Single Neuron Models (2)

1. LECTURE 4 Single Neuron Models (2)

2. Overview • Single-Compartment Models • −Integrate-and-Fire Models • − Firing rate models • −The Hodgkin-Huxley Model • −Synaptic conductance description • −The Runge-Kutta method • III. Multi-CompartmentModels • − Two-CompartmentModels

3. What is missing in single-compartment models ? • Membrane is assumed to be equipotential (at the same potential everywhere). Actually there is attenuation and delay within a neuron • It is not possible to study propagation through axon

4. Presynaptic origins are different between the apical tuft and more proximal apical dendrites or basal dendrites (Spruston 2008)

5. Multi-compartment models For simplicity, we begin by computing the coupling between two compartment that have the same length L and radius a. The total current flowing from compartment μ + 1 to compartment μ is: The surface area is: Thus, we find that

6. Realistic Neuron (and Network) Simulators The Runge-Kutta method, which is a standard numerical integration, is poorly suited for solving this multi-compartment models, because it is too slow Two freely available modeling packages for detailed neural models are in wide use, Neuron and Genesis

7. NEURON(http://www.neuron.yale.edu/neuron/) A flexible and powerful simulator of neurons and networksby Michael Hines, John W. Moore, and Ted Carnevale Neuron 7.0 / 16 January 2009;

8. Spike initiation and propagation in an anatomically detailed model of a pyramidal cell

9. Enhancements for modeling networks Although NEURON began in the domain of single-cell models, since the early 1990s it has been applied to network models that contain large numbers of cells and connections Carnevale, N.T. and Hines, M.L. The NEURON Book. Cambridge, UK: Cambridge University Press, 2006 Migliore, M., Cannia, C., Lytton, W.W., Markram, H. and Hines, M.L. Parallel network simulations with NEURON. Journal of Computational Neuroscience 21:110-119, 2006

10. GENESIS －The GEneral NEural Simulation System(http://www.genesis-sim.org/GENESIS) A general purpose software platform that was developed to support the biologically realistic simulation of neural systems, ranging from subcellular components and biochemical reactions to complex models of single neurons, simulations of large networks, and systems-level models First released to the public in 1988

11. Repeating sequences from the view widget that represents the membrane potentials for each of the cells in the network

12. Overview • Single-Compartment Models • −Integrate-and-Fire Models • − Firing rate models • −The Hodgkin-Huxley Model • −Synaptic conductance description • −The Runge-Kutta method • III. Multi-CompartmentModels • − Two-CompartmentModels

13. There are many types of two-compartmentmodels depending on the specific problems. The following is an example.

14. A a fast-activating, persistent current a slowly activating current 6 ms 225 ms A brief current injection to the dendritic compartment induces a burst that outlasts the stimulus ( a form of fast positive feedback). Burst firing terminates even for a sustained current injection (a negative feedback process) (Kepecs, Wang, and Lisman, 2002)

15. p = somatic area/total area

16. Two-Compartmentmodels are very useful! For instance ……

17. Distinct firing patterns in model neurons with identical channel distributions but different dendritic morphology 250 pm 25 mV 100 ms (Mainen and Sejnowski 1996, Nature)

18. Figure legend Digital reconstructions of dendritic arborizations of neurons from rat somatosensory cortex (a) and cat visual cortex (b-d). a, Layer 3 aspiny stellate. b, Layer 4 spiny stellate. c, Layer 3 pyramid. d, Layer 5 pyramid METHODS. Standard compartmental modelling techniques were used to simulate spatially extended neurons. All currents were calculated using conventional Hodgkin-Huxley-style kinetics 4 voltage-dependent currents: fast Na+, fast K+, slow non-inactwating K+, and high-voltage activated Ca2+; 1 Ca2+-dependent current K+ (Mainen and Sejnowski 1996, Nature)

19. Effects of electrical structure on firing pattem in a reduced two-compartment model (Mainen and Sejnowski 1996, Nature)

20. (Mainen and Sejnowski 1996, Nature)

21. burst (Mainen and Sejnowski 1996, Nature)

22. The essential behaviour of the model depends on partial electrical coupling of fast active conductances localized to the soma and axon and slow active currents located throughout the dendrites

23. Backpropagation A backpropagating action potential recordedsimultaneously from the soma and dendrite of a layer II/III pyramidal neuron in a slice from rat somatosensory cortex. (Spruston 2008)

24. Reduced two-compartment model • Including the minimalbiophysical mechanisms necessary to reproduce bursting in a pyramidalcell • Involving in effects of electrical structure on firing pattem • Involving inbackpropagating-related properties

25. Overview of the single neural models Numerical Simulation BiologicalReality • Detailed conductance based and multi-compartmentmodels • Two-compartmentmodels • Conductance based models (H-H) • Integrate-and-fire models • Firing rate neurons AnalyticalSolution Artificial

26. 作业及思考题 • 如何构造Multi-Compartment神经元模型？求解 Multi-Compartment模型的常用软件有哪些？ • 简化的Two-Compartment神经元模型可以揭示神经元的什么特性？