Some background in math analysis would be helpful. At minimum a not total revulsion to the idea of looking at a mathematical function is desirable.

Lectures

Neurobiology 1: biophysical basis of neuronal excitability and information processing

Part 1: Biophysics of excitable tissues 

1) Diffusion: from atomistic description (Brownian motion) to macroscopic interpretation (Fick's law). Diffusion coefficient and mean free path. Electrochemical potentials: mobility of charge carriers and contact potentials.

2) Equilibrium between diffusion and electrophoretic migration: Nernst equation. Equilibrium states and stationary states. Regulation of ion concentrations. Pumps and ion exchangers. Equilibrium conditions for multiple conductance: Goldman Hodgkin Katz equation.

3) Equivalent circuits. Membrane resistance and capacitance. The fundamental model of cell membrane: the RC circuit. RC circuits and low pass filtering: implications for bandwidth. Fundamentals of communication theory: sources and channels of communication. From the approximation of the spherical cell to the dendrite: equivalent models. Passive conduction of electric potentials: "telegraphist" equation. Special solutions of the cable equation. Stationary solution and space clamp. Electrotonic attenuation.

4) Phenomenology of action potential conduction. Action potential time constant and membrane time constant: a contradiction. How to solve the Telegraph equation in the presence of voltage dependent conductances. Voltage clamp and space clamp. Equations of| Hodgkin-Huxley.

5) Molecular interpretation of the HH equations. Conduction velocity (RC circuit) and geometric factors. Integration of active and passive management. Saltatory conduction: myelin. Retrograde propagation in dendrites. Biophysics of dendrites.

Part 2: Methods: electrophysiology and functional optical imaging 

1) Electrophysiology and fundamentals of signal analysis. Electrophysiology: measurements of extra and intracellular potential. Patch clamps. Quantization of ionic currents. Ionic conductances and gating currents. Single channel conductances.

2) Extracellular Field potentials: EEG and LFP (Local Field Potential). The language of oscillations: Fourier analysis for beginners. Local Field Potential and neuronal firing.

3) Functional optical imaging: ionic concentration measurements. Two-photon imaging. In vivo structural and functional imaging. Gene expression sensors.

Part 3: Biophysics and pathologies of brain functions

1) Excitatory and inhibitory synapses. shunting inhibition. Developmental regulation of chlorine homeostasis. Plasticity of inhibitory synapses. Plasticity of inhibitory synapses: post-translational regulation of chloride cotransporters.

2) Circadian rhythm, proteostasys and neuronal excitability.

3) Autism as a disease of a prediction error. Transfer function of the visual system as a tool to investigate the computational properties of the brain. Pathologies associated with the imbalance of the excitation-inhibition balance: epilepsy and cognitive deficits.

PArt 4: System Neurobiology

1) Ion channels. Structure and selectivity of ion channels; different functional state (Ohmic vs rectifying channel). Classification and functional properties of the Voltage gated Ion channels (Na, Ca, K, Cl, HCN channels)

2) Synaptic Transmission in the Central Nervous system; Distinguishing Properties of Electrical and Chemical Synapses, The Neuromuscular Junction: an Example of Synaptic Transmission, Reversal potential at the end-plate, spontaneous subtreshold activity at the motor nerve ending (Fatt and Katz), Neurotransmitters ( the experiment by Otto Loewi), synthesis of neurotransmitters and their distribution in the CNS, integrative properties and synaptic inhibition, temporal/spatial summation, excitatory/inhibitory competition

3) Neurotransmitters release. Spontaneous miniature end-plate potentials, Quantal content or Quantal output, the Poisson distribution and Binomial models for quantal release, Pre and Post-synaptic specialization. Molecular aspects of synaptic transmission; Storage/release/re cycling of synaptic vesicles; Pre-synaptic control of neurotransmitter release

4) Receptors and Transporters for neurotransmitters and their regulation. Ionotropic and metabotropic receptors (cholinergic, GABA, Glycine, Glutamate, Adrenergic, Serotonin, Dopaminergic, receptors). Transporters: the SLC6 family, catecholamine/ 5-HT/ Glycine/GABA transporters; excitatory aminoacid transporters, choline transporter; orphan neurotransmitter transporter.

5) Synaptic plasticity. Hebb’s rule, the Bienestock-Cooper-Munro threshold for synaptic modifications; Long-term and short-term synaptic plasticity (Bliss and Lomo experiment, long-term potentiation/depression); molecular mechanisms underlying synaptic plasticity; Metaplasticity.

Some notes will be provided in the form of pdf files.

Students are STRONGLY encouraged to follow the class as lots of the material presented is not really easily obtained from public sources