<< Chapter < Page Chapter >> Page >

Calcium dependent plasticity: a better model?

We introduce Calcium Dependent Plasticity (CaDP) as a more biologically realistic model for synaptic plasticity in comparison to STDP. The model was developed by Dr. Harel Shouval of the University of Texas Medical School and colleagues at Brown University (see [link] , [link] ). All of the equations and parameter values introduced in this chapter have been taken or adapted from his 2008 publication [link] . While weight changes in the STDP model were based entirely on the order of firing and the duration of the spike interval, the synaptic weights in the CaDP model incorporate spike-timing as well as a form of rate-dependent plasticity. While STDP sets arbitrary upper bounds to achieve place field stability, CaDP can be accompanied with metaplasticity to obtain a stabilized backward shift [link] . Additionally, CaDP explicitly accounts for the interactions of biological parameters known to be involved with plasticity, including calcium, magnesium, and glutamate receptors.

Plasticity equations

The CaDP rule is based upon a scheme where calcium levels directly affect the synaptic weights. At low calcium levels, there is no change in weight. At moderate calcium levels, we observe a depression of weights. At high calcium levels, we observe the potentiation of weights. To achieve this effect, we define a function, Ω , to have the above properties:

Ω ( [ C a 2 + ] ) = σ ( [ C a 2 + ] , α 2 , β 2 ) - 0 . 5 × σ ( [ C a 2 + ] , α 1 , β 1 )

where σ represents a sigmoid function, which we define as:

σ ( x , a , b ) = e b ( x - a ) 1 + e b ( x - a )

We set parameters α 1 , α 2 , to control the lower and upper calcium bounds of the LTD region, respectively. β 1 and β 2 adjust the concavity of the sigmoid function, where σ approaches the Heaviside function as β . In our analysis of CaDP, we use the parameters ( α 1 , α 2 , β 1 , β 2 ) = ( 0 . 3 , 0 . 5 , 40 , 40 ) .

While we might be inclined to base our entire weight change regime on this omega function, we must also realize that fluctuations in synaptic calcium levels would cause any increase in weight caused by high calcium levels to be nullified when calcium decreases into the LTD calcium concentrations. As such, we must also implement a rate function, η , such that potentiation due to high calcium levels would outweigh the depression caused when calcium decreases through moderate concentrations and returns to equilibrium levels. Our equation for η takes the form:

η ( [ C a 2 + ] ) = p 1 ( [ C a 2 + ] + p 4 ) p 3 ( [ C a 2 + ] + p 4 ) p 3 + ( p 2 ) p 3

We set the parameters ( p 1 , p 2 , p 3 , p 4 ) to ( 2 , 0 . 5 , 3 , 0 . 00001 ) in our simulations of CaDP. As the behavior of this equation is not intuitive, we depict η along with Ω , both as functions of calcium concentrations in figures  [link] A and  [link] B.

Plasticity Equations. (A): η as a function of Calcium concentration. Notice that η monotonically increases with calcium concentrations. (B): Ω as a function of Calcium. Note that LTD occurs when 0.2< [ C a 2 + ] <0.5 and LTP occurs when [ C a 2 + ] >0.5. (C): Weight change as a function of Calcium level.

With our two calcium dependent functions, Ω and η , we define our synaptic weight change function, depicted in [link] C as follows:

Questions & Answers

Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
Jyoti Reply
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
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
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
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
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?
Damian Reply
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
Praveena Reply
hi
Loga
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
Privacy Information Security Software Version 1.1a
Good
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply

Get the best Algebra and trigonometry course in your pocket!





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?

Ask