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Mathematics & logicExamples and counterexamples

Learn what a claim covers, explain why it works, and recognise an allowed case that shows it needs changing.

MethodMathematics & logicCounting and zero

Count each object once, explain the final count, and distinguish quantity, position and identifying labels. Make zero’s role explicit.

DefinitionMathematics & logicNumber lines and order

Use number-line positions to compare whole numbers. Read the scale, recognise equality, and distinguish numerical distance from drawing size.

DefinitionMathematics & logicAddition and subtraction

Combine separate counts, remove a part, and find differences or missing parts. Connect objects, equations and number-line moves, then use tens and ones to regroup without changing value.

DefinitionMathematics & logicMultiplication and division

Count equal groups, distinguish sharing from making groups, and check with multiplication. Split calculations into parts; interpret zero and remainders in context.

DefinitionMathematics & logicFractions

Choose a whole, count equal fractional units, and connect sharing with division. Place fractions on the number line, including values beyond one, and explain what their numerator and denominator mean.

DefinitionMathematics & logic · Physics · MeasurementRatios and rates

Distinguish part-to-part ratios, fractions of a whole and rates with units. Scale quantities together, compare unit rates, and explain when a relationship is proportional. Check zero cases, starting amounts and whether a result fits its context.

DefinitionMathematics & logic · Physics · MeasurementQuantities and units

Describe a quantity as a numerical value with a unit, and distinguish its physical kind from its dimension. Build length, area, volume and rate units, check meaningful combinations, and separate exact unit relations from measurement uncertainty.

DefinitionMathematics & logic · Physics · MeasurementUnit conversions

Convert quantities with exact unit ratios, track cancellation through compound units, and apply the correct powers to area and volume. Distinguish temperature readings from differences, check dimensions and context, and retain measurement uncertainty when reporting.

MethodMathematics & logic · Physics · MeasurementEstimation and uncertainty

Distinguish exact model values, rounded approximations and estimates from measurements. Declare the rounding rule, preserve information through calculations and unit changes, and interpret resolution, precision, accuracy and the stated uncertainty type without turning a report’s digits into guaranteed bounds.

DefinitionMathematics & logicVariables and expressions

Use symbols to name numbers or quantities, describe their allowed values, and evaluate expressions by replacing every occurrence consistently. Preserve grouping, signs, fractions and units, and distinguish a calculated value from solving an equation or proving two rules equivalent.

DefinitionMathematics & logicEquality and equations

Read equality as a relationship, find the permitted values that make an equation true, and justify one-step solutions by reversible operations on both sides. Work exactly with negative numbers and fractions, recognize all-solution and no-solution cases, and check the original equation, units and context.

DefinitionMathematics & logic · PhysicsCoordinates and tables

Locate a point from an ordered pair, read named axes and their scales, and connect the same values in words, tables and plots. Keep signs, fractions and units exact, distinguish an axis point from a quadrant point, and separate selected observations from a stated rule and its domain before drawing connections.

DefinitionMathematics & logic · PhysicsSlope and straight lines

Read a straight line as a stated relationship, calculate its slope from consistent signed coordinate changes, and interpret its intersections with the axes. Keep horizontal, vertical and coincident-point cases distinct, attach units and domain conditions to context models, and use numerical scales rather than appearance alone to judge a line’s change.

DefinitionMathematics & logic · Physics · MeasurementReading graphs

Read a graph’s quantities, units, ticks and context before judging its visual impression. Calculate differences, reference-based percentages and interval rates from the represented values; distinguish legitimate zoom from distorted spacing; and keep samples, interpolation, missing information, uncertainty and causal explanations separate.

MethodPhysics · MeasurementObservables and measurement

Choose the physical quantity you want to investigate, specify the point, event or location involved, and explain how a reading relates to that quantity.

MethodPhysicsSystems and boundaries

Choose what belongs to an investigation, describe its condition at a stated time, and identify interactions with what lies outside its boundary.

MethodPhysicsModels and assumptions

Choose what a model represents, make its simplifications explicit, and check whether its predictions answer the physical question you actually asked.

MethodPhysicsHypotheses, laws and theories

Identify what a scientific statement does, examine its evidence and conditions, and avoid treating its name as a score for certainty.

MethodMathematics & logic · PhysicsApproximations

Build a useful estimate, compare a correction with a stated reference scale, and check what is lost when you leave out a term.

ApproximationMathematics & logic · PhysicsSymmetry and invariance

Specify a transformation, identify what stays unchanged, and distinguish symmetry of an object from invariance of a physical model.

Mathematical statementPhysicsConservation laws

Use a defined system and a named quantity to track transfers, distinguish changing parts from conserved totals, and check the conditions of energy and momentum balances.

ModelPhysicsEmergence and levels of description

Choose a descriptive level, connect collective quantities with component behavior, and check when a simpler physical description answers a specified question.

ModelMathematics & logic · PhysicsVectors

Describe displacement with fixed-axis components, combine compatible vectors, and use small exact examples to introduce span, independence, basis and real vector spaces.

DefinitionPhysics · Information · MeasurementScientific records

Build an inspectable physics record, test and revise a bounded cart model, preserve processing history, and plan findable data with appropriate sharing conditions.

MethodPhysicsPosition, velocity and acceleration

Describe a point's motion on a chosen straight axis, then connect signed changes, instantaneous rates and one exact set of position, velocity and acceleration graphs.

DefinitionPhysicsNewton’s laws and forces

Choose one body, identify the forces acting on it, and use their vector sum to distinguish acceleration, balanced motion and mutual interactions.

ModelPhysicsWork, energy and power

Connect force and displacement to changes in motion, follow a spring’s stored energy, and distinguish an energy transfer from its rate.

ModelPhysics · MeasurementSpeed of light in vacuum

c denotes the speed of light in vacuum. Its numerical value is fixed exactly in SI units.

DefinitionPhysics · MeasurementPlanck constant

h denotes the Planck constant. Its numerical value is fixed exactly in SI units.

Definition
ModelSource checked

Membranes and transport

Biology

Selective membranes and transport proteins regulate movement between a cell and its surroundings.

Key knowledge

Cell membranes are selectively permeable. Passive transport allows net movement down the relevant gradient, through the membrane or transport proteins. Active transport couples movement against a gradient to an energy source, directly or through another gradient. Osmosis is passive net water movement across a selectively permeable membrane.

Conditions and scope

  • For ions, both concentration and electrical potential affect the electrochemical gradient.
  • Permeability and transport mechanisms depend on the substance and membrane; not all active transport directly hydrolyses ATP.
Sources · 3

References

Sources retain their recorded scope. A source link alone does not establish verification of every statement.

  1. Biology 2e (2018), §5.2 Passive transport: osmosis and tonicityMary Ann Clark, Matthew Douglas and Jung Choi · OpenStax/Rice UniversityTextbook chapteropenstax.orgRead source
  2. Biology 2e, 5.3: Active TransportMary Ann Clark, Matthew Douglas and Jung Choi — OpenStax, Rice UniversityTextbook chapteropenstax.orgRead source
  3. Life Sciences 10: Cell structureSiyavulaTextbook chaptersiyavula.comRead source

Evidence and review

Published selective-permeability, passive/active and primary/secondary transport accounts; no permeability or electrical measurement was made.

2026-10-10 · English transport distinctions checked against sections 5.2–5.3; medical examples and universal membrane-potential values excluded.

Foundational review

2026-10-10 · Fresh primary-source inspection of the complete compact record, including every statement, equation, quantity and material condition, followed by independent AI editorial review. This check does not certify all linked lessons or every passage of every cited publication.

Sources from other places

Scope or convention differs

Selective membranes, diffusion, osmosis and energy-dependent transport.

The introductory concentration model is narrower than ion electrochemical gradients and indirect energy coupling.

Related reference entries

Explore relationships within this area of study and its connections to other areas.

Showing 1–16 of 16 relationships

Scientific relationships · 16 / 16

The relationship type describes the connection. Its linked statements, sources and conditions define the scope.

  1. Related to
    Relationship sources · 1

    Linked statements

    • Cell membranes are selectively permeable. Passive transport allows net movement down the relevant gradient, through the membrane or transport proteins. Active transport couples movement against a gradient to an energy source, directly or through another gradient. Osmosis is passive net water movement across a selectively permeable membrane.
    • Metabolism includes chemical pathways that break down substances and build biological materials. Catabolic pathways break complex molecules into simpler ones, often releasing usable energy; anabolic pathways build complex molecules and require energy input. Enzymes catalyse many of these reactions.

    Cell metabolism can supply energy for active membrane transport.

  2. Related to
    Relationship sources · 1

    Linked statements

    • Cells couple ATP hydrolysis to otherwise energetically unfavourable processes through shared reaction steps or conformational changes. The Gibbs-energy change belongs to the overall reaction under cellular conditions; breaking an ATP bond alone is not the source of released free energy.

    The source's ATP-coupled ion pump is a membrane transport example.

  3. Related to
    Relationship sources · 1

    Linked statements

    • In many neurons, voltage-dependent ion conductances generate action potentials that propagate along excitable membranes. At chemical synapses, released neurotransmitter acts on receptors of a receiving cell. Signal integration and channel dynamics determine whether further electrical activity occurs.

    Ion conductances across membranes generate electrical activity.

  4. Related to
    Relationship sources · 1

    Linked statements

    • In mammalian kidneys, glomerular filtration forms a filtrate that renal tubules modify through reabsorption and secretion. Regulated transport of water and solutes contributes to extracellular-fluid composition and waste excretion. Other animal groups use different osmoregulatory structures.

    Tubular transport regulates water and solute reabsorption and secretion.

  5. Related to
    Relationship sources · 1

    Linked statements

    • In the mammalian nephron model, selective tubular transport modifies filtered fluid. Water permeability and salt transport differ along the loop of Henle, supporting a medullary osmotic gradient; collecting-duct water permeability helps determine how much water returns to the body. Filtration, reabsorption, secretion and excretion are distinct flows.

    Selective permeability and transport modify filtrate.

  6. Related to
    Relationship sources · 1

    Linked statements

    • In the eukaryotic secretory pathway, many membrane and exported proteins enter the rough endoplasmic reticulum, undergo processing and move in vesicles through the Golgi toward selected destinations. Endomembrane compartments coordinate synthesis, modification, sorting and degradation. Mitochondria and chloroplasts are not simply downstream secretory vesicles.

    Trafficking preserves membrane compartmentation.

  7. Related to
    Relationship sources · 1

    Linked statements

    • Animal extracellular matrix provides structural and signalling interactions through secreted proteins and cell-surface receptors. Tight junctions limit paracellular passage, anchoring junctions mechanically connect cells, and gap junctions permit exchange of selected small species. Plant plasmodesmata connect neighbouring cells through cell-wall channels.

    Selective junction permeability is distinct from membrane diffusion.

  8. Related to
    Relationship sources · 1

    Linked statements

    • A respiratory electron-transport chain couples favourable electron transfers to an electrochemical proton gradient across a membrane. ATP synthase can use proton return to synthesize ATP. In the mitochondrial aerobic example oxygen is the terminal acceptor; electron transfer, proton pumping and ATP production have distinct steps.

    An intact selective membrane supports the gradient.

  9. Related to
    Relationship sources · 1

    Linked statements

    • For an ideal dilute solution separated from pure solvent by a solvent-permeable membrane, osmotic pressure is approximately the molar concentration of osmotically active solute particles times RT. Dissociation, association and nonideal interactions can change the particle accounting and pressure.

    Osmosis depends on selective membrane permeability.

  10. Related to
    Relationship sources · 3

    Linked statements

    • Characteristic archaeal membrane lipids contain branched isoprenoid chains ether-linked to a glycerol-1-phosphate backbone, compared with the common bacterial/eukaryotic fatty-acyl ester-linked glycerol-3-phosphate model. Membrane-spanning bipolar tetraether lipids can form a monolayer. This is a characteristic chemical distinction, not an assertion that every membrane is a bilayer or that ether lipids occur only in Archaea.

    Lipid organization supports a permeability boundary.

  11. Related to
    Relationship sources · 2

    Linked statements

    • Diatoms provide a photosynthetic eukaryotic example with silica-rich cell walls. In a representative Paramecium model, cilia direct food into the oral region, food vacuoles support intracellular digestion and contractile vacuoles expel excess water. In the human–Anopheles malaria cycle, Plasmodium undergoes asexual liver/blood multiplication in the vertebrate host and gamete fusion in the mosquito host. These mechanisms illustrate distinct nutritional and lifecycle strategies rather than one protist organization.

    Water regulation depends on osmotic gradients.

  12. Related to
    Relationship sources · 1

    Linked statements

    • Water molecules are polar and can form hydrogen bonds with each other and suitable solutes. Their interactions support cohesion and help water solvate many ions and polar substances; nonpolar surfaces interact differently. Water's relatively high heat capacity buffers temperature changes, and ordinary ice is less dense than liquid water near its melting point at atmospheric pressure.

    Water's solvent behavior and nonpolar interactions supply chemical context for aqueous membranes; they do not by themselves specify membrane permeability.

  13. Related to
    Relationship sources · 1

    Linked statements

    • A spherical cell's surface-to-volume ratio is 3/r. Increasing radius therefore decreases membrane area per unit internal volume. If exchange capacity per area and demand per volume were otherwise comparable, this creates a transport constraint. Shape, membrane folds, intracellular transport and demand can change the outcome; it is not a universal maximum cell-size law.

    Membrane transport is constrained by available exchange area relative to internal volume, subject to permeability and gradients.

  14. Uses definition
    Relationship sources · 2

    Linked statements

    • Osmolarity counts osmotically active solute particles per solution volume. Tonicity describes a solution's lasting effect on cell volume relative to a specified membrane and timescale, principally through effectively nonpenetrating solutes. In the passive wall-less-cell model, a hypotonic external solution causes swelling, a hypertonic one shrinking, and an isotonic one no lasting volume change. Equal osmolarity alone need not imply equal tonicity.

    Tonicity interprets osmotic exchange through a specified selectively permeable membrane.

  15. Related to
    Relationship sources · 1

    Linked statements

    • A fatty acid has a carboxyl group and a hydrocarbon portion. Saturated fatty-acid chains lack carbon–carbon double bonds; unsaturated chains contain one or more. A triacylglycerol has three fatty-acyl groups ester-linked to glycerol. A representative glycerophospholipid has two fatty-acyl tails and a phosphate-containing polar head region: its amphipathic structure supports bilayers with tails shielded from water. Steroids instead have four fused rings, illustrating that lipid structures are diverse.

    A lipid bilayer supplies a membrane matrix; channels, carriers and other proteins specify many transport pathways.

  16. Related to
    Relationship sources · 3

    Linked statements

    • The plasma membrane separates a cell's interior from its environment and regulates exchange. Cytosol is the aqueous intracellular medium; in a eukaryotic cell, cytoplasm conventionally includes cytosol and structures outside the nucleus. A cell wall, where present, lies outside the plasma membrane and supplies support; it is not a substitute for that membrane. Typical cells contain DNA and ribosomes, while eukaryotic organelles partition functions into compartments. Specialized mature cells can lose components, so a generic diagram is not a checklist for every cell.

    A plasma membrane is the selective exchange boundary even where a supporting external cell wall is present.

Entry detailsPermanent link to this entry ↗
Record identity
bio-membranes-transport
Revision
core.1
Structured reference record
Essential core · first collection