Nine length scales · eleven claims each · not peer reviewed
Nine length scales, from a single binding pocket to the cosmic web. Where Volume XIX sorted by clock, this one sorts by ruler — and makes the same bet, that a governing ratio transfers across twenty-five orders of magnitude.
Ligand residence time is set by the ratio of binding pocket volume to ligand diffusion coefficient, so a deep pocket slows escape more than tight binding does.
Enzyme enantioselectivity is set by the ratio of transition-state geometry to active-site flexibility, so a rigid site discriminates better than a flexible one of equal affinity.
Hybridisation specificity is set by the ratio of mismatch destabilisation to duplex length, so long probes cannot distinguish a single mismatch.
A molecular motor's directionality is set by the ratio of track asymmetry to thermal noise, so a symmetric track cannot produce net motion regardless of fuel.
Quantum coherence in photosynthetic energy transfer extends only while the ratio of exciton delocalisation to protein motion is large, so flexible complexes lose coherence.
Off-target binding is set by the ratio of pocket similarity to ligand promiscuity, so a selective drug on a promiscuous ligand will still bind elsewhere.
The polymorph that forms is set by the ratio of nucleation rate to growth rate of competitors, so a slower-growing but faster-nucleating form wins.
The size of the folding nucleus is set by the ratio of contact order to chain length, so proteins with many long-range contacts nucleate a larger core.
Antibody cross-reactivity is set by the ratio of epitope similarity to affinity, so a high-affinity antibody discriminates a variant that a low-affinity one cannot.
RNA secondary structure is set by the ratio of base-pairing energy to loop entropy, so a helix forms only when the pairing gain exceeds the cost of closing a loop.
Odorant identity is set by the ratio of molecular volume to receptor pocket volume, so molecules of similar chemistry but different size smell different.
Cellular uptake of nanoparticles is set by the ratio of particle diameter to membrane thickness, with an optimum where the particle can be wrapped without being excluded.
Quantum dot emission energy is set by the ratio of dot diameter to exciton Bohr radius, so small changes in size produce large colour shifts only below that scale.
The reinforcement from nanotubes is set by the ratio of tube length to the critical transfer length, so short tubes add stiffness without strength.
Nanopore current blockade is set by the ratio of pore diameter to nucleotide size, so a tight pore reads more distinctly but blocks more often.
Nanocatalyst selectivity is set by the ratio of step sites to terrace sites, so smaller particles are more selective for structure-sensitive reactions.
The thermal conductivity enhancement of a nanofluid is set by the ratio of particle size to phonon mean free path, so the same loading enhances differently across particle sizes.
The threshold of a nanowire laser is set by the ratio of cavity length to gain length, so a short wire needs a better material to lase.
Whether nanoplastic particles enter a cell is set by the ratio of particle size to membrane pore size, not by concentration.
The relaxivity of a nanoparticle contrast agent is set by the ratio of particle size to the water diffusion length during relaxation, so larger particles do not always contrast better.
Friction at a nanocontact is set by the ratio of contact size to lattice constant, so contacts smaller than a few lattice spacings become superlubric.
Bacterial cell size is set by the ratio of biosynthetic capacity to surface area, so nutrient-rich conditions increase the ratio and the cell before division.
Organelle position is set by the ratio of motor force to cytoplasmic drag, so a large organelle sits further from the nucleus at the same motor activity.
The orientation of a dividing cell is set by the ratio of cortical tension anisotropy to spindle forces, so equal forces produce a random axis.
Bacterial cell shape is set by the ratio of wall synthesis anisotropy to turgor pressure, so higher turgor rounds the cell.
Signalling noise is set by the ratio of molecule number to cell volume, so two cells with the same concentration can differ in noise by an order of magnitude.
Autophagic flux is set by the ratio of autophagosome production to lysosomal degradation capacity, so measuring autophagosomes alone misreads flux in both directions.
Cell polarisation occurs above a threshold in the ratio of cortical reaction rate to cytoplasmic diffusion, so a fast-cycling protein can polarise in a large cell.
Segregation fidelity is set by the ratio of spindle length to kinetochore number, so a crowded spindle mis-segregates even with correct attachments.
A cell fate decision is set by the ratio of transcription factor concentration to the number of functional binding sites, so the same concentration gives different decisions in different cells.
Steady-state cell volume is set by the ratio of pump rate to passive leak, so a cell with more channels is larger at the same pump density.
Whether two cells fuse is set by the ratio of fusion protein energy to membrane tension, so a tense membrane resists fusion despite the right proteins.
Whether a tumour grows as a compact mass or an infiltrative one is set by the ratio of proliferation rate to invasion rate, so the same mutation can produce either depending on the tissue.
The depth to which oxygen reaches in tissue is set by the ratio of diffusion length to consumption rate, so dense tissue becomes hypoxic at the same vascular spacing as sparse tissue.
Whether bone adds or removes mass is set by the ratio of habitual strain to accumulated microdamage, so a bone can lose mass despite being loaded.
Cartilage friction is set by the ratio of interstitial fluid film thickness to surface roughness, so wear begins when the film falls below the asperities.
Tissue water content is set by the ratio of osmotic pressure to elastic resistance, so a stiff matrix holds less water at the same osmotic load.
Wound contraction is set by the ratio of myofibroblast force to matrix stiffness, so a stiff scar contracts less despite more force.
Capillary spacing is set by the ratio of oxygen demand to diffusive supply, so a tissue with higher metabolic rate is vascularised more densely at the same size.
Whether an appendage regenerates is set by the ratio of blastema size to body size, so small injuries in large animals fail to regenerate.
Whether inflammation stays local or spreads is set by the ratio of cytokine diffusion to cell density, so dense tissue confines a signal that sparse tissue lets spread.
The extent of thermal damage in tissue is set by the ratio of heating rate to perfusion, so a well-perfused organ requires more energy for the same lesion.
Tissue electrical conductivity is set by the ratio of extracellular volume fraction to membrane capacitance, so two tissues with the same water content can differ in impedance.
Tissue remodelling direction is set by the ratio of mechanical to biochemical signal, so a strong chemical cue can override a moderate mechanical one.
Adult body size is set by the ratio of energy intake rate to maintenance cost, so a high-cost metabolism limits size even with abundant food.
Maximum limb length is set by the ratio of bending strength to buckling load, so a slender limb fails by buckling before it fails in bending.
Heart rate is set by the ratio of metabolic rate to body mass rather than by mass alone, so animals with elevated metabolism have faster hearts than their size predicts.
Relative brain size is set by the ratio of cognitive demand to maintenance cost, so species with expensive brains need either more energy or fewer other costs.
Relative gut length is set by the ratio of diet quality to absorption rate, so low-quality diets require longer guts to extract the same energy.
Skin pigmentation is set by the ratio of UV protection needed to vitamin D synthesis needed, so the same population shifts with latitude.
Lung capacity is set by the ratio of oxygen demand to diffusing surface, so a highly active animal needs a larger surface at the same body size.
Muscle fibre composition is set by the ratio of duty cycle to fatigue resistance, so a muscle used briefly becomes fast and one used continuously becomes slow.
Eye size is set by the ratio of required acuity to photon noise, so nocturnal animals need larger eyes for the same resolution.
Wing size is set by the ratio of required lift to acceptable drag, so slow fliers need larger wings than fast ones at the same mass.
Investment in armour is set by the ratio of predation risk to growth cost, so well-defended species grow more slowly in the same habitat.
Species range size is set by the ratio of dispersal ability to habitat availability, so a good disperser in fragmented habitat has a smaller range than a poor disperser in continuous habitat.
Optimal group size is set by the ratio of predation risk to competition cost, so groups grow where predation is high and shrink where food is limiting.
Territory size is set by the ratio of resource density to defence cost, so rich habitats support small vigorously defended territories.
Population sex ratio is set by the ratio of investment in sons to investment in daughters, so species with dimorphic costs produce the rarer sex more cheaply.
Population cycles occur when the ratio of generation time to resource renewal time falls within a range, so slow-renewing resources produce longer cycles.
The Allee threshold is set by the ratio of mate encounter rate to mortality, so sparse populations decline when encounter cannot keep pace with death.
Equilibrium population density is set by the ratio of crowding mortality to resource renewal, so a productive habitat sustains more individuals at the same crowding cost.
Whether a species migrates is set by the ratio of season length to travel time, so long journeys are only worth it where the season is long.
Neutral genetic diversity is set by the ratio of mutation rate to drift rate, which is proportional to population size, so small populations lose diversity predictably.
Cooperation among non-relatives is stable only when the ratio of benefit to assortment exceeds one, so high benefit cannot compensate for random mixing.
Maximum colony size is set by the ratio of foraging range to body size, so small workers support larger colonies because they cover more ground per unit energy.
The strength of a trophic cascade is set by the ratio of predator range to prey range, so a wide-ranging predator produces a weaker cascade than a resident one.
Ecosystem stability is set by the ratio of response diversity to disturbance frequency, so a moderately disturbed system with high response diversity can be more stable than an undisturbed one.
Nutrient cycling rate is set by the ratio of decomposition to plant uptake, so a system with fast decomposition and slow uptake leaks nutrients.
Biodiversity hotspots occur where the ratio of productivity to seasonality is high, so the most productive stable regions hold the most species.
Ecosystem resilience is set by the ratio of functional redundancy to stress, so a system with high redundancy tolerates more stress before function collapses.
The depth of edge influence is set by the ratio of perimeter to area, so a long thin reserve is mostly edge while a compact one is mostly interior.
Metacommunity diversity peaks at an intermediate ratio of dispersal to competition, because too little dispersal prevents recolonisation and too much prevents specialisation.
Whether an ecosystem is a carbon sink is set by the ratio of gross primary production to ecosystem respiration, so a productive system with fast decomposition can be a source.
The spread rate of an invader is set by the ratio of population growth rate to dispersal distance, so a fast-growing invader with short dispersal can outrun a slow one with long dispersal.
The stability of a mutualistic network is set by the ratio of generalist to specialist links, so a network of specialists collapses when any partner is lost.
Soil food web complexity is set by the ratio of pore-size heterogeneity to body size, so a soil with a wide range of pore sizes supports more trophic levels.
Planetary albedo is set by the ratio of cloud cover to ice cover, so two planets with the same temperature can reflect very differently depending on which dominates.
The number and width of atmospheric circulation cells are set by the ratio of rotation rate to heating rate, so faster rotators have narrower cells.
Continental freeboard is set by the ratio of crustal thickness to ocean volume, so a planet with more water drowns its continents.
Magnetic field strength is set by the ratio of convective power to rotational constraint, so a slowly rotating planet needs more convection for the same field.
Atmospheric volatile inventory is set by the ratio of outgassing to subduction, so a planet with fast recycling has a thinner atmosphere at the same degassing rate.
The dominant mode of ocean circulation is set by the ratio of wind stress to buoyancy forcing, so a planet with weak winds and strong heating circulates differently.
Ice sheet extent is set by the ratio of accumulation to calving rate, so a cold planet with fast calving has small sheets.
Surface habitability is set by the ratio of absorbed insolation to greenhouse forcing, so a distant planet with a thick atmosphere can be as habitable as a close one with none.
Crater retention age is set by the ratio of impact flux to erosion rate, so an old surface with fast erosion looks young.
Whether an atmosphere escapes is set by the ratio of thermal velocity to escape velocity, so a warm light gas escapes from a planet that retains a cold heavy one.
Whether a planet has plate tectonics is set by the ratio of internal heat flux to lithospheric strength, so a cooling planet eventually locks its plates.
Galaxy morphology is set by the ratio of disk mass to bulge mass, so the same total mass produces spirals or ellipticals depending on the split.
Star formation rate per unit gas is set by the ratio of gas density to free-fall time, so dense clouds convert gas more efficiently.
Black hole mass is set by the ratio of accretion rate to feedback efficiency, so a high-efficiency feedback loop caps growth at a predictable mass.
The width of cosmic web filaments is set by the ratio of dark matter velocity dispersion to gravitational pull, so warmer dark matter produces broader filaments.
Supernova remnant size at a given age is set by the ratio of ejecta mass to ambient density, so the same explosion produces very different remnants in different media.
Planetary system architecture is set by the ratio of migration rate to disk lifetime, so systems that migrate far have long-lived disks.
The cosmic ray spectrum is set by the ratio of acceleration rate to escape rate, so a source that accelerates slowly produces a steep spectrum.
Cluster mass is set by the ratio of gas fraction to temperature, so a hot gas-poor cluster can have the same mass as a cooler gas-rich one.
The timing of cosmic reionisation is set by the ratio of ionising photon production to recombination rate, so a higher escape fraction reionises earlier.
The concentration of a dark matter halo is set by the ratio of its formation time to the time it has been accreting, so early-forming halos are more concentrated.
The observed merger rate of compact binaries is set by the ratio of inspiral time to the formation rate, so a population that forms early merges late and is observed at a lower rate.
A field-by-field catalogue tells you what each discipline thinks. A mechanism-by-mechanism catalogue tells you what kind of argument a discipline is making, and lets you check whether the same argument holds somewhere else. Each family here is a distinct causal shape; the eleven instances test whether it generalises.
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