Network Models, Representation and Consciousness
Lecture: Recap on Cellular Neurophysiology, reducing the neuron, Meijas 2
Lecture: Learning representations: Perceptrons & error backpropagation, Bothe 6
Lecture: Recurrent networks and auto-associative memory, Pennartz 10
Lecture: Ch 4 & 5: Networks, consciousness and panpsychism, Pennartz 15
Chapter 4 21
Chapter 5 23
Lecture: Models of Reinforcement Learning, Pennartz 24
Lecture: Predictive coding models: perceptual inference and learning, Lee 30
Lecture: Models of neural dynamics (advanced), Meijas 34
Lecture: Ch.6: Which brain structures are involved in consciousness, Pennartz 38
Chapter 6 44
Lecture: Spiking neural networks and predictive coding, Bohte 45
Lecture: Ch.8,9: Requirements and Mechanisms for conscious representation,
Pennartz 49
Chapter 8 57
Chapter 9 57
Lecture: Ch.10,11: Multi-level theory and philosophical implications, Pennartz 57
Chapter 10 57
Chapter 11 57
1
,Lecture: Recap on Cellular Neurophysiology, reducing the neuron, Meijas
computational modeling: testing, insight and predication
Hopfield model: understand different types of memory
- relies on properties of parallel-distributed processing
- Von Neumann: central processing unit, instructed by a programmed sequence
- robust and fault tolerant
- high learning capacity and flexibility
- robust to noise, and capable of handling fuzzy and incomplete information
- massive parallelism: many simultaneous operations → high speed of computation
Membrane potential: Membrane potential arises from a separation of positive and negative
charges across the cell membrane (-60 to -80 mV)
- rapid electrical signaling → you only have to open the gates
Inside Outside Eq pot
Na+ (sod) 50 440 +55mV
Cl- 52 560 -60mV
K+ (pot) 400 20 -75mV
A- 385 ~0 --
Ca2+ 0.001 2 120mV
Equilibrium potential (=reversal potential): the potential at which the electrical driving
𝑅𝑇 [𝐴]𝑜𝑢𝑡
force equals the chemical (diffusional) driving force → Nernst equation 𝐸𝑘 = 𝑧𝐹
𝐼𝑛 [𝐴]𝑖𝑛
Electrical driving force: depends on membrane potential (+ions attracted to inside)
Chemical driving force: depends on concentration difference of ion across membrane
2
,With multiple ion species:
- A: resting state
- B: both chemical and electrical driving forces go inside the cell → increasing the
number of positive charges
- C: the driving force of K+ goes to the outside of the cell
𝑅𝑇 𝑃𝑘 *[𝐾]𝑜𝑢𝑡 𝑃𝑁𝑎 *[𝑁𝑎]𝑜𝑢𝑡 𝑃𝐶𝑙 *[𝐶𝑙]𝑖𝑛
- 𝑉𝑚 = 𝐹
𝐼𝑛( 𝑃𝑘* [𝐾]𝑖𝑛
+ 𝑃𝑁𝑎*[𝑁𝑎]𝑖𝑛
+ 𝑃𝐶𝑙*[𝐶𝑙]𝑜𝑢𝑡
)
ion channel
- in the absence of the ionic gradient: the current-voltage plot is linear
- for single channel: for every ion channel there is a relationship between the current
and the voltage
- groups as electric circuits: different electrical properties with different ion channels.
different types of channels in parallel: different equilibrium potentials → different
battery-conductance combinations
capacitance: store charge in the cell → any input will not change the membrane potential
directly.
- low-pass filter: if there are lots of fluctuations → the capacitance will smooth things
out
the voltage changes slowly: charge (delta Q) / capacitance (C)
measure the voltage channel across the membrane: Vm(t) = Im *Rin (1 – e-t/tau)
time constant: tau= RinC
3
, voltage is not uniform across the membrane:
- if electrical current is injected:
- it spreads laterally because of low cytoplasmic resistivity
- current leaks through membrane depending on specific membrane resistance
- voltage will decay with distance
Potassium conductance involved in AP:
- Grows with stronger depolarization
- Does not inactivate
- Separate effects from driving force (Vm-Ek) and conductance
Sodium conductance involved in AP:
- Grows with stronger depolarization, but levels off;
- Inactivates after ~2 msec
- 3 states postulated by Hodgkin-Huxley: Active - inactivated - de-inactivated
(activatable)
time course
1) Initial depolarization needed
2) Na+ channels open
3) Further depolarization of membrane
4) More Na+ channels open → more depolarization (positive feedback loop, regenerative)
5) K+ channels start to open: repolarizing effect
6) Na+ channels inactivate
7) K+ conductance outlasts Na+ conductance: hyperpolarization
8) Refractory period → impossible or very difficult to excite membrane
- two things need to happen at the same time to reach hyperpolarization;
- sodium (Na) channels close
- potassium (K) channels open
The neuron as a computational element: McCulloch-Pitts
- tells if a neuron is going to spike or not (use them in networks)
- Synaptic weights (strengths) from pre (1,2 or 3) to postsynaptic cell (i)
- synchronous assembly of ‘neurons’ is capable of universal computation if the
synaptic weights are chosen suitably
4
Lecture: Recap on Cellular Neurophysiology, reducing the neuron, Meijas 2
Lecture: Learning representations: Perceptrons & error backpropagation, Bothe 6
Lecture: Recurrent networks and auto-associative memory, Pennartz 10
Lecture: Ch 4 & 5: Networks, consciousness and panpsychism, Pennartz 15
Chapter 4 21
Chapter 5 23
Lecture: Models of Reinforcement Learning, Pennartz 24
Lecture: Predictive coding models: perceptual inference and learning, Lee 30
Lecture: Models of neural dynamics (advanced), Meijas 34
Lecture: Ch.6: Which brain structures are involved in consciousness, Pennartz 38
Chapter 6 44
Lecture: Spiking neural networks and predictive coding, Bohte 45
Lecture: Ch.8,9: Requirements and Mechanisms for conscious representation,
Pennartz 49
Chapter 8 57
Chapter 9 57
Lecture: Ch.10,11: Multi-level theory and philosophical implications, Pennartz 57
Chapter 10 57
Chapter 11 57
1
,Lecture: Recap on Cellular Neurophysiology, reducing the neuron, Meijas
computational modeling: testing, insight and predication
Hopfield model: understand different types of memory
- relies on properties of parallel-distributed processing
- Von Neumann: central processing unit, instructed by a programmed sequence
- robust and fault tolerant
- high learning capacity and flexibility
- robust to noise, and capable of handling fuzzy and incomplete information
- massive parallelism: many simultaneous operations → high speed of computation
Membrane potential: Membrane potential arises from a separation of positive and negative
charges across the cell membrane (-60 to -80 mV)
- rapid electrical signaling → you only have to open the gates
Inside Outside Eq pot
Na+ (sod) 50 440 +55mV
Cl- 52 560 -60mV
K+ (pot) 400 20 -75mV
A- 385 ~0 --
Ca2+ 0.001 2 120mV
Equilibrium potential (=reversal potential): the potential at which the electrical driving
𝑅𝑇 [𝐴]𝑜𝑢𝑡
force equals the chemical (diffusional) driving force → Nernst equation 𝐸𝑘 = 𝑧𝐹
𝐼𝑛 [𝐴]𝑖𝑛
Electrical driving force: depends on membrane potential (+ions attracted to inside)
Chemical driving force: depends on concentration difference of ion across membrane
2
,With multiple ion species:
- A: resting state
- B: both chemical and electrical driving forces go inside the cell → increasing the
number of positive charges
- C: the driving force of K+ goes to the outside of the cell
𝑅𝑇 𝑃𝑘 *[𝐾]𝑜𝑢𝑡 𝑃𝑁𝑎 *[𝑁𝑎]𝑜𝑢𝑡 𝑃𝐶𝑙 *[𝐶𝑙]𝑖𝑛
- 𝑉𝑚 = 𝐹
𝐼𝑛( 𝑃𝑘* [𝐾]𝑖𝑛
+ 𝑃𝑁𝑎*[𝑁𝑎]𝑖𝑛
+ 𝑃𝐶𝑙*[𝐶𝑙]𝑜𝑢𝑡
)
ion channel
- in the absence of the ionic gradient: the current-voltage plot is linear
- for single channel: for every ion channel there is a relationship between the current
and the voltage
- groups as electric circuits: different electrical properties with different ion channels.
different types of channels in parallel: different equilibrium potentials → different
battery-conductance combinations
capacitance: store charge in the cell → any input will not change the membrane potential
directly.
- low-pass filter: if there are lots of fluctuations → the capacitance will smooth things
out
the voltage changes slowly: charge (delta Q) / capacitance (C)
measure the voltage channel across the membrane: Vm(t) = Im *Rin (1 – e-t/tau)
time constant: tau= RinC
3
, voltage is not uniform across the membrane:
- if electrical current is injected:
- it spreads laterally because of low cytoplasmic resistivity
- current leaks through membrane depending on specific membrane resistance
- voltage will decay with distance
Potassium conductance involved in AP:
- Grows with stronger depolarization
- Does not inactivate
- Separate effects from driving force (Vm-Ek) and conductance
Sodium conductance involved in AP:
- Grows with stronger depolarization, but levels off;
- Inactivates after ~2 msec
- 3 states postulated by Hodgkin-Huxley: Active - inactivated - de-inactivated
(activatable)
time course
1) Initial depolarization needed
2) Na+ channels open
3) Further depolarization of membrane
4) More Na+ channels open → more depolarization (positive feedback loop, regenerative)
5) K+ channels start to open: repolarizing effect
6) Na+ channels inactivate
7) K+ conductance outlasts Na+ conductance: hyperpolarization
8) Refractory period → impossible or very difficult to excite membrane
- two things need to happen at the same time to reach hyperpolarization;
- sodium (Na) channels close
- potassium (K) channels open
The neuron as a computational element: McCulloch-Pitts
- tells if a neuron is going to spike or not (use them in networks)
- Synaptic weights (strengths) from pre (1,2 or 3) to postsynaptic cell (i)
- synchronous assembly of ‘neurons’ is capable of universal computation if the
synaptic weights are chosen suitably
4
