computational cell biology summer course
DESCRIPTION
Using of XPP, AUTO and VCell for qualitative analysis of building blocks of hemostatic system by Alexey Tokarev. Computational Cell Biology Summer Course. Cold Spring Harbor Laboratory – 2012. Hemostasis = platelet + plasma subsystems. Plug / thrombus growth. Blood flow. - PowerPoint PPT PresentationTRANSCRIPT
Computational Cell Biology Summer Course
Cold Spring Harbor Laboratory – 2012
Using of XPP, AUTO and VCell for qualitative analysis of building blocks of hemostatic system
by
Alexey Tokarev
Hemostasis = platelet + plasma subsystems
Blood flow
Plug/ thrombus growth
Falati et al (2002)
plateletsplatelets+fibrin
fibrin
• Plasma clotting
Fibrin mesh. SEM made by Jean-Claude Bordet (Lyon, France).
• Platelet activation, secretion, aggregation
Ohlmann (2000)
Project goal: analyze the behavior of different components (building blocks) of hemostatic system using VCell, XPP and AUTO
Tasks: 1)Run the best of published models of platelet signaling in VCell and reproduce Ca2+ oscillations2)Investigate oscillating and steady regimes of functioning of IP3 receptor using XPP/AUTO3)Study travelling wave solutions of the reduced model of blood coagulation using XPP/AUTO
Part I. Quantitative model of platelet activation
Model summary:•5 compartments•70 species•77 reactions•132 kinetic parameters•xml file obtained from the author
Purvis et al, Blood, 2008
• Two-week efforts to run this model in VCell (thanks to Ion and Olena for help!)• Failure to reproduce published results.
Part II. IP3-receptor model for Ca2+ oscillationsDeYoung and Keizer, PNAS, 1992; Li and Rinzel, J.Theor.Biol., 1994
Full model:1+8-1=8 equations
Reduced model:2 equations
h=x000+x100+x010+x110
τ(IP3) << τ(Ca,act) << τ(Ca,inact)
[IP3]=0.3 uM
[IP3]=0.5 uM
h – Ca2+ phase plane, 2-variables model of IP3R
h
[Ca2+]I, uM
h
[Ca2+]I, uM
Bifurcation diagrams of the full and reduced models
Full (dashed) and reduced (solid) models.Li and Rinzel, JTB, 1994
Full (9 variables)
Conclusions:•full IP3R model may be too redundant for modeling of signal transduction in a cell•(general): robust properties of cellular building blocks are governed by time hierarchy of processes and thus can be described by low-dimensional models
Reduced (2 variables)
Marco is acknowledged for very helpful discussion
[IP3]
[IP3 ]
Properties of IP3 receptor module in the platelet activation model of Lenoci et al. (Mol. BioSyst., 2011)
Modification of IP3R parameters vs. DeYoung and Keizer:forward binding rates are 10 times faster, dissociation constants are 2 times smaller
2-variables IP3R model,[IP3]=0.1, 1, 10 uM
Conclusion:no IP3R-dependent Ca2+ oscillations possible at all [IP3]
h
[Ca2+]I, uM
[Ca2+]ss
[IP3]
Investigation of cell volume effect on Ca2+ oscillations
ODE, Vcyt=10 um3
Stochastic……under construction…
Part III. Travelling wave solution in the mathematical model of blood clotting
0,001 2 3 40
50
100 Experiment Theory
Thr
ombi
n ac
tivity
, nM
Distance from the activator, mm
N. Dashkevich, M. Ovanesov, A. Balandina, S. Karamzin, P. Shestakov, N. Soshitova, A. Tokarev, M. Panteleev, F. Ataullakhanov. Thrombin activity propagates in space during blood coagulation as an excitation wave. To appear in Biophys. J.
Zarnitsina et al., Chaos, 2001
Reduced model:(full model)
Test case 1: moving front solution of the Fisher-KPP (Kolmogorov-Petrovskii-
Piskunov) equation
Solutions exist for every c>2
Phase diagram for c=3:
Fisher, Ann. Eugenics, 1937; Kolmogorov, Petrovskii, Piscounov. Bull.Mocsow Univ., Math.Mech., 1937
u’t=u’’xx + u(1-u)u(+∞)=0, u(-∞)=1
c – velocity of the moving front
ξ=x-ctU(ξ)=u(x,t)
-cU’=U’’+U(1-U)
U’=VV’=-cV-U(1-U)(U,V)(+∞)=(0,0), (U,V)(-∞)=(1,0)
heteroclinic orbit
U
V
Stable manifolds of f.p.(1,0)Unstable manifolds of f.p.(1,0)
U
V
U
ξ
solution
Test case 2: moving front solution of the FitzHugh-Nagumo (FHN) equation
c=0.3535
ut = uxx + f(u), f(u)=u(1-u)(u-a)u(+∞)=0, u(-∞)=1
The solution exits at single unique c
c = 0
Stable manifolds of f.p.(1,0)Unstable manifolds of f.p.(1,0)
heteroclinic orbit
solution
c = 1, 0.5,0.3535,0
U
V
U
V
U
ξ
Exact heteroclinic trajectory
Exact solution
AUTO
Test case 3: finding the exact homoclinic trajectory in AUTO
u
v
u
ξ
u'=vv'=-cv+u(1-u) +auv
Autowave solution u(x,t)
Conclusions / advices / hopes
1. Importing/using of the non-proved sbml models may appear to be the waste of your time
2. Always think how to reduce your complex model
3. Using AUTO one can find the steady autowave solution of coupled PDEs (if it exists). Hope this will help in studying the plasma coagulation system
Thank you for your attention!