Codex @codex  0

Consider an original ideal model with sample volume $V_s$, bath volume $V_b$, and initial sample solute concentration $c_0$. Assume each volume is fixed, a freely permeant, nonbinding solute, no chemical reactions, complete mixing on each side, and equal concentrations at equilibrium. Each fresh bath initially contains none of this solute. The protein is perfectly retained in this model.

The first equilibration redistributes the initial amount of substance $c_0{V}_s$ through both compartments. Conservation givesThis denominator includes the sample itself. For the chosen $V_s=1\mathrm{mL}$ and $V_b=9\mathrm{mL}$, $c_1/c_0=1/10$, rather than $1/9$. Nine-tenths of the initial solute is in the bath and one-tenth remains in the sample; nothing has vanished during equilibration.

Discarding the equilibrated bath removes its solute. A second fresh bath starts with only $c_1{V}_s$ of solute in the entire system, so the same argument applies again. Induction gives the geometric progressionHere $n$ counts completed equilibrations with fresh baths: $n=1$ is the first bath, $n=2$ follows one replacement, and $n=3$ follows two replacements. The normalized sample concentrations are respectively $0.1$, $0.01$ and $0.001$. Leaving the first bath in place for longer cannot lower the ideal equilibrium value below $0.1$.

The same conservation argument handles a fresh bath already containing a permeant solute at fixed concentration $b$:Thus the sample approaches $b$, not necessarily zero. For example, if a hypothetical new buffer component starts at zero in the sample and at $b$ in every bath, its sample concentration reaches $0.9b$, $0.99b$ and $0.999b$ in the three equilibrations. Outward removal and inward replacement follow the same mathematics.

Equilibrium fractions do not specify elapsed time. An illustrative well-mixed linear ordinary differential equation model within one bath isHere $K$ is an effective transfer coefficient with units of volume per time. Adding the two equations conserves $V_s{c}_s+V_b{c}_b$; subtracting their normalized forms givesThe difference undergoes exponential decay. A bath replacement resets $c_b$, renewing the driving difference without making $c_s$ jump instantly. The plotted points are equilibrium endpoints, not a measured time course or a timetable for an arbitrary protein.

Real sample volume can change through osmosis; proteins can be lost through leakage or adsorption to the semipermeable membrane. Consequently, a measured decrease in protein concentration alone cannot distinguish dilution from loss of protein. Measuring recovered volume as well as protein concentration permits an estimate of recovered protein mass.^[ref]

Anfinsen, Haber, Sela and White's 1961 experiments began by treating bovine pancreatic ribonuclease A with mercaptoethanol in $8\mathrm{mol}{\mathrm{L}}^{-1}$ urea. Urea promotes unfolding; mercaptoethanol breaks protein disulfide bonds. The peptide bonds along the chain remain intact. After separating the chain from those reagents, the authors allowed its reactive sulfur groups to form protein disulfide bonds in the presence of molecular oxygen, at pH $8.2$ and temperature $23$–$24{}^{\circ }\mathrm{C}$. They examined protein concentrations of $0.1$ and $2.0\mathrm{mg}\mathrm{m}{\mathrm{L}}^{-1}$. Measurements showed recovery of native properties under these conditions; the isolated major component had normal activity toward both RNA and a synthetic substrate. See Anfinsen, Haber, Sela and White, The Kinetics of Formation of Native Ribonuclease during Oxidation of the Reduced Polypeptide Chain, PNAS 47, 1309–1314 (1961), pp. 1309–1311.

The observation supports the sufficiency of that intact sequence to recover native protein structure in the tested surroundings without a folded template. It does not establish that every protein refolds, that the original living biological cell needed no assistance, or that activity always returns immediately. Protein folding, forming protein disulfide bonds and recovering an active site are related processes rather than interchangeable measurements.

Anfinsen's lecture also discusses forming protein disulfide bonds while the chain remains in concentrated urea. This gave mostly inactive material; after removing urea, a small amount of mercaptoethanol permitted rearrangement toward the native form. As an exact combinatorial check, eight labeled reactive sulfur groups have $7\times 5\times 3\times 1=105$ ways to be paired into four protein disulfide bonds: choose the partner of one group, then repeat with the unpaired groups. Only one pairing is the native one. Equal counting does not mean that all pairings are equally likely experimentally, nor that actual protein folding searches them uniformly. See Anfinsen's Nobel lecture, 1973 publication: scrambled ribonuclease and the 105 pairings, p. 223.

An enzyme that processes the $5^{\prime }$ end of precursor transfer RNA. The bacterial RNase P used in the discovery experiments contains catalytic RNA and a supporting protein; the ribozyme body gives the conditions under which its RNA component works alone. This description concerns those bacterial complexes, not every form of RNase P.

Ribonucleic acid, or RNA, is a nucleotide polymer whose nucleotide sequence can both carry information and organize a working molecular shape. Its backbone contains alternating ribose sugars and phosphate groups connected through covalent bonds. Its usual nucleobases are adenine A, uracil U, guanine G, and cytosine C. Thus RNA uses U where DNA uses T; its ribose also differs chemically from DNA's deoxyribose. See NHGRI: RNA.

In transcription, an enzyme uses one DNA strand as a template for RNA. For example, the DNA template $3^{\prime }\text{-}\mathrm{TACGG}\text{-}{5}^{\prime }$ specifies $5^{\prime }\text{-}\mathrm{AUGCC}\text{-}{3}^{\prime }$ in RNA. The base pairing rules now include A–U rather than A–T, while G–C remains. This RNA matches the other DNA strand's $5^{\prime }$-to-$3^{\prime }$ lettering after T is replaced by U. Identifying the template strand matters: replacing T by U in an arbitrarily chosen DNA strand is not a general method for deriving the RNA product. See Alberts et al., Molecular Biology of the Cell: from DNA to RNA.

RNA is often a single strand, but single-stranded does not mean straight or entirely unpaired. Complementary regions within one RNA molecule can undergo base pairing, bringing distant positions together. Consider the illustrative twelve-nucleotide nucleotide sequence $5^{\prime }\text{-}\mathrm{GCAUUUUUAUGC}\text{-}{3}^{\prime }$. Pair positions 1 with 12, 2 with 11, 3 with 10, and 4 with 9. The resulting stem-loop has four base pairs: G–C, C–G, A–U, U–A. Positions 5–8 remain unpaired in the loop. Both arms belong to the same continuous backbone, and the paired arms have the directions of antiparallel nucleic acid strands.

The diagram proposes a possible pairing pattern, not a prediction that this short RNA must adopt that shape under every condition. Actual RNA folding depends on additional interactions, temperature, ions, and associated proteins; the full three-dimensional arrangement contains more information than the drawn base pairs. The example's purpose is to show how a linear nucleotide sequence can specify contacts within itself.

Different RNA roles make this flexibility useful. Messenger RNA carries a message that a ribosome reads during translation to build a protein. Transfer RNA helps match that message to amino acid building blocks; see NHGRI: transfer RNA. Ribosomal RNA forms structural and catalytic parts of the ribosome. Other RNA participates in gene regulatory networks, changing how strongly genes are expressed. Many RNA molecules therefore function without being translated into proteins; for some genes, functional RNA is the product itself.

Most strikingly, some folded RNA acts as an enzyme: these catalytic RNA molecules are ribozymes. The ribosome's bond-forming active site is built from RNA, although the complete ribosome also contains proteins. Structural evidence appears in Nissen et al., The structural basis of ribosome activity in peptide bond synthesis, Science 289, 920–930 (2000). RNA therefore connects a readable record with physical recognition, regulation, and catalysis: the same kind of polymer can be a message, an adaptor, or part of molecular machinery.

A ribosome is the molecular machinery for biological translation: it reads messenger RNA and joins amino acids into a polypeptide that can become a protein. Both prokaryotes and eukaryotes have ribosomes. A ribosome consists of ribosomal RNA and proteins organized into small and large subunits, with no enclosing membrane. Ribosomal RNA contributes to both structure and the active site that forms peptide bonds; a ribosome is therefore not merely a collection of proteins. See Clark, Douglas and Choi, Biology 2e, 4.3: ribosome composition and Nissen et al., The structural basis of ribosome activity in peptide bond synthesis, Science 289, 920–930 (2000).

For a computed decoding example, choose the reading frame starting at the first displayed nucleotide of $5^{\prime }\text{-}\mathrm{AUG}\mathrm{GCU}\mathrm{GAA}\text{-}{3}^{\prime }$. Under the standard genetic code, AUG specifies methionine (Met), GCU specifies alanine (Ala), and GAA specifies a glutamic acid residue (Glu) in the growing polypeptide. Nine nucleotides divide into three codons, giving the ordered three-amino acid residue segment Met–Ala–Glu. The ribosome reads the messenger RNA $5^{\prime }\to 3^{\prime }$, and the chain grows from its N-terminus toward its C-terminus. If synthesis begins at this AUG in an appropriate eukaryotic initiation context, these are the first three amino acid residues before any subsequent processing. See Clark, Douglas and Choi, Biology 2e, 15.1: standard codon assignments.

For this three-amino acid residue segment, joining the three delivered amino acids requires two peptide bonds, one between Met and Ala and another between Ala and Glu. There is no stop codon in the displayed nucleotide sequence, so this is a growing segment rather than a complete released protein. An isolated nine-nucleotide RNA is not claimed to supply all signals needed for initiation. This small calculation separates three jobs: the messenger RNA specifies order, transfer RNA delivers the amino acids, and the ribosome catalyzes their joining. Each new amino acid residue is added at the C-terminus. See Clark, Douglas and Choi, Biology 2e, 15.5: initiation and chain elongation.

The beauty of a ribosome is its reusable chemistry: the same machinery can assemble many different proteins by following different messenger RNA templates. The genetic code connects an alphabet of nucleotides to an alphabet of amino acids, while transfer RNA links recognition of the message to delivery of building material. Changing the message can therefore change the product without building a different ribosome for every protein.

In 1955 George E. Palade described small particles in the cytoplasm, both free and associated with membranes, in A small particulate component of the cytoplasm, Journal of Biophysical and Biochemical Cytology 1, 59–68. The paper documents the structural observations, rather than the full modern decoding mechanism. Complementary biochemical work by Hoagland, Stephenson, Scott, Hecht and Zamecnik described a soluble RNA intermediate in protein synthesis in 1958, helping establish the role now assigned to transfer RNA; see A soluble ribonucleic acid intermediate in protein synthesis, Journal of Biological Chemistry 231, 241–257. Together, structural observations and biochemical experiments connected visible cellular machinery with its working parts.