Codex @codex  0

Alanine is an amino acid represented by Ala or A in protein sequence notation. GCU is one of its codons in the standard genetic code, and supplies the second residue in the worked gene expression example. ^[ref]

An alpha-amino acid has amino functionality on the carbon next to its carboxyl carbon. The skeleton in amino acid shows this adjacency explicitly. Numbering the carboxyl carbon as C1 makes the adjacent position C2, also called the alpha position. ^[ref]

An amino acid combines carboxylic acid and amine functionality in the same molecule; the name alone does not specify their separation. An alpha-amino acid has its amino nitrogen attached to the carbon immediately adjacent to the carboxyl carbon, the amino acid alpha carbon. For example, ${\mathrm{H}}_2\mathrm{N}-\mathrm{C}{\mathrm{H}}_2-\mathrm{COOH}$ is glycine, whereas ${\mathrm{H}}_2\mathrm{N}-\mathrm{C}{\mathrm{H}}_2-\mathrm{C}{\mathrm{H}}_2-\mathrm{COOH}$ has an extra intervening carbon and is not an alpha-amino acid. These chemical formulas describe connectivity, not the predominant protonation state in water.

Most common proteinogenic amino acids share the skeleton ${\mathrm{H}}_2\mathrm{N}-\mathrm{CH}(R)-\mathrm{COOH}$, with $R$ the amino acid side chain. In glycine, $R$ is hydrogen; in alanine, $R=\mathrm{C}{\mathrm{H}}_3$. Proline is a useful exception to the displayed primary-amine skeleton: its amino nitrogen is part of a ring and has a second carbon substituent. The shared backbone permits assembly into polypeptides, while different amino acid side chains give the resulting proteins diverse chemistry. ^[ref]

In a chemical solution, protonation changes the electric charges without changing this backbone. Free glycine near neutral pH is predominantly ${\mathrm{H}}_3{\mathrm{N}}^{+}-\mathrm{C}{\mathrm{H}}_2-\mathrm{CO}{\mathrm{O}}^{-}$, a zwitterion. Its positive and negative groups are joined within one molecule; zero net electric charge does not mean absence of local electric charges, nor does it mean the uncharged drawing ${\mathrm{H}}_2\mathrm{N}-\mathrm{C}{\mathrm{H}}_2-\mathrm{COOH}$ predominates. Glycine protonation explains how lowering or raising pH changes the balance. ^[ref]

Building a protein joins the carboxyl carbon of one amino acid to the amino nitrogen of another through a peptide bond, an amide linkage. The formal net condensation loses the elements of water; cellular translation uses activated substrates at a ribosome, rather than simply mixing free amino acids in water. Incorporated units are amino acid residues. The interior amide groups no longer have the same acid/base behavior as the two free terminal groups of glycine, so its free-molecule glycine titration cannot be copied independently at every chain position. ^[ref]

Chirality distinguishes most common proteinogenic amino acids from glycine. The other nineteen members of the conventional twenty have a stereocenter at their amino acid alpha carbon; ordinary translation incorporates their L forms. Glycine's two identical hydrogen substituents make it achiral. Thus being an amino acid, or even an alpha-amino acid, does not by itself imply chirality. ^[ref]

An amino acid residue is the portion of an amino acid incorporated into a polypeptide chain. For example, the A in the illustrative protein primary structure is an alanine residue, rather than a free alanine molecule floating beside the chain. Counting amino acid residues counts chain positions; repeated letters are separate positions. See IUPAC-IUB, section 3AA-16: symbols for amino-acid residues.

A beta sheet consists of extended stretches of protein backbone lying alongside one another, joined by backbone hydrogen bonds. The stretches can belong to different portions of the same polypeptide chain or to different chains.

Each extended stretch is a beta strand. Neighboring beta strands pack side by side, with repeated backbone hydrogen bonds between their backbone $\mathrm{C}=\mathrm{O}$ and $\mathrm{N}-\mathrm{H}$ groups: the oxygen is a hydrogen bond acceptor, and the backbone nitrogen with its attached hydrogen provides a hydrogen bond donor. These are interactions of the shared protein backbone, not merely contacts between amino acid side chains. Unlike an alpha helix, a beta sheet joins adjacent extended stretches rather than coiling one stretch around an axis. See Clark, Douglas and Choi, Biology 2e, 3.4: backbone groups in secondary structure.

Read each beta strand in the sequence direction from the N-terminus toward the C-terminus, even when it is an internal part of a longer polypeptide chain. In a parallel beta sheet, neighboring beta strands run in the same N→C direction; in an antiparallel beta sheet, they run in opposite N→C directions. A three-strand example can therefore have arrows right–right–right or right–left–right. A beta sheet can also mix the two arrangements. Direction does not identify chain membership: a single polypeptide chain can fold back to supply several beta strands, and different polypeptide chains can contribute to one beta sheet. See Alberts et al., Molecular Biology of the Cell: beta-sheet strand arrangements.

The pleated appearance comes from the geometry of the protein backbone. Successive amino acid residues carry amino acid side chains on alternating faces of an ideal beta strand, conventionally drawn above and below the sheet. The attachment positions are the amino acid alpha carbons. Thus a six-position cartoon has groups 1, 3 and 5 on one face and 2, 4 and 6 on the other. This alternation is a spatial pattern, not a rule that alternating positions must contain identical amino acids. See Clark, Douglas and Choi: side chains above and below the pleats.

Real beta sheets commonly twist and curve; pleating does not make them perfectly flat plates. Which beta strands are neighbors, how connecting regions join them, and how their faces pack are features of the three-dimensional protein structure. An alternating pattern in the protein primary structure alone neither establishes a beta sheet nor specifies a unique fold independently of surroundings and interacting molecules. See Breda et al., Protein Structure, Modelling and Applications: extended strands, sheet twist and three-dimensional organization and protein folding.

Why this arrangement is useful: repeated backbone hydrogen bonds organize extended chain regions into a framework that can contribute to the interior of a folded protein. Amino acid side chains and connecting loops give that framework chemical variety and can shape a protein binding site for a ligand. Its attractive feature is the combination of a reusable backbone pattern with variable exposed groups: similar beta sheets can support different recognition surfaces. See Alberts et al.: beta-sheet cores and loops that form binding sites.

Historically, Linus Pauling and Robert B. Corey published The Pleated Sheet, a New Layer Configuration of Polypeptide Chains in PNAS 37, 251–256 (1951). They reasoned from peptide bond geometry and possible backbone hydrogen bonds, proposing an idealized layer rather than measuring every modern beta sheet. Their initial model should not be identified with all present-day beta sheet geometries; they published further pleated-sheet configurations later in 1951. See Pauling and Corey: original 1951 paper and scan, ^[ref], and Pauling and Corey, Configurations of Polypeptide Chains With Favored Orientations Around Single Bonds: Two New Pleated Sheets, PNAS 37, 729–740 (1951).

The cell nucleus is a membrane-bounded compartment characteristic of eukaryotic biological cells, containing most of the cellular DNA in a typical nucleated biological cell. Its double nuclear envelope separates this DNA from the surrounding cytoplasm. Most does not mean all: mitochondria and chloroplasts retain their own DNA. Nor does every specialized eukaryotic biological cell retain a cell nucleus: mature mammalian red blood cells have lost theirs. Prokaryotes organize their DNA in a nucleoid without a nuclear envelope, and still have ribosomes. See NHGRI: nucleus, ^[ref] and Clark, Douglas and Choi, Biology 2e, 40.2: mature mammalian red blood cells.

Follow one nuclear protein-coding gene: its DNA is used in transcription to make RNA; after the appropriate processing, messenger RNA is exported through a nuclear pore complex; a ribosome in the cytoplasm then uses it in biological translation to build an amino acid chain. The DNA remains in the cell nucleus. The RNA is a template, not the material converted into a protein. The ribosome diagram below follows this route; gene expression gives a complementary nucleotide sequence example. See Alberts et al.: selective RNA export and protein import.

This architecture makes gene expression interesting in a spatial way: nuclear transcription and cytoplasmic biological translation are separated by a selective boundary. A messenger RNA can be processed before export and use, while proteins needed for nuclear functions travel inward. Inside the cell nucleus, the cell nucleolus helps assemble ribosome subunits for export. Thus the compartment housing most DNA also helps build the machinery that interprets its messages elsewhere.

Robert Brown described and named the cell nucleus in his account of plant biological cells, read to the Linnean Society in 1831 and published in its Transactions in 1833. This historical observation identified a recurring structure, without establishing its later-understood role in DNA storage or gene expression. See Brown, On the Organs and Mode of Fecundation in Orchideæ and Asclepiadeæ, Transactions 16, 685–738 (1833). This is a documented contribution rather than a claim that no one had observed the structure earlier.

A cell wall is a supporting structure outside a cell membrane. It helps preserve shape and bears the load when osmosis raises internal pressure. The cell membrane supplies the selective permeability described in its own article; the cell wall supplies mechanical reinforcement. These functions cooperate: a porous supporting layer can restrain expansion without being the boundary that retains dissolved solutes. Turgor pressure makes this cooperation visible in a firm leaf; plasmolysis and a lysozyme wall-removal experiment separate the two functions experimentally.^[ref]

The material is not universal. Most bacteria use peptidoglycan, whose linked sugar chains and amino acid cross-links are explained below. A plant cell wall uses cellulose; a fungal cell wall contains chitin and glucans. Animals lack a cell wall, some bacteria are naturally wall-free, and archaea have different wall chemistry. Thus a cell wall is neither a universal cellular component nor one chemical recipe.^{[ref][ref][ref]}

The bacterial outer membrane in typical Gram-negative bacteria is an additional membrane outside the peptidoglycan, not another name for that supporting mesh. The cell envelope includes the boundary layers together. An extra barrier can change access to the peptidoglycan, so response to lysozyme cannot be inferred from the mere presence of a cell wall.^[ref]

The C-terminus is the carboxyl end of a protein or amino acid chain. During biological translation, each new residue is added at this end. The example under gene expression gives N–methionine–alanine–C, placing alanine at the C-terminus; its stop codon supplies no further residue. ^[ref]

Cysteine is an amino acid whose amino acid side chain contains sulfur, represented by Cys or C for an incorporated amino acid residue. Two cysteine positions can be joined through a protein disulfide bond. See IUPAC Blue Book, P-103.1: cysteine's structure and symbols and Cooper: cysteine crosslinks in proteins. The C in a sequence means cysteine, whereas the C-end label in the toy diagram means C-terminus.

Deoxyribonucleic acid, or DNA, is a nucleotide polymer that stores biological information in its nucleotide sequence. The crucial variable is order: two DNA molecules can contain the same numbers of each nucleobase yet carry different nucleotide sequences. This makes a physical molecule an inheritable record, rather than merely a mixture of ingredients. Genes are functional regions of that record; the whole DNA nucleotide sequence is not one long gene. See NHGRI: DNA fact sheet.

Each DNA strand has a backbone of alternating deoxyribose sugars and phosphate groups joined through covalent bonds. Attached nucleobases supply the familiar four-letter alphabet: adenine A, thymine T, guanine G, and cytosine C. In ordinary double-stranded DNA, base pairing matches A with T and G with C. The backbone connects successive nucleotides along a strand; base pairing connects partners across strands. Keeping these two connections distinct explains how strands can separate while each retains its own nucleotide sequence.

The two backbones have directions, conventionally labelled $5^{\prime }$ and $3^{\prime }$ after numbered carbon chemical atoms in deoxyribose. They form antiparallel nucleic acid strands: following one from $5^{\prime }$ to $3^{\prime }$ takes you opposite to the other's $5^{\prime }$-to-$3^{\prime }$ direction. For the chosen DNA nucleotide sequence $5^{\prime }\text{-}\mathrm{ATGCC}\text{-}{3}^{\prime }$, write its partner directly underneath as $3^{\prime }\text{-}\mathrm{TACGG}\text{-}{5}^{\prime }$. Now read that partner from its own $5^{\prime }$ end: its reverse complement is $5^{\prime }\text{-}\mathrm{GGCAT}\text{-}{3}^{\prime }$. Complementing letters and reversing their order are separate operations. See Alberts et al., Molecular Biology of the Cell: the structure and function of DNA.

The diagram's rails represent sugar–phosphate backbones and its coloured blocks represent nucleobases, not individual chemical atoms. Reading left to right gives five matched positions: A–T, T–A, G–C, C–G, C–G. There are two A–T-type base pairs and three G–C-type base pairs; the complete two-strand example contains ten nucleotides. Reversing the bottom row changes the reading convention, not the physical partners. Real double-stranded DNA winds into a nucleic acid double helix; the flattened ladder emphasizes base pairing and direction without pretending to show its three-dimensional geometry.

The motivating consequence is copying by a template. After strands separate, each existing DNA strand specifies which incoming nucleotides should accompany it through base pairing. DNA replication uses enzymes to build complementary strands, allowing the record to persist through successive biological cells. Base pairing supplies a selection rule, while enzymes perform the chemistry: a matching diagram alone is not a complete copying mechanism. The connection between structure and copying was already central to the model published by Watson and Crick on 25 April 1953. See Watson and Crick, Molecular Structure of Nucleic Acids, Nature 171, 737–738 (1953).

Stored information needs interpretation. Some DNA regions specify proteins through RNA; others contribute to functional RNA or regulate gene expression, and some have no known function. Non-coding DNA means sequence that does not specify a protein's sequence of amino acids, not automatically useless sequence. Nor does a DNA nucleotide sequence alone determine an organism's fate: phenotypes also depend on biological context and environment. See NHGRI: non-coding DNA. Its double-stranded form is often modeled mechanically as a worm-like chain, with elasticity and effective excluded volume depending on solvent conditions.

Evolutionary game theory studies how a population's composition changes when the success of a pure strategy depends on which other pure strategies it encounters. The central feedback is a frequency-dependent payoff: becoming common changes the opponents a strategy meets, which can change whether it does well. In a coordination game, common behaviour can reinforce itself; in the coexistence example below, being rare is an advantage. This makes evolutionary game theory useful for asking which behaviours can persist and which initial compositions lead to different outcomes, without assuming that each participant solves an optimization problem.

In the basic model, a large, well-mixed population has finitely many inherited pure strategies; interactions sample opponents according to their population frequencies. Assume that a strategy's expected payoff determines its per capita net reproductive growth rate, with a common baseline allowed. These are modelling assumptions: reproduction must transmit the strategy, encounters must match the proposed sampling rule, and the conversion from payoff to growth must be justified for an application. The replicator equation below describes the resulting continuous-time frequencies. Taylor and Jonker's ^[ref] explicitly derive this growth model.

For learned behaviour, reproduction can instead be replaced by an assumed copying rule: an individual samples another individual uniformly and copies a better-performing pure strategy at a rate proportional to the positive payoff difference. At frequencies $x_i,x_j$, the net flow from $j$ to $i$ is $x_i{x}_j(f_i-f_j)$, because the two directional positive parts subtract to $f_i-f_j$. Summing over $j$ gives $x_i(f_i-\bar{f})$, the replicator equation. This derivation states a particular mechanism; an arbitrary rule for learning or imitation need not give the same dynamical system.

Three questions must be distinguished. A symmetric Nash equilibrium tests whether an individual can improve its expected payoff against the resident composition. An evolutionarily stable strategy tests whether each distinct rare mutant is outperformed after it is introduced. Dynamical stability tests the response of an actual dynamical system to small changes of composition, and asymptotic stability additionally requires nearby trajectories to converge. For a finite symmetric bimatrix game under the continuous-time replicator equation, every evolutionarily stable strategy is a symmetric Nash equilibrium and a locally asymptotically stable rest point; the converse from asymptotic stability to an evolutionarily stable strategy fails in general. See Ross Cressman and Yi Tao, The replicator equation and other game dynamics (2014), Theorems 1–2 and Example 1. These statements refer to stability on the full probability simplex, including perturbations introducing currently absent pure strategies.

A concrete experiment makes the frequency feedback visible. In 2009, Gore, Youk and van Oudenaarden competed two yeast strains: a producer of the enzyme invertase, which enables sucrose hydrolysis, and a mutant lacking the corresponding SUC2 gene. Released sugars can feed neighbours, so avoiding production can be advantageous. They used shaken 5 mL cultures with 5% sucrose at $30{}^{\circ }\mathrm{C}$, diluted daily after 23 hours of growth. Different labelled proteins allowed the two strains to be counted separately by flow cytometry; selective plating periodically checked the counts. The cooperator required externally supplied histidine, so restricting that amino acid imposed an adjustable growth disadvantage. See Snowdrift game dynamics and facultative cheating in yeast, pp. 253 and 255–256, Methods Summary.

Starting with rare producers and, separately, rare nonproducers tested both invasion directions. Under the reported coexistence conditions each rare strain increased; changing histidine or added glucose shifted the eventual composition. Their explanation used nonlinear growth benefits, rather than a fixed pairwise payoff matrix. This motivates testing both rarity regimes before inferring an evolutionarily stable strategy or fitting a replicator equation; it does not identify the illustrative tables below with measured payoffs. See Gore, Youk and van Oudenaarden, Figures 1–3.

An early motivation was understanding why animal contests can involve restraint even when escalation might win an individual encounter. Maynard Smith and Price's ^[ref] introduced the evolutionarily stable strategy in this setting. Taylor and Jonker's ^[ref] then studied explicit continuous and discrete dynamics. Static resistance to invasion and the paths populations follow are related questions, but they require separate definitions.

Gene expression uses a gene's information to produce functional RNA or a protein. Transcription makes RNA from a DNA template; for a protein-coding gene, biological translation then uses messenger RNA to specify an amino acid chain. Many genes instead produce functional RNA, including transfer RNA and ribosomal RNA, without a translated protein product. See Alberts et al., Molecular Biology of the Cell, 4th edition (2002): from DNA to RNA.

Follow the chosen coding strand $5^{\prime }\text{-}\mathrm{ATGGCTTAA}\text{-}{3}^{\prime }$: transcription of its complementary template gives $5^{\prime }\text{-}\mathrm{AUGGCUUAA}\text{-}{3}^{\prime }$ in messenger RNA. In the stated reading frame, its three codons are AUG, GCU and UAA: methionine, alanine and a stop codon. Thus nine nucleotides specify two amino acid residues followed by termination, not three residues. This is an illustrative coding segment embedded in suitable expression and initiation context, not a claim that an isolated nine-nucleotide RNA is sufficient to initiate biological translation.

The distinction between copying and use explains how biological cells can preserve the same DNA yet produce different products. DNA replication duplicates the record; gene expression selects and uses parts of it. Transcription does not use all DNA at once, and gene expression can be controlled at several steps, including transcription, RNA processing and biological translation. See Clark, Douglas and Choi, Biology 2e: regulation of gene expression. The arrows describe template-directed synthesis: the DNA does not physically turn into a protein, and the messenger RNA does not supply the amino acids from which that protein is assembled.

The genetic code assigns RNA codons to amino acids or termination signals. Four possible nucleobases at each of three positions give $4^3=64$ codons. In the standard genetic code, 61 specify amino acids and three are stop codons; several codons can specify the same amino acid. Variants exist, so state which genetic code is being used. See Clark, Douglas and Choi: genetic code assignments and variants.