Conductance-Based Models Fundamentals of Computational Neuroscience, - PowerPoint PPT Presentation

2. Neurons and Conductance-Based Models Fundamentals of Computational Neuroscience, T. P . Trappenberg, 2010. Lecture Notes on Brain and Computation Byoung-Tak Zhang Biointelligence Laboratory School of Computer Science and Engineering Graduate Programs in Cognitive Science, Brain Science and Bioinformatics Brain-Mind-Behavior Concentration Program Seoul National University 1 E-mail: btzhang@bi.snu.ac.kr This material is available online at http://bi.snu.ac.kr/

Outline 2.1 Modeling biological neurons 2.2 Neurons are specialized cells 2.3 Basic synaptic mechanisms 2.4 The generation of action potentials: Hodgkin-Huxley equations 2.5 Dendritic trees, the propagation of action potentials, and compartmental models 2.6 Above and beyond the Hodgkin-Huxley neuron: fatigue, bursting, and simplifications 2 (C) 2009-2011 SNU Biointelligence Lab, http://bi.snu.ac.kr (C) 2009 SNU CSE Biointelligence Lab

2.1 Modeling biological neurons  The networks of neuron-like elements  The heart of many information-processing abilities of brain  The working of single neurons  Information transmission  Simplified versions of the real neurons  Make computations with large numbers of neurons tractable  Enable certain emergent properties in networks  Nodes  The sophisticated computational abilities of neurons  The computational approaches used to describe single neurons 3 (C) 2009-2011 SNU Biointelligence Lab, http://bi.snu.ac.kr (C) 2009 SNU CSE Biointelligence Lab

2.2 Neurons are specialized cells 4 (C) 2009-2011 SNU Biointelligence Lab, http://bi.snu.ac.kr (C) 2009 SNU CSE Biointelligence Lab

2.2.1 Structural properties (1) Fig. 2.1 5 (C) 2009-2011 SNU Biointelligence Lab, http://bi.snu.ac.kr (C) 2009 SNU CSE Biointelligence Lab

2.2.1 Structural properties (2)  Morphologies of different neurons  Pyramidal cell from the motor cortex (B)  Granule neuron from olfactory bulb (C)  Spiny neuron from the caudate nucleus (D)  Golgi-stained Purkinje cell from the cerebellum (E) Fig. 2.1 6 (C) 2009-2011 SNU Biointelligence Lab, http://bi.snu.ac.kr (C) 2009 SNU CSE Biointelligence Lab

2.2.2 Information-processing mechanisms  Neurons can receive signals from many other neurons  Synapses (contact site)  Presynaptic (from axon)  Postsynaptic (to dendrite or cell body)  Signal = action potential  Electronic pulse 7 (C) 2009-2011 SNU Biointelligence Lab, http://bi.snu.ac.kr (C) 2009 SNU CSE Biointelligence Lab

2.2.3 Membrane potential V m Membrane potential   The difference between the electric potential within the cell and its surrounding 8 (C) 2009-2011 SNU Biointelligence Lab, http://bi.snu.ac.kr (C) 2009 SNU CSE Biointelligence Lab

2.2.4 Ion channels (1) The permeability of the membrane to certain ions is achieved by ion channels  Fig. 2.2 9 (C) 2009-2011 SNU Biointelligence Lab, http://bi.snu.ac.kr (C) 2009 SNU CSE Biointelligence Lab

2.2.4 Ion channels (2)  Major ion channels  Pump: use energy  Channel: use difference of ions concentration 10 (C) 2009-2011 SNU Biointelligence Lab, http://bi.snu.ac.kr (C) 2009 SNU CSE Biointelligence Lab

2.2.4 Ion channels (3)   V rest 65 mV  Resting potential 11 (C) 2009-2011 SNU Biointelligence Lab, http://bi.snu.ac.kr (C) 2009 SNU CSE Biointelligence Lab

Supplement: Equilibrium potential and Nernst equation 12 (C) 2009-2011 SNU Biointelligence Lab, http://bi.snu.ac.kr (C) 2009 SNU CSE Biointelligence Lab

2.3 Basic synaptic mechanisms  Signal transduction within the cell is mediated by electrical potentials.  Electrical synapse or gap-junctions  Chemical synapse  Synaptic plasticity Fig. 2.3 13 (C) 2009-2011 SNU Biointelligence Lab, http://bi.snu.ac.kr (C) 2009 SNU CSE Biointelligence Lab

2.3.1 Chemical synapses and neurotransmitters  Neurotransmitters stored in synaptic vesicles  glutamate (Glu)  gamma-aminobutyric acid (GABA)  Dopamine (DA)  acetylcholine (ACh)  Synaptic cleft (a small gap of only a few micrometers)  Receptor (channel) and postsynaptic potential (PSP) 14 (C) 2009-2011 SNU Biointelligence Lab, http://bi.snu.ac.kr (C) 2009 SNU CSE Biointelligence Lab

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2.3.2 Excitatory and inhibitory synapses  Different types of neurotransmitters  Excitatory synapse  PSP: depolarization  Neurotransmitters trigger the increase of the membrane potential  Neurotransmitter: Glu, ACh  Inhibitory synapse  PSP: hyperpolarization  Neurotransmitters trigger the decrease of the membrane potential  Neurotransmitter: GABA  Non-standard synapses  Influence ion channels in an indirect way  Modulation 17 (C) 2009-2011 SNU Biointelligence Lab, http://bi.snu.ac.kr (C) 2009 SNU CSE Biointelligence Lab

 Excitatory postsynaptic potential (EPSP) resulting from non-NMDA receptors   peak     non NMDA t / t V w t e m  w : amplitude factor  strength of EPSP or efficiency of the synapse  f ( t ) =t·exp ( -t ): α -function  functional form of a PSP  Inhibitory postsynaptic potential (IPSP) resulting from non-NMDA receptors peak    non NMDA     t / t Fig. 2.4 V w t e m  EPSP resulting from NMDA receptor         t /  t / NMDA V c ( V ) e e 1 2 m m 18 (C) 2009-2011 SNU Biointelligence Lab, http://bi.snu.ac.kr (C) 2009 SNU CSE Biointelligence Lab

2.3.4 Superposition of PSP  Electrical potentials have the physical property  They superimpose as the sum of individual potentials.  Linear superposition of synaptic input  Nonlinear voltage-current relationship  Nonlinear interaction  Divisive  Shunting inhibition 19 (C) 2009-2011 SNU Biointelligence Lab, http://bi.snu.ac.kr (C) 2009 SNU CSE Biointelligence Lab

2.4 The generation of action potentials  Spike or action potential (AP)  Voltage-dependent sodium channel  Start rising phase  Neurotransmitter-gated ion channels Fig. 2.5  Depolarize  Voltage-dependent sodium channels  Influx of Na+  Falling phase  Hyperpolarization  The sodium channels inactive  Potassium channels open Fig. 2.6 20 (C) 2009-2011 SNU Biointelligence Lab, http://bi.snu.ac.kr (C) 2009 SNU CSE Biointelligence Lab

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2.4.3 Hodgkin-Huxley equations (1)  Quantified the process of spike generation   I g ( V E )  Input Current ion ion ion  Electric conductance g ion  Membrane potential relative to V the resting potential  Equilibrium potential E ion Fig. 2.7  K+, Na+ conductance dependent  4 g g n  n , The activation of the K channel K K  m , The activation of the Na channel   h , The inactivation of the Na channel 3 g g m h Na Na 22 (C) 2009-2011 SNU Biointelligence Lab, http://bi.snu.ac.kr (C) 2009 SNU CSE Biointelligence Lab

2.4.3 Hodgkin-Huxley equations (2)  n, m, h have the same form of first-order differential-equation  x should be substituted by each of the variables n, m and h t x ( V ) dt [ x - x 0 ( V )] = - dx 1 Fig. 2.8 23 (C) 2009-2011 SNU Biointelligence Lab, http://bi.snu.ac.kr (C) 2009 SNU CSE Biointelligence Lab

2.4.3 Hodgkin-Huxley equations (3)  Hodgkin-Huxley model  C , capacitance  I ( t ), external current dV     C I I ( t ) ion dt ion  Three ionic currents Fig. 2.7 dV         4 3 C g n ( V E ) g m h ( V E ) g ( V E ) I ( t ) K K Na Na L L dt dn     [ n n ( V )] n 0 dt dm     [ m m ( V )] m 0 dt dh     [ h h ( V )] h 0 dt 24 (C) 2009-2011 SNU Biointelligence Lab, http://bi.snu.ac.kr (C) 2009 SNU CSE Biointelligence Lab

2.4.4 Numerical integration A. A Hodgkin-Huxley neuron responds with constant firing to a constant external current. B. The dependence of the firing rate with the external current (nonlinear curve). (dashed line: noise added) Fig. 2.9 25 (C) 2009-2011 SNU Biointelligence Lab, http://bi.snu.ac.kr (C) 2009 SNU CSE Biointelligence Lab

2.4.5 Refractory period  Absolute refractory period  The inactivation of the sodium channel makes it impossible to initiate another action potential for about 1ms.  Limiting the firing rates of neurons to a maximum of about 1000Hz  Relative refractory period  Due to the hyperpolarizing action potential it is relatively difficult to initiate another spike during this time period.  Reduced the firing frequency of neurons even further 26 (C) 2009-2011 SNU Biointelligence Lab, http://bi.snu.ac.kr (C) 2009 SNU CSE Biointelligence Lab

2.4.6 Propagation of action potentials 27 (C) 2009-2011 SNU Biointelligence Lab, http://bi.snu.ac.kr (C) 2009 SNU CSE Biointelligence Lab

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