A Gq protein is a heterotrimeric G protein whose alpha subunit couples activated G protein-coupled receptors to effectors including phospholipase C. GTP binding changes the alpha subunit's interactions; subsequent GTP hydrolysis helps terminate the signal. The beta and gamma subunits are components of the same signalling system, not parts of the receptor. ^[ref]

The inhibitor YM-254890 supplies a molecular probe: structural work showed stabilization of a GDP-bound arrangement that impedes nucleotide exchange. Suppressing exchange is distinct from blocking the downstream enzyme directly, so an inhibitor response can help identify which stage of a signalling pathway is being controlled. ^[ref]

The Jensen functional equation on $\mathbb{R}$ isIt says that a function preserves midpoint averages. Every affine function $f(x)=ax+b$ satisfies it. The quadratic function $x^2$ does not: the midpoint of $1,-1$ is zero but the average of their squares is one.

Set $g(x)=f(x)-f(0)$. Taking $y=0$ gives $g(x/2)=g(x)/2$, and substituting this back into the equation yields $g(x+y)=g(x)+g(y)$. Thus solutions are exactly a constant plus a solution of the Cauchy functional equation. Continuity at one point forces $g(x)=ax$, first on rational multiples by additivity and then on all real inputs by rational approximation. Without a regularity hypothesis, non-linear additive solutions can occur, so the midpoint identity alone is not sufficient to infer an affine formula.

A functional calculus assigns an linear operator $f(T)$ to suitable scalar functions $f$ and an operator $T$, extending polynomial substitutionA useful calculus preserves algebraic identities, such as $(fg)(T)=f(T)g(T)$, on its allowed function class. The admissible functions and continuity properties depend on the operator: polynomial, holomorphic functional calculus, continuous and measurable spectral calculi are different constructions.

For a diagonal matrix $T=\mathrm{diag}({\lambda }_1,\dots ,{\lambda }_n)$, substitution gives $f(T)=\mathrm{diag}(f({\lambda }_1),\dots ,f({\lambda }_n))$. A nondiagonal Jordan block shows why values alone need not suffice: if $T=\lambda I+N$ with $N^2=0$, then $p(T)=p(\lambda )I+p^{\prime }(\lambda )N$. This follows by expanding each power and discarding all terms containing $N^2$.

For bounded self-adjoint operators, the spectral theorem supplies a calculus for continuous functions on the spectrum, and more generally bounded measurable functions through spectral integration. It defines objects such as positive square roots without choosing a basis of eigenvectors.

Escherichia coli fumarase C is a fumarate hydratase of Escherichia coli, commonly designated FumC. It catalyzes the reversible conversion between fumarate plus water and L-malate in the citric acid cycle. The name identifies a particular enzyme, while the broader activity name can cover related catalysts.^[ref]

The 1995 structure revealed a four-subunit assembly at $2.0\text{A˚}$ resolution, with the active site formed using atoms from three chains.^[ref] Further structures in 1996 used bound inhibitors and poor substrates to distinguish this catalytic A-site from a nearby B-site about $12\text{A˚}$ away. The second site was formed by one subunit rather than three.^[ref]

This gives a concrete interpretation problem for a binding experiment. Detecting a compound somewhere on the protein does not establish that it occupies the catalytic site. Comparing its position with substrate analogues, inhibitory behaviour and the multisubunit geometry supplies additional evidence. Similarly, a change in assembly could affect catalytic activity while retaining the same substrate-contacting amino acid residues. Structure and reaction-rate measurements describe complementary aspects of the working enzyme.

Fumarase C, often designated FumC, is a classII form of fumarate hydratase. It catalyzes reversible hydration of fumarate to L-malate. The protein designation should be tied to an organism: Escherichia coli fumarase C is a well-studied species-specific example, while the broader enzyme-activity name does not specify one protein sequence.^[ref]

The net substrate inventory makes the chemistry explicit:Four carbon atoms remain four; adding water changes hydrogen and oxygen content without changing the total charge. This hydration is chemically distinct from oxidation of L-malate to oxaloacetate. The enzyme accelerates a reversible reaction rather than making its net direction independent of conditions.^[ref]

The1995 X-ray crystallography study of the E.coli enzyme resolved an assembly of four identical protein subunits at2.0Å. Its proposed active site involved contributions from three of the four protein subunits; a local catalytic environment therefore need not lie inside just one polypeptide chain. A1996 follow-up with bound compounds distinguished the catalytic A-site from a nearby second binding site. These experiments also show why observing ligand binding does not by itself identify a catalytic site.^[ref][ref]

The pericarp is the wall of a fruit, derived from the wall of the ovary. Its regions can be distinguished as outer exocarp, middle mesocarp and inner endocarp.^[ref]

These regions need not have the same texture: in a drupe, such as a peach, the fleshy middle surrounds a hard inner stone. The stone is hardened pericarp; the seed lies inside it. In a caryopsis, by contrast, the pericarp is closely fused to the seed coat. These examples explain why a fruit's protective covering should be identified by its developmental origin as well as its appearance.

Parthenocarpy is fruit development without fertilization. Because no fertilized ovule is needed to initiate the fruit, it can produce a seedless fruit. It is distinct from apomixis, which produces an embryo or seed without the usual sexual process: a seedless fruit and an asexually formed seed solve different biological problems.

In tomato, increased auxin or gibberellin signalling can trigger parthenocarpy. Experiments with single and combined mutations affecting the two signalling systems separated the growth programme of the ovary from the usual requirement for fertilization. This makes parthenocarpy a useful test of how reproductive development is initiated.^[ref]

A caryopsis is a dry, one-seeded fruit that remains closed at maturity and has its pericarp fused to the seed coat. It is characteristic of grasses. A maize kernel is therefore a whole fruit, even though everyday language often calls it a seed.^[ref]

The developmental distinction survives the fusion: the pericarp comes from the ovary wall, whereas the seed coat comes from the coverings of the ovule. A close attachment between the two does not make them the same tissue.

A drupe is a fruit with a differentiated pericarp whose innermost region, the endocarp, forms a hard stone around the seed. The outer exocarp and middle mesocarp remain distinguishable from this stone. A peach supplies a familiar example: skin, flesh, stone and enclosed seed occupy different anatomical positions.^[ref]

The stone is therefore part of the fruit wall, rather than the seed coat. Cracking the stone exposes the seed within. This distinction matters in plant development: the pericarp derives from the ovary wall, whereas the seed develops from an ovule. A structure's hardness alone does not identify its origin.

A pome is a fleshy accessory fruit developing from an inferior ovary, with an enlarged hypanthium surrounding the central fruit tissues. An apple is a familiar example. Much of its edible flesh comes from tissue around the ovary, whereas the central core corresponds to the developed ovary. Thus the fleshy part of a pome cannot simply be identified with the pericarp, the wall derived from the ovary.^[ref]

To see the distinction, cut an apple lengthwise through its stalk and centre: locate the seeds, the enclosing core and the surrounding flesh. The fruit integrates structures with different developmental origins.

In a 2008 study, Bart J. Janssen and colleagues sampled developing apple fruits at eight times and used a DNA microarray representing roughly 13000 genes. They identified coordinated gene expression patterns associated with early cell division, later growth and starch accumulation, and ripening. The experiment illustrates how the anatomy of a pome motivates a molecular question: how are growth and maturation of its different tissues coordinated?^[ref]

Ripening is the coordinated set of developmental changes that brings a fruit toward its mature dispersal or eating state. Depending on the fruit, these changes can include altered pigmentation, softening, changes in sugars and acids, and the production of volatile compounds. They need not all occur at the same rate, so colour alone is an incomplete measure of ripening.

A particularly clear experiment established a role for Ethylene in tomato ripening. In 1991, P. W. Oeller and colleagues expressed Antisense RNA directed against 1-aminocyclopropane-1-carboxylate synthase, an enzyme required for Ethylene production. Ripening was inhibited. Supplying Ethylene from outside the plant reversed that inhibition.^[ref]

The intervention and rescue distinguish a regulating signal from a substance that merely accumulates while ripening happens. Suppressing production delays the process, while restoring the signal restores it. This establishes a causal role for Ethylene in that tomato system; the precise control of ripening must still be investigated for other fruits.

An achene is a dry, one-seeded indehiscent fruit: it remains closed at maturity, and its seed is not fused to the pericarp. Thus a seed-like object can actually be an entire fruit containing a seed. In the narrow usage of the University of Sydney eFlora, an achene develops from a superior ovary of one carpel.^[ref]

The surface units of a strawberry provide an illuminating example. Under magnification, each small unit has its own enclosing fruit wall and seed; the large fleshy region beneath the units is the receptacle. Calling every surface unit a seed hides this extra anatomical layer.^[ref]

Terminology varies between floras. PlantNET also includes comparable fruits from an inferior ovary under achene, while noting that these may be called a cypsela. The source's convention should therefore be checked when identifying a specimen.^[ref]

An accessory fruit is a mature fruit structure to which tissue outside the ovary contributes, often forming much of the flesh. The name concerns developmental origin. An apple illustrates one arrangement: the central core derives from the ovary, while the surrounding hypanthium contributes much of the edible tissue.^[ref]

A strawberry illustrates another arrangement. Its flesh is an enlarged receptacle, and the small units on the surface are individual achenes. Cutting through one of these units and separately through the flesh distinguishes the seed, the wall of its individual fruit, and the common supporting tissue.^[ref]

Accessory fruit and aggregate fruit describe different properties: the former concerns contributions from non-ovarian tissue, while the latter concerns fruits developing from several separate carpels of one flower. Both descriptions apply to the strawberry arrangement. In Fragaria vesca, dissecting tissues and profiling gene expression across developmental stages allowed researchers to investigate how these distinct parts grow together.^[ref]

An aggregate fruit develops from several separate carpels of a single flower, producing a collection of individual fruit units. The number of original flowers is crucial: a multiple fruit involves several flowers, whereas an aggregate fruit starts with one.^[ref]

A strawberry makes the arrangement tangible. Its surface bears numerous achenes, each an individual dry fruit, supported by the enlarged fleshy receptacle. The familiar edible object therefore combines many fruit units with tissue outside the individual ovaries.^[ref]

For a simple counting example, a single flower with twenty separate fertile carpels could produce twenty fruit units in one aggregate if each develops successfully. The count follows the separate carpels, not twenty separate flowers. Aggregate fruit and accessory fruit consequently describe different properties: the former concerns the collection of units, while the latter concerns contributions from non-ovarian tissue.

An indehiscent fruit remains closed at maturity instead of splitting open in a regular way to release its seeds. The category describes the opening behaviour of the fruit, rather than the number of seeds or the origin of its floral tissues.^[ref]

An achene and a caryopsis are illuminating examples. Both remain closed, but their internal construction differs: in an achene, the seed is free from the pericarp; in a caryopsis, the pericarp and seed coat are fused. Thus knowing that a fruit is indehiscent does not identify its precise fruit type.^[ref]

Closed does not mean permanently sealed against every later event. A fruit may eventually decay or be broken by an animal. The distinction from a dehiscent fruit concerns its normal opening at maturity, not whether a person can cut it open or its seed can eventually emerge during germination.