Triton 47

Triton 47 › Space, time & physics › After the PhD

Information size of cell to universe

· 2151 words · 10 min read AI-generated

Index note AI estimate: cell ~127 TB, human ~1.6e26 B, Earth ~1e51, Sun ~1.5e59, universe ~3.3e82

Mostly AI-generated: the bulk of this post is AI output that the author prompted, pasted and kept. The author's own words are typically the short prompts and the closing remarks.

(generated with AI)
Estimating the complexity of a cell and the amount of information needed to fully describe its state is a fascinating challenge. Here’s a breakdown of the components involved and an estimate of the information required:

1. DNA:

The human genome is about 3 billion base pairs long. Each base pair can be represented with 2 bits (A, T, C, G).DNA Size (bits)=3×109 base pairs×2 bits/base pair=6×109 bits.\text{DNA Size (bits)} = 3 \times 10^9 \, \text{base pairs} \times 2 \, \text{bits/base pair} = 6 \times 10^9 \, \text{bits}.DNA Size (bits)=3×109base pairs×2bits/base pair=6×109bits.

Converting to bytes:DNA Size (bytes)=6×1098=0.75 GB.\text{DNA Size (bytes)} = \frac{6 \times 10^9}{8} = 0.75 \, \text{GB}.DNA Size (bytes)=86×109​=0.75GB.

2. RNA:

In an active cell, around 10,000 to 20,000 genes are being transcribed at any time, producing various RNA molecules of different lengths. RNA molecules can vary from a few hundred to several thousand nucleotides.

  • Estimation: 10,000 molecules, average length 2,000 bases.
  • Information per RNA molecule: 2,000 bases×2 bits/base=4,000 bits2,000 \, \text{bases} \times 2 \, \text{bits/base} = 4,000 \, \text{bits}2,000bases×2bits/base=4,000bits.

Total RNA Information:10,000×4,000 bits=4×107 bits=5 MB.10,000 \times 4,000 \, \text{bits} = 4 \times 10^7 \, \text{bits} = 5 \, \text{MB}.10,000×4,000bits=4×107bits=5MB.

3. Proteins:

A cell typically contains 10 billion protein molecules of 20,000 types. Each protein can have an average length of 300 amino acids, and each amino acid requires 5 bits (there are 20 standard amino acids).

  • Information per protein: 300 amino acids×5 bits=1,500 bits300 \, \text{amino acids} \times 5 \, \text{bits} = 1,500 \, \text{bits}300amino acids×5bits=1,500bits.
  • Total protein information:

1010 proteins×1,500 bits/protein=1.5×1013 bits=1.875 TB.10^{10} \, \text{proteins} \times 1,500 \, \text{bits/protein} = 1.5 \times 10^{13} \, \text{bits} = 1.875 \, \text{TB}.1010proteins×1,500bits/protein=1.5×1013bits=1.875TB.

4. Metabolites:

Cells contain thousands of small molecules (metabolites, ions, etc.), each of which needs concentration, spatial localization, and interaction state.

  • Estimation: 10,000 types, each requiring 100 bits100 \, \text{bits}100bits.
  • Total metabolite information:

10,000×100=106 bits=125 KB.10,000 \times 100 = 10^6 \, \text{bits} = 125 \, \text{KB}.10,000×100=106bits=125KB.

5. Membranes and Organelles:

Describing the structure, composition, and dynamics of the membrane and organelles involves both spatial and compositional information.

  • Lipid molecules in a membrane: ~10810^8108, each requiring 50 bits.
  • Membrane proteins and spatial organization: ~10710^7107, each requiring 1,000 bits.

Total membrane information:108×50+107×1,000=5.5×109 bits=0.69 GB.10^8 \times 50 + 10^7 \times 1,000 = 5.5 \times 10^9 \, \text{bits} = 0.69 \, \text{GB}.108×50+107×1,000=5.5×109bits=0.69GB.

6. Cellular State Dynamics:

This includes transient interactions, signaling pathways, and changes over time. Capturing the dynamic state might require tracking:

  • Concentrations and states of all molecules over time.
  • Position and velocity for 101410^{14}1014 molecules.

Estimation: ~101510^{15}1015 bits for dynamics = 125 TB.

Total Information Required:

Summing up these components:

  • DNA: 0.75 GB
  • RNA: 5 MB
  • Proteins: ~1.875 TB
  • Metabolites: 125 KB
  • Membranes: ~0.69 GB
  • Dynamics: ~125 TB

Total= 127.3 TB.\text{Total} = \textbf{~127.3 TB}.Total= 127.3 TB.

Caveats:

  1. This estimate assumes perfect knowledge of every molecule and interaction in a single cell.
  2. It doesn’t account for quantum effects or the influence of the environment (e.g., neighboring cells, extracellular matrix).
  3. Computational models to simulate such a cell would require even more information, including initial conditions and physical laws.

Conclusion:

A single human cell’s full state might require ~127 TB of information, making it one of the most complex systems to model or describe. This underscores the incredible intricacy of life at the cellular level.

To estimate the “total human information” represented by all cells in the body, considering structure, composition, and dynamics, involves several layers:

1. Information per Cell:

  • DNA Information:
    • Each cell contains approximately 3.2×1093.2 \times 10^93.2×109 base pairs in the haploid genome.
    • Assuming 2 bits per base pair (A, T, G, C), this amounts to 6.4×1096.4 \times 10^96.4×109 bits (8×1088 \times 10^88×108 bytes).
    • Diploid cells (most somatic cells) double this, 1.6×1091.6 \times 10^91.6×109 bytes.
  • Molecular Composition:
    • Proteins, lipids, carbohydrates, water, etc., and their positions/states add information.
    • Estimated at roughly 101210^{12}1012 molecules per cell, with each molecule requiring position, state, and identity encoding.
    • Estimation for positional and state information could range to 101310^{13}1013 bits (1.25×10121.25 \times 10^{12}1.25×1012 bytes).
  • Membrane and Structure:
    • Membrane composition, topology, and structural proteins add significant data.
    • Likely on the order of 101110^{11}1011 bytes or more.
  • Dynamic State:
    • Cellular dynamics, such as ion channel states, transcriptional activity, etc., increase the informational complexity.
    • Might double or triple static information estimates.

2. Total Cells in the Human Body:

  • Human adult: 3×10133 \times 10^{13}3×1013 cells by count.
  • Adding 101410^{14}1014 microbial cells in the microbiome increases the complexity further.

3. Total Information per Body:

If we estimate:

  • 1.5×10121.5 \times 10^{12}1.5×1012 bytes per human cell.
  • 101410^{14}1014 human cells.
  • Total for human cells: 1.5×10261.5 \times 10^{26}1.5×1026 bytes (150 yottabytes, where 1 yottabyte = 102410^{24}1024 bytes).

Adding microbial information:

  • Assuming microbial cells have 10%10\%10% of the information content of human cells.
  • Microbial contribution adds 102510^{25}1025 bytes.

Total = ~1.6×10261.6 \times 10^{26}1.6×1026 bytes.

4. Considerations for Dynamics and Interactions:

  • Interaction and communication between cells: vast networks of signaling and coordination.
  • Timescale dynamics: cellular state changes (e.g., signaling, mitosis, apoptosis).
  • Adds orders of magnitude to the informational model but remains challenging to quantify exactly.

5. Comparison with Global Data:

  • The entire internet is estimated to store ~102110^{21}1021 bytes (1 zettabyte).
  • The human body’s informational complexity exceeds the internet by about 10510^5105 times, highlighting the immense complexity and data richness of biological systems.

Calculating the total information content of Earth requires considering all biological, geological, atmospheric, and human-made systems. Here’s a conceptual breakdown:

1. Biological Information

a) Humans:

  • Population: ~8×1098 \times 10^98×109 people.
  • Per Human Information: ~1.6×10261.6 \times 10^{26}1.6×1026 bytes (previous estimate).
  • Total Human Information: 1.3×10361.3 \times 10^{36}1.3×1036 bytes.

b) Animals:

  • Biomass Estimate: ~2×10152 \times 10^{15}2×1015 kg (including fish, mammals, birds, etc.).
  • Animal Cell Count: Assuming ~101310^{13}1013 cells/kg, total cells ~2×10282 \times 10^{28}2×1028.
  • Per Cell Information: ~101210^{12}1012 bytes.
  • Total Animal Information: ~2×10402 \times 10^{40}2×1040 bytes.

c) Insects:

  • Biomass Estimate: ~1×10151 \times 10^{15}1×1015 kg.
  • Insect Cell Count: Assuming ~101210^{12}1012 cells/kg, total cells ~1×10271 \times 10^{27}1×1027.
  • Per Cell Information: ~101210^{12}1012 bytes.
  • Total Insect Information: ~1×10391 \times 10^{39}1×1039 bytes.

d) Microorganisms:

  • Biomass Estimate: ~7×10147 \times 10^{14}7×1014 kg (mostly in soil and oceans).
  • Microbial Cell Count: ~103010^{30}1030.
  • Per Cell Information: ~101110^{11}1011 bytes (simpler than human cells).
  • Total Microbial Information: ~104110^{41}1041 bytes.

e) Plants:

  • Biomass Estimate: ~4×10174 \times 10^{17}4×1017 kg.
  • Plant Cell Count: ~101310^{13}1013 cells/kg, total ~4×10304 \times 10^{30}4×1030 cells.
  • Per Cell Information: ~101110^{11}1011 bytes (less complex than animal cells).
  • Total Plant Information: ~4×10414 \times 10^{41}4×1041 bytes.

Biological Subtotal:

  • Total Biological Information: ~6.3×10416.3 \times 10^{41}6.3×1041 bytes.

2. Geological Information

  • Earth’s Crust: Consists of minerals and rocks, each with atomic arrangements.
  • Atoms in Earth’s Crust: ~104910^{49}1049.
  • Per Atom Information: Assuming atomic structure, bonding, and lattice data ~10210^2102 bits/atom.
  • Crust Information: ~105110^{51}1051 bytes.
  • Oceans:
    • Water molecules: ~104610^{46}1046.
    • Per Molecule Information: ~10210^2102 bits/molecule.
    • Total Ocean Information: ~104810^{48}1048 bytes.
  • Atmosphere:
    • Air molecules: ~104410^{44}1044.
    • Per Molecule Information: ~10210^2102 bits/molecule.
    • Total Atmosphere Information: ~104610^{46}1046 bytes.

Geological Subtotal:

  • Total Geological Information: ~1.01×10511.01 \times 10^{51}1.01×1051 bytes.

3. Human-Made Systems

  • Digital Data:
    • Total stored digital data on Earth: ~102110^{21}1021 bytes (zettabytes).
  • Structures and Materials:
    • Estimating information in buildings, roads, vehicles, etc.
    • Molecules in all human-made objects: ~104210^{42}1042.
    • Per Molecule Information: ~10210^2102 bits/molecule.
    • Human-Made Structure Information: ~104410^{44}1044 bytes.

Human-Made Subtotal:

  • Total Human-Made Information: ~104410^{44}1044 bytes.

4. Total Information Content

Summing up all contributions:

  • Biological: ~6.3×10416.3 \times 10^{41}6.3×1041 bytes.
  • Geological: ~1.01×10511.01 \times 10^{51}1.01×1051 bytes.
  • Human-Made: ~104410^{44}1044 bytes.

Total:

  • Total Earth Information: ~1.01×10511.01 \times 10^{51}1.01×1051 bytes (dominated by geological and molecular structures).

Notes and Considerations

  1. Dynamics and Interactions:
    • If we include the dynamics of molecular motion, energy transfer, and environmental changes, the information content increases significantly.
  2. Quantum States:
    • Including quantum-level information (spin, position, etc.) for each particle would vastly inflate these estimates.
  3. Simplifications:
    • This model assumes static states and omits higher-order interactions, such as ecosystem dynamics and chemical reactions over time.

Earth’s total information content, when encoded, is unfathomably vast and underscores the immense complexity of our planet.

To estimate the total information content of a star system, such as our Solar System, we can use a similar methodology as for Earth. We’ll include the Sun, planets, moons, asteroids, comets, and interplanetary medium.

1. Information Content of the Sun

  • Mass: 2×10302 \times 10^{30}2×1030 kg.
  • Atoms in the Sun:
    • Assuming average atomic mass is ~1.3 u (dominated by hydrogen and helium), total atoms = 1.5×10571.5 \times 10^{57}1.5×1057.
  • Information per Atom: ~10210^2102 bits (atomic structure and quantum states).
  • Total Sun Information: 1.5×10591.5 \times 10^{59}1.5×1059 bytes.

2. Information Content of Planets

a) Earth (already calculated): ~1.01×10511.01 \times 10^{51}1.01×1051 bytes.

b) Other Planets:

  • Average planetary mass (excluding Earth): ~3×10243 \times 10^{24}3×1024 kg.
  • Total atoms across all other planets: ~6×10516 \times 10^{51}6×1051.
  • Total Planetary Information: ~6×10536 \times 10^{53}6×1053 bytes.

3. Information Content of Moons

  • Total Moons: ~200 (major moons).
  • Average Mass: ~7×10227 \times 10^{22}7×1022 kg.
  • Atoms in Moons: ~1×10501 \times 10^{50}1×1050 atoms.
  • Total Moon Information: ~1×10521 \times 10^{52}1×1052 bytes.

4. Information Content of Asteroids

  • Asteroid Belt Mass: ~3×10213 \times 10^{21}3×1021 kg.
  • Atoms in Asteroids: ~4×10494 \times 10^{49}4×1049 atoms.
  • Total Asteroid Information: ~4×10514 \times 10^{51}4×1051 bytes.

5. Information Content of Comets

  • Mass of Known Comets: ~101610^{16}1016 kg.
  • Atoms in Comets: ~1.5×10461.5 \times 10^{46}1.5×1046 atoms.
  • Total Comet Information: ~1.5×10481.5 \times 10^{48}1.5×1048 bytes.

6. Information Content of Interplanetary Medium

  • Mass: ~101610^{16}1016 kg (dust, gas, plasma).
  • Atoms in Medium: ~1.5×10461.5 \times 10^{46}1.5×1046 atoms.
  • Total Medium Information: ~1.5×10481.5 \times 10^{48}1.5×1048 bytes.

7. Information Content of Outer Planets and Kuiper Belt

  • Mass of Kuiper Belt: ~1×10231 \times 10^{23}1×1023 kg.
  • Atoms in Kuiper Belt: ~2×10492 \times 10^{49}2×1049 atoms.
  • Total Kuiper Belt Information: ~2×10512 \times 10^{51}2×1051 bytes.

8. Total Information Content of the Solar System

Summing up contributions:

  • Sun: 1.5×10591.5 \times 10^{59}1.5×1059 bytes.
  • Planets (excluding Earth): 6×10536 \times 10^{53}6×1053 bytes.
  • Earth: 1.01×10511.01 \times 10^{51}1.01×1051 bytes.
  • Moons: 1×10521 \times 10^{52}1×1052 bytes.
  • Asteroids: 4×10514 \times 10^{51}4×1051 bytes.
  • Comets: 1.5×10481.5 \times 10^{48}1.5×1048 bytes.
  • Interplanetary Medium: 1.5×10481.5 \times 10^{48}1.5×1048 bytes.
  • Kuiper Belt: 2×10512 \times 10^{51}2×1051 bytes.

Total Solar System Information:

  • Dominated by the Sun: ~1.5×10591.5 \times 10^{59}1.5×1059 bytes.

Considerations

  1. Dynamic States:
    • Including dynamics such as stellar fusion processes, orbital movements, and interplanetary interactions could vastly increase the estimate.
  2. Quantum and Relativistic Effects:
    • Accounting for quantum states of particles or general relativistic effects in spacetime would exponentially increase information content.
  3. Comparison:
    • The Sun’s contribution far outweighs the rest due to its mass and atomic density, emphasizing the centrality of stellar bodies in star system information content.

To estimate the total information content of the universe, we consider a broader scale, accounting for stars, galaxies, dark matter, intergalactic medium, and cosmic phenomena. This calculation involves assumptions about the observable universe’s composition and structure.

Key Parameters of the Universe

  1. Observable Universe:
    • Radius: ~4.4×10264.4 \times 10^{26}4.4×1026 meters (~46 billion light-years).
    • Volume: ~3.58×10803.58 \times 10^{80}3.58×1080 m³.
  2. Number of Galaxies: ~2×10122 \times 10^{12}2×1012.
  3. Average Stars per Galaxy: ~101110^{11}1011.
  4. Mass of Observable Universe: ~1.5×10531.5 \times 10^{53}1.5×1053 kg (including dark matter and energy).
  5. Baryonic Matter (~5%): ~7.5×10517.5 \times 10^{51}7.5×1051 kg.
  6. Dark Matter (~27%): ~4×10524 \times 10^{52}4×1052 kg.
  7. Dark Energy (~68%): Not yet quantifiable in classical terms.

1. Information Content of Stars

  • Total Stars: 2×1012×1011=2×10232 \times 10^{12} \times 10^{11} = 2 \times 10^{23}2×1012×1011=2×1023.
  • Mass of a Typical Star (Sun-like): ~2×10302 \times 10^{30}2×1030 kg.
  • Atoms per Star: ~1.5×10571.5 \times 10^{57}1.5×1057 atoms.
  • Total Atoms in Stars: 3×10803 \times 10^{80}3×1080.
  • Information per Atom: ~10210^2102 bits.
  • Total Star Information: 3×10823 \times 10^{82}3×1082 bytes.

2. Information Content of Galaxies

  • Mass of a Galaxy (Baryonic Matter): ~104210^{42}1042 kg.
  • Atoms in a Galaxy: ~1.5×10681.5 \times 10^{68}1.5×1068.
  • Total Atoms in All Galaxies: ~3×10803 \times 10^{80}3×1080 atoms.
  • Total Galaxy Information: Similar to stars: 3×10823 \times 10^{82}3×1082 bytes.

3. Information Content of Interstellar and Intergalactic Medium

  • Mass of Intergalactic Medium: ~5×10505 \times 10^{50}5×1050 kg.
  • Atoms in Medium: ~6.7×10776.7 \times 10^{77}6.7×1077.
  • Information per Atom: ~10210^2102 bits.
  • Total Medium Information: ~6.7×10796.7 \times 10^{79}6.7×1079 bytes.

4. Information Content of Dark Matter

  • Mass of Dark Matter: ~4×10524 \times 10^{52}4×1052 kg.
  • Particle Estimate:
    • If dark matter is composed of WIMPs (weakly interacting massive particles), with a mass ~100×100 \times100× proton mass, particles = ~2.4×10792.4 \times 10^{79}2.4×1079.
  • Information per Particle: ~10110^1101 bits (minimal interaction states).
  • Total Dark Matter Information: ~2.4×10802.4 \times 10^{80}2.4×1080 bytes.

5. Information Content of Dark Energy

  • Dark energy’s nature is unknown, but if it were describable, its impact would scale across the entire universe. The information content of dark energy may exceed the baryonic and dark matter content but is not currently quantifiable.

6. Total Information Content of the Universe

Summing major contributions:

  • Stars and Galaxies: ~3×10823 \times 10^{82}3×1082 bytes.
  • Interstellar/Intergalactic Medium: ~6.7×10796.7 \times 10^{79}6.7×1079 bytes.
  • Dark Matter: ~2.4×10802.4 \times 10^{80}2.4×1080 bytes.
  • Others (e.g., cosmic phenomena, neutrinos, etc.): Estimated as minor contributors compared to stars and galaxies.

Total Observable Universe Information:

  •  3.3×1082~3.3 \times 10^{82} 3.3×1082 bytes.

Considerations for Total Universe Information

  1. Dynamic States: Include cosmic events (e.g., black holes, supernovae), which add enormous complexity.
  2. Structure Information:
    • Galaxy distribution, large-scale structures, and cosmic microwave background (CMB) contribute further.
  3. Unobservable Universe: The observable universe is a small fraction of the entire universe (unknown factor for total size).

Conclusion

The observable universe’s information content is dominated by stars, galaxies, and dark matter, with a total estimate of approximately 3.3×10823.3 \times 10^{82}3.3×1082 bytes. Accounting for unobservable regions, quantum phenomena, and dark energy could drastically increase this estimate.

#biology #dna #health #rna #science

Original: https://triton7777.wordpress.com/2025/01/14/information-size-for-cell-simulation/

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