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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 l.jpg

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

James B.Bassingthwaighte

University of Washington

Seattle


Physiome and physiome project l.jpg
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 l.jpg
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 l.jpg
The Physiome and the Physiome Project Function:

  • 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 l.jpg
Structure with Function 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 l.jpg
Incentives for Developing the Physiome Function:

  • 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 l.jpg
An example: Function: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?


Electrical activation of the normal heart l.jpg
Electrical activation of the normal heart Function:

Prinzen et al., 2000


Slide9 l.jpg

Schematics of electrical activation Function:

RV apex pacing

left bundle branch block

X

Prinzen et al., 2000


Cardiac fiber structuring lv base lv near the apex l.jpg
Cardiac fiber structuring: Function: LV base LV near the apex

From Torrent-Guasp, 1998


Rabbit heart epicardial fibers blue subendocardial fibers yellow l.jpg
Rabbit Heart: Function:Epicardial fibers – blue Subendocardial fibers - yellow

From Vetter and McCulloch, UCSD


Spread of electrical activation in lbbb and in vf l.jpg
Spread of Electrical Activation Function: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 denis.noble@physiol.ox.ac.uk

  • 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 l.jpg
MRI tagging of Cardiac Contraction Function:

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 l.jpg

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


To explain what is seen in lbbb l.jpg
To explain what is seen Function: 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 l.jpg
The Motor Units Function:

(From Frank

Netter, Ciba)


Integrated modeling of the heart l.jpg
Integrated Modeling of the Heart Function:

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 l.jpg
Integration by Computation: The Cardiome Function:

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 l.jpg
    What are the mechanisms for the responses in Function: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 l.jpg

    Glycolysis Function:

    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 l.jpg

    ATP Function:

    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 l.jpg

    ATP Function:

    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


    Pet mid and nmr purine expts l.jpg

    ^ Function:

    PET, MID, and NMR Purine Expts.


    Circulatory dynamics center of guyton scheme l.jpg

    (Guyton et al., 1972) Function:

    Circulatory Dynamics: Center of Guyton Scheme



    It s the in vivo data that count l.jpg
    It’s the Function: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 l.jpg
    Predictive, Functional Models Function:(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 l.jpg
    A small component of the system for regulation of blood pressure: Interstitial fluid pressure-volume curves

    (Guyton et al., 1972)


    Blood pressure and volume regulation l.jpg
    Blood pressure and volume regulation: pressure:

    (Guyton et al., 1972)


    Nucleosides and nucleotides courtesy of boehringer mannheim l.jpg
    Nucleosides and nucleotides pressure:courtesy of Boehringer-Mannheim


    Sources of dynamical behavior l.jpg

    permeation, p pressure:s

    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 l.jpg

    How 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.)


    The tools systems for integrating information l.jpg
    The Tools - Systems for integrating information: pressure:

    • 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 l.jpg
    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 l.jpg
    Information Flow in Physiological Analysis:1 insight

    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 l.jpg

    XSIM insight

    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 l.jpg
    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 l.jpg

    math example1 { // simple ODEs Formulation

    // 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


    Jsim architecture l.jpg
    JSIM Architecture Formulation


    Jsim implementation l.jpg
    JSIM Formulation Implementation


    Using simulation as a mind expander l.jpg
    Using Simulation as a Mind-expander Formulation

    • 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 l.jpg

    y 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 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 l.jpg

    x Formulationi

    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 l.jpg
    Glycolysis Formulation

    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 l.jpg

    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


    Stoichiometric matrices l.jpg
    Stoichiometric Matrices Formulation

    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 l.jpg
    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 l.jpg
    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 l.jpg

    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 Cell


    Intermediary metabolism and energetics in steady state l.jpg

    Glucose 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 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 l.jpg
    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 l.jpg
    There are new tools for integrating knowledge Physiome Project are to define:

    • 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 l.jpg
    Conclusions: Physiome Project are to define:

    • 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 l.jpg
    Physiome-related Websites Physiome Project are to define:

    • 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 l.jpg
    END Physiome Project are to define:See www.physiome.organdhttp://nsr.bioeng.washington.eduDownload JSIMand try it out.It’s free.