<< Chapter < Page Chapter >> Page >

Mathematical model

Biochemical model

Ach simulation

ACH flow was simulated by using forward finite difference for time and central finite difference for space to find an explicit solution to two-dimensional heat flow. The diffusion coefficient of ACH was calculated from [link] .

[ A C H ] t = α [ A C H ] x x + [ A C H ] y y α = 0 . 4 n m 2 n s - 1

It was found experimentally that using a time step of 0.25 ns for explicit solution gave similar results as using a Gaussian lowpass filter matrix to represent a rotational symmetric point surface distribution. Since the Gaussian filter matrix, B, is built into MATLAB, it is computed faster, and thus was used for the simulation. In equation 2, B is the 3 by 3 matrix from a Gaussian lowpass filter matrix with σ = 0 . 4 . In MATLAB, B = f s p e c i a l ( ' g a u s s i a n ' , 3 , 0 . 4 ) . Time is scaled to increments of 0.25 ns.

[ A C H ] x , y t + 1 = i = - 1 1 j = - 1 1 β i , j [ A C H ] x + i , y + j t β i , j = B ( 2 + i , 2 + j )

The synaptic cleft was represented by a two-dimensional grid of length 100 nm. The width was varied from 20 to 60 nm to represent the changing distance in edematous conditions. Each cell (x, y) on the grid was 1 nm × 1 nm, and contained the concentration for that cell at a given time (t), represented in equation 2 as [ A C H ] x , y t . The initial concentration at each cell was 0 μ M , except at the neuron terminal, where the ACH was released by exocytosis at concentrations of 1000 μ M in the row of cells from [ A C H ] 45 , 2 to [ A C H ] 54 , 2 . Homogeneous Dirichlet boundary conditions were used at all boundaries except at the release site and receptor site, which were made impenetrable. These impenetrable boundaries were the row of cells from [ A C H ] 36 , 1 to [ A C H ] 63 , 1 (neuron release site) and [ A C H ] 36 , ζ to [ A C H ] 63 , ζ (membrane receptor site), where ζ was the synaptic cleft width.

Calcium control

ACH receptors influence IP3 levels, which affect cell potential, potassium channel probability, SR calcium, and intracellular calcium. The IP3 model was adapted from [link] and the remaining differential equations were adapted from [link] .

d [ I P 3 ] d t = [ A C H ] - ϵ [ I P 3 ] - V M 4 [ I P 3 ] u [ I P 3 ] u + K 4 u + P M V ( 1 - [ E ] r 2 ) K V r 2 + [ E ] r 2 d [ C a S R 2 + ] d t = B [ C a 2 + ] 2 [ C a 2 + ] 2 + C b 2 - C [ C a S R 2 + ] 2 [ C a 2 + ] 4 ( [ C a S R 2 + ] 2 + s c 2 ) ( [ C a 2 + ] 4 + c c 4 ) - L [ C a S R 2 + ] d [ W ] d t = λ ( [ C a 2 + ] + c W ) 2 ( [ C a 2 + ] + c W ) 2 + β e - ( [ E ] - v C a 3 R K ) - [ W ] d [ E ] d t = γ ( - F N a K - G C l ( [ E ] - v C l ) - 2 G C a ( [ E ] - v C a 1 ) 1 + e - [ E ] - v C a 2 R C a - G N C X [ C a 2 + ] ( [ E ] - v N C X ) [ C a 2 + ] + c N C X - G K [ W ] ( [ E ] - v K ) ) d [ C a 2 + ] d t = F [ I P 3 ] 2 [ I P 3 ] 2 + K r 2 - G C a ( [ E ] - v C a 1 1 + e - ( [ E ] - v C a 2 R C a ) + G N C X [ C a 2 + ] ( [ E ] - v N C X ) [ C a 2 + ] + c N C X - B [ C a 2 + ] 2 [ C a 2 + ] 2 + C b 2 + C [ C a S R 2 + ] 2 [ C a 2 + ] 4 ( [ C a S R 2 + ] 2 + s c 2 ) ( [ C a 2 + ] 4 + c c 4 ) - D [ C a 2 + ] ( 1 + ( [ E ] - v d ) R d + L [ C a S R 2 + ]
[ A C H ] 0 = 0 . 001 μ M Initial ACH concentration
[ I P 3 ] 0 = 0 . 49 μ M Initial IP3 concentration
[ C a S R 2 + ] 0 = 1 . 1 μ M Initial sarcoplasmic calcium concentration
[ W ] 0 = 0 . 02 Initial potassium channel probability concentration
[ E ] 0 = - 42 m V Initial cell potential
[ C a 2 + ] 0 = 0 . 17 μ M Initial intracellular calcium concentration
β = 0 . 13 μ M 2 translation factor [link]
γ = 197 m V μ M - 1 scaling factor [link]
ϵ = 0 . 015 s - 1 rate constant for linear IP3 [link]
λ = 45 channel constant [link]
B = 2 . 025 μ M s - 1 SR uptake rate constant [link]
C = 55 μ M s - 1 CICR rate constant [link]
D = 0 . 24 s - 1 Ca extrusion by ATPase constant [link]
F = 0 . 23 μ M s - 1 maximal influx rate [link]
L = 0 . 025 s - 1 leak from SR rate constant [link]
C b = 1 μ M half point SR ATPase activation [link]
c c = 0 . 9 μ M half point CICR activation [link]
c N C X = 0 . 5 μ M half point Na Ca exchange activation [link]
c W = 0 . 0 μ M translation factor [link]
F N a K = 0 . 0432 μ M s - 1 net whole cell flux [link]
G C a = 0 . 00129 μ M m V - 1 s - 1 whole cell conductance for VOCCs [link]
G C l = 0 . 00134 μ M m V - 1 s - 1 whole cell conductance Cl [link]
G K = 0 . 00446 μ M m V - 1 s - 1 whole cell conductance K [link]
G N C X = 0 . 00316 μ M m V - 1 s - 1 whole cell conductance for Na Ca exchange [link]
K 4 = 0 . 5 μ M half saturation constant IP3 degradation [link]
K r = 1 μ M half saturation constant Ca entry [link]
K V = - 58 m V half saturation constant IP3 voltage synthesis [link]
P M V = 0 . 01333 μ M s - 1 max rate voltage IP3 synthesis [link]
R 2 = 8 hill coefficient [link]
R C a = 8 . 5 m V maximum slope of VOCC activation [link]
R d = 250 . 0 m V slope of voltage dependence [link]
R K = 12 . 0 m V maximum slope Ca activation [link]
s c = 2 μ M half point CICR efflux [link]
u = 4 hill coefficient [link]
v C a 1 = 100 . 0 m V reversal potential VOCCs [link]
v C a 2 = - 24 m V half point VOCC activation [link]
v C a 3 = - 27 m V half point Ca channel activation [link]
v C l = - 25 m V reversal potential Cl [link]
v d = - 100 . 0 m V intercept voltage dependence [link]
v K = - 104 . 0 m V reversal potential K [link]
V M 4 = 0 . 0333 μ M s - 1 max nonlinear IP degradation [link]
v N C X = - 40 . 0 m V reversal potential Na Ca exchange [link]

Questions & Answers

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
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
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
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
Brooke Delaney
Start Exam
George Turner
Start Quiz
Edgar Delgado
Start Test