# The Sixth q-bio Summer School: Computational Neuroscience

### From Q-bio

In this track, students will learn how to use computational modeling for analysis of biological neural networks. We will introduce basic models including biophysical conductance-based models, simplified rate equations, fast spiking models, synaptic transmission and plasticity and memory models. We will also cover information theory and spike train analysis and provide hands-on training sessions on popular software tools used in computational neuroscience. We will apply these tools to the analysis and simulations of specific neural circuits, synaptic dynamics, learning, and control of neural systems. The relevant topics of bifurcation theory, robustness, sensitivity analysis and information theory will be reviewed in regards to the dynamics of neural circuits.

In addition, participants will have the opportunity to implement models of cortical neural dynamics in programmable and reconfigurable analog neuromorphic hardware. The course includes an introduction to neuromorphic engineering from a dynamical systems perspective, and live and interactive demonstrations.

## Contents |

# Lecturers

- Ramón Huerta, University of California, San Diego
- Mikhail I. Rabinovich, University of California, San Diego
- Nikolai Rulkov, University of California, San Diego
- Maxim Bazhenov, University of California, Riverside
- Gabriel Silva, University of California, San Diego
- Gennady Cymbalyuk, Georgia State University
- Kurt Wiesenfeld, Georgia Tech
- Gert Cauwenberghs, University of California, San Diego
- Roberto Fernández Galán, Case Western Reserve University

# Mentors

- Irma Tristan
- Alex Vergara

# Topics

- Hodgkin-Huxley model: cable equation, ionic conductances, synaptic transmission.
- Reduced models: Wilson-Cowan models, Rulkov model, Izhikevich model.
- Synaptic plasticity: long term plasticity, short term plasticity, spike-timing dependent plasticity.
- Information transmission: information flow in networks, pattern recognition, spatio-temporal decorrelation
- Models of learning: unsupervised/Hebbian learning, reinforcement learning
- Brain networks: hypothalamic circuits, central pattern generators, hypocampal networks, the insect brain.
- Neuromorphic engineering: Models of neural and synaptic implemented in analog VLSI integrated circuits.

# Suggested Reading

[1] Dayan, P. and Abbott, L.F. (2001) Theoretical Neuroscience: Computational and Mathematical Modeling of Neural Systems (MIT Press, Cambridge MA).

[2] Assisi C, Stopfer M, Bazhenov M. Using the structure of inhibitory networks to unravel mechanisms of spatiotemporal patterning. Neuron. 2011 Jan 27;69(2):373-86.

[3] Bazhenov M, Stopfer M. Forward and back: motifs of inhibition in olfactory processing. Neuron. 2010 Aug 12;67(3):357-8.

[4] R. Huerta, T. Nowotny. “Fast and robust learning by reinforcement signals: explorations in the insect brain”. Neural Computation 21(8):2123-51 (2009).

[5] A. Szucs, R. Huerta, MI Rabinovich, and AI. Selverston. “Robust microcircuit synchronization by inhibitory connections”. Neuron. 61(3):439-53 (2009).

[6] MI. Rabinovich, R. Huerta, P Varona, VS Afraimovich. “Transient cognitive dynamics, metastability, and decision making.” PLoS Comput Biol. 24(5):e1000072 (2008).

[7] R. Huerta,M. Rabinovich “Reproducible sequence generation in random neural ensembles” Physical Review Letters 93(23) epub 238104 (2004).

[8] R. Huerta, T. Nowotny, M. Garcia-Sanchez, H. Abarbanel, M. Rabinovich, “Learning Classification in the Olfactory System of Insects”, Neural Computation 16(8) 2004.

[9] Abarbanel, H.D.I.; Huerta, R.; Rabinovich, M.I. “Dynamical model of long-term synaptic plasticity.” Proceedings of the national academy of sciences of USA, 99(N15):10132-10137 (2002).

[10] Rabinovich, M. I., Volkovskii A., P. Lecanda, R .Huerta, H.D.I. Abarbanel, and G. Laurent, “Dynamical Encoding by Networks of Competing Neuron Groups: Winnerless Competition,” Physical Review Letters vol. 87 (6), p.068102/1-4 (2001).

[11] M Bazhenov, M Stopfer, M Rabinovich, R Huerta, H. D.I. Abarbanel, T. J. Sejnowski, and G. Laurent, “Model of Transient Oscillatory Synchronization in the Locust Antennal Lobe” Neuron, Vol. 30, 553 567, May, 2001.

[12] A. I. Selverston, M. I. Rabinovich, H. D. I. Abarbanel, R. Elson, A. Szucs, R. Pinto, R. Huerta, P. Varona “Reliable circuits from irregular neurons: a dynamical approach to understanding central pattern generators” J. Physiology 94 357-374 (2000).

[13] L.F. Lago-Fernandez,R. Huerta, F. Corbacho, J. A. Sigenza “Fast response and temporal coding on coherent oscillations in small-world networks” Physical Review Letters 84, 2758-2761 (2000).

[14] N.F. Rulkov, I. Timofeev, M. Bazhenov, Oscillations in Large-Scale Cortical Networks: Map-Based Model. Journal of Computational Neuroscience , 17 (2004) 203-223

[15] N.F. Rulkov, Modeling of Spiking-Bursting Neural Behavior Using Two- Dimensional Map. Phys. Rev. E, 65 (2002) 041922

[16] M Buibas, D Yu, K Chaio, and GA Silva (2010) Tracking functional signaling in neurons and glia by mapping vector fields of calcium changes using optical flow. Annals of Biomedical Engineering 38:2520-2531.

[17] C MacDonald, D Yu, Buibas, M. and GA Silva (2008) Diffusion modeling of ATP signaling suggests a partially regenerative mechanism underlies astrocyte intercellular calcium waves. Frontiers in Neuroengineering 1:1-13.

[18] Cofer, D., Cymbalyuk, G., Reid, J., Zhu, Y., Heitler, W.J., Edwards, D.H. (2010) AnimatLab: A 3D graphics environment for neuromechanical simulations. J Neurosci Methods 187(2):280-288.

[19] Shilnikov, A. L., Calabrese R. and Cymbalyuk, G.S. (2005) Mechanism of bistability: tonic spiking and bursting in a neuron model. Phys. Rev. E 71, 056214, 1-9

[20] M. Cohen, A. Wilmes, I. Vijver. Cortical electrophysiological network dynamics of feedback learning. Trends in Cognitive Sciences. Dec. 2011, Vol. 15, No. 12, 558. doi:10.1016/j.tics.2011.10.004

[21] M. I. Rabinovich, V. S. Afraimovich, C. Bick, P. Varona, Information flow dynamics in the brain. Phys. Life Rev. (2011), dol:10.1016/j.plrev.2011.11.002

[22] M. Aguiar, P. Ashwin, A. Dias, M. Field. Dynamics of Coupled Cell Networks: Synchrony, Heteroclinic Cycles and InSSation. J. Nonlinear Sci (2011) 21: 271Ð323. DOI:10.1007/ s00332-010-9083-9

[23] M. P. van den Heuvel, O. Sporns. Rich-Club Organization of the Human Connectome. The Journal of Neuroscience, November 2, 2011 ˇe 31(44):15775Ð15786.

[24] J.H. Reynolds, D.J. Heeger. The Normalization Model of Attention. Neuron 61, January 29, 2009, 168-185.

[25] K.Friston. The free-energy principle: a unified brain theory? Nature Reviews Neuroscience 11, 127-138 (February 2010) | doi:10.1038/nrn2787

[26] Ju. Schmidhuber. Formal Theory of Creativity, Fun, and Intrinsic Motivation (1990Ð 2010). IEEE Trans. Auton. Mental Dev., v. 2, No. 3, Sept. 2010. Doi: 10.1109/TAMD.2010.2056368

[27] T. Yu and G. Cauwenberghs, "Analog VLSI Biophysical Neurons and Synapses with Programmable Membrane Channel Kinetics," IEEE Trans. Biomedical Circuits and Systems, vol. 4 (3), pp. 139-148, 2010.

[28] T. Yu, T.J. Sejnowski, and G. Cauwenberghs, "Biophysical Neural Spiking, Bursting, and Excitability Dynamics in Reconfigurable Analog VLSI," IEEE Trans. Biomedical Circuits and Systems, vol. 5 (5), pp. 420-429, 2011.