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{{enzyme
| Name = polysaccharide O-methyltransferase
| EC_number = 2.1.1.18
| CAS_number = 37205-56-4
| IUBMB_EC_number = 2/1/1/18
| GO_code = 0030734
| image =
| width =
| caption =
}}
In [[enzymology]], a '''polysaccharide O-methyltransferase''' ({{EC number|2.1.1.18}}) is an [[enzyme]] that [[catalysis|catalyzes]] the [[chemical reaction]]


[[Image:SodShockTubeTest Regions.png|thumb|300px|right|Density Plot after time evolution of t=0.2[-]]]
:S-adenosyl-L-methionine + 1,4-alpha-D-glucooligosaccharide <math>\rightleftharpoons</math> S-adenosyl-L-homocysteine + oligosaccharide containing 6-methyl-D-glucose units
The '''Sod shock tube''' problem, named after Gary A. Sod, is a common test for the accuracy of [[Computational fluid dynamics|computational fluid codes]], like [[Riemann solver]]s,  and was heavily investigated by Sod in 1978.


The test consists of a one-dimensional [[Riemann problem]] with the following parameters, for left and right states of an [[ideal gas]].
Thus, the two [[substrate (biochemistry)|substrates]] of this enzyme are [[S-Adenosyl methionine|S-adenosyl methionine]] and [[1,4-alpha-D-glucooligosaccharide]], whereas its two [[product (chemistry)|products]] are [[S-adenosylhomocysteine]] and [[oligosaccharide containing 6-methyl-D-glucose units]].
<!-- Wikipedia has too many nasty admins! -->
This enzyme belongs to the family of [[transferase]]s, specifically those transferring one-carbon group [[methyltransferase]]s.  The systematic name of this enzyme class is '''S-adenosyl-L-methionine:1,4-alpha-D-glucan 6-O-methyltransferase'''. Other names in common use include '''polysaccharide methyltransferase''', and '''acylpolysacharide 6-methyltransferase'''.


<center>
==References==
<math>
{{reflist|1}}
\left( \begin{array}{c}\rho_L\\P_L\\v_L\end{array}\right)
* {{cite journal | author = Ferguson JA, Ballou CE | date = 1970 | title = Biosynthesis of a mycobacterial lipopolysaccharide. Properties of the polysaccharide methyltransferase | journal = J. Biol. Chem. | volume = 245 | pages = 4213&ndash;23  | pmid = 5503262 | issue = 16 }}
=
\left( \begin{array}{c}1.0\\1.0\\0.0\end{array} \right)
</math>
,
<math>
\left( \begin{array}{c}\rho_R\\P_R\\v_R\end{array}\right)
=
\left( \begin{array}{c}0.125\\0.1\\0.0\end{array}\right)
</math>
</center>
where
::*<math>\rho</math> is the density
::*P  is the pressure
::*v is the velocity
 
The time evolution of this problem can be described by solving the [[Euler equations]].
Which leads to three characteristics, describing the propagation speed of the
various regions of the system. Namely the rarefaction wave, the contact discontinuity and
the shock discontinuity.
If this is solved numerically, one can test against the analytical solution,
and get information how well a code captures and resolves shocks and contact discontinuities
and reproduce the correct density profile of the rarefaction wave.
 
==Analytic derivation==
The different states of the solution are separated by the time evolution of the
three [[Method of characteristics|characteristics]] of the system, which is due to the finite speed
of information propagation. Two of them are equal to the speed
of sound of the both states
::<math>cs_1 = \sqrt{\gamma \frac{P_L}{\rho_L}}</math>
::<math>cs_5 = \sqrt{\gamma \frac{P_R}{\rho_R}}</math>
The first one is the position of the beginning of the rarefaction wave while
the other is the velocity of the propagation of the shock.


Defining:
===Gene ontology (GO) codes===
::<math>\Gamma = \frac{\gamma - 1}{\gamma + 1}</math>, <math>\beta = \frac{\gamma - 1}{2 \gamma}</math>
The states after the shock are connected by the [[Rankine-Hugoniot equation|Rankine Hugoniot]]
shock jump conditions.
::<math>\rho_4 = \rho_5 \frac{P_4 + \Gamma P_5}{P_5 + \Gamma P_4}</math>
But to calculate the density in Region 4 we need to know the pressure in that region.
This is related by the contact discontinuity with the pressure in region 3 by
::<math>P_4 = P_3</math>
Unfortunately the pressure in region 3 can only be calculated iteratively, the right
solution is found when <math>u_2</math> equals <math>u_4</math>
::<math>u_4 = \left(P_3' - P_5\right)\sqrt{\frac{1-\Gamma}{\rho_R(P_3'+\Gamma P_5)}}</math>
::<math>u_2 =\left(P_1^\beta-P_3'^\beta\right) \sqrt{\frac{(1-\Gamma^2)P_1^{1/\gamma}}{\Gamma^2 \rho_L}}</math>
::<math>u_2 - u_4 = 0</math>
This function can be evaluated to an arbitrary precision thus giving the pressure in the
region 3
::<math>P_3 = \operatorname{calculate}(P_3,s,s,,)</math>
finally we can calculate
::<math>u_3 = u_5 + \frac{(P_3 - P_5)}{\sqrt{\frac{\rho_5}{2}((\gamma+1)P_3 +(\gamma-1)P_5)}}</math>
::<math>u_4 = u_3</math>
and <math>\rho_3</math> follows from the adiabatic gas law
::<math>\rho_3 = \rho_1 \left(\frac{P_3}{P_1}\right)^{1/\gamma}</math>


==References==
{{transferase-stub}}
*{{cite journal | title=A Survey of Several Finite Difference Methods for Systems of Nonlinear Hyperbolic Conservation  Laws | first=G. A. | last=Sod | year=1978 | journal=[[Journal of Computational Physics|J. Comput. Phys.]] | volume=27| pages=1–31 | url=http://www.osti.gov/energycitations/product.biblio.jsp?osti_id=6812922 | doi=10.1016/0021-9991(78)90023-2 |bibcode = 1978JCoPh..27....1S }}
*{{cite book | first=Eleuterio F.| last=Toro| year=1999 | title=Riemann Solvers and Numerical Methods for Fluid Dynamics| publisher=Springer Verlag|location=Berlin | id=ISBN 3-540-65966-8}}


==See also==
[[Category:EC 2.1.1]]
*[[Shock tube]]
[[Category:Enzymes of unknown structure]]
*[[Computational fluid dynamics]]


[[Category:Fluid dynamics]]
[[it:Polisaccaride O-metiltransferasi]]
[[Category:Computational fluid dynamics]]
[[ja:多糖-O-メチルトランスフェラーゼ]]

Revision as of 15:06, 16 August 2014

Template:Enzyme In enzymology, a polysaccharide O-methyltransferase (Air Transportation Experts Kull from Wingham, has many interests that include butterflies, property developers in singapore and digital photography. Is a travel freak and in recent past made buy a house in singapore journey to Paleochristian and Byzantine Monuments of Thessalonika.) is an enzyme that catalyzes the chemical reaction

S-adenosyl-L-methionine + 1,4-alpha-D-glucooligosaccharide ⇌ S-adenosyl-L-homocysteine + oligosaccharide containing 6-methyl-D-glucose units

Thus, the two substrates of this enzyme are S-adenosyl methionine and 1,4-alpha-D-glucooligosaccharide, whereas its two products are S-adenosylhomocysteine and oligosaccharide containing 6-methyl-D-glucose units. This enzyme belongs to the family of transferases, specifically those transferring one-carbon group methyltransferases. The systematic name of this enzyme class is S-adenosyl-L-methionine:1,4-alpha-D-glucan 6-O-methyltransferase. Other names in common use include polysaccharide methyltransferase, and acylpolysacharide 6-methyltransferase.

References

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Gene ontology (GO) codes

Template:Transferase-stub

it:Polisaccaride O-metiltransferasi ja:多糖-O-メチルトランスフェラーゼ

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