# 8.4 Modeling cell assemblies  (Page 5/9)

 Page 5 / 9
$\begin{array}{cc}\hfill \frac{\left({m}_{i+1}-{m}_{i}\right)}{dt}& ={\alpha }_{m}\left[{V}_{i}\right]\left(1-{m}_{i+1}\right)-{\beta }_{m}\left[{V}_{i}\right]{m}_{i+1}\hfill \\ & =\frac{{A}_{{\alpha }_{m}}\left({V}_{i}-{B}_{{\alpha }_{m}}\right)}{1-{e}^{\left({B}_{{\alpha }_{m}}-{V}_{i}\right)/{C}_{{\alpha }_{m}}}}\left(1-{m}_{i+1}\right)-\frac{{A}_{{\beta }_{m}}\left({B}_{{\beta }_{m}}-{V}_{i}\right)}{1-{e}^{\left({V}_{i}-{B}_{{\beta }_{m}}\right)/{C}_{{\beta }_{m}}}}{m}_{i+1}\hfill \end{array}$

Solving for ${m}_{i+1}$ gives:

${m}_{i+1}=\frac{{m}_{i}+dt{\alpha }_{m}\left[{V}_{i}\right]}{1+dt\left({\alpha }_{m},\left[{V}_{i}\right],+,{\beta }_{m},\left[{V}_{i}\right]\right)}$

Update $n,h,q,\left[C{a}_{AP}\right],\left[C{a}_{NMDA}\right]$ likewise solving for the $i+1$ step. Notice ${\alpha }_{m}$ and ${\beta }_{m}$ are functions of voltage. Plug these results into below equation which is then solved for ${V}_{i+1}$

$\frac{{V}_{i+1}-{V}_{i}}{dt}=\frac{\left({V}_{leak},-,{V}_{i+1}\right){G}_{m}+\sum \left({V}_{comp},-,{V}_{i+1}\right){G}_{core}+{I}_{Na}+{I}_{K}+{I}_{Ca}+{I}_{K\left(Ca\right)}+{I}_{syn}}{{C}_{m}}$

The ion channels have the ${V}_{i+1}$ term in them. For example the $N{a}^{+}$ channel looks like this:

${I}_{Na}=\left({V}_{Na}-{V}_{i+1}\right){G}_{Na}{m}_{i+1}^{3}{h}_{i+1}$

The final result term after solving for ${V}_{i+1}$ :

${V}_{i+1}=\frac{{C}_{m}{V}_{i}+dt\left({G}_{m}{V}_{leak}+{G}_{Na}{m}_{i+1}^{3}{h}_{i+1}{V}_{Na}+{G}_{K}{n}_{i+1}^{4}{V}_{K}+{G}_{K\left(Ca\right)}{V}_{K}\left({\left[C{a}_{AP}\right]}_{i+1}+{\left[C{a}_{NMDA}\right]}_{i+1}\right)+{I}_{Syn}+{I}_{Stim}}{{C}_{m}+dt\left({G}_{m}+{G}_{Na}{m}_{i+1}^{3}{h}_{i+1}+{G}_{K}{n}_{i+1}^{4}+{G}_{K\left(Ca\right)}\left({\left[C{a}_{AP}\right]}_{i+1}+{\left[C{a}_{NMDA}\right]}_{i+1}\right)}$

## Building networks

After constructing models for the individual neurons it is necessary to connect the cells. The mission is to have a small network (50 excitatory and 50 inhibitory neurons will be used in the simulations, more details on why in a bit) and have the cells trained with pre-selected assemblies/patterns. Given different patterns oreventswe want to construct a weighting scheme that will assign a proper weighting. Proper in the sense that cells within a pattern will have strong excitatory connections and cells that are ever in the same pattern will have inhibitory connections. The goal is to have the network able to activate patterns. This means that when a sufficient number of cells belonging a pattern are stimulated it will fully resolve.

The weighting algorithm will output weights that are effective in proportion to another, but will require proper scaling. Should the overall weighting magnitudes be too high the network will seizure (meaning all the cells start firing). If the weighting magnitudes are too low, the network will go dormant once stimulation is removed.

## Picking weights

The term weight is used loosely; it signifies the choice of the measure of conductance at synapse where two neurons meet. This parameter will suffice as way of quantifying the strength of a synapse which is physiologically determined by the amount of neurotransmitter that would be released into the cleft and the number of receptor channels. Look back at the form for a synaptic current to see the conductance term we now will give more detail on:

${I}_{syn}=\left({V}_{syn}-V\right){G}_{syn}s.$

The ${G}_{syn}$ is the conductance term that reflect the weighting. It is expressed as the product of a weighting term that is an output of the weighting algorithm and an overall weighting scale constant that will determined later. Thus, ${G}_{ij}={w}_{ij}*weigh{t}_{syn}$ . Note: there will be several different $weigh{t}_{syn}$ constants for the several synaptic currents used in the model.

The scheme used to produce weights will use a probabilistic approach. Using a simple intuitive approach we want to characterize the level ofsupporta cell gets by the term:

${s}_{q}={b}_{q}+\sum _{h}{w}_{hq}{\pi }_{h}$

Here ${s}_{q}$ is the support level of the cell. The term ${b}_{q}$ will represent a bias of a cell (this would be a way of characterizing a cells firing property independent from other cell activity, since some cells may appear simply more activate in general). ${w}_{hq}$ is the connection weight from $h$ to $q$ . Variable ${\pi }_{h}$ is the activity level of cell $h$ . Assume either 0 or 1 then we reduce this system to a summation over the active cells in all the different patterns, set A.

#### Questions & Answers

how can chip be made from sand
Eke Reply
is this allso about nanoscale material
Almas
are nano particles real
Missy Reply
yeah
Joseph
Hello, if I study Physics teacher in bachelor, can I study Nanotechnology in master?
Lale Reply
no can't
Lohitha
where is the latest information on a no technology how can I find it
William
currently
William
where we get a research paper on Nano chemistry....?
Maira Reply
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
Ali
what are the products of Nano chemistry?
Maira Reply
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
learn
Google
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
Hafiz Reply
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
Jyoti Reply
ya I also want to know the raman spectra
Bhagvanji
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
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
Brian Reply
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?
LITNING Reply
what is a peer
LITNING Reply
What is meant by 'nano scale'?
LITNING Reply
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 ?
Bob Reply
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
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply

### Read also:

#### Get Jobilize Job Search Mobile App in your pocket Now!

Source:  OpenStax, The art of the pfug. OpenStax CNX. Jun 05, 2013 Download for free at http://cnx.org/content/col10523/1.34
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'The art of the pfug' conversation and receive update notifications? By David Bourgeois By OpenStax By Anonymous User By John Gabrieli By Nicole Bartels By Cath Yu By OpenStax By OpenStax By OpenStax By Yasser Ibrahim