Designing and Constructing a Set of Fundamental Cell Models: Application to Cardiac Disease. James B.Bassingthwaighte University of Washington Seattle. Physiome and Physiome Project.
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James B.Bassingthwaighte
University of Washington
Seattle
Health
Organism
The Physiome Project
Organ
http://www.physiome.org
Tissue
Cell
Molecule
Genes
THE MORPHOME:
The Proteome, quantitative measures of structural components, content of solutes in cells and organelles, volumes, surface areas, material properties, , bilayers, organelles, organs, whole organisms.
THE PHYSIOME:
but normal septal fatty acid uptake.
How can the observations be explained through regional events at the levels of cell and molecule?
Prinzen et al., 2000
Schematics of electrical activation Function:
RV apex pacing
left bundle branch block
X
Prinzen et al., 2000
From TorrentGuasp, 1998
From Vetter and McCulloch, UCSD
The RBB is normal, and excitation spreads normally over the RV. Because the LBB is blocked, activation spreads slowly over the LV taking 50 to 100 ms, broadening the QRS complex.
Pacing
spike
ECG
...
Preset.
pulse
130ms
90ms
50ms
...
Gx
RF
Delay = 50 ms
Delay = 90 ms
Delay = 130 ms
Tagging pulse
(Prinzen, Hunter, Zerhouni,1999)
Atrial pacing Function:
LBBB: RV pacing
LV free wall pacing
anterior
base
septum
apex
posterior
Prinzen et al, J Am Coll Cardiol, 1999
Distribution of external work in the LV wall(mJ/g) 8
0
0
The CARDIOME ...with many features missing
and no connections to the body
The Whole Heart Contracting
3D Heart with
Excitationcontraction
Electrophysiology &
fibre directions
coupling
spread of excitation
Purine nucleoside and nucleotide regulation
Regional Transport
and Metabolism
Regional
Blood Flows
This is an old version, outdated:
See Hunter’s site: www.esc.auckland.ac.nz
Reneman
N.Smith, P. Hunter,et al. 1998
Glycolysis Function:
Substrate and
oxygen flow
Cardiac anatomy
and mechanics
TCA cycle
Ion pumping
Fatty acid metabolism
Phosphoenergetics
Excitatory spread
Crossbridge kinetics and energetics
Dynamic changes
in rates of expression
of contractile proteins,
enzymes, transporters
Excitationcontraction coupling
Multicomponent modelsof cardiac function and remodelingATP Function:
Ltype
Jxfer
calmodulin
Winslow et al, C.R.1999
subspace
RyR
calseq
calmodulin
ATP
ATP
Basis for the Cardiac Action PotentialICa,b
INa,Ca
Ip(Ca)
ICa,K
ICa,Na
Na+
Ca2+
Ca2+
Ca2+
K+
Na+
Luo, Rudy, C.R. 1994
ICa
Ttubule
K+
IK
[Na+]
[K+]
Ca2+
JMgxfer ,JCaADPxfer,JCaATPxfer
K+
Mg2+
IK1
ATP
Ca2+
JCaADPxfer,JCaATPxfer
ADP
K+
IKp
Mg2+
Jrel
ATP
Ca2+
JSR
Ca2+
ADP
Michailova McCulloch, Bioph.J.’01
Ins
TRPN
Ca2+
Jtr
K+
Na+
NSR
Jleak
Jup
Ca2+
Na+
Na+
Na+
Sarcoplasmic reticulum
K+
INa,K
INa
INa,b
ATP Function:
ATP
ATP
The sustainable cardiac muscle cellINaCa
ICa,b
Ip(Ca)
ICa,K
Substrates
Ca2+
Ca2+
Ca2+
Na+
K+
Glucose,
Fatty acid.
ICa
Ttubule
K+
IKr
NADH, NADPH,
ATP, PCR,
pH.
Osmolarity
charge.
K+
subspace
OxPhosph
Ca2+
IKs
TCA
K+
RyR
IK1
CalsequestrinCa
K+
IKp
Ca2+
Ca2+
CaCalmodulin
K+
Ito1
Sarcoplasmic
reticulum
Leak
Calsequestrin
Na+
Ca2+
Na+
Na+
Na+
(LuoRudy ‘94’01; Winslow et
al. ’99’00; Michailova ’01)
K+
H+
INaK
INa
INa,b
^ Function:
PET, MID, and NMR Purine Expts.(Guyton et al., 1972) Function:
Circulatory Dynamics: Center of Guyton Scheme(One doesn’t build a truck out of quarks.)
(Guyton et al., 1972)
(Guyton et al., 1972)
permeation, p pressure:s
S
E
S
P
P
high ps
Flux SP
low ps
Log [S]
Sources of dynamical behaviorHow can such information be pressure:put together to allow predictionof the results of intervention?How does one approach developing a therapy?(Most drugs block the function of a protein. But …. most genetic diseases are due to absence of a protein.)
Hypothesis
Quantitative
Hypothesis
= Model
Expt
Design
Experiment
Data
Solutions
Comparison
No
Rethink, remodel,
Redesign, redo!
OK?
Yes
Unproven but
not disproven
Hypothesis >
Working Hypothesis
XSIM insight
Information Flow in Physiological Analysis: Data AnalysisHypothesis
Systems of Equations
Observations
Solutions
XSIM is a general tool for
simulation and modeling
analysis of data: displays
while computing, finds
sensitivities, optimizes,
shows residuals,
finds parameters values and
confidence limits.
Eliminates separate graphing,
optimizing, stat.evaluation.
Comparisons, &
Characterization
Working Hypothesis
Predictions
Hypothesis
Observations
Systems of Equations
JSIM
Solutions
JSIM is a general tool
for taking sets of equations,
(algebraic, ODE, PDE, etc.)
parameter sets, i.c.’s and
b.c.’s, translating into code,
compiling and delivering to
XSIM or JSIM front end
to test model versus data.
Eliminates coding of Eqs.
Comparisons, &
Characterization
XSIM
Working Hypothesis
Predictions
math example1 { // simple ODEs Formulation
// This is a linear, constantparameter, tworegion model:
import nsrunit; unit conversion on;
realDomain t sec; t.min =0; t.max=200; t.delta=0.5; // time
real
Fp = 1.0 cm^3/(g*min), //Flow
V1 = 0.07 cm^3/g, //Plasma volume
PS= 3 cm^3/(g*min),//Permeability
V2=0.15 cm^3/g; //ISF volume
extern real Cin(t) mM; // external input
real C1(t), C2(t) mM; // conc’n in regions
when (t=0) { // initial conditions
C1 = 0;
C2 = 0;
} //end of initial conditions
// ODEs
C1:t = (Fp/V1)*(CinC1) – (PSg/V1)*(C1C2);
C2:t =(PS/V2)*(C1C2);
} //end of program
Note the use of unit conversion. Unit specification asks the parser to identify imbalances of units, and allows also conversion of units such as ergs to g.cm2.sec2 so that units may be defined either way.
Fp
Cin
C1
V1
C1
PS
V2
C2
JSIM v1.1:An example programy Formulation
y
x
Simple
System
y = f(x)
x
y = f(x,z)
Fn Gen requires line search and interpolation,
so direct computation can be as fast or faster.
x
y
Moderate
System
z
permeation, ps
high ps
S
Flux SP
E
low ps
S
P
P
Log [S]
Fn Gen requires 2dimensional search and interpolation, and iff
the local system is effectively in instantaneous steady state, then
direct computation may be almost as fast, and is more accurate.
Use Function Generators for Speed?x Formulationi
y
Complex
System
y = f (N variables)
i =1,N
Function Generators for Speed?Fn Gen requires Ndimensional search and interpolation, or
Ndimensional table lookup, but if direct computation requires
solutions to ODE’s or PDE’s or many algebraic calculations,
then the use of the function generator approach is faster.
P
Phosphocreatine
Creatine
GlucoseISF
Glycogen
CreatineKinase
Glycogen Phosphorylase
ADP
ATP
Glucose1P
Glucosecell
Phosphoglucomutase
AdenylateKinase
Glucose6P
ATP
Phosphoglucoseisomerase
ADP
ADP
AMP
Hexokinase
Fructose6P
Pi
ATP
Phosphofructokinase
ADP
ATPase
Fructose 1,6diP
ATP
1
DihydroxyacetoneP
Aldolase
Triose phosphate isomerase
Glyceraldehyde3P
1
2 NAD + 2 Pi

Glyceraldehyde3P Dehydrogenase
Glycolysis Summary:
DGlucose + 2 ADP3 + 2 Pi2
2 LLactate + 2 ATP4
2 NADH
1,3Diphosphoglycerate
2
2 ADP
Phosphoglycerate Kinase
2 ATP
3Phosphoglycerate
2
Glycogenolysis Summary:
(Glucose)n + 3 ADP3 + 3 Pi2 + H+
(Glucose)n1 + 2 LLactate + 3 ATP4
Phosphoglycerate Mutase
2Phosphoglycerate
2
Enolase
Phosphoenolpyruvate
2
2 ADP
Glucose to glycogen to glycolysis Summary:
DGlucose + ADP3 + Pi2
2 LLactate + ATP4
Pyruvate Kinase
2 ATP
Pyruvate
2
2 NADH
Lactate Dehydrogenase
2 NAD
Lactate
2
Glucose Formulation
2 pyruvate
Glycolysis
rate
2 ADP
2 ATP
2 Pi
Function generators vs. stoichiometric relationships?Using stoichiometry
is even faster:
Using stoichiometric relationships ignores kinetic
considerations, individual reaction rates, regulatory steps,
and the time required for binding and reaction. It also misses
accounting for the capacitance of a reaction network, and is
therefore unsuited for tracer kinetic and transient analysis.
But it is good for steady state analysis of large networks.
P
dCi/dt = Sij.vj  bi
where C = vector of substrate concentrations,
v = vector of reaction velocities, fluxes,
b = vector of net transport out of the system,
and S = Sm,n matrix of stoichiometric coefficients.
m = no. of metabolites, i=1,m
n = no. of reactions or fluxes, j=1,n.
In steady state: Sij.vj = b
In a closed system without synth. or degrad., b = 0.
Glucose models
f.a.
pyr
2 pyr
Glycolysis
rate
3NADH
2 ADP
2 ATP
2CO2
2 Pi
Oxidative
Phosph.
TCA
turnover
acylCoA
GTP
FADH2
(+ pentose shunt path for NADPH)
(+ ana and cataplerotic paths)
11 ADP
O2
ADP
ATP
ATP turnover
PCr buffering
2 Pi
3NADH
11 ATP
PCr
Cr
FADH2
ATPase rates:
(phosphorylation,
contraction,
pumps, etc.)
Core of Intermediary Metabolism for a Muscle CellGlucose models
f.a.
pyr
2 pyr
Glycolysis
rate
3NADH
2 ADP
2 ATP
2CO2
2 Pi
Oxid
Phosph.
TCA
turnover
acylCoA
GTP
FADH2
(+ pentose shunt path for NADPH)
(+ ana and cataplerotic paths)
11 ADP
O2
ADP
ATP
ATP turnover
PCr buffering
3NADH
11 ATP
2 Pi
PCr
FADH2
Cr
ATPase rates:
(phosphorylation,
contraction,
pumps, etc.)
Intermediary Metabolism and Energetics in Steady StateGlucose
CO2
O2
Fatty Ac.
H2O
(Not quite true, but a good approximation)