In this problem, we'll discuss some aspects of the most informative sense organ — vision. In Part A, we'll examine geometric optics and vision correction; in Part B, we'll study the properties of human rhodopsins; and in Part C, we'll learn about microbial rhodopsins.
In your answers please explicitly specify final formula and numerical answer.
Humans have binocular vision. Having two eyes separated by $s=60$ mm results in each eye forming its own image, slightly different from the image in the other eye. This difference allows us to consciously make quantitative estimates of distances to objects.
Measurement procedure:
$$ r=k \Delta x. $$
Modern ophthalmology allows for modification of the optical system itself — the cornea. In the procedure the excimer laser precisely "evaporate" tissue layers. A laser (Light Amplification by Stimulated Emission of Radiation) generates coherent radiation by stimulated photon emission in a medium with a population inversion, where the number of particles in the excited state exceeds their number in the ground state. Ophthalmology utilizes gas lasers with the active medium consists of short-lived diatomic molecules known as argon-fluoride excimers, which exist only in the excited state. When they decay, they emit light.
$E_{\mathrm{(C-C)}} = 348$ kJ/mol
$E_{\mathrm{(C-N)}} = 305$ kJ/mol
$E_{\mathrm{(N-H)}} = 391$ kJ/mol
$E_{\mathrm{(C-H)}} = 413$ kJ/mol
$E_{\mathrm{(C-O)}} = 360$ kJ/mol
$E_{\mathrm{(O-H)}} = 463$ kJ/mol
Rhodopsin (visual purple, UniProtID P08100) is a light-sensitive protein responsible for colorless night vision and is located in rods (a type of retinal cell). The functional form of the protein contains not only amino acids but also an additional cofactor molecule: retinal. The form of this protein without the cofactor is called opsin (the apo form).
Entry (amino acid sequence) P08100 from the UniProt database:
$\texttt{>sp|P08100|OPSD_HUMAN Rhodopsin OS=Homo sapiens OX=9606 GN=RHO PE=1 SV=1}$
$\texttt{MNGTEGPNFYVPFSNATGVVRSPFEYPQYYLAEPWQFSMLAAYMFLLIVLGFPINFLTLY}$
$\texttt{VTVQHKKLRTPLNYILLNLAVADLFMVLGGFTSTLYTSLHGYFVFGPTGCNLEGFFATLG}$
$\texttt{GEIALWSLVVLAIERYVVVCKPMSNFRFGENHAIMGVAFTWVMALACAAPPLAGWSRYIP}$
$\texttt{EGLQCSCGIDYYTLKPEVNNESFVIYMFVVHFTIPMIIIFFCYGQLVFTVKEAAAQQQES}$
$\texttt{ATTQKAEKEVTRMVIIMVIAFLICWVPYASVAFYIFTHQGSNFGPIFMTIPAFFAKSAAI}$
$\texttt{YNPVIYIMMNKQFRNCMLTTICCGKNPLGDDEASATVSKTETSQVAPA}$
The absorption spectrum of proteins in the UV and visible range (wavelengths $250$–$780$ nm) is determined by the amino acids that make up the protein and additional molecules (cofactors) that may also be part of the protein. Only aromatic amino acids (phenylalanine, tyrosine, and tryptophan), which are found in many proteins, absorb in this range, with an absorption maximum around $280$ nm. Cofactors typically have absorption maxima significantly different from $280$ nm.
The extinction coefficient $\varepsilon_{\lambda}^\mathrm{X}$ is a value that characterizes the absorption of light by a molecule $\mathrm{X}$ at a specific wavelength $\lambda$. This value is often used in everyday laboratory practice to quickly and conveniently determine the concentration of molecules in a solution. Absorbance $A_{\lambda}$ is related to the extinction coefficient and concentration as follows:
$$A_{\lambda}=\varepsilon_{\lambda} cl,$$where $c$ is the molar concentration of the substance and $l$ is the optical path length.
It's possible to determine the unknown extinction coefficient for rhodopsin by conducting a chemical reaction that produces a substance with a known extinction coefficient. Adding excess hydroxylamine $\mathrm{NH_2OH}$ and exposing it to light causes the following chemical reaction:
$$\mathrm{Rhodopsin} + \mathrm{NH_2 OH} \rightarrow \mathrm{Opsin} + \mathrm{Retinaloxime}.$$
The extinction coefficient of retinal oxime $\varepsilon_{365}^{\mathrm{RO}}=33600$ M$^{-1}\cdot$cm$^{-1}$. In the laboratory, the absorption spectra of the sample were measured before and after the reaction with excess hydroxylamine (Figure 4). The spectra were measured in the same cuvette.
Humans possess color vision because the retina contains light-sensitive receptor cells (cones) of three colors. Each type of cone has a maximum sensitivity near one of the three primary colors: blue, green, and red, because it expresses one of three opsin genes: OPN1SW, OPN1MW, and OPN1LW. The sensitivity (response magnitude to light with fixed intensity) of these color receptors is shown in Figure 5. If two different light signals excite these receptors equally, the colors of these light signals will be indistinguishable. For example, a mixture of red and green can be selected so that they are indistinguishable from yellow.
Color blindness is a reduced or absent ability to distinguish all or some colors. It is most often an inherited disorder associated with damage to one of the three genes listed above. The gene locations are shown in the table below; the damaged gene variant is recessive.
Disordered gene Color Disorder name Gene location (chromosome) Notation for dominant / recessive OPN1SW Blue Tritanopia 7 $\text{A}$ / $\text{a}$ OPN1MW Green Deuteranopia X $\text{X}^\text{D}$ / $\text{X}^\text{d}$ OPN1LW Red Protanopia X $\text{X}^\text{P}$ / $\text{X}^\text{p}$
Microbial rhodopsins are light-sensitive transmembrane proteins. Like animal rhodopsins, microbial rhodopsins contain retinal. The difference is that visual rhodopsins are found in animals, while microbial rhodopsins are found in bacteria, archaea, protozoan eukaryotes, and viruses.
To date, more than 10,000 genes encoding various microbial rhodopsins have been identified. While similar in structure and homology, different microbial rhodopsins contain different amino acids, which determine their function and spectral properties. The figure (Figure 6) shows photographs of solutions of different microbial rhodopsins and their possible absorption spectra (in no particular order).
Many microbial rhodopsins are proton pumps, meaning they actively pump protons through themselves when exposed to light, thereby transferring a proton from one side of the cell membrane to the other. A simple experiment to determine whether microbial rhodopsins are proton pumps is designed as follows. Microbial rhodopsins are heterologously expressed in the cell membrane of E. coli. A suspension of E. coli cells is placed in a stirred vessel (test tube, volume $V=3$ ml) containing an aqueous NaCl solution. A pH meter electrode is inserted into the vessel (Figure 7). When the vessel is illuminated, the microbial rhodopsins absorb light, transferring a proton across the membrane. The pumping rate of rhodopsins is constant.
The graph (Figure 8) shows the pH value as a function of time after the light is turned on. Before the light was turned on, the system was at equilibrium. Consider that the microbial rhodopsins are located in the inner membrane of E. coli, while the outer membrane allows protons to pass freely.
It's clear that with prolonged illumination, the pH doesn't increase infinitely, but rather settles at a new value. This can be explained by the fact that the cell membrane is actually permeable to protons, and proton leakage occurs. The flux $j$ (the number of protons passing through a unit membrane area per unit time) is linearly dependent on the difference in proton concentrations $n_1$ and $n_2$ on either side of the membrane:
$$j=\alpha (n_1-n_2 ),$$here $\alpha$ is the membrane's proton permeability. Here, the concentration is expressed in units per unit volume.