Hello, dear friend, you can consult us at any time if you have any questions, add WeChat: daixieit

MATH3888 group project

        We are using HEK293-cell. Receptors: Ryonodine receptors, IP3, endoplasmic reticulum (ER/SR), cyto-plasm, cell membrane, ...

        UTP is the agonist, Dantrolene is the inhibitors.

Possible parameters to look at for bifurcation:

● Responses to agonist: ATP/UTP concentration

● Responses to drug:

        Simple model of intracellular Ca2+ concentration c

and Ca2+ concentration in ER

where 

We have

(1) Transport between membrane and cytoplasm Jin, Jout

where c0 concentration of external Ca2+, assumed to be constant.

where the first equation is a Hill function for the pumps in the cell membrane.

(2) Transport between cytoplasm and ER JRyR, Jserca, where Jserca pumps in Ca2+ to ER, where Jserca can be given by eq. 7.34 of textbook

from Friel model of RYR (the CICR model, week 4,5 matlab, textbook pg. 302,303).

We can have

Possible model and implementation in matcont:

where the fluxes are of the form

Parameters values (from textbook[1] and Friel model [2])

● c is the Ca2+ in the cytoplasm

● ce is the Ca2+ in the ER

● Jin is the flow of Ca2+ through the cell membrane to the cytoplasm. p is the concentration of IP3 that would have effect on opening channels that would allow influx of Ca2+ (section 7.2.1 explains this). In this case, p is the agonist (either UTP or caffeine). α1, α2 are some constants

● Jpump is the flow of Ca2+ out of the system. We have a flow proportional to the amount of Ca2+ in the cytoplasm (this is retain from the Friel model)

● Jserca hill function for serca pump (from section 7.2.4) (or we could use the four-state markov model from textbook pg 295, but I test this and the behaviour is not as easy to use)

Another model for serca pump (which I have not test) is MacLennan et al (1997) from the textbook (pg 283-285) where

● JRyR from the Friel paper (week 4-5 matlab session, or textbook page 301). For n = 0, 1, the state stabilises, for n ∈ [2, 8], there are stable oscillations (for p = 0).

● Initial point (0.1, 0.1). Integrator: ODE15s, Interval: 100 (some oscillation cycles are long so might need to adjust this length).

Comment

● κ1, κ2, Kd parameters are from the Friel model [2]. They can have these values 0.054, 2.4, 1 respectively from the textbook

● δ is dependent on the membrane. δ → 0 should simulate a close system.

● γ is the ratio between volume of the cytoplasm over the ER

Observations:

● For p = 0, there is bifurcation for n, in which n ∈ [2, 8], which shows stable oscillations of c, ce.

● For p > 0, there are some k1 values s.t. the system can exhibit single pulse or multiple pulses (oscillation), i.e. there are bifurcations for k1

● There are no bifurcation for p, as p increases, the stable solution of (c, ce) increases.

1 HEK293 Cell components

● Cytoplasm -

● Endoplasmic Reticulum - Serca pump, ER calcium concentration

● RYR receptor

● IP3 receptor

● Agonist site (TO DO)

● Agonist - Caffeine?

● Cell Membrane pumps - ATPase pump