The Cell - an engineered system with a budget
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A labelled anatomical plate of the cell treated as an engineered artifact: what sets its size, what it spends, what its machines deliver under stated conditions, and where its sensing hits a physical floor. Fig. 1 is a schematic composite cell carrying nine numbered call-outs; Figs. 2-5 enlarge the membrane in section, the F1 rotary motor, kinesin on a microtubule, and the ribosome. A budget table sets E. coli against a mammalian cell WITHOUT averaging them, and a ceiling block derives why a cell is the size it is. Every printed number carries its value, units, scope and evidence class, and resolves to a row of encyclopedia/NATURE-LEDGER.md - or says, in place, that it does not: three printed numbers (mammalian power, E. coli size, the ion-pumping share) trace to NA-08 on disk but carry no ledger row, and are held here with ledger_row null as a repair queue against the ledger, not as a licence. Where the corpus carries no sourced number - the nucleus's diameter, the mitochondrion's length, the ribosome's diameter - the label reads NOT-SOURCED rather than inventing one; where nature has not been asked, it reads NOT-MEASURED. Those two fences are never merged. The drawing is schematic and not to scale: only the numbers are claims.
Claims
| ref | symbol | value | units | scope |
|---|---|---|---|---|
| d_bilayer | 4-5 | nm | lipid bilayer thickness | |
| V_m | ~-70 | mV | resting neuron | |
| E_m | 1.4-1.8 x 10^7 | V/m | V/d, 70 mV over 4-5 nm | |
| C_m | ~1 (0.01) | microfarad/cm^2 (F/m^2) | specific membrane capacitance, near-invariant across cell types | |
| E_air | ~3 x 10^6 | V/m | dry air, 1 atm - dielectric strength; COMPARISON ONLY | |
| nucleus diameter | - | micrometre | no sourced measurement in this corpus; CN-05 ASSUMES d = 6 um as a model input | |
| V_nucleus | ~113 | micrometre^3 | sphere, d = 6 um | |
| L_DNA | 1.04 (2.08) | m, haploid (diploid) | 3.055e9 bp x 0.34 nm/bp | |
| f_DNA,vol | ~5.8 | % of nuclear volume | DNA as a 1 nm-radius cylinder in a 113 um^3 sphere | |
| packing ratio | ~3.5 x 10^5 | dimensionless (linear) | 2.08 m / 6 um | |
| epsilon_final | 10^-8 - 10^-10 | per nt | genome fidelity AFTER three layers; pro- and eukaryotes | |
| epsilon_pol | ~10^-4 - 10^-5 | per nt | polymerase base selectivity ALONE - not the final figure | |
| epsilon_proof | ~10^-6 - 10^-7 (x10^2-10^3 gain) | per nt | + exonucleolytic proofreading | |
| 30 nm fibre in vivo | contested - not observed in cryo-EM of vitrified cells nor in ChromEMT | nm | in vivo chromatin structural level | |
| mitochondrion length | - | m | NA-10's scale ladder (rung 6) prints 5 x 10^-7 - 10^-6 m; NA-10's OWN gate struck it as carrying no source | |
| mitochondrion characteristic time | - | s | organelle-level dynamics | |
| mtDNA | 16,569 | bp | human mitochondrial genome, T2T-CHM13 | |
| tau_F1 | ~40 | pN.nm | F1-ATPase torque, constant across load and speed | |
| W_F1 | ~80 (vs ~90 available) | pN.nm per 120 deg step | F1, single-molecule, in vitro | |
| omega_F1 | ~130 | rev/s | F1, saturating ATP; 120 deg = ~90 deg + ~30 deg substeps | |
| dG_ATP | -47 to -50 (~20 kBT ~ 80-90 pN.nm) | kJ/mol | IN VIVO; E. coli on glucose -47 | |
| dG0'_ATP | -28 to -34 (~12 kBT) | kJ/mol | STANDARD conditions (1 M) - NOT the cell | |
| ribosome diameter | - | nm | no sourced row in this corpus | |
| r_rib,ec | ~20 (range 4-22) | aa/s | E. coli, growth-rate dependent | |
| r_rib,euk | 3-10 (yeast, 30 C); ~6 (mouse ES) | aa/s | eukaryote | |
| epsilon_rib | 10^-4 - 10^-3 | per codon | missense/misreading | |
| c_pep | 4 | ATP per peptide bond | 2 (PPi, aa-tRNA charging) + 1 GTP for each of two elongation factors | |
| d_kin | 8 | nm/step | kinesin-1 on microtubule, optical trap | |
| n_ATP,kin | 1 | ATP per 8-nm step | kinesin-1 | |
| v_kin | ~0.5-1 (commonly ~0.8) | micrometre/s | saturating ATP, near-zero load, in vitro | |
| F_stall,kin | 5-6 OR 7-8 | pN | 5-6: Svoboda & Block 1994 (optical trap). 7-8: Visscher et al. 1999 (molecular force clamp) | |
| kappa_MT | 2.2 x 10^-23 (+/-6.4%); 2.1 x 10^-23 (+/-4.7%, rhodamine) | N.m^2 | taxol-stabilised microtubule, flexural rigidity | |
| lp_MT | ~5,200 (5.2 mm) | micrometre | microtubule persistence length, lp = kappa/kBT | |
| lp_MT length-dependence | persistence length varies with filament length | - | grafted MTs | |
| lp_actin | ~17.7 | micrometre | actin filament, rhodamine-phalloidin | |
| lp_MT/lp_actin | ~294 (~300x) | dimensionless | Gittes values | |
| Re | ~6 x 10^-5 | dimensionless | E. coli: v ~ 3 x 10^-5 m/s, L = 2 um, rho = 10^3 kg/m^3, mu = 10^-3 Pa.s; inputs order-of-magnitude | |
| Pe | ~0.06-0.1 | dimensionless | same, D ~ 10^-9 m^2/s (small molecule) | |
| D_GFP,euk | 27 | micrometre^2/s | GFP-S65T, CHO cytoplasm | |
| D_GFP,ec | 7.7 +/- 2.5 | micrometre^2/s | GFP (27 kDa), E. coli cytoplasm, FRAP/photoactivation | |
| dc/c scaling | proportional to (D.a.c.T)^(-1/2) | dimensionless | diffusion-limited chemoreception | |
| dc/c prefactor | disputed - no closed form printed | - | B-P vs Bialek-Setayeshgar vs Kaizu: the B-S diffusive term is missing 1/(2(1-nbar)) | |
| ATP_ec | ~10^7 | ATP/s/cell | E. coli, growing | |
| ATP_mam | ~10^9 | ATP/s/cell | human fibroblast, ~3,000 um^3 | |
| P_ec | ~10^-12 (1,000 W/kg) | W/cell | E. coli, glucose minimal media | |
| P_mam | ~3 x 10^-10 | W/cell | mammalian cell | |
| p_cell | ~100 (mammalian) / ~1,000 (E. coli) | W/kg | specific power; cross-ref NA-08 | |
| f_prot | 61 | % of total cell ATP | E. coli, rich medium; 19.1 of 31.4 mmol ATP/g cells | |
| n_Na/ATP | 3 Na+ per 1 ATP | ions/ATP | Na+/K+-ATPase stoichiometry | |
| f_ionpump | ~50 | % of the budget | grey matter; the dominant sink, via the Na+/K+-ATPase | |
| E_neuron split | action potentials 47 / postsynaptic glutamate 34 / resting potential 13 / glutamate recycling 3 | % of signalling ATP | rodent grey matter - a MODELLED APPORTIONMENT, not per-process measurement | |
| ATP pool turnover | ~1 | s | E. coli - the 'no reservoir' claim | |
| S/V | 6 vs 0.3 | per micrometre | sphere 3/R; R = 0.5 um (E. coli) vs R = 10 um (mammalian) | |
| t(1 m) | ~6.2 x 10^9 (~195 yr) | s | 3D diffusion, D = 27 um^2/s, t = L^2/6D | |
| t_kinesin(1 m) | ~1.25 x 10^6 (~14 d) | s | 1 m at v_kin ~ 0.8 um/s | |
| L_Thio | 100-300 (max 750) | micrometre | Thiomargarita namibiensis, cell width | |
| f_vac | 80-98 | % of cell volume | Thiomargarita nitrate vacuole; living cytoplasm is a shell ~1-2 um thick | |
| V_ecoli | ~1 um x ~2 um, ~1 um^3 = 1 fL | micrometre / micrometre^3 / fL | E. coli cell size |
What this plate does NOT claim
- NOT TO SCALE. No drawn dimension, proportion, position or count on this plate is a measurement. The drawing is schematic throughout; only the printed numbers are claims. A 4-5 nm bilayer and a 6 um nucleus cannot share one drawing at one scale, and this one does not try.
- NOT ONE CELL. Fig. 1 is a composite. E. coli-scoped and mammalian-scoped numbers are labelled by scope and are never averaged. No organism has this budget.
- NOT AN OPTIMUM. Per Gould & Lewontin (1979), nothing here establishes any cellular feature as optimal. Phylogenetic inertia, drift, developmental constraint, pleiotropy and historical contingency produce features that solve nothing. Nature's authority here is precisely and only this: it has already run a very long parallel search under real physical constraints in which the failures were deleted. That makes every number here a hypothesis generator, not a proof. Per kitchen rule M7, a biomimetic design taken from this plate must still beat a tuned conventional baseline on a pre-registered metric with a load-bearing discriminator, or it is recorded NEGATIVE.
- NOT A UNI GATE. Every class on this plate is NATURA - nature's observed regularities. A nature citation NEVER raises a UNI rung. The NATURA vocabulary and the UNI ledger vocabulary (proven / designed / hypothesized / not-yet-built) describe different kinds of claim and never merge. This plate contains ZERO UNI claims.
- NOT COGNITION. 'Bounded inference' at call-out 9 is a statistical description of a physical process. Nothing here claims that a cell is aware, sentient, cognitive, or that it knows anything. Berg & Purcell bound an estimate; a bound is not an experience.
- NOT A CONSTRUCTION PLAN. Nothing here is a roadmap to building a cell, and nothing here bears on 'full human' or 'beyond human' - permanent open questions, never targets, never deliverables.
- NOT EXHAUSTIVE. Cytoplasmic streaming, syncytia and multinucleation are named size-ceiling workarounds and are not analysed here.
- NO SINGLE BERG-PURCELL PREFACTOR. The scaling is settled; the constant is disputed, and the dispute is printed instead of a number.
- THE 30-nm CHROMATIN FIBRE IS NOT DRAWN. It is OBSERVED-CONTESTED in vivo (CN05-42); chromatin is drawn as a disordered curvilinear chain per Ou et al. 2017.
- NO MAGNIFICATION IS STATED for Figs. 2-5. They are details, not calibrated micrographs.
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