f2018 lectures end

neurotransmitters2.md

@@ -450,13 +450,12 @@ IPSP
 
 * In general EPSPs in neurons are small 0.2–0.4 mV
 * Most neurons are somewhere between 10–20 mV below threshold. If everything was linear that it would take the sum of 50 or so inputs to trigger AP
-* Not so simple. Some inputs are bigger than others, the inputs can be summed differently– spatially or temporally
-* A single neuron can have as many as 10,000 different synapses. Some excitatory some inhibitory, some strong some weak. Some at the tips of dendrites, some near the cell body
-* Integration of all the postsynaptic potentials determines whether the neuron fires an action potential
+* Not so simple-- synaptic inputs can be summed in space and time within a neuron
+* Recall a single neuron may have as many as 10,000 different synapses. Some are excitatory some inhibitory, some strong some weak. Some at the tips of dendrites, some near the cell body
+* Integration of all these little postsynaptic bioelectric waves determines whether the neuron fires an action potential
 
 Note:
 
-Of course we are greatly simplifying everything here, a single neuron may have as many as 10K synaptic inputs.
 
 
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@@ -467,17 +466,33 @@ Of course we are greatly simplifying everything here, a single neuron may have a
 <div></div>
 
 * How does a neuron integrate all the information it is getting?
-* In most motor neurons and interneurons the decision to initiate an action potential is at the axon hillock. Contains a high density of voltage dependent Na⁺ channels. Contains membrane with lowest threshold
+* In many neurons the decision to initiate an action potential is at the axon hillock. Contains a high density of voltage dependent Na^+^ channels and is contains membrane with lowest threshold
 * Axon hillock is senses the local state of the cell, which is the combination of all the EPSPs and IPSPs going on at one time
-* This is mostly due potentials that spread passively
-* Temporal summation, process by which consecutive synaptic potentials at the same site are added together. Different synapses will have different time constants
-* Length constant of the cell determines the degree to which a depolarization current decreases as it spreads passively. Easier to sum inputs on the same dendritic branch than on different branches
-* Some dendrites even have voltage gated Na⁺ channels, these can amplify inputs
+* This is due graded potentials that spread passively
+* Temporal summation, process by which consecutive synaptic potentials at the same site are added together.
+* Spatial structure of the determines the degree to which a depolarization current decreases as it spreads passively. Easier to sum inputs on the same dendritic branch than on different branches
 
 </div>
 
 Note:
 
+* Different synapses will have different time constants
+* Some dendrites have voltage gated Na^+^ channels (albeit lower density than axons), these can amplify inputs
+* Length constant of the cell determines the degree to which a depolarization current decreases as it spreads passively. Easier to sum inputs on the same dendritic branch than on different branches
+
+Time constant  
+: time needed for for resistive current (I~r~, current due to ions flowing through channels) and membrane potential (V~m~) to reach **63%** of their *asymptotic values* is proportional to the combination of resistance and capacitance of the circuit in question (across the cell membrane) 
+: membrane current (I~m~) is sum of I~r~  and the capacitive current (I~c~)  
+: I~m~ = I~r~ + I~c~  
+: capacitance of membrane: during change in applied voltage or current across membrane, positively charged ions pile on surface of one side of membrane and **electrostatically** interact with cations on the other side of membrane surface (membrane acts as thin impermeable surfaces in parallel, like a capacitor), repeling them and inducing immediate, fast capacitive current along membrane
+: capacitive current falls with an exponential time course. And the membrane potential rises with **same exponential** time course  
+: Relation of membrane potential at time *t* during charging of capacitance is given by V~t~ = V~inf~(1 - *e*^-t/RC^), where V~inf~ is the membrane potential at an infinite asymptotic value of the exponential curve.  When t = RC, then we have V~t~ = V~inf~ ( 1 - *e*^-1^) ==> V~inf~ (0.63)  
+
+```javascript
+console.log( 1 - Math.E ** -1)
+```
+
+
 
 <!-- TODO: make new model neuron fig like this <div><img src="figs/image_c9ee4b6.png" height="100px"><figcaption></figcaption></div> -->