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The variable {{math|S<sub><var>ij</var></sub>}} is an occupation variable of the lattice site denoted by indices i and j. If the site is occupied, {{math|S<sub><var>ij</var></sub> {{=}} 1}}; otherwise, {{math|S<sub><var>ij</var></sub> {{=}} 0}}. Insertion of a new receptor into the membrane can occur at any unoccupied site in the lattice, and '''internalization of a receptor can occur only at occupied sites'''. In this formulation, internalization occurs at a fixed rate, independent of interaction with other receptors. I used a '''fixed internalization rate''' {{math|&mu; {{=}} 1&frasl;τ<sub><var>in</var></sub> }} in per unit time, which implies that the '''probability of internalizing''' a receptor at site (''i, j'') in a small time step Δ''t'' is:
The variable {{math|S<sub><var>ij</var></sub>}} is an occupation variable of the lattice site denoted by indices i and j. If the site is occupied, {{math|S<sub><var>ij</var></sub> {{=}} 1}}; otherwise, {{math|S<sub><var>ij</var></sub> {{=}} 0}}. Insertion of a new receptor into the membrane can occur at any unoccupied site in the lattice, and '''internalization of a receptor can occur only at occupied sites'''. In this formulation, internalization occurs at a fixed rate, independent of interaction with other receptors. I used a '''fixed internalization rate''' {{math|&mu; {{=}} 1&frasl;τ<sub><var>in</var></sub> }} in per unit time, which implies that the '''probability of internalizing''' a receptor at site (''i, j'') in a small time step Δ''t'' is:


:'''Internalization Probability'''


:<big>{{math|P<sup>in</sup>( <var>i,j, t:t</var> + Δ<sub><var>t</var></sub> ) {{=}} S<sub><var>ij</var></sub>&mu;Δ<sub><var>t</var></sub>}}</big>
:<big>{{math|P<sup>in</sup>( <var>i,j, t:t</var> + Δ<sub><var>t</var></sub> ) {{=}} S<sub><var>ij</var></sub>&mu;Δ<sub><var>t</var></sub>}}</big>


:*This equation is simply saying that the probability ({{math|P<sup>in</sup>}}) of a receptor internalizing from site (S) with coordinates ''i,j'' at time-point (''t:t'') plus the elapsed time Δ<sub>t</sub> <code>is equal to</code> the occupation state of that lattice site ({{math|S<sub><var>ij</var></sub>}} 1 or 0) &times; an internalization rate constant ({{math|&mu; {{=}} 1&frasl;τ<sub><var>in</var></sub> }}) &times; a small time step Δ<sub>t</sub>
:*This equation is simply saying that the probability ({{math|P<sup>in</sup>}}) of a receptor internalizing from site (S) with coordinates ''i,j'' at time-point (''t:t'') plus the elapsed time Δ<sub>t</sub> <code>is equal to</code> the occupation state of that lattice site ({{math|S<sub><var>ij</var></sub>}} 1 or 0) &times; an internalization rate constant ({{math|&mu; {{=}} 1&frasl;τ<sub><var>in</var></sub> }}) &times; a small time step Δ<sub>t</sub>
:* In a nutshell the probability of a receptor internalizing is equal to the internalization rate constant per unit time. Since ''S'' and &mu; {{=}} 1 and the step size for Δ<sub>time</sub> {{=}} .01 then a receptor internalizes once every 100 steps




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:'''Insertion Probability'''
:<big>{{math|P<sub>k</sub>(i,j) {{=}} 1 / ( 1 + exp( -βh<sub>k</sub>(i,j) ) )}}</big>
:<big>{{math|P<sub>k</sub>(i,j) {{=}} 1 / ( 1 + exp( -βh<sub>k</sub>(i,j) ) )}}</big>
** This equation is saying the probability of insertion varies smoothly from 0 to 1 as a function of 
** {{math|(1 / (1 - e(-50&times;1.5))) &times; 100<sub>steps</sub> {{=}} .5}}





Revision as of 12:32, 16 July 2013

Malinow Molecular Methods Quantum Dots Choquet AMPAR

Category:Malinow

Experiment Ideas

experimental notes and highlighted findings

Experiments

2000

Hayashi, Shi, Esteban, Piccini, Poncer, Malinow • 2000 • Science - PDF

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2009

Kessels, Kopec, Klein, Malinow • 2009 • Nat Neurosci. - PDF

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2007

Kopec, Real, Kessels, Malinow • 2007 • J Neuro - PDF

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Other Studies

Shouval HZ • 2005 • PNAS - PDF

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Other Notes

Lu W, Gray JA, Granger AJ, During MJ, Nicoll RA. • 2011 • J Neurophysiol - PDF

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RANDOM NOTES

{{Article|AUTHORS|YEAR|JOURNAL - [http://domain.com/linktofile.pdf PDF]|PMID|TITLE}}
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}}<!-- END ARTICLE -->