Chandrajit Bajaj cs.utexas/~bajaj

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

33. Populating the Membrane with the molecules Center for Computational Visualization Institute of Computational and Engineering Sciences Department of Computer Sciences University of Texas at Austin

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

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

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

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

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

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

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

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

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

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

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

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

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

47. 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 : Center for Computational Visualization Institute of Computational and Engineering Sciences Department of Computer Sciences University of Texas at Austin

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

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

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