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Absorption Spectra
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Absorption Spectrum
How Particle in a Box Applies to Vision

   Aside from light interacting with matter, how is this spectroscopy?  Well, as the molecule changes, the wavelength (λmax) that is absorbed changes.  In addition, the temperature and pH also has effects, as effect the distribution of electron in the orbitals of the molecule.  Different opsins have different absorption spectra as a direct result of their specific electron configuration, resulting in predictable absorption given the bonds in a molecule.
    Particle in a box can be used to determine the absorption spectra of a molecule.  Knowing the length of the “box” (bonds involved), and the number of electrons involved, one can calculate the wavelength absorbed by a molecule.

ΔE= (h2/8mL2)(N-1) 
   
    It is known that 11-cis-retinal absorbs in the visible range, and it is known that all-trans-retinal does not.  PIB can be used to explain this, demonstrating that the shortening of the box that occurs as the retinal dissociated from the opsin molecule changes the absorption spectra of the molecule, shifting it into the shorter wavelengths that are not reaching the retina, and therefore not reaching the molecule. 

    Delocalization of the pi orbitals involved in the conjugated systems play a significant role in the spectra absorbed.  Unattached 11-cis-retinal absorbs at approximately 380nm (22).  Rhodopsin absorbs at 498nm.  This difference can be explained by the increase in “box” length when the 11-cis-retinal is attached to the rhodopsin; the box length is increased, therefore shifting the absorption spectra to the red (22).  Different animal species have different protein opsin; therefore, the length of the “box” differs for each species.  Therefore, it can be understood how some animals can see higher or lower wavelengths than can humans.  (4, 22)
     
       The change in energy between the states is 28kJ/mol. (19, 29).  It can be assumed that this energy  difference is not the amount of energy needed to initaite the change from cis to trans, but rather a barrier to get over between the  two forms.

           “Dark noise” in the eye- perception by the neuron that the cis-trans isomerization has occurred, thus firing a neuron- can be traced back to a change in the size of the “box” as a result of the deprotonation of the Schiff base.  Studies are not conclusive if all rhosopsins respond to the same environments- changes in pH and temperature (1,6,8,31).  The minute differences in the opsins themselves may play a role in the discrepancies (6).  It has been hypothesized that an increase inPh should deprotanate the bse, shrinking the box and causing absorption at longer wavelengths, resulting in “dark events indistinguishable from responses the single photons” (8).  However, this has been proven untrue in some settings (6).       


Molecule
Wavelength, Max, nm
Rhodopsin
498
Bathorhodopsin
534
Lumirhodopsin
497
Metarhodopsin I
487
Metarhodopsin II
380
Free trans retinal
370
(22)


http://mcdb.colorado.edu/courses/3280/lectures/class14-2.html

The structure of colored opsin binding sites in cone cells.  The box for each molecule is colored in green. The side chains involved are coded in red. (22)  It can be seen that the lengths differ to a fair degree, and whould therefore absorb different wavelengths. 


Calculations from WebMo Job number 992    - determining ΔE for trans retinal. (Image of Webmo Molecule)
ΔE= (h2/8mL2)(N+1) 
        = (h2/8mL)(12) 
         =  6.626E-34/(8*9.10939E-3*18.486E-10)(14)
          = 805nm, longer than bis light, which makse sense as the box is smaller than the box bound to the opsin! However, PIB calculations are not accurate, only an approximation as to the predicted absortption spectra. The reported difference is likely to be different from this calculated value.  In addition, the molecule being examined in WebMo was not completely optimimized.

The actual absoption for cis-retinal as calculated by WebMo is highest at 244nm (*WebMo job number 1151) and that for all-trans-retinal is 238 (Webmo job number 1152).  The shift in absorption is minimal, with a correspoding to an energy difference of 8.06E-19kJ per molecule (485.2kJ per mole).  This does not agree with reported differences (19, 29).

Differences in absorption would not be as high between free 11-cis-retinal and 11-cis-retinal that is bonded via a Schiff base in to retinal, as that amount of conjugation is affected.  The spectrum of the all-trans-retinal should be comparable, as it is unbound in the eye in this configuration.

When the molecule is created with all single bonds, the absorption peak is at 244 nm for the cis version (Webmo  job 1103), and at 238 for the trans version (Webmo job 1105). The spesctrum has no appreciable difference between the alkene and alkane versions when analysed with WebMo using Hartree Fock 3-21G basis set.  This was not expected.

(*If you are viewing the spectrum, it may be helpful to reduce the peak with from 50 nm to 5nm.  Moving the mouse over the peaks during viewing will reveal the exact wavelength that correscponds to that point on the line.)

   
http://webvision.med.utah.edu/imageswv/spectra.jpeg



There are no sharp peaks in the absorption spectra of the rhodopsins due to the fact that the vibrational and translations states contribute slightly to the spectra (22).


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Project home
The Eye
Retinal And Rhodopsin
Absorption Spectra
WebMo Job 992
Applications
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