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Mathematics in Molecular and Cellular Biology

Mathematics in Molecular and Cellular Biology. Many thanks to Martin Burger for inviting me to his ‘Swan Song’ in Linz!. I am here for Wolfgang Nonner Many thanks to Mike Fill for help with slides. Multiscale Models of Nerve and Muscle. also called Physiology of Nerve and Muscle.

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Mathematics in Molecular and Cellular Biology

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  1. Mathematics in Molecular and Cellular Biology Many thanks to Martin Burgerfor inviting me to his ‘Swan Song’ in Linz! I am here for Wolfgang Nonner Many thanks to Mike Fill for help with slides

  2. Multiscale Models of Nerve and Muscle also called Physiology of Nerve and Muscle

  3. From Structure to Function By Fundamental Physical Laws

  4. From StructureANATOMY to Function PHYSIOLOGY using fundamental physical laws PHYSIOLOGY

  5. What is Multiscale Analysis is also called Physiology

  6. Multiscale MATHEMATICAL Analysishas rarely been possible until now

  7. Multiscale MATHEMATICAL Analysishas rarely been possible until now Except forNerve Cells Hodgkin, Huxley and Katz

  8. Multiscale Mathematical Analysis is not available for any other tissue or cell,although many are working to change this! MultiScale Analysis of Nerve Functionis more complete than of ANY other cell/tissuein Biology

  9. FromAnatomy toPhysiology using Biophysics & Biochemistry From Structure to Function using Fundamental Physical Laws

  10. PHYSIOLOGYof NerveandSkeletal Muscle

  11. Multiscale MATHEMATICAL Analysis of Musclehas not been attemptedbut structures are nearly all known now, so it may be possible

  12. Background Skeletal Cardiac Web Hyperlink EC Coupling Michael Fill, Ph.D., Dept. Physiology, Rush University

  13. Functional unit is the Motor Unit controlled by one neuron Motor Unit has 1 to ~100 muscle cells called muscle fibers Fundamental Contraction of fiber is Twitch Twitch is fast and brief Twitch is controlled by the action potential of the muscle fiber Skeletal Muscle

  14. Dreadful Design UNintelligent Design Nervous control is indirect Fundamental Contraction of fiber is long and slow Fundamental Contraction is controlled by the action potential Cardiac Muscle

  15. Excellent Design Intelligent Design Nervous control is direct Fundamental Contraction of fiber is short Fundamental Contraction is controlled by the action potential Role of myelin Why a synapse? Penalty for synapse Skeletal Muscle

  16. More Background Michael Fill, Ph.D., Dept. Physiology, Rush University

  17. Skeletal & Cardiac Muscle Membrane Systems Skeletal Cardiac Surface T-tube SR Surface T-tube SR Dyad Triad • TT signal triggers release • of Ca ions from the SR • at this junction. This Ca • is what drives muscle • contraction. • Defining the Ca release control • system here is key to … • understanding pathology • devising new therapies SR TT SR SR TT Michael Fill, Ph.D., Dept. Physiology, Rush University

  18. Actin Myosin Contractile System Controlled by Calcium and Troponin and Tropomyosin Michael Fill, Ph.D., Dept. Physiology, Rush University

  19. Dyad What are the components of the Ca release control system? Ca • the SR Ca reservoir • the SR Ca release channel • the TT signal that triggers Ca release • the signal that turns off Ca release • any local regulatory elements SR TT Don’t forget the Calcium Uptake System Don’t forget the Calcium Pump and Malignant Hyperthermia Michael Fill, Ph.D., Dept. Physiology, Rush University

  20. Dyad What are the components of the Ca release control system? Ca • the SR Ca reservoir • the SR Ca release channel • the TT signal that triggers Ca release • the signal that turns off Ca release • any local regulatory elements SR TT What are some known parameters? • the SR Ca reservoir (intra SR [Ca] = 1 mM) • the SR Ca release channel (the ryanodine receptor) • the TT signal that triggers Ca release (mediated by DHPR) • the signal that turns off Ca release (not clear yet) • any local regulatory elements (numerous proteins & factors) Michael Fill, Ph.D., Dept. Physiology, Rush University

  21. Dyad Cartoon of the Ca Release control system? Ca DHPR a2 SR TT TT g a1 d PKA AKAP b PP2A PP1 JP-45 Mitsugumin29 Junctophilin1-3 Junctate FKBP12 CaM SR RyR Junctin Triadin Calsequestrin Calsequestrin Ca2+ Michael Fill, Ph.D., Dept. Physiology, Rush University

  22. Dyad Cartoon of the Ca Release control system? Ca DHPR a2 SR TT TT g a1 d This is a complex molecular machine PKA AKAP b PP2A PP1 JP-45 Mitsugumin29 Junctophilin1-3 Junctate FKBP12 CaM SR RyR Junctin Triadin Calsequestrin Calsequestrin Ca2+ Michael Fill, Ph.D., Dept. Physiology, Rush University

  23. Dyad Stripped Down Version of Key Parts Ca DHPR SR TT TT SR RyR Junctin Triadin Calsequestrin Ca2+ Michael Fill, Ph.D., Dept. Physiology, Rush University

  24. Cardiac & Skeletal have Same Parts However, each part is tissue specific (i.e. different isoforms) Cardiac Case: Skeletal Case: DHPR-2 DHPR-1 TT SR RyR-2 RyR-1 Junctin-2 Junctin-1 Triadin-2 Triadin-1 CSQ-2 CSQ-1 Ca2+ Ca2+ Michael Fill, Ph.D., Dept. Physiology, Rush University

  25. How do these 2 control systems work? Cardiac Case: Skeletal Case: Ca2+ Ca2+ 100 ms long AP 2 ms long AP TT DHPR-1 DHPR-2 SR RyR-2 RyR-1 Ca2+ Ca2+ CSQ-2 CSQ-1 Ca2+ Ca2+ Michael Fill, Ph.D., Dept. Physiology, Rush University

  26. How do these 2 control systems work? Cardiac Case: Skeletal Case: Ca2+ Ca2+ 100 ms long AP 2 ms long AP DHPR-1 DHPR-2 DHPR loop conformation change Ca2+ influx RyR-2 RyR-1 Ca2+ Ca2+ CSQ-2 CSQ-1 Ca2+ Ca2+ Michael Fill, Ph.D., Dept. Physiology, Rush University

  27. How do these 2 control systems work? Cardiac Case: Skeletal Case: Ca2+ Ca2+ 100 ms long AP 2 ms long AP TT DHPR-1 DHPR-2 DHPR loop conformation change Ca2+ influx Ca2+ Release Ca2+ Release SR RyR-2 RyR-1 Ca2+ Ca2+ CSQ-2 CSQ-1 Ca2+ Ca2+ Michael Fill, Ph.D., Dept. Physiology, Rush University

  28. How do these 2 control systems work? Cardiac Case: Skeletal Case: Ca2+ Ca2+ DHPR-1 DHPR-2 DHPR loop conformation returns to normal and this turns off system Ca2+ influx ends here but this does not turn off this system Ca feedback here Ca2+ Release RyR-2 RyR-1 Ca2+ Ca2+ unbinding from CSQ as SR empties Ca2+ CSQ-2 CSQ-1 Ca2+ Ca2+ Michael Fill, Ph.D., Dept. Physiology, Rush University

  29. How do these 2 control systems work? Cardiac Case: Skeletal Case: Ca2+ Ca2+ DHPR-1 DHPR-2 Ca2+ Release RyR-2 RyR-1 Ca2+ Ca2+ unbinding CSQ causes sonformation changes Ca2+ CSQ-2 CSQ-1 Ca2+ Ca2+ Michael Fill, Ph.D., Dept. Physiology, Rush University

  30. How do these 2 control systems work? Cardiac Case: Skeletal Case: Ca2+ Ca2+ DHPR-1 DHPR-2 Low SR Ca2+ sensed by CSQ is what turns off this system RyR-2 RyR-1 Ca2+ Ca2+ CSQ-2 CSQ-1 Ca2+ Ca2+ Michael Fill, Ph.D., Dept. Physiology, Rush University

  31. Some Experimental Evidence: Skeletal Case • EM of the TT-SR jucntion • Short 2 ms Action Potential • Extracellular Ca entry not needed in skeletal muscle • ( the classic frog muscle Ringer story plus data like below ) Ca2+ 2 ms long AP (from a Franzini- Armstrong review) TT DHPR-1 microelectrode measurements in rat cells (text book figure) SR RyR-1 Voltage clamped frog skeletal fiber with all surface membrane channels blocked either by drugs or ion substitution. No extracellular Ca present. (from E. Rios review) Ca2+ CSQ-1 Ca2+ DHPR-mediated charge Movement (see Rios & Brum, Nature 325:717-720, 1987) Michael Fill, Ph.D., Dept. Physiology, Rush University

  32. More Experimental Evidence: Skeletal Case DHPR-mediated charge movement (more info) Ca2+ 2 ms long AP • Evidence Charge • Movement is important • Moves over right Vm range • Blocking it blocks contraction • Enhancing it promotes • muscle contraction TT DHPR-1 DHPR loop conformation change Evidence its mediated by the DHPR Dysgenic muscles lacking DHPR has no charge movement & does not contract. DHPR mutations alter charge movement DHP’s bind to DHPR and modify contraction Ca2+ Release SR RyR-1 Ca2+ Evidence DHPR loop is important. Muscle with mutant DHPR missing the loop do not have EC coupling. CSQ-1 Ca2+ Michael Fill, Ph.D., Dept. Physiology, Rush University

  33. More Experimental Evidence: Skeletal Case • Rynodine receptor is SR Ca release channel Ca2+ 2 ms long AP Low Ca2+ (1 µM) Same plus Caffeine TT DHPR-1 DHPR loop conformation change Ca2+ Release 4 pA 2 s SR RyR-1 Ca2+ CSQ-1 Ca2+ Michael Fill, Ph.D., Dept. Physiology, Rush University

  34. More Experimental Evidence: Skeletal Case • Rynodine receptor is SR Ca release channel • TT voltage changes terminates Ca release Ca2+ Low Ca2+ (1 µM) Same plus Caffeine DHPR-1 AP over....DHPR conformation returns to normal and this turns off system 4 pA 2 s RyR-1 Ca2+ Cai Transient CSQ-1 Vm step Ca2+ Michael Fill, Ph.D., Dept. Physiology, Rush University

  35. This is where modeling of this system stands Provided by E. Rios. Michael Fill, Ph.D., Dept. Physiology, Rush University

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