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Algae is a broad name for several photosynthetic eukaryotic groups, rather than one exclusive clade. The older name blue-green algae for cyanobacteria is misleading in a comparison of cellular organization: cyanobacteria are bacteria, with neither chloroplasts nor a cell nucleus.

Animals are multicellular organisms with eukaryotic cellular organization. A representative animal cell has a cell membrane, cell nucleus and mitochondria, but no cell wall or chloroplasts. A neuron illustrates how this common plan can acquire a specialized shape and signaling function. See OpenStax Biology 2e, 4.3: animal cell organization.

Archaea are a major evolutionary lineage distinct from bacteria. The cellular comparison here concerns the prokaryotic members of archaea; see two-domain system for broader clade usage. Their biological cells have a nucleoid rather than a membrane-bounded cell nucleus, yet aspects of DNA replication, transcription and biological translation resemble those of eukaryotes. Their characteristic lipids differ chemically from the usual bacterial membrane lipids, and their cell walls, when present, lack peptidoglycan. See OpenStax Biology 2e, 22.2: archaeal distinctions.

Some archaea perform methanogenesis, producing methane as part of their metabolism. Archaea also inhabit ordinary soils and oceans: extreme habitats do not define the lineage. See OpenStax Biology 2e, 22.1: moderate and extreme environments. Woese and Fox's 1977 analysis of ribosomal RNA distinguished the methanogenic group they called archaebacteria from typical bacteria. Their proposed three primary lines of descent were a historical interpretation, rather than the final resolution of deep phylogenetics. See Woese and Fox, 1977: Phylogenetic structure of the prokaryotic domain.

Bacteria are a major evolutionary lineage of organisms with prokaryotic cellular organization. Escherichia coli and cyanobacteria illustrate its variety: the same broad cellular plan supports different kinds of metabolism. Most bacteria have a cell wall containing peptidoglycan; archaea do not have peptidoglycan walls. A cell wall and a cell membrane are distinct structures, and some bacteria lack a cell wall. See OpenStax Biology 2e, 22.2: bacterial envelopes.

The usefulness of recognizing bacteria extends beyond naming: it identifies a shared evolutionary background for comparing genes, proteins and cellular mechanisms. A familiar shape or the absence of a cell nucleus alone cannot distinguish bacteria from archaea; molecular comparisons, including ribosomal RNA, supply additional evidence.

A biological cell is a membrane-bounded basic unit of living organization. In a cell-level experiment it can be an experimental unit, provided that treatment assignment and relevant interactions are handled at that level.

The shared architecture of cellular life combines a selective cell membrane, internal cytoplasm, inherited information in DNA, and ribosomes that assemble proteins. Metabolism supplies transformations of matter and energy needed for maintenance and growth. These components form a coupled system: a boundary retains useful molecules, enzymes organize chemical reactions, and inherited information supports rebuilding the machinery. See Clark, Douglas and Choi, Biology 2e: prokaryotic cells.

A worked structural comparison: in a typical prokaryote, DNA occupies a region without a surrounding cell nucleus; in a typical nucleated eukaryote, much of the DNA lies inside a membrane-bounded cell nucleus. Both still have a cell membrane, cytoplasm and ribosomes. The extra boundary compartmentalizes processes; it does not create a different basic principle of living organization. See Clark, Douglas and Choi, Biology 2e: eukaryotic cells.

Shared architecture describes cellular life and its developmental machinery, rather than requiring every specialized biological cell to retain every component. A mature mammalian red blood cell, for example, lacks a cell nucleus, although it develops from nucleated precursors. See Clark, Douglas and Choi, Biology 2e: components of blood. This distinction makes cellular unity compatible with striking specialization.

Let $n$ count chromosomes in one complete set, and let $C$ denote the nuclear DNA amount in one unreplicated haploid set of this organism. Ploidy counts sets, whereas $C$ units count material; $C$ is not a universal mass shared by all species. Here we count a paired replicated chromosome as one until its sister chromatids separate. A copied diploid genome is therefore still diploid through S phase: $2n$ persists even as $2C$ becomes $4C$.

An original bookkeeping example uses a hypothetical diploid biological cell with $n=3$. Name its three homologous chromosome pairs $A,a$, $B,b$ and $D,d$. Assume ordinary nuclear DNA replication, no chromosome loss, and one continuous double-stranded DNA molecule per unreplicated chromosome or replicated chromatid. Count nuclear material only, excluding mitochondrion DNA.

For example, $A$ becomes the paired copies $A_1,A_2$ during S phase. They remain one replicated chromosome until separation. Each completed daughter receives one $A$ copy and one $a$ copy, and similarly for the other two pairs. Across both daughters, $2\times 6=12$ double-stranded DNA molecules and $2(2C)=4C$: division allocates the copied material without another round of DNA replication.

The whole undivided anaphase biological cell transiently contains $4n$ separately counted daughter chromosomes. This counting change does not establish a four-set ploidy in a completed daughter genome: each pole receives $2n$, and each completed daughter cell nucleus is diploid. Always state whether a number refers to one cell nucleus, one pole, or the entire undivided biological cell. Compare meiotic DNA content: after meiosis I, a haploid cell nucleus can contain $2C$, so amount alone cannot determine ploidy.

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.

Cyanobacteria are bacteria that perform oxygenic photosynthesis: light-dependent reactions release oxygen from water. Their photosynthetic machinery operates on thylakoid membranes without a chloroplast or a cell nucleus. This is a particularly useful counterexample to equating photosynthesis with being a plant. Chloroplasts descend from an ancestral cyanobacterial partner through endosymbiosis; present-day cyanobacteria are independent descendants, rather than chloroplasts waiting to become plants. See Alberts et al., Molecular Biology of the Cell: chloroplasts and cyanobacteria.

The cytoplasm is the material inside a cell membrane but outside the cell nucleus, when one is present. It includes the cytosol, the organelles suspended in it, and other structures; it is not just a name for the liquid. In a prokaryote, which has no cell nucleus, the nucleoid and ribosomes are within the cytoplasm. See Clark, Douglas and Choi, Biology 2e, 4.3: cytoplasm and cytosol and Clark, Douglas and Choi, Biology 2e, 4.2: prokaryotic organization.

Try classifying four positions in the diagram. A point in the pale blue region belongs to both cytosol and cytoplasm. A point inside the mitochondrion belongs to an organelle included in the cytoplasm, but not to the surrounding cytosol. A point on a free ribosome belongs to the cytoplasm, but the ribosome itself is not cytosol. A point inside the cell nucleus belongs to neither cytoplasm nor cytosol. These distinctions prevent the misleading inference that everything outside the cell nucleus shares one undivided liquid environment.

The usefulness of the cytoplasm is this combination of shared surroundings and specialized structures: enzymes in the cytosol carry out many steps of metabolism, while organelles maintain their own internal conditions. A soluble protein made by a free ribosome may work in the cytosol or be transported elsewhere, including into the cell nucleus. Cellular organization therefore combines separation with exchange, rather than assigning each protein permanently to its place of synthesis. See Alberts et al., Molecular Biology of the Cell (2002): traffic between nucleus and cytosol.