Short Course Mathematical Molecular Biology Bob Eisenberg Shanghai Jiao Tong University Sponsor Zhenli Xu

Transcription

1 u Short Course Mathematical Molecular Biology Bob Eisenberg Shanghai Jiao Tong University Sponsor Zhenli Xu 1

2 Mathematics in Molecular and Cellular Biology Many thanks to Zhenli for inviting me!! Page 2

3 Mathematics in Molecular and Cellular Biology MUST know some elementary biology EASY to learn Compared to the books you all had to memorize in high school, I am told. Certainly EASIER THAN LEARNING AMERICAN ENGLISH Page 3

4 Elementary Material I rather patronize than mystify Few mathematicians know ELEMENTARY chemistry, biochemistry or molecular biology EASY Page 4

5 Biology is made of Devices and they are Multiscale 5

6 Device converts Input to Output by a simple law Device is ROBUST and TRANSFERRABLE because it uses POWER and has complexity! Circuit Diagram of common 741 op-amp: Twenty transistors needed to make linear robust device Power Supply Dirichlet Boundary Condition independent of time and everything else INPU T V in (t) OUTPUT V out (t) Dotted lines outline: current mirrors (red); differential amplifiers (blue); class A gain stage (magenta); voltage level shifter (green); output stage (cyan). Power Supply Dirichlet Boundary Condition independent of time and everything else 6

7 Device Amplifier Converts an Input to an Output V in Gain V out Power Supply 110 v by a simple law an algebraic equation V g V out gain in g gain positive constant real number, like 12 7

8 Device converts an Input to an Output by a simple law V g V out gain in DEVICE IS USEFUL because it is ROBUST and TRANSFERRABLE g gain is Constant!! 8

9 Device Amplifier Converts an Input to an Output V in Gain V out Power Supply 110 v Input, Output, Power Supply are at Different Locations Spatially non-uniform boundary conditions Power is needed Non-equilibrium, with flow Displaced Maxwellian of velocities Provides Flow 9

10 Device Approach to Biology is a Alan Hodgkin friendly Alan Hodgkin: Bob, I would not put it that way 10

11 Engineering is about Device Equations How Describe Biological Devices? P.S. I do not know the answer. But I know how to begin,. I think. 11

12 A few atoms make a BIG Difference Glycine G replaced by Aspartate D Ompf OmpF 1M/1M G119D 1M/1M OmpF 0.05M/0.05M G119D 0.05M/0.05M G119D Current Voltage relation determined by John Tang in Bob Eisenberg s Lab Structure determined by Raimund Dutzler in Tilman Schirmer s lab 12

13 Biological Question How do a few atoms control (macroscopic) Device Function? Mathematics of Molecular Biology is about How the device works In mathspeak: Solving Inverse Problems 13

14 Life is different because it is inherited Page 14

15 Blueprint of Life is DNA = string of genes ONLY the blueprint is inherited Page 15

16 Watson & Crick model of DNA Introduced in DNA is in the form of a regular helix containing two polynucleotide chains connected to each other by hydrogen bonds.

17 Blueprint is shown in many different ways LEARN FROM INTERNET Just search for DNA, Molecular Biology, Proteins and read in Mandarin, I imagine Page 17

18 Watson & Crick Model (DNA is polar) Right handed double helix. Chargaff s base pairing rule. Hydrogen bonding. Antiparallel. Each strand acts as template during replication.

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20 Blueprint can only make PROTEINS Page 20

21 Proteins are a String of Beads that can Make ANYthing including devices and machines Page 21

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24 PRIMARY STRUCTURE The sequence of amino acids MIL1 sequence: >gi ref NP_ MIL1 protein [Homo sapiens] MEDCLAHLGEKVSQELKEPLHKALQMLLSQPVTYQAFRECTLETTVHASGWNKILVPLVLLRQML LELTRLGQEPLSALLQFGVTYLEDYSAEYIIQQGGWGTVFSLESEEEEYPGITAEDSNDIYILPS DNSGQVSPPESPTVTTSWQSESLPVSLSASQSWHTESLPVSLGPESWQQIAMDPEEVKSLDSNGA GEKSENNSSNSDIVHVEKEEVPEGMEEAAVASVVLPARELQEALPEAPAPLLPHITATSLLGTRE PDTEVITVEKSSPATSLFVELDEEEVKAATTEPTEVEEVVPALEPTETLLSEKEINAREESLVEE LSPASEKKPVPPSEGKSRLSPAGEMKPMPLSEGKSILLFGGAAAVAILAVAIGVALALRKK length: 386amino acids Anne-Marie Ternes

25 PRIMARY STRUCTURE The numbers of amino acids vary (e.g. insulin 51, lysozyme 129, haemoglobin 574, gamma globulin 1250) The primary structure determines the folding of the polypeptide to give a functional protein Polar amino acids (acidic, basic and neutral) are hydrophilic and tend to be placed on the outside of the protein. Non-polar (hydrophobic) amino acids tend to be placed on the inside of the protein 2007 Paul Billiet ODWS

26 Infinite variety The number of possible sequences is infinite An average protein has 300 amino acids, At each position there could be one of 20 different amino acids = possible combinations Most are useless Natural selection picks out the best 2007 Paul Billiet ODWS

27 Acid = NEGATIVE (like chloride ion) BASE = POSITIVE (like sodium ion)

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30 TERTIARY STRUCTURE The folding of the polypeptide into domains whose chemical properties are determined by the amino acids in the chain MIL1 protein 2007 Paul Billiet ODWS Anne-Marie Ternes

31 Chain B of Protein Kinase C Max Planck Institute for Molecular Genetics

32 Result Protein structure depends upon the amino acid sequence This, in turn, depends upon the sequence of bases in the gene 2007 Paul Billiet ODWS

33 Multiscale Models of Nerve and Muscle also called Physiology of Nerve and Muscle Page 33

34 From Structure to Function using Fundamental Physical Laws From Anatomy to Physiology using Biophysics & Biochemistry Page 34

35 Multiscale Analysis is also called Physiology Page 35

36 Multiscale MATHEMATICAL Analysis has rarely been possible until now Page 36

37 Multiscale MATHEMATICAL Analysis has rarely been possible until now Except for Nerve Cells Hodgkin, Huxley and Katz Page 37

38 MultiScale Analysis of Nerve Function is more complete than of ANY other cell/tissue in Biology Multiscale Mathematical Analysis is not available for any other tissue or cell, although many are working to change this! Page 38

39 MultiScale Analysis of Nerve Function Multiscale Analysis is Structural. (Almost) all Structures are known and can be described on all scales. Page 39

40 MultiScale Analysis of Nerve Function Multiscale Analysis is physical, as well as mathematical. Physical variables and equations can be used in almost all steps. Description is needed only in one important case, namely gating. Page 40

41 From Structure to Function using Fundamental Physical Laws From Anatomy to Physiology using Biophysics & Biochemistry Page 41

42 PHYSIOLOGY of Nerve and Skeletal Muscle Page 42

43 Skeletal Page 43

44 Neuronal Conduction What is the information signal of a nerve? How does that signal move down a nerve fiber? What are the molecular mechanisms involved? Completely solved in outline Mathematics available Many IMPORTANT problems unsolved Optimization of function Page 44

45 Neuronal Signal Page 45

46 Voltage Signals are Found Throughout Life Page 46

47 Channels Determine Electrical Properties Page 47

48 Resting Potential Set by K Channels Page 48

49 Potential Determined by the Ion with the greatest Conductance Page 49

50 Potential Determined by the Ion with the greatest Conductance Page 50

51 Action Potential Gating Animation Action Potential Page 51

52 Propagation Page 52

53 Propagation Action Potential Propagation Page 53

54 Propagation of Action Potential

55 Myelinated Nerve Propagation Action Potential Propagation Page 55

56 Na Channel Page 56

57 K channel Page 57

58 Reminder: the Action Potential Page 58

59 Na & K channels Gating Animation Action Potential Page 59

60 Skeletal Page 60