Physical Units, Constants and Conversion Factors
Here we regroup the values of the most useful physical and chemical constants used in the book. Also some practical combinations of such constants are provided. Units are expressed in the International System (SI), and conversion to the older CGS system is also given. For most quantities and units, the practical definitions currently used in the context of biophysics are also shown.
© Springer International Publishing Switzerland 2016 609 F. Cleri, The Physics of Living Systems, Undergraduate Lecture Notes in Physics, DOI 10.1007/978-3-319-30647-6 610 Physical units, constants and conversion factors
Basic physical units (boldface indicates SI fundamental units)
SI cgs Biophysics Length (L) meter (m) centimeter (cm) Angstrom (Å) 1 0.01 m 10−10 m Time (T) second (s) second (s) 1 µs=10−6 s 1 1 1ps=10−12 s Mass (M) kilogram (kg) gram (g) Dalton (Da) −27 1 0.001 kg 1/NAv = 1.66 · 10 kg Frequency (T−1) s−1 Hz 1 1 Velocity (L/T) m/s cm/s µm/s 1 0.01 m/s 10−6 m/s Acceleration (L/T2) m/s2 cm/s2 µm/s2 1 0.01 m/s2 10−6 m/s2 Force (ML/T2) newton (N) dyne (dy) pN 1kg· m/s2 10−5 N 10−12 N Energy, work, heat joule (J) erg kB T (at T = 300 K) (ML2/T2) 1kg· m2/s2 10−7 J 4.114 pN · nm 0.239 cal 0.239 · 10−7 cal 25.7 meV 1C· 1V 1 mol ATP = 30.5 kJ = 7.3 kcal/mol Power (ML2/T3) watt (W) erg/s ATP/s 1kg· m2/s3 =1J/s 10−7 J/s 0.316 eV/s Pressure (M/LT2) pascal (Pa) atm Blood osmolarity 1 N/m2 101325˙ Pa ∼ 300 mmol/kg 1 bar = 105 Pa ∼300 Pa = 3 · 10−3 atm Electric current (A) ampere (A) e.s.u. Transmembrane 1 2.998 · 109 A current ∼1-2 mA/cm2 Electric charge (A/T) coulomb (C) statCoulomb (stC) 1A·s 2.998 · 109 C Electric volt (V) statCoulomb (stC) Neuron action potential potential (ML2/T3A) 1W/A 2.998 · 109 C ∼ 100 mV Electrical ohm () statOhm (st) Cell membrane (with K+ resistance (ML2/T3A2) 1 V/A 1.11265 · 10−12 and Na+ channels) 1-2 k · µm2 Temperature (K) kelvin (K) celsius (◦C) 1 1 Physical units, constants and conversion factors 611
Useful physical constants and their combinations
23 −1 Avogadro’s number, NAv = 6.0221409 × 10 mol = 1 (12 ) = . × −27 Atomic mass unit, mu 12 m C 1 66053904 10 kg −23 −5 Boltzmann’s constant, kB = 1.3806485 × 10 J/K (joule/kelvin degree) = 8.617×10 eV/K Planck’s constant, h = 6.62607 × 10−34 J s = 4.132 eV/fs, = h/2π Stefan-Boltzmann’s constant, σ = 5.670367 × 10−8 W/(m2K4) Gas constant, R = 8.31446 J/(K· mol) = 1.987 cal/(K· mol) = NAv · kB Molar volume at STP Vm = 22.414 litre/mol Speed of light, c = 2.99792458 × 108 m/s Elementary charge, e = 1.60217662 × 10−19 C (coulomb) −12 Vacuum dielectric constant, ε0 = 8.854 · 10 F/m (faraday/metre) 9 2 −2 Coulomb’s constant, Kc = 1/(4πε0) = 8.9875 × 10 Nm C Faraday’s constant, F = 96485.309 C/mol 2 −10 mu c = 1.4924 × 10 J = 931.494 MeV 2 −28 Kce = 2.3071 × 10 Jm=1.44eVnm c = 3.1615 × 1026 J m = 197.33 eVnm RT = kB T × NAv = 2.479 kJ/mol (at 300 K) h/kB T = 0.16 ps (at 300 K)
Useful conversion factors (with some old-fashioned units)
To convert from: To: Multiply by: radian degree arc 57.29578 angstrom nanometer 0.1 light-year metre (m) 9.461 × 1015 cm3 litre 0.001 eV joule (J) 1.6021 × 10−19 eV (wavelength) cm−1 8,065.73 eV (wavelength) nanometer 1,239.84 teraHertz (THz = 1012Hz) meV (wavelength) 4.13567 standard atmosphere kilopascal (kPa) 101.325 bar kilopascal (kPa) 100 millimeter of mercury (at 0 ◦C) kilopascal (kPa) 0.1333224 millimeter of water (at 4 ◦C) pascal (Pa) 9.80665 pound/sq.inch (lb/in2, psi) pascal (Pa) 6,900 centipoise (viscosity) pascal-second (Pa s) 0.001 horse-power (hP) watt (W) 746 kilowatt-hour (kWh) megajoule (MJ) 3.6 calorie joule (J) 4.184 eV kcal/mole 23.0609 gauss tesla (T) 0.0001 weber/sq.metre tesla (T) 1 ampere-hour coulomb (C) 3,600 Index
A ATP, adenosine triphosphate, 78, 113, 188, Accretion mechanism, 496 206, 209, 221, 240, 264, 276, 357, Acetylation, 107 430 Actin, 193, 207, 261 Autocatalysis, 507 monomer (G-actin), 226 Autocatalytic reaction, 80 polymerisation, 226 Avalon explosion, 90 polymerisation speed, 227 Average curvature, surface, 486 treadmilling effect, 228 Avogadro’s number, 11 Action potentia Axoplasm, 271 Hodgkin-Huxley experiment, 280 Action potential, 262, 275, 278 in muscle, 442 B plants, 303 Bacterial DNA, 71 post-synaptic, 291 Ballot theorem, 179 propagation speed, 282 Bartel and Szostak experiment, 80 Basal metabolic rate, 138 subthreshold, 285 Bending modulus wave-like propagation, 284 of a rmembrane, 325 Active transport, 264 of a rod, 324, 326 Adiabatic transformation, 14 Bilateral symmetry, 505 Adipocytes, 147 Binomial distribution, 66 Adiposomes, 147 Biodiversity, 554 ADP, adenosine diphosphate, 113, 215, 430 abundance, 563 Albedo, Earth surface, 39 richness, 563 Allometry, 529 Bio-geochemical cycle, 557 Amino acid, 105 Biomass, 555 Amphiphilic molecule, 169, 337 Biomass, upper bound for a species, 561 Anaerobic glycolysis, 134 Biosphere, 30 Ancient Greek medial school, 96 Biosynthesis Antiporter, ion channel, 134 clay hypothesis, 89 Apex predator, 555 iron-sulphur hypothesis, 89 Aquaporin, see ion channel Biot number, 143 Archimedean tiling, 488 Biphasic material, 387 Argentavis, 538 Biphasic model, human tissues, 390 Arrhenius law, of biodiversity, 563 Bistable oscillator, 439 Asakura and Oosawa experiment, 169 Black body, 41 Aspect ratio, 484 Body plan, 90, 505 © Springer International Publishing Switzerland 2016 613 F. Cleri, The Physics of Living Systems, Undergraduate Lecture Notes in Physics, DOI 10.1007/978-3-319-30647-6 614 Index
Boiling point, 55 Chromatin, 101, 356 Boltzmann Chromosome, 101, 356 constant, 17 Chronaxy, 278 entropy definition, 19 Cilium, 236 entropy equation, 62 Clausius, irreversible transformation, 18 kinetic theory of gas, 25 Clausius, thermodynamic entropy, 23 Boltzmann factor, 216, 345 Claverie and Rault, see mimivirus Bond number, 481 Clay hypothesis, see biosynthesis Bone size scaling, 537 Clock-and-wavefront model, 511 Brain plasticity, 292 Closed ecosystem, see ecology Brain-blood barrier, 188 Closed system, 20 Brittle, material, 374 Codon, 105 Brown fat, 147 Coenzymes, 151 Brownian motion Cohesin, 356 and membrane diffusion, 180 Cohesin, motor protein, 357 early experiments, 178 Colloid, 169 Einstein’s equations, 205 Competition, between species, 550 rectified, 216 Condensin, 356 Smoluchowski problem, 179 Condensin, motor protein, 357 Bulk modulus, 371 Conductance, neuron membrane, 269 Buoyancy force, 537 Constant, vector field, 50 Constitutive relation, 370 Contour length, 174 C Cortical tension, see membrane Calvin’s cycle, see photosynthesis Cost of transport, 541 Cambrian explosion, 90 Coupled oscillators, 513 Cantilever, 444 Creatine phosphate, 146 Capillarity, 478 Creep, 377 meniscus, 479 Crescentin, bacterial protein, 351 Capillarity length, 481 Cross bridges, sarcomere, 425 Carbohydrates, 153 Crowding agents, 172 furanose, 154 Cryptochrome, 257 monosaccharide, 153 Curl, see rotor pyranose, 154 Current summation, synaptic, 293 Carbon cycle, 558 Cyclic machine, 207, 213 Cardiac index, 139 ratchet, 216 Carnot, cyclic thermal engine, 18 Cytoskeleton, 244 Carrying capacity, 546 actin, 193 Catalyser, see enzyme centromere, 193 Catalytic efficiency, enzyme, 234 microtubules, 193 Cell cycle, 354 spectrin, 195 Cell nucleus, 337 Cellulose, 397 Central Dogma, 100 D Centromere, 101 Damping coefficient, aerodynamic, 448 Chaotic system, see deterministic chaos Debye-Huckel approximation, 175 Chemical potential, 27 Debye length, 175 Chemiosmotic theory, 120 Debye repulsion, screening, 173 Chlamydomonas, unicellular alga, 189, 255 Deformation (elastic) energy, 416 Chlorophyll, 476 Dendritic spines, 292 Cholesterol, 199 Depletion force, 169 Chondrocyte, 386 Depolarisation, membrane, 270 Chromatid, 101 Deterministic chaos, 547 Index 615
butterfly effect, 548 closed ecosystem, 556 critical bifurcation, 548 food chain, 555 loss of information, 548 mobile ecosystem, 556 Lyapunov exponent, 548 trophic level, 555 Lyapunov time, 548 Ecosystem Diastole, heart contraction, 296 producers versus consumers, 555 Diffusion Ectoderm, 505 across membrane, 176 Edema, tissue, 187 Diffusion coefficient, 177, 191, 205 Elastic compliance, 409 Diffusion equation, 180 Elastic constant, 409 Dinosaurs Elastic energy, storage, 535 extinction, 95, 539 Elastic moduli running speed, 458 bulk modulus, 411 Diodora aspera, gastropod, 191 Lamé parameters, 410 Diploblastic, body plan, 505 Poisson’s ratio, 414 Dipole moment, 167 shear modulus, 412 Dirac delta function, 45 Young’s modulus, 412 Divergence angle, 515 Elastic modulus, 370 Divergence, of a vector, 49 Electric permittivity, relative, 312 DNA Electrocardiogram, 300 exon, 77, 103 Endoderm, 505 Franklin and Wilkins x-ray diffraction, Endoergic, reaction, 69 97 Endoplasmic reticulum, 337 grooves, major and minor, 100 Energy accumulation rate, 543 intron, 77, 103 Energy barrier, 213 methylation, 107, 108 Energy budget, 543 mismatch, 99 Energy surface, 213 Nirenberg and Khorana genetic code, 97 England’s theory, maximum dissipation, 82 nucleoside, 99 Enthalpy, 27 nucleotide, 98 Entropic force, see generalised force Watson and Crick model, 97 Entropy Drag coefficient, 206 information, 36 Drag force negative, 36 in rotation, 240 Environmental pressure, 561 Stokes coefficient, 239 Enzymatic cycles, 124 Drosophila melanogaster, fruit fly, 257, 260, Enzyme, 126 428, 510 Epigenetic modification, 106 Ductile, material, 374 Equation of continuity, 180 Dulong and Petit, specific heat, 22 Equilibrium constant, 127 Dutch famine, 1944, 108 Equilibrium, statistical postulate, 12 Dynamic range, neuron, 295 Equipartition of energy, law, 22 Dynamometer, 419 Erythrocyte, red blood cell, 193 Dynein, 207, 237 Escherichia coli, bacterium, 71, 72, 104, 124, 174, 248, 328, 351, 353 Euchromatin, 101 E Euglenid, 242 Ecological niche, 537 euglenoid motion, 242 Ecology, 544 Euler equation, 404 automatic regulatory mechanism, 562 beam flexion, 404 bioaccumulation, 557 cantilever bending, 404 biomagnification, 557 Eutrophisation, 560 biovectors, 557 Exclusive competition, principle, 552 circulating reserve, 555 Extensive variable, 10 616 Index
Extinction coefficient, 249 H Extracellular potential, 281 Hagen-Poiseuille equation, 186, 483 Heart chambers, atrium, ventricle, 296 Heart vector, 301 F Heat capacity, 140 Fermentation, 135 Helmoltz free energy, 26, 82 Fermi-Dirac statistics, 172 Hemicellulose, 397 Fick’s laws, diffusion, 180 Heterochromatin, 101 Filtration coefficient, 186 Hexatic phase, 199 Flagelline, 237 Hill’s law, locomotion, 532, 534 Flagellum, 236 Hill’s law, muscle contraction, 429 and Type-III system, 237 Histone, 101, 356 axoneme, 237 acetylation, 107 proton pump, 237 Homochirality, amino acids, 89 Fluctuation therem, 82 Hydraulic resistance, 186 Foraminiferan, 95 Hydrodynamic radius, see polymer Fountain effect, liquid He, 477 Hydrogen bond, 167 Fourier series, 53 Hydrolysis, 116, 150 Fourier transform, 53 Hydrophobic Fracture strain, 416 surface, 478 Fracture stress, 416 Hydrophobic attraction, effect, 169 bone, 395 Hydrophobic force, 167 tendon, 393 Hydrophylic Froude number, 457 contact angle, 477 FtsZ, bacterial protein, 351 surface, 477 Hysteresis, 377 Hysteresis loop, 392 G Galenus, pneuma theory, 96 I Gamma function, 45 Immiscible fluids, 181 Gaussian integral, 46 Instability, dynamical, 492 Gene, 104 Intensive variable, 10 splicing, 104 Internal energy, 13 Generalised force, 160 Interneuron, 288 Gibbs free energy, 27, 29 Inversion potential, 291 Gibbs statistical factor, entropy, 18 Ion channel, 263 Gilbert, W., RNA world, 87 aquaporin-1, 264 Global heating, 40 indirect active transporter, 265 Glucose-6-phosphate, 146 ligand-gated, 264 Glucose transporter, GLUT, 145 light-gated, 264 Glycan, see polysaccharide mechanical-gated, 264 Glycerine, 152 porin, 128, 264 Glycocalyx, 337 proton pump, 265 Glycogen, 116 sodium-potassium pump, 264 Glycolysis, 116, 123 voltage-gated, 264 Golden mean, or Sectio aurea, 515 Iridescence, 486 Golgi organ, 337 Iron-sulphur theory, see biosynthesis Gonium, pluricellular alga, 189 Irreversibility, 19, 61 Gould and Eldredge theory, punctuated equi- Irrotational, vector field, 50 libria, 94 Isolated system, 12, 15 Gradient, of a scalar function, 48 Isometric effort, 427 Gravity, variations, 539 Isometry, 529 Gyration radius, 174, see also polymer Isotonic equilibrium, 165 Index 617
K Maxwell-Boltzmann distribution, 65, 329 Ketone bodies, 146 Maxwell’s equations, 311 Kinesin, 207, 222 Mayer and Joule, heat-energy equivalent, 14 KIF5, 223 Maynard-Smith, theory of proto-cell, 86 Kirchhoff’s laws, 311 Mayr theory, allopatric speciation, 94 Krebs cycle, 122 Membrane Kronecker delta function, 46 cortical tension, 193 Kuramoto model, 513 diffusion, 176 double layer, 197 semipermeable, 161 L Meniscus, 479 Lamé coefficients, 52 Mesoderm, 505 Lamé parameters, 371 Metabolic rate, 145 Laplace’s equation, 486 Metabolism Laplace’s law, 166, 193, 194, 349, 479, 486 surface scaling law, 540 Laplacian operator, 49 Metabolism, 3/4 scaling, 543 Leslie model, 568, see also population Methylation, 107, 108 dynamics Micelle, 196 Leucocyte, white blood cell, 193 Michaelis constant, 234 Lever-arm model, 220 Michaelis-Menten Liebig’s law, of the minimum, 557 equation, 234 Lift-to-weight ratio, 541 kinetics, 234 birds versus airplanes, 542 rate constants, 219 Lignin, 398 Microscopic state, 11 Limit cycle, 551 Microtubule, 193, 222 Limiting shape, 492 Miller and Urey experiment, 84 catenoid, 492 Mimivirus, 88 Linear system, 567 Minimal model, membrane, 341 Lineweaver-Burk plot, 234 Minimal surface, 484, 491 Lipid double layer, 197 Mitochondrion, 337 Lipid droplets, 146 cardiac, 436 Lipid vesicles, 338 Liposome, 198 Mitosis, 424 Lithosphere, 30 Mobility, 191, 206, 268 Logistic function, 545 Moment of inertia, 533 Loose-coupling model, 221 Monomer, 317 Lotka-Volterra equation, 550 Motility assay, 207 coexistence and symbiosis, 553 MreB, bacterial protein, 351 competition versus cooperation, 552 Muscle economic cycles, 551 antagonist, 424 non-trophic interactions, 566 contraction frequency, 423 predator-prey model, 551 direct, insect, 439 Lyapunov exponent, see deterministic chaos indirect, insect, 439 Lysis, membrane rupture, 165, 193 intrinsic rapidity, 430 sarcomere, 424 sarcosome, 424 M strain, 426 Macroscopic state, 10 stress, 423 Magnetic permeability, relative, 312 tonic, 431 Malthusian catastrophe, 545 Muscle, mechanical work, 531 Malthusian growth law, 544 Myocyte, muscle cell, 424 Mass-growth rate, 544 Myofibril, 424 Mass, maximum for an animal, 536 Myosin, 207, 261 Material surplus, 543 myosin-II average speed, 221 618 Index
myosin-V speed, 222 Phosphodiester bond, 150 myosin-V stall force, 222 Phospholipid, 195 power stroke, 209 Phosphorus cycle, 559 Myotendinous junction, 391 Photon, 35 Mytilus edulis, mollusk, 191 Photosynthesis, 35 Phototaxis, 256 Phyllotaxis, 515 N Plankton, 192 Negative entropy, 33, 34 Plasma, 193 Nernst equation, 266 Plasma membrane, 337 Neuromuscular junction, 260, 441 Poisson-Boltzmann equation, 175 Neuron, 258 Poisson’s ratio, 371 aminergic versus cholinergic, 551 Polymer, 317 mitochondria, 222 contour length, 319 Neuron refractory period end-to-end distance, 320 absolute, 285 entropic spring, 332 relative, 285 folding, 329 Newtonian fluid, 184 gyration radius, 321 Nicotinamide, 152 heteropolymer, 318 Nitrogen cycle, 559 homopolymer, 318 Nitrogen fixing bacteria, 559 hydrodynamic radius, 321 Nuclei, central nervous system, 294 Kuhn length, 327 Nucleoside, 150 Polysaccharide, 154 Nucleosome, 101 Population dynamics, 544 Nucleotide, see DNA Porin, see ion channel Post-synaptic terminal, 259 Power surplus, 543 O Pre-stress, 403 Ohm’s law, 268 Pre-synaptic terminal, 259 Oncotic pressure, 187 Prigogine theory, entropy production, 82 Open system, 27 Probability, microscopic, 61 Optical tweezers, 334 Projection matrix, see transition matrix Orthodromic conduction, 285 Protein Osmolar solution, 165 active site, 155 Oxidative phosphorylation, 133 alpha helix, 154 Oxygen cycle, 558 beta sheet, 154 homeodomain, 505 P primary structure, 154 Parenchyma, 400, 402 Protein concentration, cytoplasm, 71 Particle flux, 177 Protein, native conformation, 105 Partition coefficient, 181, 263 Proton pump, 119 Partition function, 63 ATP synthase, 237 Patch-clamp technique, 254 Pterosaurus, 538 Pauli repulsion, 172 Punctuated equilibria, see speciation Péclet number, 188 Pyrogen, 144 Pectin, 397 Pyruvate, 122 Pendulum, body oscillation, 534 Penrose tiling, 489 Permeability, 181, 263, 390 R Perrin experiments, colloids, 25 Radial symmetry, 505 Persistence length, 327, 330 Rank, see tensor Persistence length, membrane, 347 Reading frame, RNA, 105 Phenotype, 101 Redox cofactor, 151 Index 619
Redox reaction, 129, 131 Shear stress Regular polyhedra, 489 in a viscous fluid, 184 Remodelling, 368 Single-dipole model, heart, 301 Reservoir, thermodynamic, 10 Sinoatrial node, heart, 300 Resilience, 392 Skin Resilin, 440 epidermis, 381 Resting metabolic rate, O2 consumption, hypodermis, 382 145 Skin, tissue, 381 Resting potential, 269 Smoluchowski equation, 175 Retinotopy, 295 Soap bubble, surface tension, 485 Reynolds number, 183 Solar constant, CS, 38 Rheobasic current, 278 Solenoidal, vector field, 50 Riboflavin, 152 Somites, see tissue Ribose, 150 Space filling, 487 Ribosome, 102, 104 Speciation, 94 Ribozyme, 87 allopatric, 94 RNA phyletic gradualism, 94 messenger RNA, 102 punctuated equilibria, 94 ribosomal RNA, 104 Spectrin, 195 ribosome, 104 Squid, giant axon and synapse, 266 RNA-world hypothesis, 80, 87 Stahl theory of vitalism, 96 Rotor, of a vector (curl), 49 Standard solid model, 380 Starling equation, 187 Stefan-Boltzmann law, 41, 137 S Steric protection, 172 Sackur-Tetrode entropy, perfect gas, 18 Stern layer, 175 Saltatory conduction, neuron, 282 Stevin’s law, 483 Sap, see tree trunk Stick-slip, boundary, 183 Sarcomere, 209, 261, see also muscle Stirling’s approximation, factorial, 47 Sarcoplasmic reticulum, 424 Stoney equation, 445 Sarcosome, see muscle Strain, 408 Saturated fatty acid, 196 tensor, 409 Saturation, neuron receptors, 295 Strain-rate sensitivity, 377 Scalar or dot product, 48 Strength, material, 416 Scaling Stress, 407 of animal jumping, 531 tensor, 407 of animal speed, 534 Stress relaxation, 377 of moment of inertia, 533 Stress-strain diagram, 415 of muscle work, 531 Stress-strain relations, 370 of walking frequency, 533 Stride length, 533 Scaling analysis, 528 Strouhal number, 463 Scaling coefficient, 529 Structured population model, 567 Scaling exponent, 529 Supernatant, 585 Scaling factor, 528 Surface force, 476 Scaling law, metabolic, 145 Surface of revolution, 493 Scaling, of bone size, 537 Surface tension, 486 Scaling of bone size, prehistoric birds, 538 Surface tension, cell, 166 Scaling, of muscle power, 540 Surface to volume ratio, 484 Schrödinger negative entropy, 34 Symporter, 124 Sedimentation, 191 Symporter, ion channel, 134 Sedimentation coefficient, 202 Synapse, 222, 289 Shannon equation, entropy, 75 chemical, 259, 289 Shear modulus, 371 electrical, 260, 289 620 Index
excitatory, inhibitory, 292 Troponin, 210 in plants, 305 Troponin-C, 261 neuromuscular, 260, 441 Tubulin, 227, 249 Synaptic cleft, 259 Turing’s model, morphogenesis, 507 Synaptic potential, 290 Twisting modulus, 397, 405 Syncysis, 424 Systole, heart contraction, 296 U Ubiquinone, 130 Unsaturated fatty acid, 196 T Usher model, 568, see also population Tenocyte, 386 dynamics Tensor invariants, 52 V matrix form, 50 Vector product, 48 notation, 50 Verhulst model, 545 product, 51 Vesicle, 198 rank, 51 Viral capsid, 88 Thermal engine, 30 Virus, 88 Thermal ratchet, 216 Viscoelasticity, 377 Thermal receptors, skin, 139 Kelvin-Voigt model, 380 Thermal reservoir, 26 Maxwell model, 380 Thermodynamic system, 9 motor proteins, 360 Thermogenesis, plants, 148 of cartilage, 388 Thermostat, see thermal reservoir of skin, 384 Time constant, capacitor, 310 of tendon, 391 Tissue of woods, 401 blastula, 503 standard solid model, 380 diploblastic, 505 Viscosity, 206 gastrula, 503 of biological fluids, 239 segmentation, 505 of water, 206 somites, 505 Voigt notation, 409 triploblastic, 505 Voltage-clamp technique, 279 Titin, 336 Volume force, 476 Toroid, 494 Volumetric flux, 184 Torus, 494 Volvox, unicellular alga, 189, 255 Toughness of rhinoceros skin, 386 Toughness, material, 373, 416 W Transfer function, 213 Wächtershäuser iron-sulphur theory, 89 Transition matrix, 568 Water column, 192 Translation table, RNA-amino acids, 105 White fat, 147 Tree trunk Wiechert model, 381 heartwood, 398 Worm-like chain, 388 phloem, 400 sapwood, 398 X tracheids, 400 Xylem, see tree trunk xylem, 400 Triacylglycerol, 116 Triglycerides, 115, 147, 152 Y Triploblastic, body plan, 90, 505 Yield stress, 416 Trophic interaction, 563 Young’s modulus, 371 mutualism, commensalism, antagonism, 563 Z Trophic level, see ecology Zeta potential, 175