# 8.6 Mathematical models of hippocampal spatial memory  (Page 3/13)

 Page 3 / 13

We model the place cell's voltage using the Conductance-based Integrate and Fire model, as pictured by the circuit diagram above. Cell voltage, or the voltage difference across the cell membrane, which we define as ${V}_{m}$ , is modified via the flow of charged ions across the cell membrane. In our integrate and fire model, we implement three parallel components through which cell voltage is adjusted. The first parallel component represents our leak current resulting from the flow of chloride ions through leaky channels. The chloride ions will travel across the membrane to reach their resting potential, which we denote as ${V}_{Cl}$ or ${V}_{rest}$ (used later in the text), of -70 mV. The flow of ions is limited by a conductance ${g}_{Cl}$ , which remains fixed at a value of 1 mS/cm ${}^{2}$ . S represents Siemens, the reciprocal of the unit of resistance $\Omega$ . When we put these terms together using Ohm's law and solve for chloride current, we get:

${I}_{Cl}={g}_{Cl}\left({V}_{m}-{V}_{Cl}\right)$

The second parallel component of the integrate and fire model consists of a capacitor, indicative of the cell membrane's ability to separate electrical charge (in the form of ions). For this component, the capacitive current, ${I}_{C}$ represents the current due to the change in transmembrane voltage. This current takes the following form:

${I}_{C}={C}_{m}\frac{d{V}_{m}}{dt}$

Here, ${C}_{m}$ denotes the membrane's capacitance, or ability to store charge. We use the value of ${C}_{m}$ = 20 $\mu$ F/cm ${}^{2}$ .

The third parallel component of our circuit involves current from synaptic inputs. This input will act as the driving force for depolarization (in this setup we do not use any inhibitory synapses). As such, we use a excitatory reversal potential of ${V}_{syn}$ = 0 mV, which will help raise the cell voltage toward the firing threshold in the presence of input. The magnitude of the input current is limited by synaptic conductance, which we denote ${g}_{syn}$ in the circuit diagram (also referred to as ${g}_{E}$ ). The synaptic conductance, unlike the leak conductance of the chloride channels, is a variable conductance (denoted by the arrow through the resistor) whose magnitude is discussed in the next section. The synaptic input current is represented by the following:

${I}_{syn}={g}_{syn}\left({V}_{m}-{V}_{syn}\right)$

Since these three currents are in parallel, we can use Kirchhoff's current law, which states that:

${I}_{Cl}+{I}_{C}+{I}_{syn}=0$

Substituting values in for the currents yields the following:

${C}_{m}\frac{dV}{dt}+{g}_{Cl}\left(V-{V}_{Cl}\right)+{g}_{syn}\left(V-{V}_{syn}\right)=0$

Note that this differential equation only applies as long as the membrane voltage remains subthreshold. Having explained the voltage dynamics of the Integrate and Fire model, we now discuss how our variable synaptic conductance is adjusted.

## Synaptic conductance

In our model, we will represent input from external stimuli or neighboring place cells as an increase in synaptic conductance. We define our synaptic weight as the degree of increase in conductance of the postsynaptic cell due to presynaptic cell firing.As such, the excitatory synaptic conductance ( ${g}_{E}$ ) of each cell takes the following form:

are nano particles real
yeah
Joseph
Hello, if I study Physics teacher in bachelor, can I study Nanotechnology in master?
no can't
Lohitha
where we get a research paper on Nano chemistry....?
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
Ali
what are the products of Nano chemistry?
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
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da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
hey
Giriraj
Preparation and Applications of Nanomaterial for Drug Delivery
revolt
da
Application of nanotechnology in medicine
has a lot of application modern world
Kamaluddeen
yes
narayan
what is variations in raman spectra for nanomaterials
ya I also want to know the raman spectra
Bhagvanji
I only see partial conversation and what's the question here!
what about nanotechnology for water purification
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
what is the stm
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
what is Nano technology ?
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
what king of growth are you checking .?
Renato
how did you get the value of 2000N.What calculations are needed to arrive at it
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