DD2435 Mathematical modeling of biological systems

Reading directions for Johnston D. and Wu S. M.-S.: Fundamentals of Cellular Neurophysiology, TheMIT Press, ISBN 0-262-10053-3.

Directions: 1 = chapter of fundamental character/highest importance; 2 = chapter of intermediate importance, 3 = chapter with additional information. A number for a superior section/level only relates to the text on that level, and does not concern subsequent subsections.

1 INTRODUCTION 2

2 ION MOVEMENT IN EXCITABLE CELLS

2.1 INTRODUCTION 2

2.2 PHYSICAL LAWS THAT DICTATE ION MOVEMENT 2

2.2.1 Fick’s law for diffusion 1

2.2.2 Ohm’s law for drift 1

2.2.3 The Einstein relation between diffusion and mobility 1

2.2.4 Space-charge neutrality, s 11,12 1

2.2.4 Space-charge neutrality , s 13 2

2.3 THE NERNST-PLANCK EQUATION (NPE) 1

2.4 THE NERNST EQUATION 1

2.5 ION DISTRIBUTION AND GRADIENT MAINTENANCE 2

2.5.1 Active transport of ions 2

2.5.2 Passive distribution of ions and Donnan equilibrium 1

2.6 EFFECTS OF CI- AND K+ ON MEMBRANE VOLTAGE 2

2.7 MOVEMENT OF IONS ACROSS BIOLOGICAL MEMBRANES 2

2.7.1 Membrane permeability 2

2.7.2 The Goldman-Hodgkin-Katz (GHK) model 1

2.7.3 Applications of GHK equations 2

2.7.3.1 Resting potential 1

2.7.3.2 Action potential 1

2.7.3.3 Effects of electrogenic pumps on membrane potential 2

3 ELECTRICAL PROPERTIES OF THE EXCITABLE MEMBRANE

3.1 EQUIVALENT CIRCUIT REPRESENTATION 1

3.2 MEMBRANE CONDUCTANCE 2

3.2.1 Linear membrane 2

3.2.2 Nonlinear membrane 2

3.3 IONIC CONDUCTANCES 2

3.4 THE PARALLEL CONDUCTANCE MODEL 1

3.5 CURRENT-VOLTAGE RELATIONS 2

4 FUNCTIONAL PROPERTIES OF DENDRITES 1

4.1 INTRODUCITON 3

4.2 SIGNIFICANCE OF ELECTROTONIC PROPERTIES OF NEURONS 2

4.3 ISOPOTENTIAL CELL (SPHERE) 1

4. NONISOPOTENTIAL CELL (CYLINDER) 1

1 Alternativt läses motsvarande i Bower & Beeman: Genesis

2D1435 Neuronnäts- och Biomodellering

4.4.1 Units and definitions 1

4.4.2 Solutions of cable equations 2

4.4.2.1 Infinite cable, current step 2

4.4.2.2 Finite cable, current step 2

4.5 RALL MODEL OF NEURONS

4.5.1 Derivation of the model 2

4.5.1.1 Equivalent (semi-infinite) cylinder 1

4.5.1.2 Eqivalent (finite) cylinder 2

4.5.1.3 Finite cylinder with lumped soma 2

4.5.2 Experimental determination of l, ρ, and τm 2

4.5.3 Application to synaptic inputs 1

4.6 TWO-PORT NETWORK ANALYSIS OF ELECTROTONIC STRUCTURE 3

5 NONLINEAR PROPERTIES OF EXCITABLE MEMBRANE

5.1 INTRODUCTION

5.2 MEMBRANE RECTIFICATION

5.3 MODELS FOR MEMBRANE RECTIFICATION

5.3.1 Constant field (GHK) model 2

5.3.2 Energy- barrier model (Eyring rate theory) 2

5.3.3 The gate model (Hodgkin and Huxley’s model) 1

6 HODGKIN AND HUXLEY’S ANALYSIS OF THE SQUID GIANT AXON

6.1 INTRODUCTION

6.2 VOLTAGE-CLAMP EXPERIMENTS OF THE SQUID AXON 2

6.3 HODGKIN AND HUXLEY’S MODEL 1

6.4 NONPROPAGATING AND PROPAGATING ACTION POTENTIALS 2

6.4.1 Hodgkin-Huxley equations for non-propagating and propagating action potentials 2

6.4.2 Variations in voltage and current for non-propagating and propagating action potentials 2

7 FUNCTIONAL DIVERSITY OF VOLTAGE-GATED ION CONDUCTANCES 3

8 MOLECULAR STRUCTURE AND UNITARY CURRENTS OF ION CHANNELS

8.1 INTRODUCTION 3

8.2 MOLECULAR STRUCTURE OF ION CHANNELS 3

8.3 PATCH-CLAMP RECORDS OF SINGLE-CHANNEL CURRENTS 2

9 STOCHASTIC ANALYSIS OF SINGLE-CHANNEL FUNCTION

9.1 INTRODUCTION 3

9.3 STATISTICAL ANALYSIS OF CHANNEL GATING 1

9.4 PROBABILITY DENSITY FUNCTION OF CHANNEL GATING 1

10 FORMULATION OF STOCHASTIC CHANNEL MECHANISMS 3

11 SYNAPTIC TRANSMISSION I: PRESYNAPTIC MECHANISMS

11.1 ELECTRICAL TRANSMISSION 1

11.2 CHEMICAL TRANSMISSION 2

11.3 EXPERIMENTS AT THE NEUROMUSCULAR JUNCTION 2

11.4 STATISTICAL TREATMENT OF THE QUANTUM HYPOTHESIS 2

11.5 USE-DEPENDENT SYNAPTIC PLASTICITIES 1

11.6 SYNAPTIC TRANSMISSION BETWEEN CENTRAL NEURONS 2

12 SYNAPTIC TRANSMISSION II: CA2+ AND TRANSMITTER RELEASE

12.1 INTRODUCTION 3

12.2 FORMULATION OF THE CA2+ HYPOTHESIS 3

12.3 COOPERATIVE ACTION OF CA2+ IONS ON TRANSMITTER RELEASE 2

12.4 BIOPHYSICAL ANALYSIS OF CA2+ AND TRANSMITTER RELEASE 2

12.4.5 A model for transmitter release at the squid synapse 1

12.5 CA2+ AND SYNAPTIC PLASTICITY 2

12.6 MOLECULAR MECHANISMS OF RELEASE 3

13 SYNAPTIC TRANSMISSION III: POSTSYNAPTIC MECHANISMS

13.1 INTRODUCTION 3

13.2 GENERAL SCHEME FOR LIGAND-GATED CHANNELS 2

13.3 SYNAPTIC CONDUCTANCES AND REVERSAL POTENTIALS

13.3.1 Definitions of excitatory and inhibitory responses 1

13.3.2 Voltage-clamp anslysis of synaptic parameters (I-V curves) 2

13.3.3 Conductance and reversal potentials for nonisopotential synaptic inputs 3

13.3.3.1 Reversal potentials and conductance ratios: General 1

13.4 SYNAPTIC KINETICS 1

13.5 EXCITATORY AMINO ACID RECEPTORS 2

13.6 FUNCTIONAL PROPERTIES OF SYNAPSES 1

13.7 SLOW SYNAPTIC RESPONSES: CONDUCTANCE-DECREASE PSP:S 2

13.8 DIVERSITY OF NEUROTRANSMITTERS IN THE CENTRAL NERVOUS SYSTEM 3

13.9 ELECTRICAL TRANSMISSION 2

13.10 COMPARTEMENTAL MODELS (ERSÄTTS AV GENESIS-KAPITEL) 3

13.11 DENDRITIC SPINES ADN THEIR EFFECTS ON SYNAPTIC INPUTS 2

15 CELLULAR NEUROPHYSIOLOGY OF LEARNING AND MEMORY

15.1 INTRODUCTION 3

15.1.1 Spine shape changes as a substrate for synaptic plasticity 3

15.1.1.1 Examples for spine shape changes and synaptic plasticity 3

15.1.2 Summary of the possible effects of dendritic spines 2

15.2 LONG-TERM SYNAPTIC PLASTICITY 1

15.3 ASSOCIATIVE AND NON-ASSOCIATIVE FORMS OF LEARNING 1

15.4 ROLE OF HIPPOCAMPUS IN LEARNING AND MEMORY 2

15.5 COMPUTATIONAL MODELS OF LEARNING AND MEMORY 2