Could Muons Be the Unseen Architects of Biological Evolution?

I was having a discussion with my elder kid, who is working on ‘Muon Tomography Simulation’ to map the contents of structures hidden in the Earth as part of his summer job (he is an undergrad at Berkeley focused on Quantum Physics and Pure Math). The discussion veered to how many muons travel through the human body in our lifetime and if they have any biological impact given their ionizing radiation.

The pervasive nature of cosmic rays and their interactions with Earth’s atmosphere gives rise to a constant shower of secondary particles, among which muons are a prominent component. While muons are known for their ability to penetrate deep into materials, including human tissue, the biological effects of these particles are often understated.

In this blog I delve into the nature of muons, their interactions with human cells, and a detailed statistical analysis of the potential biological effects over a human lifespan and over millions of years.

Understanding Muons

Muons are elementary particles similar to electrons but with a mass approximately 200 times greater. They originate from the decay of pions and kaons, which are produced when high-energy cosmic rays collide with nuclei in the upper atmosphere. Muons, due to their high mass and weak interaction with matter, can travel through several kilometers of rock, making them valuable for geological and sub-surface imaging.

Muon Flux and Human Exposure

At sea level, the average muon flux is approximately 10,000 muons per square meter per minute. This translates to roughly 167 muons per square meter per second. Considering an average human body surface area of 0.35 square meters, the body is exposed to approximately 58.45 muons per second. Over an 80-year lifespan (equivalent to 2.52 × 10⁹ seconds), this results in a substantial number of muons interacting with the body:

Biological Interaction and Damage

To estimate the probability of biological damage, we did not initially have evidence on how much energy is needed to cause a mutational impact at the cellular level. Upon searching, not to my surprise, Piet D. Groen has already pondered and worked on the energy requirement and the muon impact on cells in an NIH paper titled “Muons, mutations, and planetary shielding”

Through this paper, I consider the energy deposition required to cause a biological mutation, which is approximately 30 eV.

Energy of Muons:

Average energy of a cosmic ray muon at sea level: 4 GeV (4 × 10⁹ eV).

Energy Deposition:

The ionization potential of biological tissue is approximately 30 eV per ion pair.

The average energy deposition per muon track is around 1.5 MeV/cm (1.5 × 10⁶ eV/cm).

Given that muons can traverse several centimeters of tissue, the total energy deposited in a cell (assuming a cell diameter of about 10 micrometers, or 10^-3 cm) can be estimated as:

Number of Ionizations:

The number of ionizations (or interactions that could potentially lead to mutations) per muon per cell can be estimated by dividing the total energy deposition by the energy required for one ionization (30 eV):

Aggregate Biological Impact

To understand the aggregate impact, we calculate the expected number of significant interactions for all cells over a lifetime (I am assuming average lifetime to be 80 years).

Total Ionizations Over 80 Years:

Total muons over 80 years: 1.47×1⁰¹¹

Total ionizations per cell over 80 years:

Total Significant Interactions:

Given the probability that any given ionization event will cause a significant biological mutation is very low, we can assume a small fraction of these ionizations lead to mutations. For simplicity, assume 1 in 10⁷ ionizations leads to a mutation:

This result suggests that over an 80-year lifespan, each cell (through mitosis which may retain the mutations) might experience approximately 735 biological mutations due to muon interactions. Are these significant mutations? Maybe not. Can they be? Statistically it could but I have no way to find the probability of that as there are not much experiments done. Given the vast number of cells in the human body, the aggregate number of mutations is substantial (assuming 37 trillion cells per human).

Cellular Repair Mechanisms

Despite the large number of potential mutations, individual cells have robust repair mechanisms that mitigate these effects. Cells have evolved several DNA repair pathways to maintain genomic integrity:

Direct Repair:

Some DNA damage can be directly reversed by specific enzymes. For example, photolyase enzymes can repair UV-induced thymine dimers.

Base Excision Repair (BER):

BER corrects DNA damage involving small, non-helix-distorting base lesions. The damaged base is removed by a glycosylase enzyme, followed by removal of the abasic site and filling in of the correct nucleotide.

Nucleotide Excision Repair (NER):

NER fixes bulky, helix-distorting lesions. This process involves removal of a short single-stranded DNA segment containing the lesion, followed by DNA synthesis to fill the gap.

Mismatch Repair (MMR):

MMR corrects base-pairing errors that escape proofreading during DNA replication. This system increases the fidelity of DNA replication.

Double-Strand Break Repair:

Double-strand breaks (DSBs) are repaired by non-homologous end joining (NHEJ) or homologous recombination (HR). NHEJ directly ligates the broken ends, while HR uses a homologous sequence as a template for repair.

These repair mechanisms significantly reduce the probability that muon-induced DNA damage will lead to permanent mutations. Most DNA lesions are promptly and accurately repaired, preventing them from causing long-term harm to the cell.

Accounting for Repair Efficiency

To quantify how much DNA repair mechanisms reduce the probability of muon-induced DNA damage leading to permanent mutations, we need to understand the efficiency of these repair mechanisms. Various studies suggest that DNA repair mechanisms can correct a large fraction of the damage caused by ionizing radiation. However, for a precise calculation, let’s use some general assumptions based on empirical data.

Assumptions

Initial Probability of Damage:

From our previous calculations, each cell might experience approximately 735 significant biological mutations due to muon interactions over an 80-year lifespan.

Repair Efficiency:

Studies indicate that DNA repair mechanisms can correct about 99.9% of DNA lesions caused by low-LET radiation (which includes muons). This translates to a repair efficiency of 0.999.

Calculation

Given:

Initial number of mutations per cell over 80 years: 735

Repair efficiency: 99.9% or 0.999

The remaining number of mutations after repair mechanisms have acted can be calculated as follows:

Remaining mutations per cell = Initial mutations per cell × (1−Repair efficiency)

735 × (1−0.999)

735 × 0.001

Hence, remaining mutations per cell = 0.735

Total Remaining Mutations in the Human Body

To find the total number of remaining mutations in the human body, multiply the remaining mutations per cell by the total number of cells in the human body:

Total remaining mutations= 0.735 × 3.72 × 10¹³

Total remaining mutations ≈ 2.73 × 10¹³

Thus, after accounting for the repair mechanisms, the total number of mutations in the entire human body over an 80-year lifespan is reduced from approximately 2.73 × 10¹⁶ to approximately 2.73 × 10¹³.

These calculations illustrate the profound impact of DNA repair mechanisms in mitigating the potential damage caused by muons and other low-LET ionizing radiation.

Cumulative Effects Over A Million Years

To understand the cumulative impact of muons on biological systems over geological timescales, we need to consider the total biomass and the constant exposure to muons over millions of years.

Estimating Muon Flux Over Millions of Years

Average Muon Flux:

Average muon flux: 10,000 muons per square meter per minute.

Convert to annual flux:

Total Muons Over 1 Million Years:

Estimating Biomass Exposure

Global Biomass Estimate:

The total biomass on Earth is estimated to be around 550 × 10¹⁵ grams of carbon (approximately 5.5 × 10¹⁴ kg).

Cell Density and Surface Area:

Assuming an average cell mass of 1 nanogram, the total number of cells in the Earth’s biomass is approximately 5.5 × 10²⁶ cells.

Assuming an average surface area per organism, consider an estimated average surface area per cell exposed to muons. For simplicity, we’ll use a spherical approximation.

Calculating Cumulative Biological Impact

Total Muons Interacting with Biomass:

Assuming an average surface area exposed to muons per cell and the global biomass spread across the Earth’s surface, we can estimate the number of muons interacting with the biomass.

The Earth’s surface area is approximately 5.1 × 10 ¹⁴ m².

Total Significant Interactions:

Using the previously established estimate of 50 ionizations per muon per cell, we can calculate the cumulative number of significant interactions over 1 million years:

Total muons over 1 million years interacting with Earth’s surface:

Total ionizations:

Assuming 1 in 10⁷ ionizations leads to a mutation:

At 99.9% repair efficiency, that will have a remaining mutation of 1.34 x 10²⁴ over a million years.

This result suggests that over millions of years, the cumulative number of significant biological interactions due to muons across the entire biomass of Earth is substantial. Could this cumulative effect have played a role in evolutionary processes, potentially contributing to mutations and biodiversity? 🤷‍♂️

I am not suggesting it actually did. I have no evidence to consider if this is relatively small or large on a cosmic scale spread across a million years across all bio mass. My guess is as good as yours, but the remaining mutations seems statistically substantial to ruminate over.

Worth pondering.