1. September 2005 Center for Computational Visualization Institute of Computational and Engineering Sciences Department of Computer Sciences University of Texas at Austin Lecture 7: Multiscale Bio-Modeling and Visualization Cell Structures: Membrane and Intra-Cellular Molecule Models (NMJ) Chandrajit Bajaj http://www.cs.utexas.edu/~bajaj

2. September 2005 Center for Computational Visualization Institute of Computational and Engineering Sciences Department of Computer Sciences University of Texas at Austin Molecules of the Cell

3. September 2005 Center for Computational Visualization Institute of Computational and Engineering Sciences Department of Computer Sciences University of Texas at Austin Bacterial Cell

4. September 2005 Center for Computational Visualization Institute of Computational and Engineering Sciences Department of Computer Sciences University of Texas at Austin Functions performed by Cells Chemical – e.g. manufacturing of proteins Information Processing – e.g. cell recognition of friend or foe

5. September 2005 Center for Computational Visualization Institute of Computational and Engineering Sciences Department of Computer Sciences University of Texas at Austin Neuromuscular Junction (NMJ) http://fig.cox.miami.edu/~cmallery/150/neuro/neuromuscular-sml.jpg Movie!

6. September 2005 Center for Computational Visualization Institute of Computational and Engineering Sciences Department of Computer Sciences University of Texas at Austin Cells of the Central Nervous System Figure 8-3 Anatomic and functional categories of neurons

7. September 2005 Center for Computational Visualization Institute of Computational and Engineering Sciences Department of Computer Sciences University of Texas at Austin How do Nerve Cells Function ?

8. September 2005 Center for Computational Visualization Institute of Computational and Engineering Sciences Department of Computer Sciences University of Texas at Austin Axonal transport of membranous organelles

9. September 2005 Center for Computational Visualization Institute of Computational and Engineering Sciences Department of Computer Sciences University of Texas at Austin Synapse Dendrite receives signals Terminal buttons release neurotransmitter Terminal button pre-synaptic Dendrite post synaptic

10. September 2005 Center for Computational Visualization Institute of Computational and Engineering Sciences Department of Computer Sciences University of Texas at Austin Membrane Proteins Ligand Gated channels bind neurotransmitters Voltage gated channels propagate action potential along the axon

11. September 2005 Center for Computational Visualization Institute of Computational and Engineering Sciences Department of Computer Sciences University of Texas at Austin

12. September 2005 Center for Computational Visualization Institute of Computational and Engineering Sciences Department of Computer Sciences University of Texas at Austin Neurotransmitters Released from the terminal buttons Bind to ligand gated receptors on the post-synaptic membrane Can excite or repress electrical activity in neuron

13. September 2005 Center for Computational Visualization Institute of Computational and Engineering Sciences Department of Computer Sciences University of Texas at Austin Electrical Excitation Excitatory neurotransmitters in brain such as Glutamate released from terminal button, bind ligand gated post synaptic ionotrophic membrane proteins Opens Ca+ channels and excites the neuron

14. September 2005 Center for Computational Visualization Institute of Computational and Engineering Sciences Department of Computer Sciences University of Texas at Austin All or None If threshold potential reached, the axon hillock generates an action potential Voltage dependent Na and K channels propagate along the axon

15. September 2005 Center for Computational Visualization Institute of Computational and Engineering Sciences Department of Computer Sciences University of Texas at Austin Propagation of an action potential along an axon without attenuation Action potentials are the direct consequence of the properties of voltage-gated cation channels

16. September 2005 Center for Computational Visualization Institute of Computational and Engineering Sciences Department of Computer Sciences University of Texas at Austin Action Potential I

17. September 2005 Center for Computational Visualization Institute of Computational and Engineering Sciences Department of Computer Sciences University of Texas at Austin Action Potential II

18. September 2005 Center for Computational Visualization Institute of Computational and Engineering Sciences Department of Computer Sciences University of Texas at Austin Propagation in Axons The narrow cross-section of axons and dendrites lessens the metabolic expense of carrying action potentials Many neurons have insulating sheaths of myelin around their axons. The sheaths are formed by glial cells. The sheath enables the action potentials to travel faster than in unmyelinated axons of the same diameter whilst simultaneously preventing short circuits amongst intersecting neurons.

19. September 2005 Center for Computational Visualization Institute of Computational and Engineering Sciences Department of Computer Sciences University of Texas at Austin Terminal Buttons Electrical excitation signals the release of neurotransmitters at terminal button Neurotransmitters stored in fused vesicles Release at pre-synaptic membrane by exocytosis

20. September 2005 Center for Computational Visualization Institute of Computational and Engineering Sciences Department of Computer Sciences University of Texas at Austin Chemical synapses can be excitatory or inhibitory Excitatory neurotransmitters open cation channels, causing an influx of Na + that depolarizes the postsynaptic membrane toward the threshold potential for firing an action potential. Inhibitory neurotransmitters open either Cl - channels or K + channels, and this suppresses firing by making it harder for excitatory influences to depolarize the postsynaptic membrane.

21. September 2005 Center for Computational Visualization Institute of Computational and Engineering Sciences Department of Computer Sciences University of Texas at Austin Neuromuscular Junction (NMJ) http://fig.cox.miami.edu/~cmallery/150/neuro/neuromuscular-sml.jpg Movie!

22. September 2005 Center for Computational Visualization Institute of Computational and Engineering Sciences Department of Computer Sciences University of Texas at Austin How do Synapses Occur at the Neuro-Muscular Junction ?

23. September 2005 Center for Computational Visualization Institute of Computational and Engineering Sciences Department of Computer Sciences University of Texas at Austin Biological / Modeling Motivation - NMJ Complex model with intricate geometry, intriguing physiology and numerous applications Many diseases/disorders can be traced back to problems in the Synaptic well –Myasthenia Gravis: muscle weakness –Snake venom toxins: block synaptic transmission Holds the key to understanding numerous biological processes

24. September 2005 Center for Computational Visualization Institute of Computational and Engineering Sciences Department of Computer Sciences University of Texas at Austin Populating the Domain with ≈ 1 million molecules Image from : www.mcell.cnl.salk.edu [5]

25. September 2005 Center for Computational Visualization Institute of Computational and Engineering Sciences Department of Computer Sciences University of Texas at Austin NMJ Multi-Scale Modeling Length Scale –The cell membranes are ≈ Microns –The receptor molecules are ≈ nanometers –The ions are ≈ Angstroms –The packing density is non-uniform Time Scale –The Neurotransmitters diffuse in microseconds –The Ion channels open in milliseconds –The ACh hydrolyzation is in microseconds

26. September 2005 Center for Computational Visualization Institute of Computational and Engineering Sciences Department of Computer Sciences University of Texas at Austin Extracting Domain Information from Imaging data Cellular Membrane Geometry can be extracted (meta- balls) Receptors are concentrated in certain areas along the pots-synaptic membrane Acetyl-Cholinesterase exists in clusters in the synaptic cleft Images from : www.starklab.slu.edu

27. September 2005 Center for Computational Visualization Institute of Computational and Engineering Sciences Department of Computer Sciences University of Texas at Austin Synaptic Cleft Geometry Twin resolution models for the Ce From 14813 vertices and 29622 triangles to 4825 vertices and 9636 triangles (~67% decimation)

28. September 2005 Center for Computational Visualization Institute of Computational and Engineering Sciences Department of Computer Sciences University of Texas at Austin Acetylcholinesterase in Synaptic Cleft Activity Sites

29. September 2005 Center for Computational Visualization Institute of Computational and Engineering Sciences Department of Computer Sciences University of Texas at Austin Activity Sites AchE molecule (PDBID = 1C2B) Cell Membrane Enlarged View Datasets from www.pdb.org and Dr. Bakers groupwww.pdb.org

30. September 2005 Center for Computational Visualization Institute of Computational and Engineering Sciences Department of Computer Sciences University of Texas at Austin Nictonic-Acetyl-Choline Receptor Pentameric Symmetry in AchR molecule (PDBID: 2BG9) Image from Unwin [8]

31. September 2005 Center for Computational Visualization Institute of Computational and Engineering Sciences Department of Computer Sciences University of Texas at Austin AChBP (1I9B.pdb) Active Sites Complementary component Primary Component ACh Binding Site

32. September 2005 Center for Computational Visualization Institute of Computational and Engineering Sciences Department of Computer Sciences University of Texas at Austin Specificity Ion channels are highly specific filters, allowing only desired ions through the cell membrane.

33. September 2005 Center for Computational Visualization Institute of Computational and Engineering Sciences Department of Computer Sciences University of Texas at Austin Populating the Membrane with the molecules NamePDBIDSize ( o A)Weight (kDa) Density (/µm 2 ) Number- Atoms AChE1C2B(58, 65, 58) 160600 - 2500 4172 AChR2BG9(84, 85, 162) 2902500 - 10000 14929 ACh1AKG(13, 22, 13) 13.430000 - 50000 18

34. September 2005 Center for Computational Visualization Institute of Computational and Engineering Sciences Department of Computer Sciences University of Texas at Austin RBF Spline Representations of 3D Maps Local maxima and minima of the original density map Thin-plate spline interpolation with centers at local max & min 1139 centers, 9.55% error (middle); 7649 centers, 7.36% error (right) Original Map RBF Approximation (5891 centers, 7.88% error)

35. September 2005 Center for Computational Visualization Institute of Computational and Engineering Sciences Department of Computer Sciences University of Texas at Austin Fast and Stable Computation of RBF Representation of 3D Maps Interpolate Map with an analytic basis of the form p = polynomial of degree k-1 = Radial basis function (thin-plate spline kernel) Make Coefficients orthogonal to polynomials of degree k-1

36. September 2005 Center for Computational Visualization Institute of Computational and Engineering Sciences Department of Computer Sciences University of Texas at Austin One choice for It minimizes “bending energy”: It is conditional positive definite Memory storage Computational cost Thin-Plate Spline Kernel

37. September 2005 Center for Computational Visualization Institute of Computational and Engineering Sciences Department of Computer Sciences University of Texas at Austin Matrix Form function value at x i, where p i (x) forms a basis for polynomial of degree k-1 coefficients of the RBF kernel at x i

38. September 2005 Center for Computational Visualization Institute of Computational and Engineering Sciences Department of Computer Sciences University of Texas at Austin Matrix A (1065x1065) Condition number = 2.95E+06 (non-positive definite) Poor Conditioning

39. September 2005 Center for Computational Visualization Institute of Computational and Engineering Sciences Department of Computer Sciences University of Texas at Austin Matrix A (1065x1065) Condition number = 2.95E+06 (non-positive definite) Multi Scale matrix after HB wavelet pre-conditioning/sparsification Condition number = 332 (positive definite) Use of Pre-conditioners/Sparsifiers

40. September 2005 Center for Computational Visualization Institute of Computational and Engineering Sciences Department of Computer Sciences University of Texas at Austin Synaptic Cleft Modeling

41. September 2005 Center for Computational Visualization Institute of Computational and Engineering Sciences Department of Computer Sciences University of Texas at Austin NMJ – Physiology: Synaptic Transmission Ach = AcetylCholine, AchE = AcetyleCholinEsetrase, AchR = AcetylCholineReceptor Image from : Smart and McCammon [1]

42. September 2005 Center for Computational Visualization Institute of Computational and Engineering Sciences Department of Computer Sciences University of Texas at Austin Modeling Physiology I : Electrostatics Potential dielectric properties of the solute and solvent, ionic strength of the solution, solute atomic partial charges. Poisson-Boltzmann

43. September 2005 Center for Computational Visualization Institute of Computational and Engineering Sciences Department of Computer Sciences University of Texas at Austin Fas2 meets AChE

44. September 2005 Center for Computational Visualization Institute of Computational and Engineering Sciences Department of Computer Sciences University of Texas at Austin Adaptive Boundary Interior-Exterior Meshes (a) monomer mAChE (b) cavity (c) interior mesh (d) exterior meshes Y. Zhang, C. Bajaj, B. Sohn, Special issue of Computer Methods in Applied Mechanics and Engineering (CMAME) on Unstructured Mesh Generation, 2004.

45. September 2005 Center for Computational Visualization Institute of Computational and Engineering Sciences Department of Computer Sciences University of Texas at Austin AChE Tetramer Conformations

46. September 2005 Center for Computational Visualization Institute of Computational and Engineering Sciences Department of Computer Sciences University of Texas at Austin Model Physiology II Reaction Diffusion Models Time dependent equations to model the diffusion of ACh across the synaptic cleft Initial Condition Boundary Conditions On the domain at the AchR boundaries

47. September 2005 Center for Computational Visualization Institute of Computational and Engineering Sciences Department of Computer Sciences University of Texas at Austin Steady State Smulochowski Equation (Diffusion of multiple particles in a potential field)  -- entire domain  -- biomolecular domain  -- free space in   a – reactive region  r – reflective region  b – boundary for  Diffusion-influenced biomolecular reaction rate constant :

48. September 2005 Center for Computational Visualization Institute of Computational and Engineering Sciences Department of Computer Sciences University of Texas at Austin Active Sites of AChE Y. Song, Y. Zhang, C. Bajaj, N. A. Baker, Biophysical Journal, Volume 87, 2004, Pages 1-9 Y. Song, Y. Zhang, T. Shen, C. Bajaj, J. A. McCammon and N. A. Baker, Biophysical Journal, 86(4):2017-2029, 2004

49. September 2005 Center for Computational Visualization Institute of Computational and Engineering Sciences Department of Computer Sciences University of Texas at Austin Many Next Steps Poisson-Boltzmann equation for electrostatic potential in the presence of a membrane potential, and coarse-grained dynamics Poisson-Nernst-Plank equations for Ion Permeation through Membrane Channels Ion Permeation with coupled Dynamics of Membrane Channels

50. September 2005 Center for Computational Visualization Institute of Computational and Engineering Sciences Department of Computer Sciences University of Texas at Austin More Reading Model Validation : Reaction Diffusion MCell Bartol and Stiles [2001] Continuum models Smart and McCammon [1998] Diffusion Simulations Naka et al [1999]

51. September 2005 Center for Computational Visualization Institute of Computational and Engineering Sciences Department of Computer Sciences University of Texas at Austin How do muscle cells function ?