Modelling the Brain, Cognitive Models & AI PDF

Modelling the brain Cognitive models and AI Alex Cayco Gajic Fall 2024 M1. Origins of cognitive modelling L1. Modelling the mind L2. Modelling the brain !  Does a single neuron matter for cognition ? Mice trained to lick for a water reward to microstimulation (ac...

Modelling the brain Cognitive models and AI Alex Cayco Gajic Fall 2024 M1. Origins of cognitive modelling L1. Modelling the mind L2. Modelling the brain !  Does a single neuron matter for cognition ? Mice trained to lick for a water reward to microstimulation (activates local population of neurons) What happens if we stimulate only one neuron? Houweling and Brecht, 2008  Activating a single neuron can bias decision making Single ? neuron No stimulation Local population First lick response Houweling and Brecht, 2008  Activating a single neuron can bias decision making Single neuron No stimulation Local population First lick response Houweling and Brecht, 2008  What is a neuron ? Dendrites Axon (receive input from (sends signal to other neurons) other neurons) Soma (processe s inputs) Neurons generate electrical signals called action potentials (APs) – “All or none” events: either it happens (“spike”) – To generate an AP, input must be greater than an intrinsic threshold Neurons communicate by transmitting APs The Action Potential Fluctuations in membrane potential (voltage across membrane) Electrode Voltage The Action Potential Fluctuations in membrane potential (voltage across membrane) Electrode Voltage The Action Potential Fluctuations in membrane potential (voltage across membrane) After initiation, all APs are about the same – Information carried by timing or frequency (not shape) Electrode Voltage  The Action Potential First discovered in 1865 – However, missed some details due to imperfect technology Caused by flow of positively- charged ions across cell membrane – Mechanism not understood for >100 years J. Bernstein  Electrochemical potential across cell membrane Cell membrane Intracellular Potassium (K+) Extracellular Sodium (Na+) Negatively charged ions At rest: -70 mV How does the membrane potential change? – Must be some flow of ions  Electrochemical potential across cell membrane Cell membrane Intracellular Potassium (K+) Extracellular Sodium (Na+) At rest: 0 mV If ions could move freely, would diffuse to concentrations inside and outside the cell  Electrochemical potential across cell membrane Cell membrane Intracellular Potassium (K+) Extracellular Sodium (Na+) At rest: -70 mV AP must be due to ions crossing semi-permeable cell membrane : allows some ions to pass through, but not others  What we now know : ion channels control permeability to specific ions (cell membrane) Abbott & Dayan Configurational change in channel structure changes whether a particular ion can pass through – Triggered by a chemical messenger, mechanical forces, or the voltage itself  Bernstein’s Membrane Theory (1902) Bernstein hypothesized that AP occurs due to a non-specific increase J. Bernstein of the membrane permeability – Causes ions to equilibrate (i.e. voltage à 0) Problem : subsequent experiments showed that the membrane potential goes beyond zero!  Integrate-and-fire model (1907) Phenomenological model of the membrane potential as an electrical circuit, ignoring AP generating mechanism From basic physics: dV (t) C = I(t) L Lapicque dt AAACAnicbZDLSgMxFIYzXmu9jboSN8Ei1E2ZWvGyEIrd6K6CvUBbSiaTaUMzmSE5I5ShuPFV3LhQxK1P4c63MZ0WUesPgY//nMPJ+d1IcA2O82nNzS8sLi1nVrKra+sbm/bWdl2HsaKsRkMRqqZLNBNcshpwEKwZKUYCV7CGO6iM6407pjQP5S0MI9YJSE9yn1MCxurauxXc9hWhiVfPw+Eo8WCEL/C14a6dcwpOKjwLxSnk0FTVrv3R9kIaB0wCFUTrVtGJoJMQBZwKNsq2Y80iQgekx1oGJQmY7iTpCSN8YBwP+6EyTwJO3Z8TCQm0Hgau6QwI9PXf2tj8r9aKwT/rJFxGMTBJJ4v8WGAI8TgP7HHFKIihAUIVN3/FtE9MImBSy6YhnI918n3yLNSPCsVSoXRznCtfTuPIoD20j/KoiE5RGV2hKqohiu7RI3pGL9aD9WS9Wm+T1jlrOrODfsl6/wIFh5YJ Capacitance : Current: Change in voltage Ability of cell membrane Flow of charge across over time (slope) to store charge cell membrane V(t) Voltage (V) Time  Integrate-and-fire model (1907) Phenomenological model of the membrane potential as an electrical circuit, ignoring AP generating mechanism From basic physics: dV (t) C = I(t) L Lapicque dt AAACAnicbZDLSgMxFIYzXmu9jboSN8Ei1E2ZWvGyEIrd6K6CvUBbSiaTaUMzmSE5I5ShuPFV3LhQxK1P4c63MZ0WUesPgY//nMPJ+d1IcA2O82nNzS8sLi1nVrKra+sbm/bWdl2HsaKsRkMRqqZLNBNcshpwEKwZKUYCV7CGO6iM6407pjQP5S0MI9YJSE9yn1MCxurauxXc9hWhiVfPw+Eo8WCEL/C14a6dcwpOKjwLxSnk0FTVrv3R9kIaB0wCFUTrVtGJoJMQBZwKNsq2Y80iQgekx1oGJQmY7iTpCSN8YBwP+6EyTwJO3Z8TCQm0Hgau6QwI9PXf2tj8r9aKwT/rJFxGMTBJJ4v8WGAI8TgP7HHFKIihAUIVN3/FtE9MImBSy6YhnI918n3yLNSPCsVSoXRznCtfTuPIoD20j/KoiE5RGV2hKqohiu7RI3pGL9aD9WS9Wm+T1jlrOrODfsl6/wIFh5YJ Capacitance : Current: Change in voltage Ability of cell membrane Flow of charge across over time (slope) to store charge cell membrane V(t) V(t+dt) Differential equation Voltage (V) : allows calculation of voltage based on slope at each time Time dt  Integrate-and-fire model (1907) dV (t) Inject a square wave of current into the C = I(t) neuron. What happens? dt AAACAnicbZDLSgMxFIYzXmu9jboSN8Ei1E2ZWvGyEIrd6K6CvUBbSiaTaUMzmSE5I5ShuPFV3LhQxK1P4c63MZ0WUesPgY//nMPJ+d1IcA2O82nNzS8sLi1nVrKra+sbm/bWdl2HsaKsRkMRqqZLNBNcshpwEKwZKUYCV7CGO6iM6407pjQP5S0MI9YJSE9yn1MCxurauxXc9hWhiVfPw+Eo8WCEL/C14a6dcwpOKjwLxSnk0FTVrv3R9kIaB0wCFUTrVtGJoJMQBZwKNsq2Y80iQgekx1oGJQmY7iTpCSN8YBwP+6EyTwJO3Z8TCQm0Hgau6QwI9PXf2tj8r9aKwT/rJFxGMTBJJ4v8WGAI8TgP7HHFKIihAUIVN3/FtE9MImBSy6YhnI918n3yLNSPCsVSoXRznCtfTuPIoD20j/KoiE5RGV2hKqohiu7RI3pGL9aD9WS9Wm+T1jlrOrODfsl6/wIFh5YJ I(t) 0 V(t) Vrest Time  Integrate-and-fire model (1907) dV (t) Inject a square wave of current into the C = I(t) neuron. What happens? dt AAACAnicbZDLSgMxFIYzXmu9jboSN8Ei1E2ZWvGyEIrd6K6CvUBbSiaTaUMzmSE5I5ShuPFV3LhQxK1P4c63MZ0WUesPgY//nMPJ+d1IcA2O82nNzS8sLi1nVrKra+sbm/bWdl2HsaKsRkMRqqZLNBNcshpwEKwZKUYCV7CGO6iM6407pjQP5S0MI9YJSE9yn1MCxurauxXc9hWhiVfPw+Eo8WCEL/C14a6dcwpOKjwLxSnk0FTVrv3R9kIaB0wCFUTrVtGJoJMQBZwKNsq2Y80iQgekx1oGJQmY7iTpCSN8YBwP+6EyTwJO3Z8TCQm0Hgau6QwI9PXf2tj8r9aKwT/rJFxGMTBJJ4v8WGAI8TgP7HHFKIihAUIVN3/FtE9MImBSy6YhnI918n3yLNSPCsVSoXRznCtfTuPIoD20j/KoiE5RGV2hKqohiu7RI3pGL9aD9WS9Wm+T1jlrOrODfsl6/wIFh5YJ I(t) 0 V(t) Vrest Time  Integrate-and-fire model (1907) dV (t) Inject a square wave of current into the C = I(t) neuron. What happens? dt AAACAnicbZDLSgMxFIYzXmu9jboSN8Ei1E2ZWvGyEIrd6K6CvUBbSiaTaUMzmSE5I5ShuPFV3LhQxK1P4c63MZ0WUesPgY//nMPJ+d1IcA2O82nNzS8sLi1nVrKra+sbm/bWdl2HsaKsRkMRqqZLNBNcshpwEKwZKUYCV7CGO6iM6407pjQP5S0MI9YJSE9yn1MCxurauxXc9hWhiVfPw+Eo8WCEL/C14a6dcwpOKjwLxSnk0FTVrv3R9kIaB0wCFUTrVtGJoJMQBZwKNsq2Y80iQgekx1oGJQmY7iTpCSN8YBwP+6EyTwJO3Z8TCQm0Hgau6QwI9PXf2tj8r9aKwT/rJFxGMTBJJ4v8WGAI8TgP7HHFKIihAUIVN3/FtE9MImBSy6YhnI918n3yLNSPCsVSoXRznCtfTuPIoD20j/KoiE5RGV2hKqohiu7RI3pGL9aD9WS9Wm+T1jlrOrODfsl6/wIFh5YJ I(t) 0 V(t) Problem : Vrest Does not return to Vrest Time  Leaky integrate-and-fire model Solution : Add extra current dV (t) to compensate for leak of C ḡL (V (t) = I(t) EL ) + I(t) dt ions over time (Ohm’s law) AAACFXicbZDJSgNBEIZ74hbjFvXopTEICZowMeJyC4qg4CGCWSATQk+nJ2nSs9BdI4YhL+HFV/HiQRGvgjffxk4yuP/Q8PNVFdX124HgCkzz3UhMTc/MziXnUwuLS8sr6dW1mvJDSVmV+sKXDZsoJrjHqsBBsEYgGXFtwep2/2RUr18zqbjvXcEgYC2XdD3ucEpAo3Z6B+ctm0jcbUcWsBvAF8NsLQu5/OkXyGG8jc81bKczZsEcC/81xdhkUKxKO/1mdXwauswDKohSzaIZQCsiEjgVbJiyQsUCQvuky5raesRlqhWNrxriLU062PGlfh7gMf0+ERFXqYFr606XQE/9ro3gf7VmCM5hK+JeEALz6GSREwoMPh5FhDtcMgpioA2hkuu/YtojklDQQabGIRyNtP958l9T2y0US4XS5V6mfBzHkUQbaBNlUREdoDI6QxVURRTdonv0iJ6MO+PBeDZeJq0JI55ZRz9kvH4A4W6cPg== AAACAnicbZDLSgMxFIYzXmu9jboSN8Ei1E2ZWvGyEIrd6K6CvUBbSiaTaUMzmSE5I5ShuPFV3LhQxK1P4c63MZ0WUesPgY//nMPJ+d1IcA2O82nNzS8sLi1nVrKra+sbm/bWdl2HsaKsRkMRqqZLNBNcshpwEKwZKUYCV7CGO6iM6407pjQP5S0MI9YJSE9yn1MCxurauxXc9hWhiVfPw+Eo8WCEL/C14a6dcwpOKjwLxSnk0FTVrv3R9kIaB0wCFUTrVtGJoJMQBZwKNsq2Y80iQgekx1oGJQmY7iTpCSN8YBwP+6EyTwJO3Z8TCQm0Hgau6QwI9PXf2tj8r9aKwT/rJFxGMTBJJ4v8WGAI8TgP7HHFKIihAUIVN3/FtE9MImBSy6YhnI918n3yLNSPCsVSoXRznCtfTuPIoD20j/KoiE5RGV2hKqohiu7RI3pGL9aD9WS9Wm+T1jlrOrODfsl6/wIFh5YJ Leak current Conductance (gL) : I(t) How easily current passes 0 Reversal potential (EL) : Voltage at which there V(t) is no net flow of the passive corresponding current Vrest Time What about the AP?  Leaky integrate-and-fire model Solution : Add extra current dV (t) to compensate for leak of C ḡL (V (t) = I(t) EL ) + I(t) dt ions over time (Ohm’s law) AAACFXicbZDJSgNBEIZ74hbjFvXopTEICZowMeJyC4qg4CGCWSATQk+nJ2nSs9BdI4YhL+HFV/HiQRGvgjffxk4yuP/Q8PNVFdX124HgCkzz3UhMTc/MziXnUwuLS8sr6dW1mvJDSVmV+sKXDZsoJrjHqsBBsEYgGXFtwep2/2RUr18zqbjvXcEgYC2XdD3ucEpAo3Z6B+ctm0jcbUcWsBvAF8NsLQu5/OkXyGG8jc81bKczZsEcC/81xdhkUKxKO/1mdXwauswDKohSzaIZQCsiEjgVbJiyQsUCQvuky5raesRlqhWNrxriLU062PGlfh7gMf0+ERFXqYFr606XQE/9ro3gf7VmCM5hK+JeEALz6GSREwoMPh5FhDtcMgpioA2hkuu/YtojklDQQabGIRyNtP958l9T2y0US4XS5V6mfBzHkUQbaBNlUREdoDI6QxVURRTdonv0iJ6MO+PBeDZeJq0JI55ZRz9kvH4A4W6cPg== AAACAnicbZDLSgMxFIYzXmu9jboSN8Ei1E2ZWvGyEIrd6K6CvUBbSiaTaUMzmSE5I5ShuPFV3LhQxK1P4c63MZ0WUesPgY//nMPJ+d1IcA2O82nNzS8sLi1nVrKra+sbm/bWdl2HsaKsRkMRqqZLNBNcshpwEKwZKUYCV7CGO6iM6407pjQP5S0MI9YJSE9yn1MCxurauxXc9hWhiVfPw+Eo8WCEL/C14a6dcwpOKjwLxSnk0FTVrv3R9kIaB0wCFUTrVtGJoJMQBZwKNsq2Y80iQgekx1oGJQmY7iTpCSN8YBwP+6EyTwJO3Z8TCQm0Hgau6QwI9PXf2tj8r9aKwT/rJFxGMTBJJ4v8WGAI8TgP7HHFKIihAUIVN3/FtE9MImBSy6YhnI918n3yLNSPCsVSoXRznCtfTuPIoD20j/KoiE5RGV2hKqohiu7RI3pGL9aD9WS9Wm+T1jlrOrODfsl6/wIFh5YJ Leak current I(t) 0 V(t) passive Vrest V(t) Threshold with spike Vrest Time  Leaky integrate-and-fire model Solution : Add extra current dV (t) to compensate for leak of C ḡL (V (t) = I(t) EL ) + I(t) dt ions over time (Ohm’s law) AAACFXicbZDJSgNBEIZ74hbjFvXopTEICZowMeJyC4qg4CGCWSATQk+nJ2nSs9BdI4YhL+HFV/HiQRGvgjffxk4yuP/Q8PNVFdX124HgCkzz3UhMTc/MziXnUwuLS8sr6dW1mvJDSVmV+sKXDZsoJrjHqsBBsEYgGXFtwep2/2RUr18zqbjvXcEgYC2XdD3ucEpAo3Z6B+ctm0jcbUcWsBvAF8NsLQu5/OkXyGG8jc81bKczZsEcC/81xdhkUKxKO/1mdXwauswDKohSzaIZQCsiEjgVbJiyQsUCQvuky5raesRlqhWNrxriLU062PGlfh7gMf0+ERFXqYFr606XQE/9ro3gf7VmCM5hK+JeEALz6GSREwoMPh5FhDtcMgpioA2hkuu/YtojklDQQabGIRyNtP958l9T2y0US4XS5V6mfBzHkUQbaBNlUREdoDI6QxVURRTdonv0iJ6MO+PBeDZeJq0JI55ZRz9kvH4A4W6cPg== AAACAnicbZDLSgMxFIYzXmu9jboSN8Ei1E2ZWvGyEIrd6K6CvUBbSiaTaUMzmSE5I5ShuPFV3LhQxK1P4c63MZ0WUesPgY//nMPJ+d1IcA2O82nNzS8sLi1nVrKra+sbm/bWdl2HsaKsRkMRqqZLNBNcshpwEKwZKUYCV7CGO6iM6407pjQP5S0MI9YJSE9yn1MCxurauxXc9hWhiVfPw+Eo8WCEL/C14a6dcwpOKjwLxSnk0FTVrv3R9kIaB0wCFUTrVtGJoJMQBZwKNsq2Y80iQgekx1oGJQmY7iTpCSN8YBwP+6EyTwJO3Z8TCQm0Hgau6QwI9PXf2tj8r9aKwT/rJFxGMTBJJ4v8WGAI8TgP7HHFKIihAUIVN3/FtE9MImBSy6YhnI918n3yLNSPCsVSoXRznCtfTuPIoD20j/KoiE5RGV2hKqohiu7RI3pGL9aD9WS9Wm+T1jlrOrODfsl6/wIFh5YJ Leak current I(t) 0 V(t) passive Vrest “Pasted” spike V(t) Threshold with spike Vrest Reset voltage Time  Leaky integrate-and-fire model Solution : Add extra current dV (t) to compensate for leak of C ḡL (V (t) = I(t) EL ) + I(t) dt ions over time (Ohm’s law) AAACFXicbZDJSgNBEIZ74hbjFvXopTEICZowMeJyC4qg4CGCWSATQk+nJ2nSs9BdI4YhL+HFV/HiQRGvgjffxk4yuP/Q8PNVFdX124HgCkzz3UhMTc/MziXnUwuLS8sr6dW1mvJDSVmV+sKXDZsoJrjHqsBBsEYgGXFtwep2/2RUr18zqbjvXcEgYC2XdD3ucEpAo3Z6B+ctm0jcbUcWsBvAF8NsLQu5/OkXyGG8jc81bKczZsEcC/81xdhkUKxKO/1mdXwauswDKohSzaIZQCsiEjgVbJiyQsUCQvuky5raesRlqhWNrxriLU062PGlfh7gMf0+ERFXqYFr606XQE/9ro3gf7VmCM5hK+JeEALz6GSREwoMPh5FhDtcMgpioA2hkuu/YtojklDQQabGIRyNtP958l9T2y0US4XS5V6mfBzHkUQbaBNlUREdoDI6QxVURRTdonv0iJ6MO+PBeDZeJq0JI55ZRz9kvH4A4W6cPg== AAACAnicbZDLSgMxFIYzXmu9jboSN8Ei1E2ZWvGyEIrd6K6CvUBbSiaTaUMzmSE5I5ShuPFV3LhQxK1P4c63MZ0WUesPgY//nMPJ+d1IcA2O82nNzS8sLi1nVrKra+sbm/bWdl2HsaKsRkMRqqZLNBNcshpwEKwZKUYCV7CGO6iM6407pjQP5S0MI9YJSE9yn1MCxurauxXc9hWhiVfPw+Eo8WCEL/C14a6dcwpOKjwLxSnk0FTVrv3R9kIaB0wCFUTrVtGJoJMQBZwKNsq2Y80iQgekx1oGJQmY7iTpCSN8YBwP+6EyTwJO3Z8TCQm0Hgau6QwI9PXf2tj8r9aKwT/rJFxGMTBJJ4v8WGAI8TgP7HHFKIihAUIVN3/FtE9MImBSy6YhnI918n3yLNSPCsVSoXRznCtfTuPIoD20j/KoiE5RGV2hKqohiu7RI3pGL9aD9WS9Wm+T1jlrOrODfsl6/wIFh5YJ Leak current I(t) 0