
Original Article

Abstract

Channelrhodopsins-2 (ChR2) are a class of light sensitive proteins that offer the ability to use light stimulation to regulate neural activity with millisecond precision. In order to address the limitations in the efficacy of the wild-type ChR2 (ChRwt) to achieve this objective, new variants of ChR2 that exhibit fast mon-exponential photocurrent decay characteristics have been recently developed and validated. In this paper, we investigate whether the framework of transition rate model with 4 states, primarily developed to mimic the biexponential photocurrent decay kinetics of ChRwt, as opposed to the low complexity 3 state model, is warranted to mimic the mono-exponential photocurrent decay kinetics of the newly developed fast ChR2 variants: ChETA (Gunaydin et al., Nature Neurosci. 13:387–392, 2010) and ChRET/TC (Berndt et al., Proc. Natl. Acad. Sci. 108:7595–7600, 2011). We begin by estimating the parameters of the 3-state and 4-state models from experimental data on the photocurrent kinetics of ChRwt, ChETA, and ChRET/TC. We then incorporate these models into a fast-spiking interneuron model (Wang and Buzsaki, J. Neurosci. 16:6402–6413, 1996) and a hippocampal pyramidal cell model (Golomb et al., J. Neurophysiol. 96:1912–1926, 2006) and investigate the extent to which the experimentally observed neural response to various optostimulation protocols can be captured by these models. We demonstrate that for all ChR2 variants investigated, the 4 state model implementation is better able to capture neural response consistent with experiments across wide range of optostimulation protocol. We conclude by analytically investigating the conditions under which the characteristic specific to the 3-state model, namely the monoexponential photocurrent decay of the newly developed variants of ChR2, can occur in the framework of the 4-state model.

Keywords

Model Neuron Closed State Neural Response Root Means Square Deviation Hippocampal Pyramidal Cell 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgements

We would like to thank Lisa Gunaydin and Andre Berndt for sharing their data with us. This research was funded by startup funds to SST; the intramural grant on Computational Biology at the University of Florida; and the Wilder Center of Excellence for Epilepsy Research and the Children’s Miracle Network. P.P.K. was partially supported by the Eckis Professor Endowment at the University of Florida.

Supplementary material

11538_2013_9888_MOESM1_ESM.pdf (408 kb)
(PDF 408 kB)

References

  1. Bass, C. E., Grinevich, V. P., Vance, Z. B., Sullivan, R. P., Bonin, K. D., & Budygin, E. A. (2010). Optogenetic control of striatal dopamine release in rats. J. Neurochem., 114(5), 1344–1352. Google Scholar
  2. Berndt, A., Schoenenberger, P., Mattis, J., Tye, K., Deisseroth, K., Hegemann, P., & Oertner, T. (2011). High-efficiency channelrhodopsins for fast neuronal stimulation at low light levels. Proc. Natl. Acad. Sci. USA, 108(18), 7595–7600. CrossRefGoogle Scholar
  3. Boyden, E. S., Zhang, F., Bamberg, E., Nagel, G., & Deisseroth, K. (2005). Millisecond-timescale, genetically targeted optical control of neural activity. Nat. Neurosci., 8(9), 1263. CrossRefGoogle Scholar
  4. Braun, F. J., & Hegemann, P. (1999). Two light-activated conductances in the eye of the green alga volvox carteri. Biophys. J., 76(3), 1668–1678. CrossRefGoogle Scholar
  5. Cardin, J., Carlén, M., Meletis, K., Knoblich, U., Zhang, F., Deisseroth, K., Tsai, L., & Moore, C. I. (2009). Driving fast-spiking cells induces gamma rhythm and controls sensory responses. Nature, 459(7247), 663–667. CrossRefGoogle Scholar
  6. Crick, F. H. (1979). Thinking about the brain. Sci. Am., 241(3), 219–232. CrossRefGoogle Scholar
  7. Deisseroth, K., Feng, G., Majewska, A. K., Miesenböck, G., Ting, A., & Schnitzer, M. J. (2006). Next-generation optical technologies for illuminating genetically targeted brain circuits. J. Neurosci., 26(41), 10380. CrossRefGoogle Scholar
  8. Golomb, D., Yue, C., & Yaari, Y. (2006). Contribution of persistent na+ current and m-type k+ current to somatic bursting in ca1 pyramidal cells: combined experimental and modeling study. J. Neurophysiol., 96(4), 1912–1926. CrossRefGoogle Scholar
  9. Gradinaru, V., Mogri, M., Thompson, K. R., Henderson, J. M., & Deisseroth, K. (2009). Optical deconstruction of parkinsonian neural circuitry. Science, 324(5925), 354. CrossRefGoogle Scholar
  10. Grossman, N., Nikolic, K., Toumazou, C., & Degenaar, P. (2011). Modeling study of the light stimulation of the neuron cell with channelrhodopsin-2 mutants. In IEEE trans, biomedical eng (pp. 1742–1751). Google Scholar
  11. Gunaydin, L., Yizhar, O., Berndt, A., Sohal, V., Deisseroth, K., & Hegemann, P. (2010). Ultrafast optogenetic control. Nat. Neurosci., 13(3), 387–392. CrossRefGoogle Scholar
  12. Hegemann, P., Ehlenbeck, S., & Gradmann, D. (2005). Multiple photocycles of channelrhodopsin. Biophys. J., 89(6), 3911–3918. CrossRefGoogle Scholar
  13. Huber, D., Petreanu, L., Ghitani, N., Ranade Hromádka, T., Mainen, Z., & Svoboda, K. (2008). Sparse optical microstimulation in barrel cortex drives learned behaviour in freely moving mice. Nature, 451(7174), 61–64. CrossRefGoogle Scholar
  14. Ishizuka, T., Kakuda, M., Araki, R., & Yawo, H. (2006). Kinetic evaluation of photosensitivity in genetically engineered neurons expressing green algae light-gated channels. Neurosci. Res., 54(2), 85–94. CrossRefGoogle Scholar
  15. Koch, C., & Segev, I. (1998). Methods in neuronal modeling. Cambridge: MIT Press. Google Scholar
  16. Kravitz, A. V., Freeze, B. S., Parker, P. R. L., Kay, K., Thwin, M. T., Deisseroth, K., & Kreitzer, A. C. (2010). Regulation of parkinsonian motor behaviours by optogenetic control of basal ganglia circuitry. Nature, 466(7306), 622–626. CrossRefGoogle Scholar
  17. Kuehn, B. (2010). Optogenetics illuminates brain function. JAMA, 303, 20. CrossRefGoogle Scholar
  18. Nagel, G., Szellas, T., Huhn, W., Kateriya, S., Adeishvili, N., Berthold, P., Ollig, D., Hegemann, P., & Bamberg, E. (2003). Channelrhodopsin-2, a directly light-gated cation-selective membrane channel. Proc. Natl. Acad. Sci. USA, 100(24), 13940–13945. CrossRefGoogle Scholar
  19. Nikolic, K., Degenaar, P., & Toumazou, C. (2006). Modeling and engineering aspects of channelrhodopsin2 system for neural photostimulation. Conf. Proc. IEEE Eng .Med. Biol. Soc., 1, 1626–1629. CrossRefGoogle Scholar
  20. Nikolic, K., Grossman, N., Grubb, M. S., Burrone, J., Toumazou, C., & Degenaar, P. (2009). Photocycles of channelrhodopsin-2. Photochem. Photobiol., 85(1), 400–411. CrossRefGoogle Scholar
  21. Schoenlein, R. W., Peteanu, L. A., Mathies, R. A., & Shank, C. V. (1991). The first step in vision: femtosecond isomerization of rhodopsin. Science, 254(5030), 412–415. CrossRefGoogle Scholar
  22. Talathi, S. S., Carney, P. R., & Khargonekar, P. P. (2011). Control of neural synchrony using channelrhodopsin-2: a computational study. J. Comput. Neurosci., 31(1), 87–103. MathSciNetCrossRefGoogle Scholar
  23. Tønnesen, J., Sørensen, A. T., Deisseroth, K., Lundberg, C., & Kokaia, M. (2009). Optogenetic control of epileptiform activity. Proc. Natl. Acad. Sci. USA, 106(29), 12162. CrossRefGoogle Scholar
  24. Wang, Q., Schoenlein, R. W., Peteanu, L. A., Mathies, R. A., & Shank, C. V. (1994). Vibrationally coherent photochemistry in the femtosecond primary event of vision. Science, 266(5184), 422–424. CrossRefGoogle Scholar
  25. Wang, X., & Buzsaki, G. (1996). Gamma oscillation by synaptic inhibition in a hippocampal interneuronal network model. J. Neurosci., 16(20), 6402–6413. Google Scholar
  26. Zhang, F., Wang, L.-P., Brauner, M., Liewald, J. F., Kay, K., Watzke, N., Wood, P. G., Bamberg, E., Nagel, G., Gottschalk, A., & Deisseroth, K. (2007). Multimodal fast optical interrogation of neural circuitry. Nature, 446(7136), 633–639. CrossRefGoogle Scholar

Copyright information

© Society for Mathematical Biology 2013

Authors and Affiliations

  • Roxana A. Stefanescu
    • 1
  • R. G. Shivakeshavan
    • 2
  • Pramod P. Khargonekar
    • 3
  • Sachin S. Talathi
    • 1
    • 2
    • 4
    Email author
  1. 1.Department of Pediatrics, Division of NeurologyUniversity of FloridaGainesvilleUSA
  2. 2.Department of Biomedical EngineeringUniversity of FloridaGainesvilleUSA
  3. 3.Department of Electrical EngineeringUniversity of FloridaGainesvilleUSA
  4. 4.Department of NeuroscienceUniversity of FloridaGainesvilleUSA

Personalised recommendations