SYDE 556/750: Simulating Neurobiological Systems

Accompanying Readings: Chapter 1

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Overall Goal

  • Building brains!
  • Why?
    • To figure out how brains work (health applications)
    • To apply this knowledge to building systems (AI applications)

Administration

Coursework

  • Four assignments (60%)

    • 20%, 20%, 10%, 10%
    • About two weeks for each assignment
    • Everyone writes their own code, generates their own graphs, writes their own answers
  • Final project

    • Make a novel model of some neural system
    • For 556 students, this can be an extension of something seen in class
    • For 750 students, this must be more of a research project
    • ideas
    • Get your idea approved via email before Reading Week

Schedule

WeekReadingTopicAssignments
Jan 5Chpt 1Introduction
Jan 9, 12Chpt 2,4Neurons, Population Representation#1 posted
Jan 16, 19Chpt 4Temporal Representation
Jan 23, 26, 30Chpt 5,6Feedforward Transformations#1 due (23rd at midnight); #2 posted
Feb 2, 6, 9Chpt 6,8Dynamics
Feb 13, 16Chpt 7Analysis of Representations#2 due (18th at midnight); #3 posted
Feb 20, 23*Reading Week*
Feb 27, Mar 2ProvidedSymbols
Mar 6, 9Chpt 8Memory#3 due (6th at midnight)
Mar 13, 16ProvidedAction Selection#4 due (13th at midnight)
Mar 20, 23Chpt 9Learning
Mar 27Conclusion
Mar 30, Apr 3Project Presentations

To Do:

  • Get textbook (Eliasmith & Anderson, 2003, Neural Engineering), start reading.
  • Be able to run Juypter (old: ipython) notebooks
  • Decide what language you'll do your assignments in (Matlab or Python; see webpage)
  • Start thinking about a project... already!

Focus of the Course

Theoretical Neuroscience

  • How does the mind work?
  • Most complex and most interesting system humanity has ever studied
    • Why study anything else?
  • How should we go about studying it?
    • What techniques/tools?
    • How do we know if we're making progress?
    • How do we deal with the complexity?

A Useful Analogy

  • What is Theoretical Neuroscience?
  • A useful analogy is to theoretical physics
    • Similarities
      • Methods are similar
      • Goals are similar (quantification)
    • Differences
      • Central question "What exists? vs Who are we?"
      • More simulation (because of nonlinearities) in biology

Neural Modelling

  • Let's build it
    • Specify theory in enough detail that this is possible
    • Tends to get complex, so need computer simulation
  • Bring together levels and modeling methods
    • Single neuron models (levels of detail; e.g. spikes, spatial structure, various ion channels, etc.)
    • Small network models (levels of detail; e.g. spiking neurons, rate neurons, mean fields, etc.)
    • Large network/cognitive models (levels of detail; e.g. biophysics, pure computation, anatomy, etc.)
    • Ideally allow all levels of detail below any higher level to be included as desired.
    • 'Correct' level depends on questions being asked.

Problems with current approaches

Large-scale neural models (e.g. Human Brain Project, Synapse Project, etc.)

  • Lack of function or behaviour
    • Can't compare to psychological data
  • Assumes canonical algorithm repeats

    • e.g., Measurements from one small part (hippocampus) are valid everywhere
    • But, different parts of the brain are very different (connectivity, cell types, inputs/outputs)
  • Expects intelligence to 'emerge'

    • Unclear what 'emergence' means, how it will work, or what it explains
    • Wishful thinking?

Cognitve models (e.g. ACT-R, Soar, etc.)

  • Disconnected from neuroscience, can't compare to neural data
    • Trying to map components of the model to brain areas
    • When a component is active, maybe neurons in that area are more active?
  • No "bridging laws"
    • Like having rules of chemistry that never mention that it's all built out of atoms and electrons
  • No constraints on the equations
    • Just anything that can be written down
    • Many possibilities; hard to figure out what matches human data best
  • Maybe that's okay
    • Do we understand the brain enough to make this connection and constrain theories?
    • When understanding a word processor, do we worry about transistors?

The Brain

  • 2 kg (2% of body weight)
  • 20 Watts (25% of power consumption)
  • Area: 4 sheets of paper
  • Neurons: 100 billion (150,000 per $mm^2$)
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Brain structures

  • Lots of visually obvious structure
  • Lots of greek and latin names to remember
    • locus coeruleus, thalamus, amygdala, hypothalamus, substantia nigra, etc etc

<img src="lecture1/brain2.png" width="300" float:right>

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A Neuron

Neurons in the brain

  • 100 billion
  • 100's or 1000's of distinct types (distinguished via anatomy and/or physiology)
  • Axon length: from $10^{-4}$ to $5$ m
  • Each neuron: 500-200,000 inputs and outputs
    • 72km of axons
  • Communication: 100's of different neurotransmitters

Neuron communication: Synapses

What it really looks like

What it really really looks like

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Kinds of data from the brain

Lesion studies

  • What are the effects of damaging different parts of the brain?
    • Occipital cortex: blindness (really blindsight)
    • Inferior frontal gyrus: can't speak (Broca's area)
    • Posterior superior temporal gyrus: can't understand speech (Wernicke's area)
    • Fusiform gyrus: can't recognize faces (and other visually complex objects)
    • Ventral medial prefrontal cortex: moral judgement??? (Phineas Gage)
    • etc, etc, etc

fMRI

  • Functional Magnetic Resonance Imaging
  • Measure blood oxygenation levels in the brain
    • show the difference between two tasks
    • averaged over many trials and patients
  • Measured while performing tasks
    • ~4 second between scans
    • some attempts at going faster, but blood vessels don't change much faster than this
  • Shows where energy is being used in the brain
    • equivalent to figuring out how a CPU works by measuring temperature
    • a bit more fine-grained than lesion studies
  • Good spatial resolution, low temporal resolution
  • Neurosynth

EEG

  • Electrical activity at the scalp
  • Large-scale communication between areas
  • High time resolution, low spatial resolution

Single cell recording

  • Place electrodes (one or many) into the brain, record from it
    • not necessarily right at a neuron
  • Pick up local electrical potentials
    • You can hear neural 'spikes'
  • High temporal resolution only one (or a few) cells
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Multielectrode recordings

  • Put 'tetrodes' or multi-electrode arrays into the brain
  • Post-processing:
    • "Spike sorting"
    • Local field potentials (LFPs)
  • High temporal resolution, max ~100 cells

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Calcium Imaging

  • Use calcium to glow when Ca2+ ions bond
    • Happens a lot during neural activity and spike generation
  • Good spatial and good temporal resolution

  • E.g. In a fish embryo

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  • In a stalking fish
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Optogenetics

  • Allows stimulation and recording from select parts of the brain
    • Just those parts expressing a light sensitive proteins that are stimulated
  • High spatial and temporal resolution (but local)
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What do we know so far?

  • Lots of details
    • Data: "The proportion of type A neurons in area X is Y"
    • Conclusion: "Therefore, the proportion of type A neurons in area X is Y".
  • Hard to get a big picture

    • No good methods for generalizing from data
  • "Data-rich and theory-poor" (Churchland & Sejnowski, 1994; still true)

    • Need some way to connect these details
    • Need unifying theory

Recall: Neural Modeling

  • What I cannot create, I do not understand
  • Build a computer simulation
    • Do to neuroscience what Newton did to physics
    • Too complex to be analytically tractable, so use computer simulation
  • Can we use this to connect the levels?

Single neuron simulation

  • Hodgkin & Huxley, 1952

Single neuron simulation

  • Hodgkin & Huxley, 1952

Single neuron simulation

Millions of neurons

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Billions of neurons

  • Simplify the neuron model and you can run more of them
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The controversy

  • What level of detail for the neurons? How should they be connected?
  • IBM SyNAPSE project (Dharmendra Modha)
    • Billions of neurons, but very simple models
    • Randomly connected
    • 2009: "Cat"-scale brain (1 billion neurons)
      • 2012: "Human"-scale brain (500 billion neurons; 5x human!)
    • Called a "hoax and PR stunt" by:
  • Blue Brain (Henry Markram)
    • Much more detailed neurons
    • Statistically connected (i.e. similar to hippocampus)
  • How much detail is enough?
    • How could we know?

What actually matters...

  • Connecting brain models to behaviour
    • How can we build models that actually do something?
    • How should we connect realistic neurons so they work together?

The Neural Engineering Framework

  • Our attempt
    • Probably wrong, but got to start somewhere
  • Three principles
    • Representation
    • Transformation
    • Dynamics
  • Building behaviour out of detailed low-level components

Representation

  • How do neurons represent information? (What is the neural code?)
  • What is the mapping between a value to be stored and the activity of a group of neurons?
  • Examples:
    • Edge detection in retina
    • Place cells
  • Every group of neurons can be thought of as representing something
    • Each neuron has some preferred value(s)
    • Neurons fire more strongly the closer the value is to that preferred value
    • Values are vectors

Transformation

  • Connections compute functions on those vectors
  • Activity of one group of neurons causes another group to fire
    • One group may represent $x$, connected to another group representing $y$
    • Whatever firing pattern we get in $y$ due to $x$ is a function $y = f(x)$
  • Can find what class of functions are well approximated this way
  • Puts limits on the algorithms we can implement with neurons

Dynamics

  • Recurrent connections (feedback)
  • Turns out to allow us to compute functions of this form:
    • ${dx \over dt} = f(x, u)$
    • $x$ is what the neurons represent, $u$ is the input neurons and $f()$ is the transformation
  • Great for implementing all of control theory (i.e., dynamical systems)
    • Example:
      • memory: (${dx \over dt} = u$)

Examples

  • This approach gives us a neural compiler
  • Given a quantitative description of a behaviour (e.g. an algorithm), you can solve for the connections between neurons that will approximate that behaviour
    • Works for a wide variety of neuron models
    • Number of neurons affects accuracy
    • Neuron properties influence timing and computation
    • Can make predictions (e.g. rats head direction and path integration)

Vision: character recognition

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Problem solving: Tower of Hanoi

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Spaun: digit recognition

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Spaun: copy drawing

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Spaun: addition by counting

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Spaun: pattern completion

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Benefits

  • No one else can do this
  • New ways to test theories (neurological constraints)
  • Suggests different types of algorithms
  • Potential medical applications
  • New ways of understanding the mind and who we are