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The New Head hypothesis offers a plausible developmental explanation for vertebrate cranial innovation: migratory neural crest biological cells helped build a feeding and sensory apparatus that could diversify. Its strongest form is a hypothesis about integration of several innovations, not a claim that neural crest alone produced every part of the vertebrate head or directly proves evolutionary success.

neural crest arises near the border of the neural and non-neural ectoderm. Cells undergo an epithelial-to-mesenchymal transition, migrate and generate diverse derivatives. Cranial populations contribute substantially to facial and pharyngeal cartilage, bone and connective biological tissues; other populations supply peripheral neurons, glial cells and pigment biological cells. These are regionally restricted potentials, not a claim that every crest biological cell makes every derivative. Importantly, neural crest remains ectodermal in origin even when it makes biological tissues often associated with mesoderm.

The hypothesis proposed by Carl Gans and R. Glenn Northcutt linked the new head to a transition from passive suspension feeding toward more active food acquisition, with an expanded cranial skeleton, sensory systems and muscularised pharyngeal apparatus. neural crest, ectodermal placodes and mesodermal muscle contributions were complementary. A support skeleton allows feeding surfaces and sensory organs to be positioned; sensory organs guide action; muscles supply force. Their integration gives a more convincing functional explanation than a list of crest derivatives alone.^[ref]

Several distinctions keep this argument anatomically accurate. The brain largely develops from the neural tube; ectodermal placodes contribute important cranial sensory components; much cranial muscle comes from mesoderm. neural crest provides connective and skeletal organisation around those biological tissues and contributes to their interactions. The pharyngeal arches are multicellular constructions involving neural crest, mesoderm, ectoderm and endoderm. Thus loss of cranial neural crest can secondarily disrupt biological tissues it does not itself become. Fate mapping distinguishes cellular contribution, while selective ablation and rescue test developmental necessity and interaction.

There is direct experimental support for a role in diversification. Reciprocal cell transplantation of prospective beak neural crest between quail and duck shifted beak morphology toward the donor species and altered nearby host biological tissues. This connects intrinsic properties of the crest population with instructions to its environment, explaining how changes in one interacting population can reshape a complex organ. Same-species grafts, developmental-stage matching and permanent donor labels are needed to distinguish patterning information from surgical effects or simple replacement. The result supports a mechanism for morphological variation; it does not by itself establish which ancestral feeding behaviour was favoured by natural selection.^[ref]

Comparative evidence also qualifies an abrupt invention narrative. Neural-border regulatory and sensory programmes have antecedents outside vertebrates. In Ciona, a pigment-cell lineage with parts of a crest-like regulatory programme can acquire migratory behaviour after experimental manipulation. Such a rudiment supports stepwise assembly of properties; a migrating pigment precursor is not automatically equivalent to the full multipotent, skeletogenic vertebrate neural crest. Compare origin, regulatory dependencies, migration and derivative range separately.^[ref]

Jawless vertebrates are another important logical control. Their existence prevents equating the origin of neural crest with the later origin of jaws: cranial contributions preceded the particular jawed-vertebrate feeding apparatus. Later modifications of an inherited developmental system can support new structures without repeating its original evolutionary origin. Conversely, retention of homologous genes does not establish identical biological cell types; comparative experiments must test how those genes interact and what the biological cells actually produce.

A strong research programme would combine lineage tracing and selective perturbation across vertebrate and non-vertebrate chordates, compare homologous regulatory elements and ask whether reconstructed changes alter migration, skeletal competence or biological tissue interactions. Fossils constrain when hard cranial structures appeared, but rarely identify the embryonic source directly. Modern ablation establishes a present-day requirement, not the sequence of ancestral events. Likewise, species richness is influenced by many ecological and historical factors, so it is not a direct experimental readout of one developmental innovation.

The defensible conclusion is that neural crest supplied a versatile developmental substrate for cranial construction and diversification, acting with placodes and other biological tissues. Experimental grafting and comparative developmental evidence make that causal contribution substantial. The specific ecological transition proposed in the New Head hypothesis remains an evolutionary reconstruction whose details require evidence beyond the existence of crest derivatives.

DNA repair preserves usable inherited information, while genetic recombination can improve the combinations in which that information is transmitted. Their evolution need not have the production or prevention of diversity as an ultimate goal. natural selection favors consequences for survival and reproduction in particular contexts; novelty is neither automatically beneficial nor something an organism must maximize.

mutation creates new sequence variants; genetic recombination usually rearranges variants already present. A chromosomal crossover can produce a new haplotype without changing the allele frequency at either of two genetic loci. Conversely, DNA repair can restore sequence integrity after damage without eliminating the inherited differences between individuals. In particular, a normal alternative allele is not an error merely because it differs from another individual's sequence. These operations address different features of inheritance.

Unrepaired damage can block DNA replication or transcription, break a chromosome, or generate a harmful mutation. DNA repair thus has immediate benefits to a biological cell and can reduce the future burden of deleterious changes in descendants. In multicellular organisms, somatic mutation can compromise tissue function, while germline mutation changes what offspring inherit. The relevant balance includes the biochemical costs of DNA repair, the probability and severity of damage, and the possibility of DNA repair errors. natural selection for increased fidelity can become weak relative to genetic drift when an additional improvement is extremely small; perfect fidelity need not evolve. Some error-prone damage responses can also improve immediate survival even if surviving descendants carry more mutations.

The biochemical relationship is complementary. homologous recombination repairs a DNA double-strand break by using a related intact sequence as a template. In meiosis, programmed breaks can be repaired using a homologous chromosome, sometimes producing chromosomal crossovers and sometimes noncrossover products. Biochemical identification of Spo11 linked a component of the meiotic machinery to programmed break formation, demonstrating that meiotic diversification can begin with a controlled DNA-damage-and-repair process.^[ref] Crossovers also help establish the physical connections needed for reliable segregation in many meiotic systems. This immediate transmission function can favor the machinery independently of any later benefit from a novel haplotype. DNA repair with sister chromatids in another context can preserve sequence without the same exchange between parental homologues.

There are also population-level benefits of reshuffling. Suppose two favorable alleles, $A$ and $B$, occur in different lineages as $Ab$ and $aB$. With no exchange, their lineages compete and either favorable allele can be lost when the other lineage prevails. genetic recombination can create $AB$, allowing selection to combine their benefits; it can also separate a favorable allele from linked harmful changes. This is the core of the Fisher-Muller hypothesis and relates to Hill-Robertson interference, the reduction in the efficacy of natural selection caused by associations among selected genetic loci. Recreating low-load genotypes can also slow Muller's ratchet in finite biological populations.

The bookkeeping illustrates why this is not simply increasing all diversity. Let $x_{AB},x_{Ab},x_{aB},x_{ab}$ be haplotype frequencies and $D=x_{AB}{x}_{ab}-x_{Ab}{x}_{aB}$ be linkage disequilibrium. Under the standard random-mating model with recombination fraction $r$ and no other evolutionary forces,For $x_{Ab}=x_{aB}=1/2$ and the other two zero, $D=-1/4$. At $r=0.1$, the next frequencies are $x_{AB}^{\prime }=x_{ab}^{\prime }=0.025$ and $x_{Ab}^{\prime }=x_{aB}^{\prime }=0.475$. Each favorable allele still has frequency $1/2$: the process creates both the favorable combination and its unfavorable counterpart. Subsequent natural selection determines their fates. If the original associations are already advantageous, breaking them can instead impose a recombination load.

In controlled yeast experimental evolution, sexual and asexual treatments differed in their rates and genomic routes of adaptation, with the sexual treatment more efficiently separating beneficial from deleterious changes.^[ref] A mechanistic test should control the costs and bottlenecks of the sexual cycle, compare otherwise matched genetic backgrounds, and use reconstructed changes to distinguish genetic linkage from intrinsically different effects of a mutation. Such results establish a benefit under the tested population regime, not an unconditional advantage of sex in every environment. genetic recombination can disrupt favorable epistasis, and the costs of mating are distinct from those of crossover formation.

For an explanation of the evolution of the machinery itself, the association with its bearer matters. A recombination modifier must on average increase the representation of its own descendants, perhaps through improved segregation or through association with combinations that selection favors. Merely increasing long-run adaptability of the species is insufficient. Similarly, a mutator allele can spread in an asexual lineage by hitchhiking with a beneficial mutation it helped generate despite producing many harmful ones; exchange can weaken that association. The advantages of fidelity and of exchange consequently depend on genetic linkage, population size, environmental change and the current supply of beneficial variants.

DNA repair can regulate which exchanges are permitted as well. DNA mismatch repair corrects copying errors and can reject exchange between sufficiently diverged sequences. In bacteria, disabling mismatch-repair functions greatly relaxed a barrier to genetic recombination between divergent lineages.^[ref] An experiment separating these roles should compare DNA repair of copying errors with exchange between templates of controlled divergence, using a restored DNA repair gene as a rescue. DNA repair and genetic recombination can therefore be parts of the same evolved solution: preserve functional sequence, transmit chromosomes reliably, and reshuffle existing alleles when doing so improves reproductive success.

The substrate contact area is the square bottom face, so the total traction force magnitude is stress times area:By Newton's third law, the force exerted by the substrate on the biological cell has the same magnitude and opposite direction to the cell's force on the substrate.

In this two-pool calcium model, $c$ is the cytosolic calcium ion concentration, and $c_s$ measures calcium in an intracellular store, such as the endoplasmic reticulum. The variables in these balances are expressed using compatible effective volumes, so internal transfers enter their two equations with equal and opposite signs. If actual compartment concentrations use different reference volumes, the corresponding volume ratio must first be included in their balances.

The flux $J_{+}$ pumps calcium from the cytosol into the store, $J_{-}$ releases it back, and $k_s{c}_s$ is passive store leakage back to the cytosol. The external input $r$ supplies cytosolic calcium, while $kc$ exports it from the biological cell. Thus $k,k_s$ have units of inverse time and all five fluxes have units of concentration per time. Their directions can be sketched asAdding the two ordinary differential equations verifies the total calcium balanceInternal uptake, release and leakage redistribute calcium; only the exchanges across the cell membrane change this total. In particular any equilibrium must have $c=r/k$ when $k>0$.

If the biological cells are initially interchangeable, randomly allocate them to five groups of ten for the days. Within each day, independently choose a uniform distribution on a finite set over assignments having two occurrences of each dose level to the ten experimental units. One implementation is a random permutation of a list containing two labels of each level; the duplicate labels give every admissible assignment the same number of underlying permutations.

Randomize the processing order within each day as well, while pairing each preparation with its immediate measurement. Randomize dose within day, not merely the names of the days. This restricted randomization preserves the planned balance while protecting treatment contrasts against systematic order effects. Conceal the dose labels from the assessor where practical.

Use a randomized complete block design, with day as block and each biological cell as an experimental unit. Each day should contain two biological cells at each of the five dose levels. Each level then has ten replicates overall and occurs equally often in every day: the resulting block design is an orthogonal block design.

This spreads any day-to-day changes in preparation, temperature or measurement across all levels instead of confounding dose with day. Treat the zero level as a control with otherwise comparable handling. Keep the treatment-to-measurement delay standardized because the response variable is a diffusion rate measured immediately after preparation.

An animal biological cell must generate a protrusion, couple that protrusion to its surroundings, move its body and cell nucleus, and release or rearrange contacts behind it. Cell polarity makes these events persistent in one direction. At cellular scales, inertia is usually negligible: active forces balance resistance continuously, rather than giving the cell momentum that carries it forward after propulsion stops. ATP consumption maintains the system away from thermodynamic equilibrium.

At the front, actin polymerization can push the cell membrane into a lamellipodium. Whether this produces advance depends on coupling to the environment: without a mechanical grip, the actin network can move backward instead. On a flat adhesive substrate, integrins bind the extracellular matrix and connect through focal adhesions to the cytoskeleton. Regulated engagement transmits traction, while rearward myosin contraction and adhesion turnover move the rest of the cell. Adhesions must resist slipping long enough to transmit force but release to avoid anchoring the rear indefinitely. Another protrusive mechanism is a membrane bleb: local separation of the cell membrane from the cell cortex, driven by intracellular pressure, expands the membrane before a new cortex assembles underneath it.

A two-dimensional culture surface offers a broad basal contact area and little geometrical obstruction above the cell. A three-dimensional environment adds pore size, fibre orientation, matrix stiffness, and resistance from surrounding cells. The same cells may switch between elongated, strongly adhesive migration and more rounded, weakly adhesive movement. Proteolysis can enlarge a path through the extracellular matrix, but a sufficiently permissive existing pore need not require digestion. The relatively stiff cell nucleus can become the main bottleneck; its passage depends on deformation, confinement and force transmission. Extensive squeezing can damage the nuclear envelope, so migration speed alone is not a sufficient measure of successful transit.

A decisive experiment removed all functional integrins from mouse leukocytes. Their interstitial migration in three-dimensional environments persisted, and myosin became particularly important for passage through narrow gaps. This distinguishes force generation from a particular adhesion mechanism: confinement and friction can provide useful coupling even without integrin anchoring.^[ref]

Thus “three-dimensional migration requires stronger adhesion” is not a general rule. A useful comparison holds ligand density, matrix stiffness and pore geometry as independently controlled as possible, measures whole-cell and nuclear movement, and perturbs actin, myosin, integrins and matrix digestion separately. Differences then identify which mechanical requirement has changed, rather than treating dimensionality as a single unexplained variable.

Patch-clamp series resistance, also called patch-clamp access resistance, is the effective electrical resistance between the pipette's sensed voltage and the cell interior. It includes tip access and any remaining obstruction after break-in. For injected electric current $I$ into the biological cell, an ideal resistive access path givesThus $1\mathrm{nA}$ through $20\mathrm{M\Omega }$ produces a $20\mathrm{mV}$ difference: a substantial possible voltage clamp error. The electric current in this equation is the access-path current, excluding any bypass seal leak current. In current clamp, the same access drop contaminates the pipette voltage during injection. Bridge compensation subtracts an estimated $I{R}_s$; an estimate that changes during recording leaves an error.

An independent passive voltage clamp calculation makes both speed and error visible. Write $v=V-E_L$ and $v_p=V_p-E_L$, with fixed leak reversal potential $E_L$, constant membrane electrical resistance $R_m$ and membrane capacitance $C_m$. Assume an ideal command at the pipette node and omit seal leak current and pipette capacitance. Electric charge conservation givesFor a step $v_p=\Delta V$ from $v(0)=0$, the ordinary differential equation givesWith the figure's parameters and $\Delta V=10\mathrm{mV}$, the time constant is $0.909\mathrm{ms}$, the final membrane rise is $9.091\mathrm{mV}$, and access-path electric current falls from $500$ to $45.45\mathrm{pA}$. Only when $R_m\gg R_s$ does the time constant approach $R_s{C}_m$ and the final voltage approach the command. Actual voltage clamp also depends on amplifier feedback control and the space clamp problem.

A permeating solute can cross the specified membrane appreciably during the observation interval. This is a property of a solute-membrane-time comparison, not an immutable label attached to a molecule. Passage can reduce a concentration difference through passive transport while water is also moving; it does not require water to wait.

For an original dilute ideal example, stipulate a flexible model biological cell with $20\mathrm{mmol}{\mathrm{L}}^{-1}$ retained particles and an external reservoir with $10\mathrm{mmol}{\mathrm{L}}^{-1}$ retained particles plus $10\mathrm{mmol}{\mathrm{L}}^{-1}$ freely permeating neutral solute. Initially the total osmolarities are equal. Suppose the permeating solute eventually has equal internal and external concentrations, there is negligible pressure difference, no active transport, and the internal retained particle amount is conserved. The permeating contributions cancel from the final osmotic balance; the internal retained concentration must fall from $20$ to $10\mathrm{mmol}{\mathrm{L}}^{-1}$. The required volume is twice its initial value. This illustrates an initially equal-osmolarity but hypotonic solution; it assumes the boundary can survive that expansion and predicts no universal time course.

Phase-contrast microscopy converts specimen-dependent phase differences into visible light intensity differences. It can reveal structures in living, unstained biological cells, allowing their changes to be followed without first making an absorbing preparation.^[ref] The key question is how an optical microscope can read a phase when an ordinary detector records light intensity.

Consider a transparent specimen with complex amplitude transmission $t(x,y)=e^{i\varphi (x,y)}$. In ideal in-focus coherent imaging with all relevant spatial frequencies transmitted, its image has $I=|t{|}^2=1$: varying $\varphi$ alone produces no brightness detail. This is a particular model, not a claim that all transparent specimens are invisible. Diffraction, defocus, absorption and a finite optical pupil can already change a real image.

A phase-contrast microscope images an illuminating annulus onto a phase plate ring near the objective's rear focal plane. The aligned ring attenuates and shifts direct light relative to most diffracted light; their interference changes image brightness.^[ref]

The method is beautiful because the bright direct beam becomes its own reference: a small specimen-dependent complex amplitude can interfere with it and change the image at first order. Merely magnifying an invisible phase pattern would leave $|t{|}^2$ unchanged.

Phospholipids are lipids containing a phosphate group as part of their structure linked by covalent bonds. The familiar membrane-forming phospholipids are amphiphilic: a hydrophilic head region with chemical polarity coexists with a hydrophobic, largely nonpolar hydrocarbon region. These descriptions refer to different parts of the same molecule, not to two separate substances. See IUPAC Gold Book: phospholipids and IUPAC Gold Book: amphiphilic.

A typical two-chain glycerophospholipid provides a useful example: a glycerol scaffold carries two fatty acid-derived acyl groups through ester linkages, plus a phosphate-containing head region. Phosphatidylcholine is one example. This scaffold describes an important subclass, rather than all phospholipids: sphingomyelin has a different backbone, and even glycerophospholipids need not all have two acyl groups. See IUPAC–IUB, Nomenclature of Lipids (1976), Lip-1.5 and Lip-2.1–2.6.

Polar does not mean negatively charged overall. At near-neutral pH, phosphatidylcholine is zwitterionic: its phosphate region carries negative electric charge and its choline region positive electric charge, with zero net electric charge for the molecule. Counting those opposite charges gives $(-1)+(+1)=0$; it does not remove their local interactions with water. See Lodish et al., Molecular Cell Biology: membrane lipids.

In a lipid bilayer, two membrane leaflets orient their hydrophilic heads toward the water on either side and their hydrophobic chains toward the shared interior. The hydrophobic effect helps explain this organization through the free energy of the water and lipids together. It is not a special repulsive chemical bond between chains and water. Which organization is favored also depends on molecular geometry, temperature, concentration, and the surrounding chemical solution; a phospholipid label alone does not guarantee a lipid bilayer. See Alberts et al., Molecular Biology of the Cell: the lipid bilayer.

This organization supplies a flexible barrier for compartments. A fluid lipid bilayer allows lipids to undergo diffusion within each membrane leaflet; barrier function therefore coexists with motion of molecules, as in the fluid mosaic model. It is not completely impermeable: small nonpolar molecules such as molecular oxygen and carbon dioxide cross much more readily than ions. In a cell membrane, ion channels and other membrane transport proteins provide selective routes; the existing membrane transport article explains their driving forces. See Alberts et al.: principles of membrane transport.

In 1925, E. Gorter and F. Grendel extracted lipids from red blood cells and compared the surface area of a one-molecule-thick film on water with the estimated total surface area of the red blood cells. Their table gave ratios near two, supporting a two-layer covering; they also proposed heads facing the aqueous surroundings on both sides. The inference depends on recovering the relevant lipids, estimating the red blood cell surface area correctly, and comparing compatible packing in the film and the cell membrane. It was indirect evidence, not an image of the lipid bilayer. The paper itself notes possible losses during evaporation. See Gorter and Grendel, On Bimolecular Layers of Lipoids on the Chromocytes of the Blood, Journal of Experimental Medicine 41 (1925), 439–443.

Photosynthesis captures light energy and transforms it into chemical forms that a biological cell can use. In plants, algae and cyanobacteria, this supports carbon fixation: incorporation of carbon from carbon dioxide into chemical compounds used to build living material. Capturing light and incorporating carbon are distinct processes coupled through metabolism. See OpenStax Biology 2e, 8.1: overview of photosynthesis.

For oxygenic photosynthesis, a simplified net equation writes a six-carbon sugar, glucose, as the representative product:This is net stoichiometry, not a one-step mechanism. A worked bookkeeping check counts six carbon chemical atoms, twelve hydrogen chemical atoms, and eighteen oxygen chemical atoms on each side: the product side has six oxygen chemical atoms in the sugar and twelve in molecular oxygen. The light label supplies energy, not additional chemical atoms.

Crucially, the released molecular oxygen comes from water, not carbon dioxide. Cancelling water made and consumed in different steps hides this distinction in the net equation. The Calvin cycle supplies a net three-carbon triose phosphate, such as glyceraldehyde 3-phosphate, for subsequent sugar synthesis; it does not directly export glucose. See OpenStax Biology 2e, 8.2: light-dependent reactions and OpenStax Biology 2e, 8.3: using light energy to make organic molecules.

The useful achievement is connecting incoming light to both usable energy and new biological material. ATP is an immediate energy currency; NADPH supplies electrons for synthesis; carbon dioxide supplies the carbon incorporated into carbohydrates. These roles are complementary. Conservation of energy still holds: photosynthesis transforms energy, never creates it, and some absorbed energy is dissipated as heat. A plant also carries out cellular respiration, including in biological cells that perform photosynthesis. Gas exchange reflects both processes. Oxygenic photosynthesis remains central to interpreting terrestrial molecular oxygen as an atmospheric biosignature gas. See OpenStax Biology 2e, 8.3: photosynthesis and respiration.

A physiological integrator combines regulatory inputs to select a response; it need not perform the mathematical integral action used in control theory. In thermoregulation, the hypothalamus participates in combining internal and skin signals. The term describes a role, which can be distributed across interacting biological cells, rather than a mandatory single comparator.

A plant cell wall provides reinforcement outside the cell membrane, with cellulose as a major structural component. It is a composite rather than a solid sheet of pure cellulose. Wall construction varies with the kind and developmental state of the biological cell.

A grouping of biological cells in a plant with related functions. In a seed, plant embryo tissues and endosperm have distinct developmental identities.

Plasmolysis is withdrawal of the membrane-bounded contents from parts of a cell wall after water loss. A sufficiently concentrated external hypertonic solution, with solutes effectively excluded by the cell membrane over the observation time, can cause this. The cell wall remains; the enclosed material contracts. Plasmolysis is therefore distinct from osmotic lysis, which breaks the cellular boundary during excessive swelling. A return to a less concentrated surrounding chemical solution can reverse plasmolysis if the biological cell remains functional.^[ref]

Growth concentrated at a selected part of the biological cell surface. Spatial selection can be controlled at transport, vesicle docking or fusion rather than only by directed vesicle motion.

An angiosperm pollen grain is a small male gametophyte, not itself a seed or a single gamete. Its tube-forming biological cell supports delivery of sperm.^[ref]

The polymerase chain reaction amplifies a selected DNA region using repeated copying steps. Amplified material can be examined by DNA sequencing; appropriate template controls help distinguish a new rearrangement from material already present in the starting preparation.

The essential trick is to choose two PCR primers on opposite DNA strands with their extendible $3^{\prime }$ ends facing into the same interval. A DNA polymerase extends each PCR primer $5^{\prime }\to 3^{\prime }$; the resulting DNA can itself become a template. The amplicon is therefore selected by two opposed PCR primers, rather than by the DNA polymerase recognizing a named gene. This makes PCR amplification useful for inspecting one interval within a much larger genome. Here PCR means polymerase chain reaction; the statistical abbreviation PCR means principal component regression.^[ref]

For a deliberately tiny nucleotide sequence example, display the upper strand as $5^{\prime }\text{-}\mathrm{ACGT}\text{-}\mathrm{GGAATT}\text{-}\mathrm{CAGC}\text{-}{3}^{\prime }$. The left PCR primer is $5^{\prime }\text{-}\mathrm{ACGT}\text{-}{3}^{\prime }$ and binds the lower strand. The right PCR primer, written in its own $5^{\prime }$-to-$3^{\prime }$ direction, is $5^{\prime }\text{-}\mathrm{GCTG}\text{-}{3}^{\prime }$: the reverse complement of CAGC. It binds the upper strand and extends leftward in the drawing. With flanks outside this interval, the bounded amplicon contains $4+6+4=14$ base pairs, including both PCR primer sequences. These four-nucleotide PCR primers illustrate direction and counting only; they are not a proposed experimental design.

A useful way to understand the polymerase chain reaction is to separate recognition from construction. Base pairing positions a PCR primer; a DNA polymerase then joins new nucleotides onto that existing strand. The PCR primer becomes part of the copied DNA, rather than merely marking a place for an independent strand to start. A PCR thermal cycle repeatedly exposes templates, positions starting ends and permits construction. This makes DNA copying possible outside biological cells, with the chosen PCR primers specifying which interval is repeatedly accessible.

Variation among biological cells in states such as cell-cycle stage, expression level and responsiveness. Population averages can agree even when individual-cell histories differ.