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Non hereditary mutations are much more common because hereditary ones get eliminated by natural selection. As for why non hereditary mutations turn into cancer and not grow into some monstrous organs must be related to self destruction (apoptosis) and tissue compatibility (but mostly self destruction).

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Different tissue types do cell division with different rates. As mutations are mostly errors while copying during division the fast ones have a higher likelihood.

Some tissue types may have more contact with carcinogens. Your skin is basically the only tissue to get contact with UV light for instance.

Some kinds of cancer may have multiple possible mutations to cause them and some may need multiple specific ones, influencing their likelihood.

Of cause there are also cancers linked to certain virus infections.

there are certain sequences or portions of a chromosome that for reasons we still are trying to understand, are more susceptible to mutation, or damage. For example the Brca1 gene is susceptible to mutation to cause breast cancer

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Oh, huh. The BRCA1 gene doesn't always mutate in a similar way, does it? What I mean is, if the cancers caused by BRCA1 aren't all formed by the same mutations and subsequently behave the same way. I've definitely heard that every cancer is unique to the individual, so maybe I'm working under the wrong assumption that everyone with BRCA1 related cancers has the "same" type of cancer (all equally aggressive, all immune/responsive to the same treatments, etc).

There are some great answers here, just adding a bit based off your recent edit.

"Evolution" is a great way to frame development of cancer cell lineages. For a cell to develop into malignant growth, it has to be able to "outcompete" neighboring cells to go from cellular expansion > avoidance of immune system > invasion of extracellular matrix > treatment resistance. One of the core concepts is the idea of driver mutations, where certain mutations are more likely to lead to further mutations hence "driving" to cancerous developments.

The infamous BRCA gene is one such example. If one person inherits a mutated copy and then develops a mutation in the other copy, they lose the capability to prevent damaged cells to undergo programmed cell death (apoptosis). When combined with other risk factors (female sex, radiation exposure, OCP use, etc.), random mutations can pile up that would normally be prevented by functioning BRCA gene products. Colon cancers also show a similar line of progression (APC > KRAS > p53 > VEGF genes) where the initial inherited mutation increases risk of developing cancers.

Another classic example would be the Li Fraumeni Syndrome, inherited dysfunctional p53 gene. The p53 protein is crucial to detecting damage to DNA and then initiating repair or cell death. Cells with one inherited mutated copy of this gene who further develop "non-hereditary" mutation in the other copy now lack this the capability for DNA repair in future cell divisions (two-hit hypothesis). Most of the time, other repair/immune mechanisms will prevent cells without a single functioning copy from turning cancerous; however, in cell lines that physiologically divide rapidly (skin cells, GI cells, bone marrow), cells can escape these mechanisms. Families with Li Fraumeni Syndrome can present with a variety of cancers in their medical history ranging from breast cancer to brain cancer.

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Just adding this: although genetic mutations are “random” in the sense that whether they happen or not in an individual is, effectively, a roll of the dice, that doesn’t mean the dice are equally likely to land on all numbers. For example, it’s known that one nucleobase (cytosine, C) has an outsized tendency to mutate to thymine (T) because it only has to lose one amino group to turn into uracil, which looks to many enzymes indistinguishable from T. This even happens when you heat DNA in a test tube - a very small fraction of the C’s in that test tube will lose an amino group and become U. (Edit: and if the C was already methylated, it will turn into T if it loses the amino group.) This is actually a nuisance when you are looking for rare mutations in a sample, and can lead to false positives unless you correct for it somehow.

There are many other examples, but even at a chemical level certain DNA bases and sequences are more susceptible to mutation than others. This is at least part of the answer to your question.

Edit: So, while the occurrence of a mutation or not in an individual can be considered an essentially random process in most cases, not all random mutations are equally likely. It’s like if you had a hat full of names and drew a name at random: the likelihood that the name begins with S isn’t the same that it begins with X, just because S names tend to be more common (at least in English). The process can be random and still generate certain outcomes more than others.

not an oncologist, but there are only so many nucleotides in that gene. yes all cancer is personal but they all have similarities. p53 for example, is often inactivated; it is the gene that makes cancer cells suicide. no single mutation causes cancer, it is a combinations of them. in short, our DNA gets mutated daily no matter what we do and if we live long enough cancer will kill us, but some regions are more susceptible and other have no effect (called silent mutations)

If you are looking for further reading with regard to cancers specifically, see Hanahan and Weinberg "the hallmarks of cancer" papers. They cover the last 40+ years of our understanding of cancer genetics and molecular mechanisms.

https://www.cell.com/fulltext/S0092-8674(00)81683-9

https://www.cell.com/fulltext/S0092-8674(11)00127-9

https://aacrjournals.org/cancerdiscovery/article/12/1/31/675608/Hallmarks-of-Cancer-New-DimensionsHallmarks-of

There are certain functions a cancer cell needs to perform and thus certain gene types that need to be mutated. It’s by no means an intentional action on the part of the cancer, but if the cancer can’t grow uncontrollably, get blood flow, evade the immune system, and eventually metastasize it’s not a very effective cancer. The most common cancer types are also often in cells exposed to carcinogens in the environment (lung, skin, etc.).

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Even if two mutations had the exact same chance of happening in a given organism, if one of those would confer much greater chance of evading the immune system that the other, you would end up seeing a lot more cancers with the 1st mutation, even if the mutation itself didn't have a higher chance of appearing.

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>For example, why do some types of cancer account for the majority of cases while others are rare?

Different cancers are not simply different mutations. The same mutation can cause different cancers and the same cancer can be caused by different mutations. Rare cancers tend to be those in tissues/organs that have little cell division, so there is less opportunity for mutations to arise and spread.

There are oncogenes, genes sequences known to cause cancer, and there is also epigenetics. Epigenetics says that your environment and even thoughts regulate gene expression. Just because you have it doesnt mean it will ever express itself. Genetics is a very complicated system of 3 billion base pairs constantly being edited by proteins. Some sequences upregulate, some downregulate. UV rays from the sun, for example, create Thymine dimers (separates the DNA and damages it with long enough exposure so that when there are 2 T's in sequence, it separates the pair of T's from the rest of the DNA. This damage is usually fixed by proteins that relentlessly edit and repair, so there are tons of things that cause damage, and often times it has to do with age, and how well the body repairs damaged sequences.

It's always important to remember that "random" does not mean "equal chance".

Yep, a common misconception. I can’t count the number of times I’ve heard something like:

“Either you’ll get cancer or you won’t, it’s 50/50.”

No, 2 options doesn’t mean it’s a 50% chance of each!

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There are many different types of mutations in the BRCA1 gene. And having the mutation just makes you more susceptible to cancer so even within the same family with same mutation what type of cancer you get can be different since cancer is at its core multifactorial.

I think a better example of this is Achondroplasia caused by a mutation in the FGFR3 gene there are like two very specific mutations that cause almost all of these cases which are usually random and not inherited.

Edit: check out this article about mutation hot spots https://pubmed.ncbi.nlm.nih.gov/27070266/

Certain mutations, random or not, cause things which become apparent (such as cancer) while others go unnoticed.

Some tissues have extra exposure, such as the liver, skin, mouth, etc.

Some cell types are more or less resistant based on their function, location, age, etc.

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