Molecular mechanisms of long-term memory

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Molecular mechanisms of long-term memory
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LTP an increase in synaptic strength
Long-term potentiation (LTP)
Bliss and Lomo J Physiol, 1973
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LTP an increase in synaptic strength
Long-term potentiation (LTP)
LTP protocol induces postynaptic influx of Ca2
with CaMKII inhibitor or knockout
Postsynaptic current
Time (mins)
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0
Lledo et al PNAS 1995, Giese et al Science 1998
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Calcium-calmodulin dependent kinase II (CaMKII)
One holoenzyme 12 subunits
Kolodziej et al. J Biol Chem 2000
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Model of bistability in the CaMKII-PP1 system
autocatalytic activation and saturating
inactivation.
a) Autophosphorylation of CaMKII (2 rings per
holoenzyme)
P0
P1
slow
P2
P1
fast
Lisman and Zhabotinsky, Neuron 2001
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b) Dephosphorylation of CaMKII by PP1
(saturating inactivation)
E
phosphatase, PP1
k1
k2
k-1
Total rate of dephosphorylation can never exceed
k2.PP1 Leads to cooperativity as rate per
subunit goes down Stability in spite of turnover
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Bistability in total phosphorylation of CaMKII
Ca20.1?M (basal level)
Rate of dephosphoryation
Rate of phosphorylation
Total reaction rate
0
0
No. of active subunits
12N
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Phosphorylation dominates at high calcium
Ca2 2?M (for LTP)
Rate of dephosphoryation
Rate of phosphorylation
Total reaction rate
0
0
No. of active subunits
12N
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The Normal State of Affairs (one stable state,
no bistability)
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How to get bistability
1) Autocatalysis k increases with C 2)
Saturation total rate down, (k-)C, is limited
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Reaction pathways
14 configurations of phosphorylated subunits per
ring
P0 P1 P2 P3 P4 P5 P6
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Phosphorylation to clockwise neighbors
P0 P1 P2 P3 P4 P5 P6
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Phosphorylation to clockwise neighbors
P0 P1 P2 P3 P4 P5 P6
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Random dephosphorylation by PP1
P0 P1 P2 P3 P4 P5 P6
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Random dephosphorylation by PP1
P0 P1 P2 P3 P4 P5 P6
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Random turnover included
P0 P1 P2 P3 P4 P5 P6
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Stability of DOWN state
PP1 enzyme
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Stability of DOWN state
PP1 enzyme
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Stability of DOWN state
PP1 enzyme
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Stability of UP state
PP1 enzyme
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Stability of UP state
PP1 enzyme
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Stability of UP state
PP1 enzyme
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Stability of UP state
PP1 enzyme
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Stability of UP state
PP1 enzyme
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Protein turnover
PP1 enzyme
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Stability of UP state with turnover
PP1 enzyme
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Stability of UP state
PP1 enzyme
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Stability of UP state
PP1 enzyme
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Stability of UP state
PP1 enzyme
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Stability of UP state
PP1 enzyme
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Stability of UP state
PP1 enzyme
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Stability of UP state
PP1 enzyme
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Stability of UP state
PP1 enzyme
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Stability of UP state
PP1 enzyme
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Stability of UP state
PP1 enzyme
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Stability of UP state
PP1 enzyme
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Small numbers of CaMKII holoenzymes in PSD
Petersen et al. J Neurosci 2003
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Simulation methods
Stochastic implementation of reactions, of rates
Ri(t) using small numbers of molecules via
Gillespie's algorithm
1) Variable time-steps, ?t P(?t) ?Ri exp(-?t
?Ri) 2) Probability of specific reaction P(Ri)
Ri/?Ri 3) Update numbers of molecules
according to reaction chosen 4) Update reaction
rates using new concentrations 5) Repeat step 1)
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System of 20 holoenzymes undergoes stable LTP
1
Pulse of high Ca2 here
Fraction of subunits phosphorylated
0
0
10
20
Time (yrs)
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Slow transient dynamics revealed
Fraction of subunits phosphorylated
Time (mins)
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Spontaneous transitions in system with 16
holoenzymes
Fraction of subunits phosphorylated
Time (yrs)
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Spontaneous transitions in system with 4
holoenzymes
Fraction of subunits phosphorylated
Time (days)
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Average lifetime between transitions increases
exponentially with system size
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Large-N limit, like hopping over a potential
barrier
Reaction rates
Effective potential
12N
No. of active subunits
0
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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
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Why is this important?
Transition between states loss of
memory Transition times determine memory decay
times.
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Something like physics
Barrier height depends on area between rate
on and rate off curves, which scales with
system size.
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Physics analogy barriers with noise ...
Inherent noise because reactions take place one
molecule at a time.
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 )
?
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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 pN
time to wait increases as (1/p)N expN.ln(1/p)
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Change of concentration ratios affects balance
between UP and DOWN states.
System of 8 CaMKII holoenzymes
9 PP1 enzymes
7 PP1 enzymes
Phosphorylation fraction
Time (yrs)
Time (yrs)
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Optimal system lifetime is a trade-off between
lifetimes of UP and DOWN states
10 yrs
DOWN state lifetime
1 yr
UP state lifetime
Average lifetime of state
1 mth
1 day
Number of PP1 enzymes
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Optimal system lifetime is a trade-off between
lifetimes of UP and DOWN states
10 yrs
DOWN state lifetime
1 yr
UP state lifetime
Average lifetime of state
1 mth
1 day
Number of PP1 enzymes
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Analysis Separate time-scale for ring switching
In stable UP state
Preceding a switch down
Turnover
Turnover
No. of active subunits, single ring
Total no. of active subunits
Time (hrs)
Time (hrs)
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(No Transcript)
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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.
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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, rn, and off, r-n. 8)
Continue with new value of n.
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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, rn, and off, r-n. 8)
Continue with new value of n.
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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, rn, 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, rn, 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, rn, 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, rn, 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, rn, and off, r-n. 8)
Continue with new value of n.
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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, rn, and off, r-n. 8)
Continue with new value of n.
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Analysis Solve 1D model exactly
rn-1
rn1
rn
N1
N0
n1
n-1
n
n2
r-n2
r-n1
r-n
Time to hop from N0 to N1
Use rn Tn 1 r-n1Tn1 for N0 n lt N1
rn Tn r-n1Tn1 for n lt N0
Tn 0 for n N1 Average total time for
transition, Ttot ?Tn
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Optimal system lifetime is a trade-off between
lifetimes of UP and DOWN states
10 yrs
DOWN state lifetime
1 yr
UP state lifetime
Average lifetime of state
1 mth
1 day
Number of PP1 enzymes
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Optimal system lifetime is a trade-off between
lifetimes of UP and DOWN states
10 yrs
DOWN state lifetime
1 yr
UP state lifetime
Average lifetime of state
1 mth
1 day
Number of PP1 enzymes