Team:Oxford/what are microcompartments

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<h1>The ellipsoid packing problem</h1>
<h1>The ellipsoid packing problem</h1>
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Once treated as ellipsoids, the problem was then reduced to the classical ‘sand packing’ problem. Because the dimensions of these proteins was substantially smaller than the icosahedron (by approximately a factor of 20 in every dimension), I assumed that the geometry of the container i.e. the microcompartment, was not significant.
Once treated as ellipsoids, the problem was then reduced to the classical ‘sand packing’ problem. Because the dimensions of these proteins was substantially smaller than the icosahedron (by approximately a factor of 20 in every dimension), I assumed that the geometry of the container i.e. the microcompartment, was not significant.
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<br><br>
Another assumption made in these calculations was that the enzymes could be treated as homogenous. They are of very similar dimensions, varying by no more than 20-30% on any axis, and also have very similar sphericities- the key variable in determining the packing efficiency of the molecules. Sphericity is defined as:
Another assumption made in these calculations was that the enzymes could be treated as homogenous. They are of very similar dimensions, varying by no more than 20-30% on any axis, and also have very similar sphericities- the key variable in determining the packing efficiency of the molecules. Sphericity is defined as:
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φ=( π^(1⁄3) 〖(6V_p)〗^(2⁄3))/A_p
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<img src="https://static.igem.org/mediawiki/2014/1/1a/Oxford_Leroy_eqn1.png" style="float:left;position:relative; width:30%;" />
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<li>φ = sphericity</li>
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<li>V_p = volume of ellipsoid (nm^3)</li>
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<li>A_p = surface area of ellipsoid (nm^2)</li>
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For ellipsoids, a surface area approximation was used:
For ellipsoids, a surface area approximation was used:
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A_p≈4π((〖(ab)〗^(1.6)+〖(ac)〗^(1.6)+〖(bc)〗^(1.6))/3)^(1⁄(1.6))
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<img src="https://static.igem.org/mediawiki/2014/a/ac/Oxford_Leroy_eqn2.png" style="float:left;position:relative; width:50%;" />
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After calculating the sphericities of the enzymes, the porosity of the system could then be determined through empirical data from literature. Because the DcmA and FdhA sphericities were very similar (0.953 and 0.981 respectively), we considered the system to be composed of a homogenous spheroid species of porosity 0.973 i.e. the weighted average of the two species.
After calculating the sphericities of the enzymes, the porosity of the system could then be determined through empirical data from literature. Because the DcmA and FdhA sphericities were very similar (0.953 and 0.981 respectively), we considered the system to be composed of a homogenous spheroid species of porosity 0.973 i.e. the weighted average of the two species.

Revision as of 13:34, 19 September 2014

#list li { list-style-image: url("https://static.igem.org/mediawiki/2014/6/6f/OxigemTick.png"); } }


What are micro-compartments?


Introduction

BIOREMEDIATION INTRODUCTION PLUS QUOTES BIOREMEDIATION INTRODUCTION PLUS QUOTES BIOREMEDIATION INTRODUCTION PLUS QUOTES BIOREMEDIATION INTRODUCTION PLUS QUOTES BIOREMEDIATION INTRODUCTION PLUS QUOTES BIOREMEDIATION INTRODUCTION PLUS QUOTES BIOREMEDIATION INTRODUCTION PLUS QUOTES BIOREMEDIATION INTRODUCTION PLUS QUOTES BIOREMEDIATION INTRODUCTION PLUS QUOTES BIOREMEDIATION INTRODUCTION PLUS QUOTES BIOREMEDIATION INTRODUCTION PLUS QUOTES BIOREMEDIATION INTRODUCTION PLUS QUOTES
Structure
Structure
Information Information Information Information Information Information Information Information Information Information Information Information Information Information Information Information Information Information Information
Mutated micro-compartment structures model
Mutated micro-compartment structures model
Information Information Information Information Information Information Information Information Information Information Information Information Information Information Information Information Information Information Information
Abundance
Abundance
Information Information Information Information Information Information Information Information Information Information Information Information Information Information Information Information Information Information Information
Modelling the number of enzymes in a micro-compartment
Modelling the number of enzymes in a micro-compartment
The aim of this model was to predict a theoretical maximum number of enzyme molecules that can be packed into a single microcompartment. To get a first estimate, without taking into consideration whether this volume of protein would interrupt the biological processes in the cell, we approached this problem volumetrically.

Due to the complexity of the enzyme movements and their interactions, I simplified their structures by approximating them as ellipsoids with axes lengths calculated through modelling the monomers and predicting the structures of the FdhA tetramer and DcmA hexamer respectively.





Oxford iGEM 2014

The ellipsoid packing problem

Once treated as ellipsoids, the problem was then reduced to the classical ‘sand packing’ problem. Because the dimensions of these proteins was substantially smaller than the icosahedron (by approximately a factor of 20 in every dimension), I assumed that the geometry of the container i.e. the microcompartment, was not significant.

Another assumption made in these calculations was that the enzymes could be treated as homogenous. They are of very similar dimensions, varying by no more than 20-30% on any axis, and also have very similar sphericities- the key variable in determining the packing efficiency of the molecules. Sphericity is defined as:



  • φ = sphericity
  • V_p = volume of ellipsoid (nm^3)
  • A_p = surface area of ellipsoid (nm^2)


    • For ellipsoids, a surface area approximation was used:



    After calculating the sphericities of the enzymes, the porosity of the system could then be determined through empirical data from literature. Because the DcmA and FdhA sphericities were very similar (0.953 and 0.981 respectively), we considered the system to be composed of a homogenous spheroid species of porosity 0.973 i.e. the weighted average of the two species.