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

1. Designing and Constructing a Set of Fundamental Cell Models:Application to Cardiac Disease James B.Bassingthwaighte University of Washington Seattle

2. 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

3. 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

4. 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.

5. 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).

6. 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.

7. 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?

8. Electrical activation of the normal heart Prinzen et al., 2000

9. Schematics of electrical activation RV apex pacing left bundle branch block X Prinzen et al., 2000

10. Cardiac fiber structuring: LV base LV near the apex From Torrent-Guasp, 1998

11. Rabbit Heart: Epicardial fibers – blue Subendocardial fibers - yellow From Vetter and McCulloch, UCSD

12. 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 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.

13. 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)

14. 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

15. 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.

16. The Motor Units (From Frank Netter, Ciba)

17. 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

18. 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

19. 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?

20. 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

21. 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

22. 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

23. ^ PET, MID, and NMR Purine Expts.

24. (Guyton et al., 1972) Circulatory Dynamics: Center of Guyton Scheme

25. BTEX for nucleosides/-tides

26. 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.

27. 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.)

28. A small component of the system for regulation of blood pressure: Interstitial fluid pressure-volume curves (Guyton et al., 1972)

29. Blood pressure and volume regulation: (Guyton et al., 1972)

30. Nucleosides and nucleotides courtesy of Boehringer-Mannheim

31. 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.

32. 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.)

33. 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

34. 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.

35. 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

36. 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

37. 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

38. 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

39. JSIM Architecture

40. JSIM Implementation

41. 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

42. 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?

43. 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

44. 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

45. 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

46. 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.

47. 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.

48. 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.

49. 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

50. 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)