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BMED 3510 Multi-Scale Models The Heart as Example Book Chapter 12 What Does “Multi-Scale” Mean? Length, Time, and Functional Scales years mosquitos days human cells hours minutes seconds bacteria, parasites human organs ecosystems Heart large molecules, viruses Calcium small milliseconds molecules 1nm 1mm 1mm 1cm 1m 1km Issues Different “players” at different levels Number of players large at each level Combinatorial explosion if all lower levels are retained in detail E.g., number of molecules involved in heart function is enormous. Not feasible to describe the function, aging, and diseases of the heart by accounting for all molecular processes all the time. Most relevant in physiology: Physiome Project (http://physiomeproject.org/) Current “Solutions” Focus on one or two levels Use only one (most appropriate) time scale 3 Separation of Time Scales Implementation (Theoretically) start with large system with many variables All very slow processes are considered constant (dX / dt = 0) All very fast processes are assumed to be in steady state (dX / dt = 0) Retain only processes at just the right time scale of interest 4 Different Models of the Same Subject Examples Light: Light as wave or light as “corpuscles” (little particles) Heart: Pump Big muscle Oscillator Chemical system (Ion flow) Electrical system Very many examples, not just of organs, but: Cancer, infectious diseases, inflammation, ecosystems, … 5 Stats of the Heart Amazing facts Was (is?) thought to be the location of love and emotions, no “broken brain” Size of a fist; weighs about half a pound Moves blood through a network of about 60,000 miles of arteries, veins and capillaries Pumps over 7,000 liters of blood per day Beats roughly 100,000 times every day Beats 2 to 3 billion times in a normal life time Miss a few beats in a row: game over! 6 The Heart as a Peristaltic Pump http://www.dovercorporation.com/Image%20Library/DoverCorpImages/articles-engineered-systems/Abaque-Pump7 components.jpg?code=3cf4e99f-b1e7-46d3-b28e-d9fd9931a89d, http://www.thevintnervault.com/category/435/Peristaltic-Pumps.html The Heart as a Very Sophisticated Pump Actually: Two pumps that drive different portions of the circulation of blood (to the lungs; to the rest of the body) In contrast to almost all engineered pumps: Sensitive and adaptable to momentary needs Constantly adjusts influx – efflux in response to demands Adjustments are “autonomous” Increasing the venous blood input to the ventricle stretches the ventricular wall, enhances contractility, and elevates the diastolic pressure and volume of the ventricle, which in turn leads to an increased stroke volume Very complicated fluid dynamics Long-term adaptation possible 8 The Heart as a Muscle Systems 9 www.helicalheart.com/index_files/h3.gif; www.knowyourbody.net/wp-content/uploads/2012/06/Papillary-muscle-Picture.gif The Heart as a Muscle Systems 10 The Heart as a Muscle Systems Imagine what it would take to develop a dynamic model describing the heart on the basis of contraction and relaxation of myofibrils! 11 The Heart as an Chemical Systems Repeated contraction and relaxation of heart cells associated with: Periodic movement of calcium ions between three locations: extracellular fluid cytosol, and intracellular sarcoplasmic reticulum (SR) 12 The Heart as an Chemical Systems 13 The Heart as an Chemical Systems 1. Electrical signal: influx of sodium; small amount of calcium flows from the extracellular space into the cytosol 2. Calcium triggers a mechanism called calcium-induced calcium release: results in the flow of large amounts of calcium from the SR into cytosol 3. Calcium binds to troponin; leads to sliding action of the myfibrils actin and myosin 4. Myocyte contracts 5. Calcium unbinds and is pumped back into the SR; cell relaxes. 14 The Heart as an Electrical Systems Normal heart beat Electrical signals that start from the Sinoatrial node (SA node) Move to the Atrioventricular Node (AV node). Moves down the Bundle of His in the septum and Purkinje fibers. Electrical signal causes contraction first of the atrium and then the ventricles. 15 The Heart as an Electrical Systems Normal heart beat Electrical signals that start from the Sinoatrial node (SA node) Move to the Atrioventricular Node (AV node). Moves down the Bundle of His in the septum and Purkinje fibers. Electrical signal causes contraction first of the atrium and then the ventricles. 16 Rhythm of the Electrical System PR Segment QRS Complex ST Segment PR Interval 1 mV QT Interval 0 0.2 0.4 0.6 Time (sec) 0.8 17 http://www.austincc.edu/apreview/PhysText/Cardiac.html; WikiCommons File ECG-PQRST+popis.svg The Electrical System Oscillates Contraction and relaxation switch off regularly: Oscillations Why do we see different oscillatory patterns in an EKG? 18 Myocardial Infarction Problems in electro-chemical activity lead to fibrillation Many possible reasons, including genetics 19 Myocardial Infarction 20 http://thevirtualheart.org/FentonCherry/Newecg_n_vt_vf.s2.gif Heart Models: Pure Math (x y 1) x y 0 2 2 3 2 3 (x 2 (9 / 4)y 2 z 2 1)3 x 2 z 3 (9 /80)y 2 z 3 0 3 x , y , z 3 21 Modeling a Peristaltic Pump Instantaneous volumetric flow rate: Pressure drop: 22 Linear Oscillator Models 23 Nonlinear Oscillator Models Limit Cycle Model of van der Pol (1928) v k (1 v 2 )v v 0 Write as two first-order ODEs: w k (1 v 2 ) w v vw 24 Nonlinear Oscillator Models Flexible Alternative for Limit Cycles: S-system models (Yin and Voit; 2008) X 1 2.5 ( X 26 X 13 X 23.2 ) X 2 1.001 2.5 (1 X 15 X 23 ) X 1 1.005 ( X 28 X 17 X 25 ) X 2 X 16 X 25 X 11 X 24 25 Toward Fibrillation S-system model B, “poked” with a sine function (spurious signal with frequency A) A=0 A = 10 26 Toward Fibrillation A = 0.5 A = 0.42 27 Toward Fibrillation A = 0.4 A = 0.394 28 Calcium Flow 29 Calcium Flow Model rEC y = [Ca2+]cyt ctSC f(y) pCS rSC x = [Ca2+]SR x pCS y rSC ( x y) ct SC y rEC rSC ( x y) ct SC pCE yh ( x y) h h K y yh ( x y) pCE y pCS y h h K y 30 Models of Action Potentials Hodgkin and Huxley (1952) showed that an action potential can be modeled as an electrical circuit Important difference to electrical circuits The lipid bilayer ~ capacitance (Cm) Voltage-gated and leak ion channels ~ nonlinear (gn) and linear (gL) conductances Electrochemical gradients driving the flow of ions ~ batteries (E) Ion pumps and exchangers ~ current sources (Ip). 31 File:Hodgkin-Huxley.svg Models of Action Potentials dn n (v)(1 n) n (v)n dt dm m (v)(1 m) m (v)m dt dh h (v)(1 h) h (v)h dt Voltage (mV) 100 45 -10 0 10 20 time [msec] Voltage (mV) 100 + calcium oscillation model 45 -10 0 40 time (msec) 80 32 Heart Disease Numerous causes Aging, stress, hereditary factors Always molecular events involved Need to span the gap from genes and ions to malfunctioning physiology 33 Multi-Scale Heart Disease Raymond Winslow’s group (Johns Hopkins) connected: specific gene mutation to malfunction of dyad to malfunction of calcium release to formation to spiral waves to fibrillation 34 Summary of Heart Chapter Multi-scale models pose an unsolved problem Current approaches: Isolated models at different levels Bridging two levels Mesoscopic models as starting points Template-and-anchor models (coarse high-level template models; fine-grained anchor models of selected details) Hybrid agent-based models with dynamic (ODE) submodels 35 Frontiers of Systems Biology Modeling Needs Data pipelines Automation of translation from biology to models Multi-scale modeling More effective hybrid modeling (e.g., ODE + ABM for spatial features and stochasticity) Improved guidelines for choosing optimal mathematical formats Parameter estimation Theory of biology (why?) 36 Frontiers of Systems Biology The Brain Several hundred cell types in human brain 100 billion neuronal components 100s of trillions of interconnections between neurons Multi-scale combination of electrical and chemical activities within complex anatomy Emerging features such as cognition, learning, memory, consciousness Start with Caenorhabditis elegans with 959 somatic cells and 302 neurons? 37 Frontiers of Systems Biology The Immune System Actually two systems: innate and adaptive (acquired) immune systems Complex generation of cells responding to new agents like pathogens Huge variability in antibodies Confusing system of cytokines Immunological memory Inflammatory and autoimmune diseases Immunodeficiency, cancer 38 Frontiers of Systems Biology The Immune System 39 Frontiers of Systems Biology Metapopulations Usually microbial Examples: Gut, skin, oral cavity; soil, lakes, moist environments Often thousands of species (definition of species in question) Complicated biofilms; quorum sensing Unclear how important rare species are Species compete for resources and depend on each other Most species cannot be cultured in the lab, so how can we study them? 40 Frontiers of Systems Biology Whole cell models Account for all types of molecules Markus Covert’s group (Stanford): “A whole-cell computational model predicts phenotype from genotype,” Cell 150, 2012 Very simple cell (Mycoplasma genitalium) Fifteen person-years to construct this model Our Hope in BMED 3510 …is that: You have learned how to approach complexity in biology with computational means You recognize that all biological components are parts of systems You realize that our intuition is not sufficient to analyze complex systems, even if they are fairly small You have started to see the biological world with different eyes 42 Wrap-Up Please: Participate in CIOS Be constructive Send us emails with additional suggestions Send problems with the book Good Luck with the Final!
