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Molecular mechanisms of long-term memory Spine Shaft of Dendrite Axon Presynaptic Postsynaptic Synapse PSD.

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Presentation on theme: "Molecular mechanisms of long-term memory Spine Shaft of Dendrite Axon Presynaptic Postsynaptic Synapse PSD."— Presentation transcript:

1 Molecular mechanisms of long-term memory Spine Shaft of Dendrite Axon Presynaptic Postsynaptic Synapse PSD

2 LTP: an increase in synaptic strength Long-term potentiation (LTP) Time (mins) 0 60 Postsynaptic current LTP protocol induces postynaptic influx of Ca 2+ Bliss and Lomo J Physiol, 1973

3 LTP: an increase in synaptic strength Long-term potentiation (LTP) Time (mins) 0 60 Postsynaptic current LTP protocol induces postynaptic influx of Ca 2+ Lledo et al PNAS 1995, Giese et al Science 1998 with CaMKII inhibitor or knockout

4 Calcium-calmodulin dependent kinase II (CaMKII) One holoenzyme = 12 subunits Kolodziej et al. J Biol Chem 2000

5 Model of bistability in the CaMKII-PP1 system: autocatalytic activation and saturating inactivation. P0 P1 P2 slow fast a) Autophosphorylation of CaMKII (2 rings per holoenzyme): Lisman and Zhabotinsky, Neuron 2001

6 E = phosphatase, PP1 b) Dephosphorylation of CaMKII by PP1 (saturating inactivation) k2k2 k1k1 k -1 Total rate of dephosphorylation can never exceed k 2.[PP1] Leads to cooperativity as rate per subunit goes down Stability in spite of turnover

7 Bistability in total phosphorylation of CaMKII 0 12N No. of active subunits Total reaction rate 0 Rate of phosphorylation Rate of dephosphoryation [Ca 2+ ]=0.1  M (basal level)

8 Phosphorylation dominates at high calcium 0 12N No. of active subunits Total reaction rate 0 Rate of phosphorylation Rate of dephosphoryation [Ca 2+ ] = 2  M (for LTP)

9 The “Normal” State of Affairs (one stable state, no bistability)

10 How to get bistability 1) Autocatalysis: k+ increases with [C] 2) Saturation: total rate down, (k-)[C], is limited

11 Reaction pathways 14 configurations of phosphorylated subunits per ring P0 P1P2 P3 P4 P5 P6

12 Phosphorylation to clockwise neighbors P0 P1P2 P3 P4 P5 P6

13 Phosphorylation to clockwise neighbors P0 P1P2 P3 P4 P5 P6

14 Random dephosphorylation by PP1 P0 P1P2 P3 P4 P5 P6

15 Random dephosphorylation by PP1 P0 P1P2 P3 P4 P5 P6

16 Random turnover included P0 P1P2 P3 P4 P5 P6

17 Stability of DOWN state = PP1 enzyme

18 Stability of DOWN state = PP1 enzyme

19 Stability of DOWN state = PP1 enzyme

20 Stability of UP state = PP1 enzyme

21 Stability of UP state = PP1 enzyme

22 Stability of UP state = PP1 enzyme

23 Stability of UP state = PP1 enzyme

24 Stability of UP state = PP1 enzyme

25 Protein turnover = PP1 enzyme

26 Stability of UP state with turnover = PP1 enzyme

27 Stability of UP state = PP1 enzyme

28 Stability of UP state = PP1 enzyme

29 Stability of UP state = PP1 enzyme

30 Stability of UP state = PP1 enzyme

31 Stability of UP state = PP1 enzyme

32 Stability of UP state = PP1 enzyme

33 Stability of UP state = PP1 enzyme

34 Stability of UP state = PP1 enzyme

35 Stability of UP state = PP1 enzyme

36 Stability of UP state = PP1 enzyme

37 Small numbers of CaMKII holoenzymes in PSD Petersen et al. J Neurosci 2003

38 Stochastic implementation of reactions, of rates R i (t) using small numbers of molecules via Gillespie's algorithm: 1) Variable time-steps, ∆t: P(∆t) = ∑R i exp(-∆t ∑R i ) 2) Probability of specific reaction: P(R i ) = R i /∑R i 3) Update numbers of molecules according to reaction chosen 4) Update reaction rates using new concentrations 5) Repeat step 1) Simulation methods

39 Time (yrs) Fraction of subunits phosphorylated Pulse of high Ca 2+ here System of 20 holoenzymes undergoes stable LTP

40 Time (mins) Fraction of subunits phosphorylated Slow transient dynamics revealed

41 Spontaneous transitions in system with 16 holoenzymes Time (yrs) Fraction of subunits phosphorylated

42 Spontaneous transitions in system with 4 holoenzymes Time (days) Fraction of subunits phosphorylated

43 Average lifetime between transitions increases exponentially with system size

44 Large-N limit, like hopping over a potential barrier 0 12N No. of active subunits Reaction rates Effective potential

45 1) Chemical reactions in biology: x-axis = “reaction coordinate” = amount of protein phosphorylation 2) Networks of neurons that “fire” action potentials: x-axis = average firing rate of a group of neurons

46 Why is this important? Transition between states = loss of memory Transition times determine memory decay times.

47 Something like physics Barrier height depends on area between “rate on” and “rate off” curves, which scales with system size.

48 Physics analogy: barriers with noise... Rate of transition over barrier decreases exponentially with barrier height... (like thermal physics, with a potential barrier, U and thermal noise energy proportional to kT ) Inherent noise because reactions take place one molecule at a time. ?

49 General result for memory systems Time between transitions increases exponentially with scale of the system. Scale = number of molecules in a biochemical system = number of neurons in a network Rolling dice analogy: number of rolls needed, each with with probability, p to get N rolls in row, probability is p N time to wait increases as (1/p) N = exp[N.ln(1/p)]

50 Change of concentration ratios affects balance between UP and DOWN states. System of 8 CaMKII holoenzymes: Time (yrs) Phosphorylation fraction 7 PP1 enzymes 9 PP1 enzymes

51 Number of PP1 enzymes Average lifetime of state 10 yrs 1 yr 1 mth 1 day Optimal system lifetime is a trade-off between lifetimes of UP and DOWN states UP state lifetime DOWN state lifetime

52 Number of PP1 enzymes Average lifetime of state 10 yrs 1 yr 1 mth 1 day Optimal system lifetime is a trade-off between lifetimes of UP and DOWN states UP state lifetime DOWN state lifetime

53 Analysis: Separate time-scale for ring switching Turnover Preceding a switch down In stable UP state Time (hrs) Total no. of active subunits No. of active subunits, single ring Turnover

54

55 Analysis: Separate time-scale for ring switching Goal Rapid speed-up by converting system to 1D and solving analytically. Method Essentially a mean-field theory. Justification Changes to and from P0 (unphosphorylated state) are slow.

56 Analysis: Project system to 1D 1) Number of rings “on” with any activation, n. 2) Assume average number, P, of subunits phosphorylated for all rings “on”. 3) Calculate reaction rates for one ring, assuming contibution of others is (n-1)P. 4) Calculate average time in configurations with these reaction rates. 5) Hence calculate new value of P. 6) Repeat Step 2 until convergence. 7) Calculate rate to switch “on”, r + n, and “off”, r - n. 8) Continue with new value of n.

57 Analysis: Project system to 1D 1) Number of rings “on” with any activation, n. 2) Assume average number, P, of subunits phosphorylated for all rings “on”. 3) Calculate reaction rates for one ring, assuming contibution of others is (n-1)P. 4) Calculate average time in configurations with these reaction rates. 5) Hence calculate new value of P. 6) Repeat Step 2 until convergence. 7) Calculate rate to switch “on”, r + n, and “off”, r - n. 8) Continue with new value of n.

58 Analysis: Project system to 1D 1) Number of rings “on” with any activation, n. 2) Assume average number, P, of subunits phosphorylated for all rings “on”. 3) Calculate reaction rates for one ring, assuming contibution of others is (n-1)P. 4) Calculate average time in configurations with these reaction rates. 5) Hence calculate new value of P. 6) Repeat Step 2 until convergence. 7) Calculate rate to switch “on”, r + n, and “off”, r - n. 8) Continue with new value of n.

59 Analysis: Project system to 1D 1) Number of rings “on” with any activation, n. 2) Assume average number, P, of subunits phosphorylated for all rings “on”. 3) Calculate reaction rates for one ring, assuming contibution of others is (n-1)P. 4) Calculate average time in configurations with these reaction rates. 5) Hence calculate new value of P. 6) Repeat Step 2 until convergence. 7) Calculate rate to switch “on”, r + n, and “off”, r - n. 8) Continue with new value of n.

60 Analysis: Project system to 1D 1) Number of rings “on” with any activation, n. 2) Assume average number, P, of subunits phosphorylated for all rings “on”. 3) Calculate reaction rates for one ring, assuming contibution of others is (n-1)P. 4) Calculate average time in configurations with these reaction rates. 5) Hence calculate new value of P. 6) Repeat Step 2 until convergence. 7) Calculate rate to switch “on”, r + n, and “off”, r - n. 8) Continue with new value of n.

61 Analysis: Project system to 1D 1) Number of rings “on” with any activation, n. 2) Assume average number, P, of subunits phosphorylated for all rings “on”. 3) Calculate reaction rates for one ring, assuming contibution of others is (n-1)P. 4) Calculate average time in configurations with these reaction rates. 5) Hence calculate new value of P. 6) Repeat Step 2 until convergence. 7) Calculate rate to switch “on”, r + n, and “off”, r - n. 8) Continue with new value of n.

62 Analysis: Project system to 1D 1) Number of rings “on” with any activation, n. 2) Assume average number, P, of subunits phosphorylated for all rings “on”. 3) Calculate reaction rates for one ring, assuming contibution of others is (n-1)P. 4) Calculate average time in configurations with these reaction rates. 5) Hence calculate new value of P. 6) Repeat Step 2 until convergence. 7) Calculate rate to switch “on”, r + n, and “off”, r - n. 8) Continue with new value of n.

63 Analysis: Project system to 1D 1) Number of rings “on” with any activation, n. 2) Assume average number, P, of subunits phosphorylated for all rings “on”. 3) Calculate reaction rates for one ring, assuming contibution of others is (n-1)P. 4) Calculate average time in configurations with these reaction rates. 5) Hence calculate new value of P. 6) Repeat Step 2 until convergence. 7) Calculate rate to switch “on”, r + n, and “off”, r - n. 8) Continue with new value of n.

64 Analysis: Solve 1D model exactly Time to hop from N 0 to N 1 Use: r + n T n = 1 + r - n+1 T n+1 for N 0 ≤ n < N 1 r + n T n = r - n+1 T n+1 for n < N 0 T n = 0 for n ≥ N 1 Average total time for transition, T tot = ∑T n N0N0 N1N1 n n+1 n-1 n+2 r - n+1 r+nr+n r - n+2 r-nr-n r + n-1 r + n+1

65 Number of PP1 enzymes Average lifetime of state 10 yrs 1 yr 1 mth 1 day Optimal system lifetime is a trade-off between lifetimes of UP and DOWN states UP state lifetime DOWN state lifetime

66 Number of PP1 enzymes Average lifetime of state 10 yrs 1 yr 1 mth 1 day Optimal system lifetime is a trade-off between lifetimes of UP and DOWN states UP state lifetime DOWN state lifetime


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