Neuroscience

From the membrane potential to circuits, memory and neural codes

About this course

The nervous system from the cell up — membrane potentials, action potentials and cable properties, synapses and receptors, circuits, sensation and receptive fields, plasticity and memory, energy use and population codes.

What you will be able to do

  • Explain the ionic basis of the resting potential and the action potential
  • Apply cable theory to predict how signals spread along dendrites
  • Describe synaptic transmission and the receptors that mediate it
  • Explain how sensory transduction and receptive fields encode stimuli
  • Relate synaptic plasticity to memory and population codes to information in the brain

What this course covers

  • The Nernst Equation and Ionic Batteries
  • Evolutionary Origin of Ionic Concentration Gradients
  • Goldman Equation: Resting Potential as a Weighted Mean
  • Steady State, the Sodium–Potassium Pump, and ATP Cost of Rest
  • Membrane Capacitance and the Surface-Charge Nature of Voltage
  • Membrane Time Constant, Input Resistance, and the Brain's Energy Bill
  • Worked Example: Goldman vs. Nernst Across Clinical Potassium Range
  • The ATP cost of one spike: the ledger
  • The resting metabolic rent
  • The 20-watt budget and the 4 Hz rate
  • Brain efficiency vs. silicon: architectural comparison
  • Sparse coding as the cheapest code
  • Scaling the ledger to humans and across species
  • BOLD signal: flow, oxygen mismatch, and the 8-second clock
  • Sensory transduction: threshold and range
  • Hecht's photon threshold and Poisson decision
  • Rhodopsin cascade: single-photon amplification
  • Weber's law from Poisson counting (root-N noise)
  • Dynamic range and the sliding adaptation window
  • Hair-cell Fermi: detection below thermal noise
  • Physics-to-biology handover: quantum vs. circuit limit
  • Spike-timing-dependent plasticity (STDP) window
  • NMDA receptor as coincidence detector
  • LTP and LTD: calcium dose determines sign
  • BCM sliding threshold
  • Unifying STDP, calcium, and BCM across timescales
  • Synaptic scaling (homeostatic plasticity)
  • Information capacity of synaptic weights
  • The Quantum: Vesicles, Poisson, and Failures
  • Calcium as the Dice-Loader: Fourth-Power Rule
  • Synaptic Strength and Reliability: NPQ and CV
  • The Quantum as a Voltage: Channels, Receptors, and Spread
  • The Synaptic Cleft: Diffusion Time and Concentration
  • Short-Term Plasticity: Depression, Facilitation, and the Tsodyks–Markram Model
  • Worked Example: Cortical Synapse, Train, and Cell Firing
  • Population Vector Decoding
  • Fisher Information and the Cramér-Rao Bound
  • Information per Spike: Rate vs. Timing Codes
  • Neural Readout as Weighted Sums (No Decoder)
  • Noise Correlations and the Saturation of Averaging
  • Cue Combination by Inverse Variance
  • Brain-Computer Interface: Capstone Application
  • Transmitter as concentration read against time
  • Receptor binding kinetics and two decay clocks
  • NMDA receptor magnesium block and coincidence detection
  • Why the brain uses many transmitters
  • Shunting inhibition as division, not subtraction
  • Drug occupancy and the therapeutic window
  • Worked example: NMDA current, charge, and calcium threshold
  • The Forgetting Curve as a Power Law
  • Synaptic Persistence: Fast Receptors vs. Slow Structure
  • Hippocampal–Cortical Handover and Consolidation Clock
  • Reconsolidation: Recall as Rewriting
  • Place Cells and Grid Cells as a Spatial Code
  • Hopfield Network Capacity and the Storage Cliff
  • Spaced Repetition as the Forgetting Curve Applied
  • Receptive field as a spatial filter
  • Center-surround receptive field (difference of Gaussians)
  • Retinal wiring that produces center-surround
  • Cortical simple cell as a Gabor filter
  • Orientation map and hypercolumn
  • Linearity, rectification, and normalization in visual cells
  • Retinal compression and efficient coding
  • Cortical magnification factor
  • Spike as threshold crossed and reset
  • Hodgkin–Huxley gates and the computed spike
  • Voltage-clamp technique
  • Threshold, all-or-none firing, and refractory period
  • Axon conduction velocity and myelin
  • Generality and limits of the Hodgkin–Huxley model
  • Integrate-and-fire rate curve (Lapicque/Fermi)
  • Dendrite as leaky cable: length constant
  • Cable equation: heat diffusion with leak
  • Transient vs. steady-state attenuation and delay
  • Active dendrite tricks that compensate passive loss
  • Temporal and spatial summation of synaptic inputs
  • Three-halves rule and the equivalent cylinder
  • Fermi estimate: synapses needed to fire a cell
  • Threshold unit as a logic gate
  • McCulloch–Pitts universality and its limits
  • Lateral inhibition and edge detection
  • Subtractive vs. divisive inhibition
  • Half-center oscillator
  • Reflex arc latency ledger
  • Four circuit motifs as universal building blocks
  • Isotropic fractionator: counting neurons by dissolving brains
  • Sleep as the brain's maintenance window
  • Brain scaling laws: rodents vs. primates
  • Human brain as a scaled primate brain, not a special case
  • Reaction-time ledger: accounting for 200 milliseconds
  • Fermi estimation of synapses and axon length
  • The connectome as tile repeated: limits and meaning of the arithmetic
  • Chemoaffinity and the two-gradient map
  • Growth cone mechanics
  • Critical period and ocular dominance competition
  • Limits of correlation-based refinement and the rotated-newt question
  • The genome ledger
  • Map refinement by retinal waves and Hebb's rule
  • Worked example: two-eye competition and amblyopia patching

Syllabus

  1. Neural Signalling

    1. L1 · The Resting Membrane
    2. L2 · The Action Potential
    3. L3 · Cables and Dendrites

  2. Synapses and Circuits

    1. L4 · The Synapse
    2. L5 · Transmitters and Receptors
    3. L6 · Circuits

  3. Sensation and Maps

    1. L7 · Sensation and Transduction
    2. L8 · Receptive Fields
    3. L9 · Maps and Development

  4. Plasticity and Memory

    1. L10 · Plasticity
    2. L11 · Memory

  5. Energy, Codes and the Human Brain

    1. L12 · The Energy Budget
    2. L13 · Population Codes
    3. L14 · The Human Brain, and the Close