Why we sleep. Overview Estimates: brain consists of 100 billions of neurons that are connected with about 10 14 of synapses Function of the brain is based.

Why we sleep

Hsin-Hua WeiHsin-Hua Wei

Stefanie LutzStefanie Lutz

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

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

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

Classical Interpretation

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

New Interpretation

By Giulio Tononi, a neuroscientist at the University of Wisconsin

“Going up and down, up and down, basically all the neurons fire and then all are silent – it’s a wonderful way for the brain to tell the synapses to get weaker”

The progressive weakening allows only the strong connections to survive.

Tononi’s 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.

Development of the model

discrete model for strength of the synapses during our sleep

simulate two interpretations:1. brain bursts cause strengthening2. brain bursts cause weakening of synapses

include influence of neighbouring synapses

General equations

syn(i,j),t+1 = syn(i,j),t + α * (g(t) + f(t));

g(t) = β * (syn(i-1,j),t + syn(i+1,j),t + syn(i,j-1),t + syn(i,j+1),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

Graph of f and c

Choice of signs and parameters leads to different interpretations

classical interpretation:

syn(i,j),t+1 = syn(i,j),t + α * (g(t) + f(t)) , α = 0.01 new interpretation:

syn(i,j),t+1 = syn(i,j),t - α * (g(t) + f(t)) , α = 0.01 our interpretation:

syn(i,j),t+1 = syn(i,j),t + α * (g(t) + f(t))

for syn(i,j),t ≥ threshold

syn(i,j),t+1 = syn(i,j),t + α * (g(t) - f(t)) , α = 0.01

for syn(i,j),t < threshold

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)

Simulations – part I

Classical

syn(i,j),t+1 = syn(i,j),t + 0.01 * (g(t) + f(t));

g(t) = 0.001* (syn(i-1,j),t + syn(i+1,j),t + syn(i,j-1),t + syn(i,j+1),t)

f(t) = -c(n) * (t - n) * (t - n - 1) , c(n) = (n + 0.5)(-0.1)

New

syn(i,j),t+1 = syn(i,j),t - 0.01 * (g(t) + f(t));

g(t) = 0.001* (syn(i-1,j),t + syn(i+1,j),t + syn(i,j-1),t + syn(i,j+1),t)

f(t) = -c(n) * (t - n) * (t - n - 1) , c(n) = (n + 0.5)(-0.1)

Threshold

syn(i,j),t+1 = syn(i,j),t + 0.01 * (g(t) + f(t))

for syn(i,j),t ≥ threshold

syn(i,j),t+1 = syn(i,j),t + 0.01 * (g(t) - f(t))

for syn(i,j),t < threshold

synthres = 0.5

Comparison: initial conditions vs. model with threshold

Simulations – part II:Bigger bursts

Classical

syn(i,j),t+1 = syn(i,j),t + 0.01 * (g(t) + f(t));

g(t) = 0.001* (syn(i-1,j),t + syn(i+1,j),t + syn(i,j-1),t + syn(i,j+1),t)

f(t) = -c(n) * (t - n) * (t - n - 1) , c(n) = 1.5 * (n + 0.5)(-0.1)

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

New

syn(i,j),t+1 = syn(i,j),t - 0.01 * (g(t) + f(t));

g(t) = 0.001* (syn(i-1,j),t + syn(i+1,j),t + syn(i,j-1),t + syn(i,j+1),t)

f(t) = -c(n) * (t - n) * (t - n - 1) , c(n) = 1.5 * (n + 0.5)(-0.1)

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

Threshold

syn(i,j),t+1 = syn(i,j),t + 0.01 * (g(t) + f(t))

for syn(i,j),t ≥ threshold

syn(i,j),t+1 = syn(i,j),t + 0.01 * (g(t) – f(t))

for syn(i,j),t < threshold

synthres = 0.5

Comparison: higher vs. lower initial bursts (with threshold)

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

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 brain’s selection of the most

important things to retain (new interpretation or our model?)