Calcium dynamics in dendritic spine and spine motility

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Calcium dynamics in dendritic spine and spine
motility
David Holcman Dept. of mathematics, Weizmann
Institute of Science
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Collaborators

• E. Korkotian, Weizmann Institute of Science
• M Segal, Weizmann Institute of Science
• Z. Schuss, Tel Aviv University

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Harris
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(No Transcript)
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Spine fast motility
Korkotian et.al, Neuron 2001
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Aims

• Based spine fast motility at a molecular level
• Study calcium dynamics
• Model the coupling between calcium dynamics and
  Spine motility
• Consequence of the model?Computed bonds of Ca
  to molecule, involved in induction of plasticity

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Talk organization
I. Physiological evidence of fast motility -
movement - Spine contents
II. Modeling Calcium dynamics - At a
molecular - a nonlinear effect
III. From model to the simulations comparaison
with experimental data - Time course Ca2
(t)
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I-Physiological evidence of fast motility
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Spine fast motility
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Spine fast contraction
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Fast motility is induced by Ca binding to actin
type molecule
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Spine contents

• Ca sensitive molecule CaM, Buffers,
• Actin, Myosins
• Actin filament
• Channels, Pumps
• Organelles, ER

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Shape of a dentritic
R

• RRadius of the head lt1,5 µ m
• Llength of the neck 0 1,5 µ m
• F0.1, 0.6 µ m

l
?
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Modeling Calcium dynamics
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Langevin dynamics

• Particle X(x,t) follows

• Neglect electrostatic interaction V(x)0
• V(x,t) flow field
• Need to restore binding interactions

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Spine Model

• CaM, Actin Myosin interactions
• Calcineurin
• Pumps
• Absorption of ions at the dendrite site

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Schematic model
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Molecular rules

• When an ion meet a molecule
• Calibration of the radius R
• Mean Time to stay backward binding rate
• (Poisson Process)
• 4 ions at a Actin-Myosin create a drift of
  amplitude

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Dynamics and model of the drift

• Contraction produce a flow field for the free
  ions
• Vhydrodynamical flow due to the cytoplasm
  incompressibility
• N(t)number of molecules containing 4 Ca ions

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Hydrodynamics effect

• Using the Greens function

• K Constant

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Fokker-Planck equations

• Evolution of the concentration

• With boundary conditions

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Time scale

• Hydrodynamic Time scale
• Diffusion Time Scale
• Diffusion and reaction

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Summary

• Nonlinear effectbond calcium induce a
  contraction for free calcium
• Two times scales

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From model to the simulations comparaison with
experimental data
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Ca trajectories
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Simulation of 100 ions
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Post-Synaptic versus Uniform Distribution
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Number of bonds
With push
no push (PSD)
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Comparison with experimental data
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Fast decay time scale
Majewska et.al JNS2001
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Conclusion

• Spine fast motility based at molecular level
• Ca dynamics Double exponential decay
• Hydrodynamics
• Diffusion
• binding
• Contraction effect push the ion toward the
  dendrite.
• No contraction majority of ions pump out
• Fast motility may be imply in targeting important
  organelles.
• Holcman et.al. Biophys, July 2004

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Ability of spine to compartmentalize Calcium

• Aspiny neuron have micro-structures
• Ca compartmentalizes in dendrite, as in spine
  Goldberg et.al 2003, Neuron
• Role of dendritic spine?

In Collaboration with E Korkotian, M.Segal
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Spine changes geometrical shape

• Spine highly dynamics change shape constantly
  (length of the neck)
• Calcium dynamics
• induction of calcium increase
• Head long/short spine equal
• Dendrite CaLongltlt CaShort

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Spine motility, real time
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Change of Spine shape induced by Ca release

• 1,2 Spines change
• 3 Control

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Morphological changes induced by Glutamate release

• Small Concentration?
• increase in spine length
• Large Concentration?
• decrease in spine length

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Calcium dynamics as a function of the spine length
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Calcium dynamics after shrinkage
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Calcium dynamics after elongation
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Consequences

• Calcium extrusion depend on the spine neck length
• Active processes involved
• Pumps
• Stores
• Exchanges
• Conclusion
• Property of spinedynamically changes the length.
  
• Neck length regulate the number of calcium
  reaching the dendrite
• How calcium dynamics is related to the neck
  length?

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Model calcium extrusion distribution

• Calcium can
• reach the dendrite
• Pumped out
• How to quantify it?
• No quantitative measurements

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Modeling Calcium

• One dimensional model for the neck
• Ca move by diffusion and
• can be absorbed at a pump

Flux through a pump
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Ratio Ca to dendrite/pumped
The flux of the ions arriving at the dendrite is
given by


The total number of ions pumped out is given by

.
The ratio is given by
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Analysis

• In the steady state regime

Asymptotic
Conclusion Predict a sharp transition between
isolate and conducting state
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Transition point

• Critical length
• ? 16.66 and a cutoff length at L1.5 µm
  imposes that Np 20.
• For Lgt spine is isolated
• for Llt spine is coupled to the dendrite.

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Ratio as a function of spine length
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Distribution of Pumps

• Extrusion Flux1600 (Sabatini et al. 2002),
• the number of pumps that produce a ratio of ?
  16.66 should be around 100.
• a spine becomes isolated when 1/4 of the pumps
  are located on the spine neck.

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Consequences

• spine can become isolated by two different ways
• increase the spine neck length
• increase the number of pumps.
• But two procedures not equivalent, number of
  pumps has to increase quadratically in order to
  produce a similar effect that would be achieved
  by changing linearly the spine length.
• L1.5 µm and Np 20, r(1.5) 0.95,
• 10 ions pumped out, 9 arrive to the dendrite
• L1 µm, r(1) 2.33,
• 10 ions pumped out, 23 arrive to the dendrite

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Conclusions

• Spine are highly dynamic
• spine neck length controls the magnitude of
  spine/dendrite communication by the presence of
  active calcium removal mechanisms
• Spine neck can be considered as an active filter
  for the passage of calcium
• a dendritic spine can become isolated by two
  different ways increase the spine neck length,
  and the other is to increase the number of pumps
• Since a dendrite is a stable structure whereas a
  dendritic spine is flexible, having the ability
  to change its length, only dendritic spine can
  be coupled or/and uncoupled dynamically by
  changing both the neck length and the number of
  pumps.
• Comparing the time needed for a pump to be
  functionally active after being synthesized with
  the time to change the spine geometry, our
  computation suggests that it is more efficient
  and fast for the spine head to be
  compartmentalized by increasing the length,
  rather than adding pumps.