= Disulfide bond
{title2=$\mathrm{S-S}$}
A <disulfide bond> is the single <covalent bond> between the two adjacent <sulfur> <chemical atoms> in a <disulfide>, conventionally written $\mathrm{R-S-S-R'}$. Here $R$ and $R'$ stand for the attached organic groups; they may belong to the same <molecule> or to initially separate <molecules>. A <disulfide bond> is a chemical bridge, rather than a <hydrogen bond> or a mere contact between nearby groups. Two <thiols>, $\mathrm{R-SH}$ and $\mathrm{R'-SH}$, can supply its two <sulfur> endpoints. https://openstax.org/books/organic-chemistry/pages/18-7-thiols-and-sulfides[John McMurry, Organic Chemistry, 18.7: thiol oxidation and disulfides]{ref}
The <stoichiometry> of forming a <disulfide bond> is especially revealing. Written as an <oxidation> <half-reaction>, it is
$$
\mathrm{R-SH+R'-SH\longrightarrow R-S-S-R'+2H^++2e^-}.
$$
The reverse <reduction> <half-reaction> consumes two <Electrons> and two <hydrogen ions> to restore two <thiols>. Both sides contain two <sulfur> <chemical atoms>; the two <hydrogen> <chemical atoms> have moved into the two <hydrogen ions>, and the net <electric charge> remains zero because $+2-2=0$. Thus one <disulfide bond> corresponds to two <thiol> groups and two transferred <Electrons>. These <half-reactions> describe <redox> bookkeeping, not a complete standalone <chemical reaction>: an accompanying <reactant> must accept or supply the <Electrons>, and <pH> affects the actual <protonation> of the groups. <Mercaptoethanol> can promote <reduction> through exchange of <disulfide bonds>, but adequate excess and appropriate conditions are needed; adding it does not by itself prove complete <reduction>. https://pmc.ncbi.nlm.nih.gov/articles/PMC3766385/[Jakob R. Winther and Colin Thorpe, Quantification of Thiols and Disulfides (2014), section 3: reducing reagents and completeness]{ref}
In a <protein disulfide bond>, the endpoints are normally the <amino acid side chains> of two <cysteine> <amino acid residues>. An intrachain <protein disulfide bond> closes an intramolecular bridge within one <polypeptide chain>; an interchain <protein disulfide bond> connects different <polypeptide chains>, and can arise by intermolecular crosslinking of initially separate <molecules>. Forming or reducing these bridges changes <covalent bond> connectivity and can change <protein structure>, while preserving the order of <amino acid residues> and the <peptide bonds> in the <protein backbone>. A complete chemical account of <protein primary structure> includes crosslinks as well as sequence, so preservation of sequence does not imply preservation of every <covalent bond>. Mature <insulin> has two interchain <protein disulfide bonds> and one intrachain <protein disulfide bond>. https://pubmed.ncbi.nlm.nih.gov/14744022/[Seung-Gu Chang, Ki-Doo Choi, Seung-Hwan Jang and Hang-Cheol Shin, Role of disulfide bonds in the structure and activity of human insulin (2003)]{ref}
\Image[/disulfide-bonds-redox-and-bridges.png]
{title=<Disulfide bond> <redox> bookkeeping and schematic intrachain and interchain <protein disulfide bonds>}
{description=Original connectivity cartoons, not measured <protein structures>. Blue and green traces preserve their numbered <amino acid residues>; amber S-S links connect <amino acid side chains> without replacing a <peptide bond>. The cartoons are invented examples, not <insulin> coordinates.}
A bridge is useful because it constrains which parts of a <polypeptide chain> can move apart without breaking a <covalent bond>. Its placement therefore matters as well as its presence. The <ribonuclease A refolding experiment> provides the existing experimental example: breaking and reforming four <protein disulfide bonds> can accompany loss and recovery of function. Counting four bridges alone cannot tell whether their endpoints have the native pairing. This is an attractive connection between simple chemical counting and the richer problem of <protein folding>.
How can an experiment reveal an initially hidden <disulfide bond>? <Ellman's reagent>, also called <DTNB>, measures free <thiols> by producing a yellow absorbing species. Its reactive <disulfide bond> undergoes exchange with the <conjugate base> $\mathrm{R-S^-}$ of a <thiol>, producing a mixed <disulfide> attached to $R$ and one released 2-nitro-5-thiobenzoate species, abbreviated TNB. At the assay <pH>, the strongly colored form is the dianion $\mathrm{TNB^{2-}}$: one negative charge is on <sulfur> and the other is on the <carboxylic acid>-derived $\mathrm{COO^-}$ group. With excess <DTNB> and complete reaction, one released TNB reports one reacted <thiol>. George L. Ellman's 1959 paper introduced the tissue assay; it was subsequently reexamined quantitatively. https://pubmed.ncbi.nlm.nih.gov/13650640/[George L. Ellman, Tissue sulfhydryl groups (1959)]{ref} https://assets.thermofisher.com/TFS-Assets/LSG/manuals/MAN0011216_Ellmans_Reag_UG.pdf[Pierce Biotechnology, Ellman's Reagent instructions, introduction and reaction diagram]{ref}
The modern apparatus can be simple: tubes, pipettes, a <buffer solution>, <cysteine> standards, <DTNB>, and an instrument that measures <absorbance> through a cuvette at <wavelength> $412\,\mathrm{nm}$. The Pierce protocol uses $50\,\mathrm{\mu L}$ of a $4\,\mathrm{mg\,mL^{-1}}$ <DTNB> stock, $2.50\,\mathrm{mL}$ of <buffer solution>, and $250\,\mathrm{\mu L}$ of sample. Its <buffer solution> is $0.1\,\mathrm{mol\,L^{-1}}$ sodium <phosphate> at <pH> 8.0 with a metal-binding additive. After 15 minutes at room <temperature>, measure <absorbance> against a <buffer solution> plus <DTNB> blank; run known <cysteine> <concentrations> in parallel. The observable is increased yellow color and increased blank-corrected <absorbance> as more accessible <thiols> react, rather than direct imaging of <disulfide bonds>. These are published protocol conditions, not measurements performed for this article. https://assets.thermofisher.com/TFS-Assets/LSG/manuals/MAN0011216_Ellmans_Reag_UG.pdf[Pierce Biotechnology, Ellman's Reagent instructions, page 2: standard and cuvette procedures]{ref}
For a before/after test, split a purified <protein> sample into matched aliquots. Measure accessible free <thiols> in one aliquot; subject the other to complete <reduction> of its <disulfide bonds>, remove the reducing <reagent>, then measure the resulting <thiols> with fresh <DTNB>. Process the unreduced aliquot through a matching cleanup. Normalize to recovered <protein> and known <dilution>, since cleanup can change both. To estimate all reducible <protein disulfide bonds>, expose buried groups using matching <protein denaturation> conditions in both aliquots and calibrate in that same <chemical solution>; a native-accessibility measurement answers a different question. A larger corrected reading after <reduction> supports conversion of previously unreactive groups into detectable <thiols>. Attribution to <disulfide bonds> requires excluding other reducible <sulfur> modifications. This is a proposed comparison based on the detection principles, not a reconstruction of Ellman's original tissue measurements. https://pmc.ncbi.nlm.nih.gov/articles/PMC3766385/[Winther and Thorpe (2014), sections 1.2 and 4.1: indirect disulfide detection and assay limitations]{ref}
\Image[/disulfide-bonds-ellman-workflow.png]
{title=Matched <Ellman's reagent> assay workflow and an explicitly hypothetical <disulfide bond> count}
{description=Original apparatus and workflow schematic. The displayed <absorbances> are calculated illustrations for two free <thiols> and two <disulfide bonds> per model <protein> at equal final <protein> <concentration>; they are not measured data or a calibration curve. Reducing <reagent> removal and matched accessibility are prerequisites for interpreting the difference.}
Under the <Beer-Lambert law>, the blank-corrected <absorbance> is $A=\varepsilon lc$, where $l$ is the cuvette path length, $c$ is the released TNB <concentration>, and $\varepsilon$ is its molar absorption coefficient. Riddles, Blakeley and Zerner measured $\varepsilon_{412}=14150\,\mathrm{L\,mol^{-1}\,cm^{-1}}$ in dilute aqueous salt <chemical solutions>, confirming the value independently using <cysteine>. It must not be applied indiscriminately to other <solvents> or <protein denaturation> mixtures. https://www.sciencedirect.com/science/article/pii/0003269779907929[Peter W. Riddles, Robert L. Blakeley and Burt Zerner, Ellman's reagent: a reexamination (1979)]{ref} For aliquots compared on the same final volume and <protein> <concentration> basis, the ideal estimate is
$$
c_{\mathrm{S-S}}=\frac{c_{\mathrm{SH,after}}-c_{\mathrm{SH,before}}}{2}
=\frac{A_{\mathrm{after}}-A_{\mathrm{before}}}{2\varepsilon l},
\qquad
\bar n_{\mathrm{S-S}}=\frac{c_{\mathrm{S-S}}}{c_{\mathrm{protein}}}.
$$
The factor of two follows from the <reduction> <stoichiometry>; $\bar n_{\mathrm{S-S}}$ is the number of <disulfide bonds> per <protein> <molecule>, or an average for a mixed population. If the aliquots have different <dilutions> or recoveries, convert each reading to a common sample basis before subtracting.
As a hypothetical calculation, choose $c_{\mathrm{protein}}=10\,\mathrm{\mu mol\,L^{-1}}$ in each final cuvette, two free <thiols> and two <disulfide bonds> per <protein> <molecule>, and $l=1\,\mathrm{cm}$. Before <reduction>, $c_{\mathrm{SH}}=20\,\mathrm{\mu mol\,L^{-1}}$ gives $A=0.283$; complete <reduction> adds four <thiols> per <protein> <molecule>, so $c_{\mathrm{SH}}=60\,\mathrm{\mu mol\,L^{-1}}$ gives $A=0.849$. The difference $0.566$ gives $c_{\mathrm{S-S}}=20\,\mathrm{\mu mol\,L^{-1}}$ and $\bar n_{\mathrm{S-S}}=2$. The published tube volumes imply a <dilution> factor $2.80/0.250=11.2$; reversing that <dilution> multiplies both <thiol> and <protein> <concentrations> by 11.2 and leaves the bridge count per <protein> <molecule> unchanged.
Controls determine whether that arithmetic has chemical meaning. Use fresh <cysteine> standards and a processed blank without <protein> to detect color generated by residual reducing <reagent>. Even a reducing <reagent> containing no <thiols> can interfere: Han and Han showed that tris(2-carboxyethyl)phosphine, abbreviated TCEP, reduces <DTNB> to two TNB equivalents per TCEP. https://doi.org/10.1006/abio.1994.1290[J. C. Han and G. Y. Han, A Procedure for Quantitative Determination of Tris(2-Carboxyethyl)phosphine (1994)]{ref} In the hypothetical model, $5\,\mathrm{\mu mol\,L^{-1}}$ residual TCEP in only the reduced cuvette would add $A=0.1415$ and falsely add $0.5$ bridge per <protein> <molecule>. A stable endpoint and agreement after a further <reduction> treatment help check completion. A sample without <DTNB> checks its own color; cloudy samples can also attenuate light without producing TNB. Match <pH>, <temperature>, accessibility and calibration <chemical solution>, and minimize delay that permits reoxidation. If two already-free but buried <thiols> become accessible only in the reduced aliquot, they mimic one new <disulfide bond> per <protein> <molecule>. Finally, bulk <absorbance> supplies a count under these assumptions: it does not locate the <cysteine> endpoints, distinguish intrachain from interchain bridges, or establish the native pairing of a <protein disulfide bond>.
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