# 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.

What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
why we need to study biomolecules, molecular biology in nanotechnology?
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
why?
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
what does nano mean?
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
it is a goid question and i want to know the answer as well
Maciej
Abigail
for teaching engĺish at school how nano technology help us
Anassong
Do somebody tell me a best nano engineering book for beginners?
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
what is fullerene does it is used to make bukky balls
are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
what is the Synthesis, properties,and applications of carbon nano chemistry
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
so some one know about replacing silicon atom with phosphorous in semiconductors device?
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
for screen printed electrodes ?
SUYASH
What is lattice structure?
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
what's the easiest and fastest way to the synthesize AgNP?
China
Cied
how did you get the value of 2000N.What calculations are needed to arrive at it
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