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Chemical stripping of organic material, commonly photoresist, by reactive species produced in a plasma. oxygen radicals convert suitable organic material into volatile oxidation products. A remote source reduces direct energetic ion bombardment, but exposed materials can still oxidize and inorganic residue can remain.

A plasma is a gas of mobile charged particles whose collective electromagnetic response is important to its dynamics. It commonly contains ions and electrons, and may also contain a neutral component: complete ionization is not required. A multi-species fluid description has current density $\mathbf{J}={\sum }_s{q}_s{n}_s{\mathbf{u}}_s$. The relative motion of the species can matter even when a single-fluid magnetohydrodynamics approximation describes the large-scale dynamics.

A mean-field coupling of the Poisson equation to an ideal Boltzmann distribution of mobile ions. In Gaussian units with uniform dielectric constant $ϵ$, ${\nabla }^2\varphi =-(4\pi /ϵ)[{\rho }_f+{\sum }_i{q}_i{n}_{i,0}{e}^{-\beta q_i\varphi }]$. The potential reference and chemical potentials determine the normalization factors. It neglects discrete-ion correlations and assumes local thermal equilibrium. A counterion-only model is not the same equation as a symmetric salt reservoir.

A polyatomic ion consists of a bound group of two or more chemical atoms with nonzero total electric charge. Hydronium, ${\mathrm{H}}_3{\mathrm{O}}^{+}$, contains three hydrogen and one oxygen chemical atom; its net electric charge is $+e$, where $e$ is the elementary charge. This is a discrete charged group, while an ionic crystal can contain an extended arrangement of ions.^[ref]

A chemical element of atomic number 59. Its trivalent ion has a $4f^2$ open-shell electron configuration. In LS coupling, Hund's rules select $L=5$, $S=1$, $J=4$, the ${}^3{H}_4$ term symbol. The corresponding free-ion Landé g-factor is $4/5$ and its effective paramagnetic moment is $(4/5)\sqrt{20}{\mu }_B\simeq 3.58{\mu }_B$.

Consider an original toy AB salt model with $K_{\mathrm{sp},c}=10^{-8}{\mathrm{M}}^2$ stipulated at fixed temperature and fixed activity coefficient product. This is a conditional concentration constant, not measured data for calcium carbonate or any identified material. A stock contains A cations and X anions; another contains Y cations and B anions. All four ions have unit electric charge magnitude. Only AB can form a solid; X and Y remain spectator ions. Assume full dissociation, no other chemical reactions, and a mixed volume equal to the sum of the initial volumes.

Mix two stocks, each of volume $V$,, each at molar concentration $C$ of its indicated salt. Before any precipitation, the mixed volume is $2V$, soMultiplying the two stock concentrations would overestimate the mixed ion product by a factor of four. The saturation threshold is $C=2\sqrt{K_{\mathrm{sp},c}}=2\times 10^{-4}\mathrm{M}$.

If $C=10^{-4}\mathrm{M}$, mixing gives $Q_{c,0}=2.5\times 10^{-9}{\mathrm{M}}^2<K_{\mathrm{sp},c}$: no AB precipitate is favored. If $C=4\times 10^{-4}\mathrm{M}$, mixing gives $Q_{c,0}=4\times 10^{-8}{\mathrm{M}}^2>K_{\mathrm{sp},c}$. Suppose nucleation occurs and bulk AB solid remains at chemical equilibrium. Equal starting inventories and one-to-one stoichiometry require equal remaining concentrations, henceFor two $10\mathrm{mL}$ portions in the second case, each reacting ion starts with $4\mu \mathrm{mol}$; the final $20\mathrm{mL}$ chemical solution retains $2\mu \mathrm{mol}$ of each, and $2\mu \mathrm{mol}$ of AB enters the solid. The respective X and Y inventories stay at $4\mu \mathrm{mol}$. Exactly half of each reacting inventory precipitates in this toy model.

The chemical equilibrium calculation adds a phase constraint to the inventory balance. Write $x=n_{\mathrm{AB},s}/(2V)$ and $c=C/2-x$. In the equilibrated bulk model,When $x>0$, the last condition requires saturation; when $x=0$, the inventory can leave an undersaturated chemical solution. Together these give $x=\max \{0,C/2-\sqrt{K_{\mathrm{sp},c}}\}$. This excludes a persistent supersaturated solution by its explicit chemical equilibrium assumption; it does not model a nucleation delay.

Precipitation is formation of a solid from a chemical solution; the formed solid is a precipitate. Dissolved chemical species enter a separate thermodynamic phase. A newly formed solid can create a surface for heterogeneous catalysis; observing it does not establish the composition or catalytic role of that surface.

For example, mixing suitable chemical solutions of calcium chloride and sodium carbonate can form calcium carbonate:Here $aq$ means dissolved in water, and $s$ marks the solid. Both sides contain one calcium chemical atom, one carbon chemical atom, and three oxygen chemical atoms; net electric charge is $+2-2=0$ on the left and zero on the right. The arrow describes the net change when precipitation occurs, rather than promising complete removal of either ion. The calcium carbonate precipitation experiment makes this phase separation visible.^[ref]

The attraction is that an invisible dissolved inventory becomes a recoverable solid. Net ionic equations track that transfer; the saturation criterion for precipitation determines whether it is favored under specified conditions. This combination supports separations and chemical analysis.^[ref]

Pump-probe spectroscopy measures a sample's response to a probe pulse at a controlled delay after an exciting pump pulse. Varying delay follows dynamics; selecting frequency and wave polarization can distinguish different contributions. Spectroscopic measurement of hydration dynamics is an application to water surrounding ions.

A radical has one or more unpaired electrons. In a simple atomic orbital or molecular orbital occupancy picture, an unpaired electron occupies a spatial orbital without an opposite-spin partner in that orbital. A dot such as ${\mathrm{H}}^{\bullet }$ marks this electronic property; it does not mean a missing electron or positive electric charge. Free radicals can be neutral or charged. Terminology also has a boundary: metal ions exhibiting paramagnetism are not normally called free radicals just because they have unpaired electrons.^[ref]

Compare three species containing the same single proton. The hydrogen atom ${\mathrm{H}}^{\bullet }$ has one electron in its $1s$ atomic orbital, and is a neutral radical. The hydrogen cation ${\mathrm{H}}^{+}$ has no electrons, so no unpaired electron. The hydrogen anion ${\mathrm{H}}^{-}$ has two electrons paired in its $1s$ atomic orbital. It is charged but is not a radical in its ground state. With $N_p$ protons, $N_e$ electrons, and positive elementary charge $e$, the independent electric charge count isThe electron pair and electric charge questions require different information. An odd $N_e$ ensures that not all electrons can be paired; an even $N_e$ alone does not ensure pairing, as the molecular orbital description of molecular oxygen illustrates.

The distinction matters whenever a chemical reaction mechanism uses dots and charge signs together. Homolysis gives one bonding electron to each fragment, while heterolysis assigns both to one fragment. A radical chain reaction can pass an unpaired electron from one species to another without generating net electric charge. Detection then exploits the unpaired electron's spin and magnetic moment, rather than merely measuring whether the sample carries an electric charge.

A radical ion is both a radical and an ion. Removing one electron from neutral benzene can produce ${{\mathrm{C}}_6{\mathrm{H}}_6}^{\bullet +}$, a radical cation; adding one can produce ${{\mathrm{C}}_6{\mathrm{H}}_6}^{\bullet -}$, a radical anion. These formulae specify net electric charge and an unpaired electron, without claiming that both reside on one chemical atom.^[ref]

A hard-sphere model relating the radius ratio of opposite-charge ions to a possible coordination number. For a cube of eight mutually touching anions around a touching cation, $r_c/r_a=\sqrt{3}-1$; real bonding and coordination-dependent radii limit its predictive power.

In 1995, Christopher Monroe and collaborators cooled one ${}^9{\mathrm{Be}}^{+}$ ion in a ring/endcap Paul trap. They used $313\mathrm{nm}$ Doppler cooling and optical pumping into $|F,m_F⟩=|2,2⟩$. Red-sideband Raman transitions transferred population to $|1,1⟩$, followed by dissipative recycling. Repeating across three directions yielded a reported three-dimensional ground state population of about $92\%$.^[ref]

A variable-frequency Raman transition probe, an exchange pulse and a cycling detection beam converted state populations into fluorescence collected through $f/2$ optics onto a position-sensitive photomultiplier. Red/blue asymmetry inferred motional occupation; varying probe duration tested the thermal assumption. Off-resonant processes and independently observed heating limited cooling.^[ref]

Patterned material removal by chemically reactive plasma species and directional ion bombardment.

A redox chemical reaction couples oxidation and reduction. In the electrode examples here, oxidation releases electrons and reduction accepts them. ^[ref]

Redox can be recognized by changes in oxidation state: an increase records oxidation, a decrease reduction. These are formal electron assignments, distinct from measured partial atomic charges. Half-reactions expose the matching loss and gain, making electric charge conservation visible.^[ref]

The electron accounting need not describe free electrons travelling between spatially separated chemical species. For example, in $2{\mathrm{H}}_2+{\mathrm{O}}_2⟶2{\mathrm{H}}_2\mathrm{O}$, hydrogen changes from oxidation state $0$ to $+1$ and oxygen from $0$ to $-2$. Four hydrogen chemical atoms lose four formally assigned electrons in total; two oxygen chemical atoms gain four. The water product has covalent bonds, and these assignments do not turn it into separated ions. See ionic approximation of bonds and electron transfer and ionic character.

By contrast, neutralization can rearrange chemical bonds without changing oxidation states:Hydrogen remains $+1$ and oxygen remains $-2$. The aqueous proton notation abbreviates its interaction with water. This acid-base chemistry example conserves electric charge but has no matching increase and decrease of oxidation state; movement of ions or a change of chemical bonds alone does not establish redox.

A single nitrate Lewis structure singles out one N=O connection, yet the three N–O chemical bonds of the isolated symmetric ion are equivalent. Chemical resonance reconciles that symmetry with the integer electron pair allocations of a Lewis structure. The equal chemical bond lengths in nitrate are discussed in The Open University, Discovering chemistry: resonance structures.

Chemical resonance uses several Lewis structures with the same chemical atom connections and total electric charge to describe electronic structure that one allocation cannot fully express. The chemical atoms stay in place; the positions of bond pairs, lone pairs, and formal charges differ between drawings. A two-headed arrow $\leftrightarrow$ connects the drawings and is distinct from a chemical equilibrium arrow $\rightleftharpoons$. See the IUPAC Gold Book, resonance form.

In each nitrate resonance structure, use the existing formal charge convention $\mathrm{FC}=v-n-b/2$:Here $v$ counts neutral-chemical atom valence electrons, $n$ counts nonbonding electrons, and $b$ counts incident bonding electrons. The sum is $+1-1-1+0=-1$, agreeing with the nitrate ion's net electric charge. The formal charge rules and their distinction from actual atomic electric charge are given in Flowers et al., Chemistry 2e, 7.4: formal charges and resonance.

Keep one labelled oxygen fixed while reading the three nitrate resonance structures. Its connection is double in one drawing and single in two. Equal weighting within this three-contributor Lewis structure model gives the average bond orderThe same calculation applies to all three N–O connections. Averaging the drawn formal charges similarly gives $-2/3$ per oxygen, while nitrogen retains $+1$; $+1+3(-2/3)=-1$. These fractions summarize the chosen contributors. They are not a measurement of partial atomic charge, a literal fraction of an electron sitting on an oxygen, or time spent in one drawing.

The resonance hybrid has one spatially continuous electron density extending over the ion. None of its N–O chemical bonds is permanently selected as the double connection of one contributor. The dashed marks above are symbols; electrons do not travel along them or make the marks float between chemical atoms. For isolated symmetric nitrate, symmetry makes the three N–O chemical bonds equivalent; an environment that distinguishes the oxygen sites can remove that equivalence. The fraction $4/3$ alone predicts neither a chemical bond length nor a dissociation energy. The general relation between multiple chemical bonds, lengths, and strengths is discussed in 7.5 Strengths of Ionic and Covalent Bonds; its tabulated averages are not a nitrate-specific calibration of $4/3$.

Ozone provides a useful two-contributor comparison. Its $3\times 6=18$ valence electrons give three bond pairs and six lone pairs. One resonance structure has a double O–O connection on the left and a single one on the right; the other reverses these allocations while retaining the same chemical atom positions and connections. The central oxygen has one lone pair and formal charge $+1$; the singly connected terminal oxygen has three lone pairs and formal charge $-1$; the doubly connected terminal oxygen has two lone pairs and formal charge zero. Thus $6+12=18$ electrons and zero net electric charge are conserved. The equal-contributor bond order count is $(2+1)/2=3/2$ for either connection. See MIT 5.111, lecture 10, pp. 4–5: ozone resonance structures.

For carbon dioxide, $\mathrm{O}=\mathrm{C}=\mathrm{O}$ and ${\mathrm{O}}^{-}-\mathrm{C}\equiv {\mathrm{O}}^{+}$ share sixteen valence electrons and the same O–C–O connections. The mirror drawing ${\mathrm{O}}^{+}\equiv \mathrm{C}-{\mathrm{O}}^{-}$ is also possible. The two charge-separated drawings are equivalent to one another for an isolated symmetric carbon dioxide molecule, but neither is equally dominant with $\mathrm{O}=\mathrm{C}=\mathrm{O}$ in the elementary formal charge comparison.

Chemical resonance does not mean that a molecule rapidly flips between drawings, nor that separate molecules at chemical equilibrium carry the individual drawings. The actual electron density belongs to one combined electronic description. In a quantum mechanics treatment, contributors enter a linear combination of many-electron wavefunctions; a molecular orbital treatment can describe the extended electronic arrangement through molecular orbitals. The drawings alone provide neither a measured density nor numerical weights. Their usefulness is to expose the limitations of one localized allocation without pretending that every algebraically allowed Lewis structure contributes equally.

A resonance hybrid is the combined electronic description expressed using several resonance structures. The word does not describe a mixture of separate molecules or ions: a nitrate ion has one electron density, rather than three species in chemical equilibrium. Equal weighting is appropriate for the equivalent nitrate contributors in the elementary model; the unequal carbon dioxide contributors illustrate why it is not a general rule. See Chemistry 2e, 7.4: resonance hybrids do not fluctuate between forms.

A reversal potential $E_{\mathrm{rev}}$ is a membrane potential at which a specified open ion channel, or specified combination of ion channels, carries zero net electric current, with the surrounding conditions fixed; the electric current changes sign across that voltage. Specifying which current matters: an individual ion contribution and a sum of several contributions can reverse at different voltages. Zero net electric current does not mean that all ions have stopped moving. See Purves et al., Neuroscience, 2nd edition (2001): reversal of a mixed-ion channel current.

Throughout these examples, membrane potential is $V=V_{\mathrm{inside}}-V_{\mathrm{outside}}$, and conventional current is inward-positive. Positive electric current corresponds to net positive electric charge entering or net negative electric charge leaving. Negative electric current corresponds to the reverse charge transfer. A convenient Ohmic approximation iswhere $g$ is the available electrical conductance. For fixed $g>0$, $V<E_{\mathrm{rev}}$ gives positive electric current, $V=E_{\mathrm{rev}}$ gives zero, and $V>E_{\mathrm{rev}}$ gives negative electric current; the line has slope $-g$. If $g=0$, the modeled pathway carries zero electric current at every voltage: closing it does not locate its reversal potential. 3.1 Synapses (§3.1: conductance-based synaptic current) uses outward-positive $g(V-E)$; the formula here reverses that sign to match this wiki's inward-positive convention.

For the stipulated single-pathway example from ion channel, $E_{\mathrm{rev}}=-80\mathrm{mV}$ and $g=10\mathrm{nS}$ giveThe open ion channel carries zero net electric current at $-80\mathrm{mV}$ even though $g$ remains positive. Near that point a change of membrane potential changes the electric current, which is why zero current at one voltage does not make an open pathway electrically irrelevant; see shunting inhibition.

For an ion channel passing only one ion species by passive transport, its reversal potential can equal that species' Nernst equilibrium potential, where the chemical and electrical contributions to electrochemical potential balance. At that thermodynamic equilibrium, passage in both directions can continue with no net transport. For an ion channel admitting several ion species, opposing contributions can cancel while each species continues to have net transport. Such a reversal potential is not generally any one species' Nernst equilibrium potential. See the Purves reference above.

To work out that cancellation explicitly, put two Ohmic ion channel populations across the same cell membrane. Stipulate constant electrical conductances and fixed reversal potentials:The potassium and sodium contributions add because both pathways experience the same membrane potential:Thus $I_{\mathrm{total}}=12\mathrm{nS}(E_{\mathrm{eff}}-V)$. This weighted mean follows simply by expanding and regrouping the two current terms; it assumes additive Ohmic contributions and a positive total electrical conductance. At $V=E_{\mathrm{eff}}$, the inward-positive individual electric currents areThe potassium contribution is outward and the sodium contribution inward. Equal and opposite electric currents give $I_{\mathrm{total}}=0$; neither pathway has stopped transporting its ions. The calculation treats two distinct pathways. Applying it to one mixed-species ion channel would additionally require a justified decomposition into independent Ohmic contributions; a general mixed-channel reversal potential cannot be obtained by assuming those hypotheses silently.

This is an instantaneous balance of the specified passive electric currents. It would be the stationary voltage of a passive capacitance model containing only these constant pathways and no applied electric current, but it is not a complete prediction of a living cell's resting membrane potential. Other electric currents, voltage-dependent gating, and pumps involved in active transport can matter. Pumps that transfer net electric charge are electrogenic and contribute their own electric current. See Purves et al.: functional properties of the sodium/potassium pump.

The toy model holds ion concentrations and therefore the stipulated reversal potentials fixed. Continuing inward sodium and outward potassium transport would change finite reservoirs unless active transport or external control maintained them. Transport can be a small fraction of the reservoir's ions over a short interval, making fixed concentrations a useful approximation; it is not a claim that the reservoirs never change. See Gerstner et al., Neuronal Dynamics (2014), §2.1: equilibrium potentials, channel currents and maintained gradients.

A reversal potential makes the effect of opening an ion channel predictable from the present membrane potential. The same open pathway can carry inward or outward electric current as $V$ crosses its reversal potential. The two-pathway example reveals a particularly useful distinction: zero net charge transfer can coexist with continuing exchange of different substances. That distinction connects membrane transport to electric current measurements without mistaking electrical balance for thermodynamic equilibrium.

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 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.

The rock salt structure of ordinary sodium chloride has a coordination number of six for each kind of ion: six nearest neighbours of the opposite sign surround each ion along three perpendicular directions. Its conventional cubic unit cell contains four formula units; sharing corner, face, and edge sites between adjacent cells must be included in that count. Sixfold local coordination is compatible with $1:1$ overall stoichiometry.^[ref]

The checkerboard plane in the diagram is a slice through this three-dimensional arrangement. It leaves out the two nearest neighbours above and below the plane. Repeating a complete even-by-even patch gives equal numbers of signs; the displayed odd-by-odd crop has a boundary imbalance and is not a complete neutral ionic crystal or a unit cell. Other salts need not have the rock salt structure or the same coordination number.