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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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designing and constructing a set of fundamental cell models application to cardiac disease

Designing and Constructing a Set of Fundamental Cell Models:Application to Cardiac Disease

James B.Bassingthwaighte

University of Washington

Seattle

physiome and physiome project
Physiome and Physiome Project
  • Integrative models of genomic, metabolic, and intact in vivo systems should, via iteration with carefully designed experiments, resolve contradictions among prior observations and interpretations.
  • Comprehensive, accurate and realistic models will demonstrate emergent properties not inherent to the individual components, but apparent in the intact organism.
  • The “reverse engineering” of biology will aid clinical diagnosis and the design and the evaluation of therapy.
  • Databases, concepts, descriptions, and models are best put in the public domain, an open system to foster rapid progress.
  • James B.Bassingthwaighte
  • University of Washington
  • Seattle
slide3
Engineering and reverse engineering the route from Genome to Function:(Integrating Biological Systems Knowledge)

Health

Organism

The Physiome Project

Organ

http://www.physiome.org

Tissue

  • Structure to Function:
  • Experiments, Databases
  • Problem Formulation
  • Engineering the Solutions
  • Quantitative System Modeling
  • Archiving & Dissemination

Cell

Molecule

Genes

the physiome and the physiome project
The Physiome and the Physiome Project
  • The “Physiome” is the quantitative description of the functional behavior of the physiological state of an individual of a species. In its fullest form it should define relationships from organism to genome.
  • The “Physiome Project” is a concerted effort to define the Physiome through databasing and through the development of a sequence of model types: schema of interactions, descriptions of structure and functional relationships, and integrative quantitative modeling for logical prediction and critical projections.
structure with function
Structure with Function
  • The Genome, and the Transcriptome.

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:

  • The physico-chemical status.
  • Schema of interactions between the components. Regulatory apparatus for gene expression and metabolism, etc. Functional models describing all from genes + milieu organism).
incentives for developing the physiome
Incentives for Developing the Physiome
  • To develop understanding of a mechanism or a phenomenon: fundamental science.
  • To determine the most effective targets for therapy, either pharmaceutic or genomic.
  • To design artificial or tissue-engineered, biocompatible implants.
an example the pathophysiology of left bundle branch block in the cardiac conduction system
An example: The Pathophysiology of Left Bundle Branch Block in the Cardiac Conduction System
  • Auscultation: Reverse splitting of the second heart sound
  • ECG: Wide QRS complex, implying asynchronous activation
  • X-ray: Modest cardiac enlargement, septal atrophy and hypertrophy of the LV free wall
  • Thallium scan: Low flow in the septum
  • PET scan: Decreased septal glucose uptake,

but normal septal fatty acid uptake.

How can the observations be explained through regional events at the levels of cell and molecule?

slide9

Schematics of electrical activation

RV apex pacing

left bundle branch block

X

Prinzen et al., 2000

rabbit heart epicardial fibers blue subendocardial fibers yellow
Rabbit Heart: Epicardial fibers – blue Subendocardial fibers - yellow

From Vetter and McCulloch, UCSD

spread of electrical activation in lbbb and in vf
Spread of Electrical Activation in LBBB and in VF
  • Spread of excitation computed from multicell model of action potential was developed by Dennis Noble and colleagues at Oxford, UK in collaboration with Rai Winslow and colleagues at Johns Hopkins University in 1998.
  • See www.bme.jhu.edu/ccmb and [email protected]
  • ECG: Wide QRS complex and often late T wave

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.

mri tagging of cardiac contraction
MRI tagging of Cardiac Contraction

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)

distribution of external work in the lv wall

Atrial pacing

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

to explain what is seen in lbbb
To explain what is seen in LBBB:
  • Thallium scans: Decreased septal blood flow relative to rest of LV is due to reduced local demand. Decreased septal mass is the result of local atrophy. Increased mass of LV free wall is local hypertrophy.
  • PET: Decreased Septal Glucose Uptake: There is a shift away from using glucose as local work is lessened. PET data show normal FA uptake. Regional FA uptake is matched to local flow.
  • X-ray: LV hypertrophy: Hypertrophic free wall due to increased workload and low contractile efficiency. This is partially attributable to increased wall tension with LV cavity volume increase: Tension=Pressure x Radius.
the motor units
The Motor Units

(From Frank

Netter, Ciba)

integrated modeling of the heart
Integrated Modeling of the Heart

The CARDIOME ...with many features missing

and no connections to the body

The Whole Heart Contracting

3-D Heart with

Excitation-contraction

Electrophysiology &

fibre directions

coupling

spread of excitation

Purine nucleoside and nucleotide regulation

Regional Transport

and Metabolism

Regional

Blood Flows

integration by computation the cardiome
Integration by Computation: The Cardiome

This is an old version, outdated:

See Hunter’s site: www.esc.auckland.ac.nz

  • Transport:
      • UW: (Our group) Flows, uptake (O2, fats), nucleotide energetics
  • Cardiac Mechanics:
      • Auckland Univ: P.Hunter
      • UCSD: McCulloch
      • Maastricht: Arts, Prinzen,

Reneman

      • JHU: W.Hunter
  • Action Potentials:
      • Oxford U: D. Noble
      • Johns Hopkins: Winslow
      • Case-Western: Rudy
  • Cardiac excitatory spread:
      • CWRU: Rudy et al.
      • Johns Hopkins: Winslow
      • Syracuse: Jalife
      • UCSD: McCulloch

N.Smith, P. Hunter,et al. 1998

what are the mechanisms for the responses in left bundle branch block
What are the mechanisms for the responses in Left Bundle Branch Block?
  • Thallium scans: How is local flow regulated?
  • PET Glucose Uptake: How is glycolysis regulated?
  • MR Strain Patterns: How do structure, excitation, and contraction combine to produce these?
  • X-ray LV hypertrophy: What regulates actin and myosin expression?
multicomponent models of cardiac function and remodeling

Glycolysis

Substrate and

oxygen flow

Cardiac anatomy

and mechanics

TCA cycle

Ion pumping

Fatty acid metabolism

Phosphoenergetics

Excitatory spread

Cross-bridge kinetics and energetics

Dynamic changes

in rates of expression

of contractile proteins,

enzymes, transporters

Excitation-contraction coupling

Multicomponent modelsof cardiac function and remodeling
basis for the cardiac action potential

ATP

L-type

Jxfer

calmodulin

Winslow et al, C.R.1999

subspace

RyR

calseq

calmodulin

ATP

ATP

Basis for the Cardiac Action Potential

ICa,b

INa,Ca

Ip(Ca)

ICa,K

ICa,Na

Na+

Ca2+

Ca2+

Ca2+

K+

Na+

Luo, Rudy, C.R. 1994

ICa

T-tubule

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

the sustainable cardiac muscle cell

ATP

ATP

ATP

The sustainable cardiac muscle cell

INaCa

ICa,b

Ip(Ca)

ICa,K

Substrates

Ca2+

Ca2+

Ca2+

Na+

K+

Glucose,

Fatty acid.

ICa

T-tubule

K+

IKr

NADH, NADPH,

ATP, PCR,

pH.

Osmolarity

charge.

K+

subspace

OxPhosph

Ca2+

IKs

TCA

K+

RyR

IK1

Calsequestrin-Ca

K+

IKp

Ca2+

Ca2+

Ca-Calmodulin

K+

Ito1

Sarcoplasmic

reticulum

Leak

Calsequestrin

Na+

Ca2+

Na+

Na+

Na+

(Luo-Rudy ‘94-’01; Winslow et

al. ’99-’00; Michailova ’01)

K+

H+

INaK

INa

INa,b

it s the in vivo data that count
It’s the in vivo data that count!
  • The cell is a high-concentration, intricately structured milieu.
  • Enzymes are usually attached to membranes.
  • Behavior inside cells is unlike that in vitro.
  • Bucket-brigade handling of substrates is common.
  • A cell’s behavior depends on its neighbors.
  • Different species have different parameters.
slide27
Predictive, Functional Models(They have to be “complete” with respect to the question or problem to be predictive.)
  • Levels of reduction
  • Classes of Models:
    • Behavioral models
    • Mechanistic models
    • Biophysical and molecular models
  • Dynamical versus steady state models
  • Parts lists suited to the level of reduction.

(One doesn’t build a truck out of quarks.)

slide28
A small component of the system for regulation of blood pressure: Interstitial fluid pressure-volume curves

(Guyton et al., 1972)

sources of dynamical behavior

permeation, ps

S

E

S

P

P

high ps

Flux SP

low ps

Log [S]

Sources of dynamical behavior
  • Non-linearities
  • Delays giving phase lags.
  • High gain feedback
  • Spatial differentiation
  • E.g.: Enzyme sequestration  delayed response and high gain, a “switch”
  • Microcompartments inside cells do this, e.g. G-6-Pase in liver endoplasmic reticulum.
slide32

How can such information beput 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.)

the tools systems for integrating information
The Tools - Systems for integrating information:
  • Data:
    • Databases
    • Search engines
    • Relationships:
      • Charts and diagrams: nodes and edges
      • Quantitation: chemistry and kinetics, equations
  • Models:
    • Parts list or ingredients in the recipe
    • Schema of relationships
    • Qualitative modeling of incomplete systems
    • Equation-based modeling (continuous or stochastic)
  • Strategies:
    • Use sensitivity analysis used in experiment design and analysis
    • Parameterize observations by fitting models to data
    • Use failures to fit the data to improve ideas and models
    • Have alternative hypotheses to aid progress: expt–model–expt loop
modeling tools aids to intuition and the developers of insight
Modeling tools: Aids to intuition and the developers of insight
  • Equation-based and icon-based programming
  • System for modeling analysis of data.
  • Optimization routines for automated data fitting and estimation of parameters and confidence limits.
  • Displays of behavioral analysis to show the changing forms of model solutions with parameter changes.
  • Displays of residuals to show error and bias.
  • Multiple solutions with parameter changes
  • Solutions from multiple models to fit data
  • Simultaneous fitting of multiple data sets by one comprehensive model to reveal and eliminate contradictions.
  • Convenient display of multiple variables.
  • Movies and 2- and 3-D plots of data and model solutions.
  • Monte Carlo tests for model behavior and data fitting.
information flow in physiological analysis 1
Information Flow in Physiological Analysis:1

Hypothesis

Quantitative

Hypothesis

= Model

Expt

Design

Experiment

Data

Solutions

Comparison

No

Rethink, remodel,

Redesign, redo!

OK?

Yes

Unproven but

not disproven

Hypothesis ->

Working Hypothesis

information flow in physiological analysis data analysis

XSIM

Information Flow in Physiological Analysis: Data Analysis

Hypothesis

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

information flow in physiological analysis model formulation
Information Flow in Physiological Analysis: Model Formulation

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

jsim v1 1 an example program
math example1 { // simple ODEs

// This is a linear, constant-parameter, two-region 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)*(Cin-C1) – (PSg/V1)*(C1-C2);

C2:t =(PS/V2)*(C1-C2);

} //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.sec-2 so that units may be defined either way.

Fp

Cin

C1

V1

C1

PS

V2

C2

JSIM v1.1:An example program
using simulation as a mind expander
Using Simulation as a Mind-expander
  • Compute at the speed of thought
  • Adjust parameters manually, quickly
  • Use repetitive operation mode for exploration
  • Change parameters during solutions
  • Control solution speed
  • Show interdependencies with phase plane plots
  • Switch model components on or off
  • Modify the model program rapidly
use function generators for speed

y

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 SP

E

low ps

S

P

P

Log [S]

Fn Gen requires 2-dimensional 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?
function generators for speed

xi

y

Complex

System

y = f (N variables)

i =1,N

Function Generators for Speed?

Fn Gen requires N-dimensional search and interpolation, or

N-dimensional 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

glycolysis
Glycolysis

Phosphocreatine

Creatine

GlucoseISF

Glycogen

CreatineKinase

Glycogen Phosphorylase

ADP

ATP

Glucose-1-P

Glucosecell

Phosphoglucomutase

AdenylateKinase

Glucose-6-P

ATP

Phosphoglucoseisomerase

ADP

ADP

AMP

Hexokinase

Fructose-6-P

Pi

ATP

Phosphofructokinase

ADP

ATPase

Fructose 1,6-diP

ATP

1

Dihydroxyacetone-P

Aldolase

Triose phosphate isomerase

Glyceraldehyde-3-P

1

2 NAD + 2 Pi

-

Glyceraldehyde-3-P Dehydrogenase

Glycolysis Summary:

D-Glucose + 2 ADP3- + 2 Pi2-

2 L-Lactate + 2 ATP4-

2 NADH

1,3-Diphosphoglycerate

2

2 ADP

Phosphoglycerate Kinase

2 ATP

3-Phosphoglycerate

2

Glycogenolysis Summary:

(Glucose)n + 3 ADP3- + 3 Pi2- + H+

(Glucose)n-1 + 2 L-Lactate + 3 ATP4-

Phosphoglycerate Mutase

2-Phosphoglycerate

2

Enolase

Phosphoenolpyruvate

2

2 ADP

Glucose to glycogen to glycolysis Summary:

D-Glucose + ADP3- + Pi2-

2 L-Lactate + ATP4-

Pyruvate Kinase

2 ATP

Pyruvate

2

2 NADH

Lactate Dehydrogenase

2 NAD

Lactate

2

function generators vs stoichiometric relationships

Glucose

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

stoichiometric matrices
Stoichiometric Matrices

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.

applying the stoichiometric matrix idea to sets of reactions
Applying the Stoichiometric Matrix Idea to Sets of Reactions
  • Instead of a matrix of individual reactions, consider a matrix of sets of reactions, in which each node is a set (e.g. TCA, glycolysis) linked to other sets by a finite number of fluxes.
  • The sets should have non-overlapping reactions. Sets are composed of enzymes or transporters, but not substrates (e.g. glucose, ATP, NAD, CO2).
  • Mapping sets of sets summarizes connectivity of large numbers of reactions, parameterizing them describes the functional relationships specifically.
functional metabolic groupings sets and the linking of models
Functional Metabolic Groupings (sets) and the linking of models
  • The core of cell metabolism consists of glycolysis, pentose shunt, TCA, oxidative phosphorylation, ATP synthesis and use.
  • Mass, redox state, free energy, charge, pH, osmolarity must balance within narrow limits.
  • Each “set” (e.g.TCA) has fixed matrix S, but the fluxes can depend on conditions outside of the set.
  • Each set is a submodel, separable from other sets, essential for model development and maintenance.
  • Each submodel may have two forms, dynamical or steady state.
core of intermediary metabolism for a muscle cell

Glucose

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 Cell
intermediary metabolism and energetics in steady state

Glucose

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 State

Glucose

CO2

O2

Fatty Ac.

H2O

(Not quite true, but a good approximation)

the long term goals of the physiome project are to define
The Long Term Goals of the Physiome Project are to define:
  • The generic Human Physiome, and those of other species.
  • The bases for improving therapies:
    • To design gene or multidrug therapy
    • To enhance targeting in drug design
    • To treat the individual patient (while accounting for side effects, when enough is known)
  • The links from genomics to function
  • An individual’s genome/physiome
there are new tools for integrating knowledge
There are new tools for integrating knowledge
  • Better, bigger databases
  • Models summarizing decades of learning
  • New methods of systems analysis:
    • Control analysis in metabolism and physiology
    • Networks of models
  • Large multi-institutional collaborations
  • Public access to models
  • Models should be entries to databases
conclusions
Conclusions:
  • Data should be obtained in vivo if possible.
  • Modeling system should aid thinking and analysis
  • Conservative cell models provide a basis for a host of specific applications.
  • Their behavior is innately complex and highly dependent on the conditions.
  • Computability is a major issue if models are to be used are practical aids to thinking.
  • Even now models do provide short-term prediction of the consequences of intervention.
physiome related websites
Physiome-related Websites
  • www.physiome.org (U.Washington site)
  • www.bme.jhu.edu/news/microphys (microvascular physiome)
  • www.bme.jhu.edu/ccmb (Center for Comp. Med. & Biol.)
  • bionome.sdsc.edu (UCSD cardiome site)
  • biomodel.georgetown.edu/model/ (Model library)
  • nsr.bioeng.washington.edu (Circulatory Transport and Exchange)
  • www.esc.auckland.ac.nz (Hunter group)
  • www.iups2001.org.nz (IUPS 2001 meeting)
  • www.vcell.uconn.edu (Virtual cell)
  • www.cordis.lu (“cell factory”, supported by European Commission)
  • www.genesis.caltech.edu (Genesis, neural modeling)
  • www.chaos.harvard.edu (Ary Goldberger’s site for signal analysis)
end see www physiome org and http nsr bioeng washington edu download jsim and try it out it s free
ENDSee www.physiome.organdhttp://nsr.bioeng.washington.eduDownload JSIMand try it out.It’s free.
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