Overview of Heart Models

Designing and Constructing a Set of Fundamental Cell Models: Application to Cardiac Disease James B.Bassingthwaighte University of Washington Seattle 23jul01: http://nsr.bioeng.washington.edu NLM7.01 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 23jul01: http://nsr.bioeng.washington.edu NLM7.01 Engineering and reverse engineering the route from Genome to Function: (Integrating Biological Systems Knowledge) Organism The Physiome Project http://www.physiome.org Health Organ Tissue Cell Molecule Genes Structure to Function: • Experiments, Databases • Problem Formulation • Engineering the Solutions • Quantitative System Modeling • Archiving & Dissemination NLM7.01 23jul01: http://nsr.bioeng.washington.edu 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. 23jul01: http://nsr.bioeng.washington.edu NLM7.01 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). 23jul01: http://nsr.bioeng.washington.edu NLM7.01 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. 23jul01: http://nsr.bioeng.washington.edu NLM7.01 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? 23jul01: http://nsr.bioeng.washington.edu NLM7.01 Electrical activation of the normal heart sinus node left atrium His bundle AV node bundle branches right ventricle Purkinje fibers Prinzen et al., 2000 23jul01: http://nsr.bioeng.washington.edu NLM7.01 Schematics of electrical activation RV apex pacing left bundle branch block X Prinzen et al., 2000 23jul01: http://nsr.bioeng.washington.edu NLM7.01 Cardiac fiber structuring: LV base From Torrent-Guasp, 1998 LV near the apex 23jul01: http://nsr.bioeng.washington.edu NLM7.01 Rabbit Heart: Epicardial fibers – blue Subendocardial fibers - yellow From Vetter and McCulloch, UCSD 23jul01: http://nsr.bioeng.washington.edu NLM7.01 Spread of Electrical Activation in LBBB and in VF 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. 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 denis.noble@physiol.ox.ac.uk and 23jul01: http://nsr.bioeng.washington.edu NLM7.01 MRI tagging of Cardiac Contraction Pacing spike ECG ... Preset. pulse 50ms 90ms 130ms ... Gx RF Delay = 50 ms Delay = 90 ms Delay = 130 ms Tagging pulse (Prinzen, Hunter, Zerhouni,1999) 23jul01: http://nsr.bioeng.washington.edu NLM7.01 Distribution of external work in the LV wall Atrial pacing LBBB: RV pacing . LV free wall pacing (mJ/g) 8 anterior . . septum * posterior * 0 0 Prinzen et al, J Am Coll Cardiol, 1999 F ib e r s tre s s F ib e r s tre s s 23jul01: http://nsr.bioeng.washington.edu Fiber length F ib er s tre s s Fiber length Fiber length NLM7.01 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. 23jul01: http://nsr.bioeng.washington.edu NLM7.01 The Motor Units (From Frank Netter, Ciba) 23jul01: http://nsr.bioeng.washington.edu NLM7.01 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 fibre directions Excitation-contraction coupling Electrophysiology & spread of excitation Purine nucleoside and nucleotide regulation Regional Transport and Metabolism Regional Blood Flows 23jul01: http://nsr.bioeng.washington.edu NLM7.01 Integration by Computation: The Cardiome • 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 This is an old version, outdated: See Hunter‟s site: www.esc.auckland.ac.nz • 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 23jul01: http://nsr.bioeng.washington.edu NLM7.01 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? 23jul01: http://nsr.bioeng.washington.edu NLM7.01 Multicomponent models of cardiac function and remodeling Substrate and Cardiac anatomy oxygen flow Glycolysis and mechanics Ion pumping Phosphoenergetics Fatty acid metabolism TCA cycle Dynamic changes in rates of expression of contractile proteins, enzymes, transporters NLM7.01 Excitatory spread Cross-bridge kinetics and energetics Excitation-contraction coupling 23jul01: http://nsr.bioeng.washington.edu Basis for the Cardiac Action Potential ICa,b ICa,K ICa,Na Na+ ATP INa,Ca Ip(Ca) Luo, Rudy, C.R. 1994 T-tubule ICaL-type Ca2+ Mg2+ Ca2+ RyR Ca2+ K+ Na+ [Na+] Ca2+ [K+] Ca2+ K+ IK IK1 IKp Ins Na+ Winslow et al, C.R.1999 Michailova McCulloch, Bioph.J.’01  calmodulin ATP ADP subspace calseq Ca2+ Jrel Jxfer JMgxfer , JCaADPxfer, JCaATPxfer JCaADPxfer, JCaATPxfer Mg2+ ATP Ca2+ K+ K+ JSR NSR Jtr Ca2+  ADP calmodulin TRPN Ca2+ J Jup ATP leak Na+ ATP K+ Na+ Sarcoplasmic reticulum Na+ K+ INa,K 23jul01: http://nsr.bioeng.washington.edu INa INa,b NLM7.01 The sustainable cardiac muscle cell ICa,b ICa,K Substrates INaCa Ip(Ca) ATP Ca2+ T-tubule ICa subspace K+ Glucose, Fatty acid. Na+ Ca2+ NADH, NADPH, ATP, PCR, pH. Osmolarity charge. Ca2+ K + + IKr IKs IK1 IKp Ito1 Ca2+ RyR OxPhosph TCA K K + Calsequestrin-Ca Ca2+ K + Ca2+ Sarcoplasmic reticulum Calsequestrin Leak Ca-Calmodulin K + ATP Ca2+ Na+ Na+ ATP Na+ Na+ (Luo-Rudy „94-‟01; Winslow et al. ‟99-‟00; Michailova ‟01) 23jul01: http://nsr.bioeng.washington.edu H+ K + INaK INa INa,b NLM7.01 PET, MID, and NMR Purine Expts. ^ 23jul01: http://nsr.bioeng.washington.edu NLM7.01 (Guyton et al., 1972) Circulatory Dynamics: Center of Guyton Scheme 23jul01: http://nsr.bioeng.washington.edu NLM7.01 BTEX for nucleosides/-tides 23jul01: http://nsr.bioeng.washington.edu NLM7.01 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. 23jul01: http://nsr.bioeng.washington.edu NLM7.01 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.) 23jul01: http://nsr.bioeng.washington.edu NLM7.01 A small component of the system for regulation of blood pressure: Interstitial fluid pressure-volume curves (Guyton et al., 1972) 23jul01: http://nsr.bioeng.washington.edu NLM7.01 Blood pressure and volume regulation: (Guyton et 23jul01: http://nsr.bioeng.washington.edu al., 1972) NLM7.01 Nucleosides and nucleotides courtesy of Boehringer-Mannheim 23jul01: http://nsr.bioeng.washington.edu NLM7.01 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. S permeation, ps S E P P Flux SP high ps low ps Log [S] 23jul01: http://nsr.bioeng.washington.edu NLM7.01 How can such information be put together to allow prediction of 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.) 23jul01: http://nsr.bioeng.washington.edu NLM7.01 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) 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 NLM7.01 • Strategies: 23jul01: http://nsr.bioeng.washington.edu 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. 23jul01: http://nsr.bioeng.washington.edu NLM7.01 Information Flow in Physiological Analysis:1 Hypothesis Expt Design Quantitative Hypothesis = Model Solutions Experiment Data Comparison OK? No Yes Hypothesis -> 23jul01: http://nsr.bioeng.washington.edu Rethink, remodel, Redesign, redo! Unproven but not disproven NLM7.01 Working Hypothesis Information Flow in Physiological Analysis: Data Analysis Hypothesis Observations Systems of Equations Solutions XSIM XSIM is a general tool for simulation and modeling Comparisons, & analysis Characterization of data: displays while computing, finds sensitivities, optimizes, Working Hypothesis residuals, shows finds parameters values and confidence limits. PredictionsEliminates separate graphing, optimizing, stat.evaluation. 23jul01: http://nsr.bioeng.washington.edu NLM7.01 Information Flow in Physiological Analysis: Model Formulation Hypothesis Observations Systems of Equations Solutions JSIM JSIM is a general tool Comparisons, & XSIM for taking sets of equations, Characterization (algebraic, ODE, PDE, etc.) parameter sets, i.c.‟s and b.c.‟s, Working Hypothesis translating into code, compiling and delivering to XSIM or JSIM front end Predictions to test model versus data. Eliminates coding of Eqs. 23jul01: http://nsr.bioeng.washington.edu NLM7.01 JSIM v1.1: An example program Cin Fp V1 PS C1 C1 extern real Cin(t) mM; real C1(t), C2(t) mM; when (t=0) { C1 = 0; // external input // conc’n in regions // initial conditions V2 C2 C2 = 0; } // ODEs C1:t = (Fp/V1)*(Cin-C1) – (PSg/V1)*(C1-C2); C2:t =(PS/V2)*(C1-C2); //end of initial conditions math example1 { // simple ODEs // This is a linear, constant-parameter, two-region model: import nsrunit; unit conversion on; } //end of program realDomain t sec; t.min =0; t.max=200; t.delta=0.5; // time real Fp = 1.0 PS= 3 cm^3/(g*min), //Flow V1 = 0.07 cm^3/g, V2=0.15 cm^3/g; //Plasma volume //ISF volume 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. cm^3/(g*min),//Permeability 23jul01: http://nsr.bioeng.washington.edu NLM7.01 JSIM Architecture 23jul01: http://nsr.bioeng.washington.edu NLM7.01 JSIM Implementation 23jul01: http://nsr.bioeng.washington.edu NLM7.01 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 NLM7.01 23jul01: http://nsr.bioeng.washington.edu Use Function Generators for Speed? y = f(x) x Simple System y y x Fn Gen requires line search and interpolation, so direct computation can be as fast or faster. S permeation, ps Flux SP y = f(x,z) S E P x z P Moderate System y high ps low ps 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. 23jul01: http://nsr.bioeng.washington.edu NLM7.01 Function Generators for Speed? y = f (N variables) xi i =1,N Complex System y 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, P then the use of the function generator approach is faster. 23jul01: http://nsr.bioeng.washington.edu NLM7.01 Glycolysis Phosphocreatine Creatine Creatine Kinase GlucoseISF Glucosecell ATP ADP Glycogen Glycogen Phosphorylase ADP ATP Adenylate Kinase Glucose-1-P Phosphoglucomutase Phosphoglucoseisomerase Phosphofructokinase Glucose-6-P Fructose-6-P ATP ADP ADP Pi ATPase AMP Hexokinase Fructose 1,6-diP 1 Dihydroxyacetone-P Triose phosphate isomerase ATP Aldolase 1 Glyceraldehyde-3-P 2 NAD + 2 Pi 2 NADH 2 ADP 2 ATP Glycolysis Summary: D-Glucose + 2 ADP3- + 2 Pi2-  2 L-Lactate + 2 ATP4- Glyceraldehyde-3-P Dehydrogenase Phosphoglycerate Kinase Phosphoglycerate Mutase Enolase - 2 1,3-Diphosphoglycerate 2 3-Phosphoglycerate 2 2-Phosphoglycerate 2 ADP 2 ATP Glycogenolysis Summary: (Glucose)n + 3 ADP3- + 3 Pi2- + H+ (Glucose)n-1 + 2 L-Lactate + 3 ATP4Glucose to glycogen to glycolysis Summary: D-Glucose + ADP3- + Pi2-  2 L-Lactate + ATP4- 2 Phosphoenolpyruvate Pyruvate Kinase Lactate Dehydrogenase 2 2 Pyruvate 2 NAD 2 NADH Lactate NLM7.01 23jul01: http://nsr.bioeng.washington.edu Function generators vs. stoichiometric relationships? Using stoichiometry is even faster: Glucose 2 ADP 2 Pi Glycolysis rate 2 pyruvate 2 ATP Using stoichiometric relationships ignores kinetic considerations, individual reaction rates, regulatory steps, and the time required for binding and reaction. It also misses P 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. 23jul01: http://nsr.bioeng.washington.edu NLM7.01 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. 23jul01: http://nsr.bioeng.washington.edu NLM7.01 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. 23jul01: http://nsr.bioeng.washington.edu NLM7.01 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. 23jul01: http://nsr.bioeng.washington.edu NLM7.01 Core of Intermediary Metabolism for a Muscle Cell Glucose 2 ADP 2 Pi pyr Glycolysis rate f.a. TCA turnover 2 pyr 2 ATP 3NADH acylCoA 2CO2 GTP FADH2 (+ pentose shunt path for NADPH) (+ ana- and cataplerotic paths) 11 ADP O2 3NADH FADH2 Oxidative Phosph. ATP 11 ATP PCr ATP turnover PCr buffering ATPase rates: (phosphorylation, contraction, pumps, etc.) ADP 2 Pi Cr 23jul01: http://nsr.bioeng.washington.edu NLM7.01 Intermediary Metabolism and Energetics in Steady State Glucose 2 ADP Glucose O2 Fatty Ac. Glycolysis rate 2 pyr 2 ATP pyr 2 Pi 3NADH 2CO2 TCA acylCoA GTP turnover FADH2 (+ ana- and cataplerotic paths) f.a. (+ pentose shunt path for NADPH) CO2 H2O 11 ADP ATP O2 3NADH FADH2 PCr Oxid Phosph. 11 ATP ATP turnover PCr buffering ATPase rates: (phosphorylation, contraction, pumps, etc.) 2 Pi Cr ADP (Not quite true, but a good approximation) 23jul01: http://nsr.bioeng.washington.edu NLM7.01 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 23jul01: http://nsr.bioeng.washington.edu NLM7.01 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 23jul01: http://nsr.bioeng.washington.edu NLM7.01 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. 23jul01: http://nsr.bioeng.washington.edu NLM7.01 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) 23jul01: http://nsr.bioeng.washington.edu NLM7.01 END See www.physiome.org and http://nsr.bioeng.washington.edu Download JSIM and try it out. It‟s free. 23jul01: http://nsr.bioeng.washington.edu NLM7.01