ReDiClus

Receptor Diffusion & Cluster Model - ReDiClus Model

Diffusion and Cluster Model of LTP

Diffusion and Cluster Model of LTP

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Model Space

The model is simulated in a 3D space with the following parameters

• There is a 3D XYZ coordinate grid
• The X-Y plane has 60x60 area
• The X-Y plane consists of real numbers: -30 to +30
• The Z axis is only 2 levels: 0 and -1
  • 0 represents the membrane surface
  • -1 represents intracellular space

Particle Types

There are 2 types of particles in the simulation

• 'Red' particle dots represent AMPA receptors
  • Red dots can randomly diffuse anywhere on the X-Y plane
  • Red dots only diffuse on the surface Z = 0
• 'Blue' particle dots represent PSD-95 molecules
  • Blue dots are contained in predefined PSD areas and cannot leave
  • Blue dots can exist at the surface Z = 0 or intracellularly Z = -1

Visual Representations

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two independent processes

In this model, there are two independently occurring processes.

• 1. Blue dots can be expressed at the surface or internalized within their PSD area
  • The Blue dot internalization/externalization rate properties are set by the Shouval cluster model equations.
• 2. Red dots diffuse on the X-Y plane with brownian motion
  • Each Red dot has an initial step size randomly drawn from a normal distribution with a mean = 1 and sd = .2

The step size for Red dots is dynamically altered when it's located in a PSD area

• In a PSD, the step size is reduced by a by some factor based on the number of Blue dots currently expressed at the surface of that PSD
• The more Blue dots at the surface, the more the step size is reduced
• The current step size function is:
  • f(R_step) = R * (10*(1 ⁄ B_n))
    • where R_step is the baseline Red dot step size
    • where B_n is number of Blue dots currently expressed at the PSD surface

Several screen shots of the dynamic graphs in the model

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MEAN SQUARED DISPLACEMENT

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Quantitative Review

Quantitative Physiology of the Dendrite

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Harris Website

The Size of Dendrites

adapted from Sheng and Hoogenraad (2007) ^FIG: {{#info

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• Dendrite: 1–10 spines per 10 μm
  
• Spines: 0.5–2 μm in length
  
• PSD: 100 - 300 nm diameter
  
• PSD95: within 12 nm of surface
  

adapted from Harris ^FIG: {{#info

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• proximal dendrite diameter: 1 - 3 µm
• distal dendrite diameter: 0.2 - 2 µm
• dendrite length: 2000 - 9000 µm
• dendrite tip to soma: 100 - 200 µm
• dendrites at soma: 1 - 5
• dendrite branches (granual): 10 - 30
• dendrite branches (purkinje): 400-500

Particle Counts

adapted from Sheng and Hoogenraad (2007) ^FIG: {{#info

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• PSD: 10,000 proteins (or 100 copies of 100 proteins)
  
• CaMKIIα: 7.4%
  
• CaMKIIβ: 1.3%
  
• SynGap: 2.1 pmol/20 μg
  
• NMDAR: 20 proteins
  
• AMPAR: 15 proteins
  
• GluR: 60 subunits, 15 tetramers, 80% or 12 GluR1/GluR2 heteromers
  
• PSD95: within 12 nm of surface
  

Diffusion Rates

from Choquet 2010 ^FIG: {{#info

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• extrasynaptic: 0.1 µm²⁄s
• synaptic: 0.05 µm²⁄s
• synaptic after glu/gly: 0.01 µm²⁄s

Images

From Sheng and Hoogenraad 2007

• Spine morphology ^FIG: {{#info: Error creating thumbnail: File missing{{{2}}} CLICK AWAY FROM IMAGE TO CLOSE }}

From Harris KM and Weinberg 2012

• Spine morphology ^FIG: {{#info: 3D reconstruction of a proximal CA3 pyramidal cell dendrite (blue) and a large mossy fiber bouton (translucent yellow). The cut-away in C2 shows synapses (red) onto multiple dendritic spines, some of which are highly branched. The bouton also forms nonsynaptic cell adhesion junctions (fuchsia). CLICK AWAY FROM IMAGE TO CLOSE }}
• Hippocampal dendrite ^FIG: {{#info: {{{2}}} CLICK AWAY FROM IMAGE TO CLOSE }}

Choquet 2007 Real Time Receptor Diffusion

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Choquet 2007 Real Time Receptor Diffusion Analysis

• The video represents a 10µm × 10µm section scaled to a 535px × 535px video.
  • 1_µm : 53.5_px
• The analysis below documents one instance of Qdot diffusion, between the 6s-7s time points.
• This instance was chosen because of the clarity of motion and no Qdot flicker.
• The Qdot (center) moves from pixel location (X:291, Y:302) at 6.78s to (X:319, Y346) at 6.98s
  • That is a distance of 52.2px in 200ms
  • Qdot velocity: Q_v ≈ 1_µm ⁄ 200_ms
  • Note this diffusion rate of 5µm/s is 10-fold higher than the median diffusion rate reported above.
  • An upper bound of 5µm/s means that receptors can move between synapses in fractions of a second.

Figures:

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Receptor Diffusion Rate Best Estimates

• GABAA: .01 - .05 µm²/s ^FIG: {{#info: Choquet 2010 CLICK AWAY FROM IMAGE TO CLOSE }}

Malinow

Molecular Methods

Quantum Dots

Choquet

AMPAR