Why%20we%20sleep

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Why we sleep

• Hsin-Hua Wei
• Stefanie Lutz

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Overview

• Estimates brain consists of 100 billions of
  neurons that are connected with about 1014 of
  synapses
• Function of the brain is based on interaction
  between highly networked neurons by means of
  electrical impulses
• Typically neurons connect to at least a thousand
  other neurons

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• Neurons are typically composed of a soma, a
  dendritic tree and an axon
• The axon extends away from the cell body and is
  the main conducting unit for carrying signals to
  other neurons.
• Signals flow in only one direction

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• About 1000 times a night, billions of neurons
  undergo a synchronous one-second burst of non-REM
  electrical activity.
• Throughout the night, the bursts become smaller.
• The bursts disappear completely just before
  waking
• The longer a person has been sleep-deprivated,
  the bigger the initial burst

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Classical Interpretation
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The waves of brain activity during deep sleep

• reactivate neurons
• strengthen neuronal connection
• The bursts let the brain slowly reinforce
  synaptic connections that already exist.
• ? We sleep to remember

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New Interpretation

• By Giulio Tononi, a neuroscientist at the
  University of Wisconsin

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• Going up and down, up and down, basically all
  the neurons fire and then all are silent its a
  wonderful way for the brain to tell the synapses
  to get weaker
• The progressive weakening allows only the strong
  connections to survive.

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Tononis theory

• Without paring unneeded information, our brains
  would face space crunch
• By proportionally weakening synapses, the brain
  ensures that they retain the same strength
  relative to each other.

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Development of the model

• discrete model for strength of the synapses
  during our sleep
• simulate two interpretations
• 1. brain bursts cause strengthening
• 2. brain bursts cause weakening of synapses
• include influence of neighbouring synapses

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General equations

• syn(i,j),t1 syn(i,j),t a (g(t) f(t))
• g(t) ß (syn(i-1,j),t syn(i1,j),t
  syn(i,j-1),t syn(i,j1),t)
• f(t) -c(n) (t - n) (t - n - 1)
• Parabola with negative coefficient in front of t2
• 0, 1 , 3, 4 , 6, 7 , ...
• Maximum at t n 0.5
• c(n) µ (n 0.5)(-0.1)
• ? strictly decreasing

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Graph of f and c
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Choice of signs and parameters leads to different
interpretations

• classical interpretation
• syn(i,j),t1 syn(i,j),t a (g(t) f(t)) ,
  a 0.01
• new interpretation
• syn(i,j),t1 syn(i,j),t - a (g(t) f(t)) ,
  a 0.01
• our interpretation
• syn(i,j),t1 syn(i,j),t a (g(t) f(t))
• for syn(i,j),t threshold
• syn(i,j),t1 syn(i,j),t a (g(t) - f(t)) ,
  a 0.01
• for syn(i,j),t lt threshold

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Realisation of function g(t) of neighbours

• Assumptions
• cell represents neuron with synapses
• strength of synapses is proportional to strength
  of neuron ? focus on synapses
• simplification neuron sends signals only to one
  neighbour, but can be reached by 0 to 4
  neighbours (von Neumann neighbourhood)

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Simulations part I
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Classical

• syn(i,j),t1 syn(i,j),t 0.01 (g(t) f(t))
• g(t) 0.001 (syn(i-1,j),t syn(i1,j),t
  syn(i,j-1),t syn(i,j1),t)
• f(t) -c(n) (t - n) (t - n - 1) ,
• c(n) (n 0.5)(-0.1)

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New

• syn(i,j),t1 syn(i,j),t - 0.01 (g(t) f(t))
• g(t) 0.001 (syn(i-1,j),t syn(i1,j),t
  syn(i,j-1),t syn(i,j1),t)
• f(t) -c(n) (t - n) (t - n - 1) ,
• c(n) (n 0.5)(-0.1)

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Threshold

• syn(i,j),t1 syn(i,j),t 0.01 (g(t) f(t))
• for syn(i,j),t threshold
• syn(i,j),t1 syn(i,j),t 0.01 (g(t) - f(t))
• for syn(i,j),t lt threshold
• synthres 0.5

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Comparison initial conditions vs. model with
threshold
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Simulations part IIBigger bursts
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Classical

• syn(i,j),t1 syn(i,j),t 0.01 (g(t) f(t))
• g(t) 0.001 (syn(i-1,j),t syn(i1,j),t
  syn(i,j-1),t syn(i,j1),t)
• f(t) -c(n) (t - n) (t - n - 1) ,
• c(n) 1.5 (n 0.5)(-0.1)

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Comparison higher vs. lower initial bursts (old
interpretation)
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New

• syn(i,j),t1 syn(i,j),t - 0.01 (g(t) f(t))
• g(t) 0.001 (syn(i-1,j),t syn(i1,j),t
  syn(i,j-1),t syn(i,j1),t)
• f(t) -c(n) (t - n) (t - n - 1) ,
• c(n) 1.5 (n 0.5)(-0.1)

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Comparison higher vs. lower initial bursts (new
interpretation)
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Threshold

• syn(i,j),t1 syn(i,j),t 0.01 (g(t) f(t))
• for syn(i,j),t threshold
• syn(i,j),t1 syn(i,j),t 0.01 (g(t) f(t))
• for syn(i,j),t lt threshold
• synthres 0.5

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Comparison higher vs. lower initial bursts (with
threshold)
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Why do we sleep?

• Conservation of metabolic energy, higher mental
  function, heat retention, learning and memory?
• highly simplifying assumptions
• ideas which you could base further models on
• Classical interpretation 170 (200) of original
  strength after a few iterations ? every memory
  reinforces
• New interpretation significant weakening of
  synapses, only the initially strongest survive ?
  principally we forget

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• Bigger bursts cause stronger synapses at the end
  (classical), more vanishing (new), both for our
  model ? after sleep loss our brain has to process
  more data, more extreme results
• Our model growing and diminishing synapses,
  depending on the initial conditions ? strong
  memories persist and reinforce, unimportant ones
  disappear
• nobody can retain every cognition
• sleep as the brains selection of the most
  important things to retain (new interpretation or
  our model?)