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R. E. Humbel coauthored experimental work identifying the chemical structure of human insulin-like growth factors with E. Rinderknecht. Their 1978 study determined the complete sequence of serum-derived insulin-like growth factor 1: a single chain of seventy amino acid residues connected by three disulfide bonds.^[ref]

The comparison with proinsulin connected a biological activity to a molecular relationship. Corresponding regions resembled the insulin chains, while an intervening connecting segment remained in the growth factor. Conserved residues were compatible with a related folded structure; sequence similarity was evidence for that inference, not an atomic structure determination.^[ref]

This research illustrates why a bioassay and sequence analysis complement one another. Two preparations can produce similar responses without containing identical proteins. Establishing residue order and covalent connections provides an independent way to distinguish related signaling molecules.

Reinhold Benesch was a biochemist who investigated hemoglobin function in collaboration with Ruth E. Benesch. Their 1969 account of intracellular organic phosphates explained a mechanism by which 2,3-Bisphosphoglycerate changes oxygen affinity: the regulator binds preferentially to deoxyhemoglobin, making oxygen release more favourable at a specified oxygen partial pressure. This identifies a chemical regulator of oxygen transport, rather than treating hemoglobin affinity as an immutable property of the isolated protein.^[ref]

The discovery is an example of allostery: ligand binding at one part of a molecular system affects binding elsewhere. A short equilibrium argument shows why the effect is reciprocal. Consider an original four-state model with one oxygen ligand $O$ and one regulator $B$, allowing states $H$, $HO$, $HB$ and $HOB$. Define dissociation constantsMultiplying around the two possible binding paths givesThus, if regulator binding makes oxygen ten times harder to bind in this model, $K_{O\mid B}/K_O=10$, oxygen binding must likewise increase the regulator's dissociation constant tenfold. An equilibrium coupling cannot act in only one direction. The four-state construction is an illustrative reduction, not a claim that the four oxygen-binding subunits of real hemoglobin behave as one physical site.

This reasoning motivates a controlled measurement: compare oxygen-equilibrium curves for matched hemoglobin preparations with different regulator concentrations, while controlling pH, temperature and solution composition. Measuring regulator binding as well tests the reciprocal side of the proposed mechanism. His coauthored 1969 paper with Ruth E. Benesch and Chi Irg Yu explicitly examined how several of these conditions enter the oxygenation problem.^[ref]

The scientific contribution is collective in these sources. Their joint paper does not establish a separate personal allocation of the chemical preparation, measurements and interpretation. The photograph below is the institutionally identified joint image, credited to Columbia University's Department of Biochemistry.^[ref]

A release factor is a protein involved in terminating biological translation and releasing the completed polypeptide at a stop codon.^[ref]

Amyloid deposition involving the kidney. Depending on the distribution, it can disrupt filtration-barrier function and produce protein loss or progressive renal impairment.

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]

An assay in which a measurable output is linked to a chosen regulatory sequence or activity. Reporter RNA abundance, biological translation and protein stability can affect the same endpoint differently.

An experimentally introduced gene whose measurable output reports a specified regulatory process. A change in protein output alone cannot distinguish altered transcription, RNA decay and biological translation.

A light-absorbing aldehyde related to vitamin A, used as a chromophore in rhodopsin-family proteins. Its local packing and bonding connect light absorption to structural changes.

The RGD motif is the three-amino acid sequence arginine–glycine–aspartic acid, abbreviated R–G–D in one-letter notation. In fibronectin, this sequence contributes to cell adhesion and recognition by integrins. A protein primary structure can therefore contain a short recognizable region whose activity depends on its molecular presentation.

The originating 1984 experiment measured attachment-promoting activity of synthetic fragments from fibronectin. Its reported active sequence was the four-residue peptide RGDS, with serine following the RGD motif. The three-letter name of the core and the four-residue experimental fragment must be kept distinct.^[ref]

For an original sequence example, the invented five-residue string ARGDS contains the RGD motif at positions 2–4; ARGES does not. The two strings have equal length, but substituting glutamic acid for aspartic acid changes their local sequence. This inspection identifies a motif, not an experimentally established attachment activity. A folded protein, a surface-presented peptide and a soluble peptide present different physical contexts; the activity of one preparation does not specify every function of full-length fibronectin.

Rhodopsin is the light-sensitive G protein-coupled receptor of vertebrate rod photoreceptors. It consists of the protein opsin bound to the light-absorbing molecule 11-cis-retinal. Absorbing a photon changes the retinal configuration toward all-trans-retinal, initiating structural changes that activate the signaling partner transducin. The visual cycle supplies fresh 11-cis-retinal so the pigment can be regenerated.^[ref]

The 2000 bovine rhodopsin structure, obtained by X-ray crystallography at $2.8$ angstrom resolution, showed seven membrane-spanning alpha helices surrounding the bound chromophore. The dark-state retinal helps stabilize an inactive receptor configuration. The structure made a molecular question visible: how can a small rearrangement of a bound light absorber alter the intracellular surface that engages another protein?^[ref]

The distinction between opsin and functional pigment matters experimentally. In mice lacking RPE65, investigators detected rod opsin but no normal rhodopsin, together with loss of rod responses on electroretinography. Having the receptor chain is insufficient when the required retinal supply is disrupted.^[ref]

Riboflavin kinase is an enzyme that phosphorylates riboflavin to form flavin mononucleotide, using ATP and producing ADP. It is EC 2.7.1.26, with systematic activity name ATP:riboflavin 5′-phosphotransferase. The reaction supplies a flavin cofactor and also a substrate for FAD synthase.^[ref]

The two reactions can be kept chemically distinct:Their sum requires two ATP molecules per flavin adenine dinucleotide made from riboflavin, producing one ADP and one diphosphate. The flavin mononucleotide intermediate cancels in the net equation, but must still be formed during the pathway.^[ref]

A constructed inventory makes the limitation explicit. With 8 nanomoles of riboflavin and 12 nanomoles of ATP, no more than 6 nanomoles of flavin adenine dinucleotide can be formed through the complete two-step route if there are no other ATP sources. This is a stoichiometric ceiling. If the first reaction instead converts all eight nanomoles before the second proceeds, only four nanomoles of ATP remain, allowing four nanomoles of flavin adenine dinucleotide and leaving four of flavin mononucleotide. The same initial inventory permits different intermediate distributions.

A divalent metal ion is required for riboflavin kinase activity, with preferences depending on the biological source. Some bacteria place this activity and FAD synthase in one bifunctional protein.^[ref] The activity names distinguish reactions, while protein architecture describes how an organism implements them.

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 ribonucleoprotein is an association of RNA with proteins.

A protein component of a ribosome. The machinery can combine products of different genomes, especially in an organelle.

Ribosomal protein L22 is a bacterial ribosomal protein with a tunnel-facing contribution to the environment encountered by an emerging polypeptide chain. Its molecular identity and its role in a particular regulatory stall are separate levels of description: showing that a residue affects one nascent-chain response does not establish that every translation event is affected equally.

A 2002 genetic experiment provided a concrete functional connection. Mutations bypassing SecM-dependent elongation arrest were found in ribosomal protein L22 and 23S ribosomal RNA. The altered residues faced the narrow constriction of the ribosomal exit tunnel. Their positions and effects supported an interaction between that region and the nascent chain.^[ref]

An original comparison illustrates how to distinguish a sequence-sensitive effect from a general failure of translation. Suppose an assay measures the arrested fraction for an arrest-capable peptide and for a control peptide:These invented values show a change associated mainly with the arrest-capable sequence. Measuring only its0.8-to-0.2 change would omit the comparison supplied by the control. Such a pattern would motivate a sequence-sensitive explanation, but additional checks of assembly, abundance and general translation competence would still be needed.

The experiment also separates an affected protein component from the larger molecular apparatus. L22 acts within a ribosome containing ribosomal RNA and many other components. A mutation's effect can depend on that surrounding structure and on the peptide being synthesized. Functional perturbation and structural location therefore complement one another without making the isolated protein the entire arrest mechanism.

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.

Sequencing of RNA fragments protected by ribosomes to measure their positions on transcripts. Occupancy measures a combination of entry, passage and dwell time; more footprints can reflect slower elongation rather than more completed protein.

A ribozyme is an RNA molecule whose folded structure provides catalysis of a chemical reaction. A protein enzyme builds its active site from an amino acid chain; a ribozyme builds a working active site from RNA, sometimes with metal ions and associated proteins. Base pairing can help recognize a substrate, but recognition alone does not establish catalysis: the RNA must promote chemical conversion. A passive messenger RNA template being read by a ribosome is not thereby a ribozyme. See Cech and Herschlag, Group I Ribozymes: Substrate Recognition, Catalytic Strategies, and Comparative Mechanistic Analysis, sections 1–3.

The surprise is that an information-bearing polymer can also perform chemistry. Examples include the self-splicing group I intron of Tetrahymena thermophila and the catalytic RNA component of bacterial RNase P, discussed below. The ribosome supplies an everyday example: its peptide bond-forming active site is made of ribosomal RNA, although the complete machine also contains proteins. Nissen and colleagues examined structures of a large ribosome subunit with substrate analogues and found RNA contacting those analogues at the catalytic centre. This supports an RNA active site, not a claim that isolated ribosomal RNA can carry out all of biological translation. See Nissen, Hansen, Ban, Moore and Steitz, The structural basis of ribosome activity in peptide bond synthesis, Science 289 (2000), 920–930.

For the Tetrahymena group I intron, RNA splicing removes the intron and joins its flanking exons. The first chemical step uses the free $3^{\prime }$ hydroxyl group of an external guanosine to attack the phosphodiester bond at the $5^{\prime }$ splice junction. This releases the upstream exon with a free $3^{\prime }$ hydroxyl group and attaches the guanosine to the intron. That newly freed hydroxyl group then attacks the phosphodiester bond at the other splice junction, joining the exons and releasing the linear intron. Each step exchanges one backbone connection for another; it is not simply separation of base pairs. See Cech, Zaug and Grabowski, 1981: the phosphoester-transfer mechanism.

The motivating experiment began with an unexpected control. As Cech recounts, Zaug purified a ribosomal RNA precursor from Tetrahymena using a detergent and phenol extraction, then compared test tubes with and without added cell nucleus extract. Incubation in salts and nucleotides released the same amount of small intron RNA in both cases, detected by gel electrophoresis. Repetition made a missing ingredient or accidental omission less plausible. Activity also survived treatments intended to destroy proteins. Nevertheless, absence of added extract did not by itself exclude a tightly attached, resistant protein, or prove that the small RNA had been newly excised rather than released from an already processed complex. See Thomas R. Cech, 1989 Nobel lecture, pp. 655–659: the unexpected control and alternative explanations.

An independent chemical readout addressed the latter problem. Cech mixed precursor RNA with phosphorus-32-labelled guanosine bearing three phosphate groups (GTP), and used gel electrophoresis followed by exposure to X-ray film to locate the label. Label appeared in the excised intron with magnesium present; it was absent when magnesium was omitted or labelled ATP replaced the labelled guanosine reagent. This experiment is described in Cech, 1989 Nobel lecture, pp. 657–658: labelled-guanosine controls. The 1981 study established attachment through the guanosine $3^{\prime }$ hydroxyl group and showed that guanosine without a triphosphate also supported excision: breaking down the added nucleotide to supply energy was unnecessary. See Cech, Zaug and Grabowski, In vitro splicing of the ribosomal RNA precursor of Tetrahymena, Cell 27 (1981), 487–496: primary abstract. Separately, sequencing and terminal analysis found an extra $5^{\prime }$ guanosine absent from the corresponding DNA sequence. See Zaug and Cech, The intervening sequence excised from the ribosomal RNA precursor of Tetrahymena contains a 5-terminal guanosine residue not encoded by the DNA, Nucleic Acids Research 10 (1982), 2823–2838. Together, incorporation and sequence evidence support a new covalent bond, beyond a change in how RNA associates.

Kruger, Grabowski, Zaug, Sands, Gottschling and Cech's 1982 test removed dependence on a precursor purified from Tetrahymena. They cloned the intron and adjacent exons into a DNA template, made precursor RNA with purified bacterial RNA polymerase under conditions suppressing RNA splicing, and removed proteins by detergent–phenol extraction. Denaturing gel electrophoresis separated precursor species. Purified precursor was then incubated with the guanosine reagent, magnesium and salt; matched samples without this incubation supplied a precursor baseline. Their standard assay used $10\mathrm{mM}$ magnesium chloride, $0.1\mathrm{mM}$ of that guanosine reagent, $100\mathrm{mM}$ ammonium sulfate and a buffer solution at pH $7.5$, for $30$ minutes at temperature $37{}^{\circ }\mathrm{C}$, with specified variations in individual experiments. Gel electrophoresis and radioactive-film detection showed excised intron RNA; sequencing verified its $5^{\prime }$ junction. See Kruger et al., Self-Splicing RNA, Cell 31 (1982), 147–157, figures 3–4 and Experimental Procedures.

Excision alone could leave disconnected exons. To test joining, the authors paired labelled RNA with DNA spanning the joined-exon sequence, removed exposed RNA with enzymes, and separated the protected pieces by denaturing gel electrophoresis. Spliced samples yielded protected RNA long enough to span the junction. See Kruger et al., 1982, figure 6: independent evidence for exon ligation. The experimental logic matters: an intron-sized band identifies a candidate product, while sequence and junction assays test its chemical identity.

These controls support sufficiency of the prepared RNA under the assay conditions. They do not show that every RNA self-splices, or that proteins are dispensable inside a biological cell. Many group I introns use proteins to help attain an active fold. See Cech and Herschlag, Group I Ribozymes, section 6: protein facilitation. Nor does a failed assay necessarily identify an inactive nucleotide sequence: unsuitable ions, pH, or temperature can prevent a working active site from forming.

The distinction between self-processing and repeated use became especially clear with bacterial RNase P. In 1983 Guerrier-Takada, Gardiner, Marsh, Pace and Altman separated the RNA and protein components of RNase P from two bacteria. Purified RNA cleaved precursor transfer RNA under conditions containing $60\mathrm{mM}$ magnesium ions, or $10\mathrm{mM}$ magnesium ions plus $1\mathrm{mM}$ spermidine. The protein components alone had no catalytic activity. At $5$–$10\mathrm{mM}$ magnesium without spermidine, both components were needed. Thus the comparison demonstrated an RNA catalyst while also explaining why protein assistance could matter under other conditions. RNase P produces the mature $5^{\prime }$ end of transfer RNA by removing its leader; it acts on a separate substrate and can be used again. See Guerrier-Takada et al., The RNA moiety of ribonuclease P is the catalytic subunit of the enzyme, Cell 35 (1983), 849–857: primary abstract.

Self-splicing demonstrates RNA chemistry, but one precursor completing one rearrangement is not yet evidence for catalytic turnover: repeated conversion of separate substrates by a regenerated catalyst. The self-splicing precursor changes its own connectivity and incorporates external guanosine. In 1986 Zaug and Cech showed that a shortened Tetrahymena intron RNA could cleave and rejoin separate short RNA substrates in a sequence-dependent reaction. This demonstrated an RNA enzyme acting beyond its own self-processing. See Zaug and Cech, The intervening sequence RNA of Tetrahymena is an enzyme, Science 231 (1986), 470–475: primary abstract.

Read the second figure as a counting argument. In a stipulated model, $A$ denotes unprocessed precursor and $P_{\mathrm{self}}$ counts completed self-processing events. Set $A(0)=R_0$, $P_{\mathrm{self}}(0)=0$ and $dA/d\tau =-A$. The exponential function solution gives $P_{\mathrm{self}}/R_0=1-e^{-\tau }$, never exceeding one. Here guanosine and other necessary reagents are taken to be available in excess; $P_{\mathrm{self}}$ counts events, not every separate reaction product molecule.

For a second stipulated model, let an unchanged ribozyme $R$ perform $R+S⟶R+P$ on a separate substrate $S$. Assume the effective law of mass action $dS/dt=-kRS$, no reverse reaction, no ribozyme loss and no inhibited or long-lived bound states. Set $R=R_0$, $S(0)=5R_0$, $P(0)=0$ and $\tau =k{R}_{0}t$. Then $S/R_0=5e^{-\tau }$ and $P/R_0=5(1-e^{-\tau })$, with $S+P=5R_0$. At $\tau =1$, self-processing gives about $0.632$ completed events per initial RNA, whereas the regenerated ribozyme gives about $3.161$ reaction product molecules per initial ribozyme. More than one substrate conversion per initial ribozyme, with appropriate background and identity controls, is evidence for turnover. Product accumulation below that threshold alone cannot distinguish a reusable catalyst from one-shot chemistry. These models illustrate that distinction; actual enzyme kinetics can include folding delays, binding, saturation and product release.