1. Multiscale Modeling in Biology Scientific Computing and Numerical Analysis Seminar CAAM 699

2. Outline Biology and Mathematical Biology Multiscale Modeling Strategies Example 1: The Heart Example 2: Cancer Example 3: Intestinal Edema

3. Biology The study of life is extremely complex Biologists have become highly specialized in their fields Fields are divided by scales: – Molecular Biology – Cell Biology – Organism Biology – Population Biology

4. Mathematical Biology Biology, science based on observation, experiment and data Mathematical modeling of biology is a newer field of research Improvements in computer power made simulations of complex biological systems possible Mathematical Biology now utilized for understanding and prediction

5. Multiscale Modeling Math. Biology also sliced into distinct scales Models created for particular scale of interest Finer scale processes often govern processes seen at coarser scales and vice versa One scale models quite sophisticated Multiscale Modeling: combining models from different scales, still in its early stages of development

6. Multiscale Modeling Strategies Assuming Quasi-Equilibrium: – Microscopic Scale, fast process – Macroscopic Scale, slow process – Assume quasi-equilibrium of micro – Use info in constitutive laws at macro scale Example: Complex Fluid (Ren, 2005) – Constitutive Law: Momentum Flux Equation – Microscopic Level: Molecular Dynamics used on fluid particles to estimate viscous stress for macro

7. Multiscale Modeling Strategies Time Splitting: – Microscopic Scale, slow process – Macroscopic Scale, fast process – Split the simulation into two time scales Example: Thrombus Development (Xu, 2008) – Fast, macroscopic blood flow solved first – Used as boundary conditions for slow thrombus growth, modeled by Cellular Potts model (accumulation of cells via probabilities)

8. Multiscale Modeling Strategies In all strategies the common goal is to create constitutive laws and continuum-level equations of a biological system, whose parameters are computed from finer scale models of the system Microscopic Continuum

9. Example 1: The Heart The Heart – Physical Scale: 10 cm = 10 -1 m http://www.healthcentral.com/heart- disease/what-is-heart-disease-000003_1- 145.html

10. Example 1: The Heart Artery Physical Scale: mm = 10 -3 m Red Blood Cell Physical Scale: μm = 10 -6 m http://www.pennmedicine.org/health_in fo/bloodless/000209.html http://www.fi.edu/learn/heart/blood/red.html

11. Modeling ISR Coronary Artery Disease: Accumulation of plaque in the arteries Treatment: place a metal stent in artery to keep it open, blood flowing In-Stent Restinosis (ISR): build-up of new cells in the area where initial problem was Goal is to prevent ISR from occurring in patients

12. Example 1: ISR Scale of Interest: – Physical Scale: Cell to Artery (micron to cm) – Time Scale: Seconds to Months Processes of Interest: – Initial injury due to stent – Platelet aggregation – Red blood cell Thrombus formation – Cell cycle, cell signaling – Blood Flow – Drug Diffusion

13. Modeling ISR Visual Map of Processes and Scales

14. Modeling ISR Single Process Models are available Integration done using a coupling computer program (COAST) Example Simulation:

15. Example 2: Cancer Destructive disease, develops through complex interactions between genetics, cell mechanics and environmental factors Processes in Cancer Development: – Genetic mutations – Overcoming normal cell death processes – Tumor growth Multiple scales exist in each of these processes: focus on cell death: apoptosis

16. Animal Cell Image from: www.cellsalive.com

17. The Cellular Components Organelles: nucleus, mitochondria, endoplasmic reticulum Cytosol: Fluid within the cell, has an internal overpressure 20-200 Pa over ambient http://www.enchantedlearning.com /subjects/animals/cell/

18. The Cellular Components Cytoskeleton: mesh of cross-linked actin filaments, which can be contracted by myosin II Membrane: Lipid bilayer covering the cell cortex; it has folds and ruffles to allow for shape changes Alberts, Molecular Biology of the Cell http://www.dreamingintechnicolor.com/IdeaLab/

19. Actin-Myosin Myosin filaments are intertwined with the actin filaments in the cytoskeleton When activated, myosin II attaches itself to two actin filaments and pulls them inward Alberts, Molecular Biology of the Cell

20. Apoptosis During apoptosis cells break down into fragments that are then taken in by phagocytes (garbage collecting cells) Triggered/Inhibited by toxins, hormones, stresses, nutrient deprivation, etc

21. Apoptosis The apoptotic pathway, a set of chain reactions involving many proteins that together lead to the degradation of the cell Mechanically: – Cell condensation, Bleb Formation – Cytoskeleton collapses – Nucleus disassembles – Cell breaks into vesicle fragments – Fragments engulfed by phagocytes

22. Blebbing Blebs are balloon-like protrusions Membrane and cytoskeleton become detached, cytosol inflates membrane Charras et al. Nature, May 2005

23. Blebbing Actin cytoskeleton contracts due to myosin II Membrane/Cytoskeleton separate Due to pressure gradients, cytoplasm flows into detached region forcing the membrane outward to form the bleb Fluorescently labeled actin (green) during bleb formation (Charras et al. Nature, May 2005)

24. Scales in this Problem Continuum Level: Cell level – Overall cell deformation due to formation of blebs stems from varying forces on and mechanical properties of membrane, cytosol and cytoskeleton Microscopic Level: Cytoskeleton, cross-linked fiber network – Mechanical response of the network to various local stresses and strains

25. Multiscale Modeling Mechanical properties of they cytoskeleton will vary spatially and with time as the apoptotic process proceeds One cannot use a strictly continuum level equation where the elastic properties are assumed to be homogeneous or static Goal is to couple the continuum model to a microscopic model in order to continuously provide updated info on mechanical parameters

26. Cancer Summary In cancer, the normal apoptotic process does not occur Cancer cells continue to proliferate Choke out the normal, healthy cells Understanding the mechanics to the apoptotic process is one piece to the puzzle of finding a cure for cancer

27. Example 3: Intestinal Edema Intestine: organ that moves food through its tract via peristalsis, coordinated muscle contractions Muscle cells contract by the actin-myosin process Alberts, Molecular Biology of the Cell

28. Example 3: Intestinal Edema Edema is an abnormal accumulation of fluid in the interstitium (cavities between organs, tissues, cells) Normally fluid levels are regulated by the pressure gradients (hydrostatic and osmotic) After a trauma, patients are often given fluids to maintain blood pressure Excess fluid seeps into interstitium

29. Example 3: Intestinal Edema Excess fluid around the muscle cells of the intestine, interrupts peristalsis via mechanotransduction (the conversion of a mechanical signal into a chemical one) Build-up of fluid initiates a pathway that results in the cessation of myosin production Goal is to model intestinal edema to determine a threshold when this pathway is turned on

30. Example 3: Intestinal Edema Physical Scales of Interest: – Macro-scale: Intestine (centimeters) – Micro-scale: Individual cells and chemical ions (microns and nanometers) Time Scales: – Edema Formation: minutes – Signaling Pathway: Seconds, Fractions of Seconds

31. Summary Goal of mathematical biology: understanding and prediction Inclusion of multiple spatial and temporal scales is a MUST for realistic biological models Three examples were presented to give a small taste as to the complexity faced developing multiscale models for these systems

32. References Sloot P and Hoekstra A (2009) “Multi-scale modelling in computational biomedicine”, Briefings in Bioinformatics, Vol II, No. I, p. 142-152 Hegewald J, Krafczyk M, Tolke J, Hoekstra A and Chopard B, (2008) “An Agent-Based Coupling Platform for Complex Automata”, Lectures in Computer Science, Vol 5102, p. 227- 233 Schnell S, Grima R and Maini P, (2007) “Multiscale modeling in biology” American Scientist, Vol 95:2, p. 134-142 Alberts B, Johnson A, Lewis J, Raff M, Roberts K, Walter P, Molecular Biology of the Cell, Garland Science, 1994