The number of MHC class I loci. As the number of loci increases, the organism gains an ability to respond to a greater diversity of pathogens and avert evasion of an immune response. At the same time, with each new locus, any T cells that respond to self peptides bound to the new MHC class I molecule must be removed to maintain self tolerance. There is an optimal balance of MHC class I diversity and T cell count. In the case of humans, the optimal number of MHC class I loci appears to be 3.
This is a knowledge gap I’ve always been missing about how the immune system works.
I love it and would love to get some sources I can read up on how immunity works, described in Mathy terms that I as a non biology person can understand.
I’m glad it excites you! Please bear in mind it’s just a hypothesis, from a biomedical engineering graduate student enrolled in his first immunology survey class :)
As a fellow mathy person, I’ll say that one of the most important things to bear in mind is that, like all biology, formal mathematical modeling only allows us to predict the immune system’s behavior in bits and pieces.
This is partly due to the shortcomings of current methods. For example, we don’t really have a good way to continuously monitor the course of a particular infection in vivo. Instead, we have to give a bunch of inbred mice the same infection, sacrifice them at intervals, take tissue samples, stain them for things like cell count or quantity and location of protein, and try to make sense of the jumble.
An analogy might be trying to infer the “dynamics of an action movie” by taking still frames at roughly the same time points from all six Die Hard movies and looking at specific metrics, like whether or not there was a weapon in the shot.
It’s also because biological behavior at the level of the cell, especially that of the immune system, is so heterogeneous and dynamically interconnected. We understand that processes like feedback loops are important, and we can also gather the “data still frames” I just described to inform us about the causes and effects of these processes.
For example, the adaptive immune response is to some extent a product of a positive feedback loop, in which activating cytokines and attracting chemokines cause an influx of immune cells to a site of infection. We can empirically determine how long that takes to happen in a particular infection, in a particular model organism, under particular treatment conditions. Sometimes, we can generalize, to give an estimate of how long a primary adaptive immune response takes to develop across many diseases.
But my experience thus far is that understanding immunity, or any other biological process, really depends on having a deep awareness of an immense number of different types of biological structures, and how they interact. In conjunction with knowledge of lots of factoids about norms and patterns (i.e. how long cell type X takes to reach 60-90% confluence in medium Y at temperature Z), you can make more and more useful predictions about what will happen if you intervene in a certain way.
Math is useful for understanding and using what models we do have, as well as potentially for producing more of them. It improves your reasoning and helps avoid this being the limiting factor in your progress (as it can be for some biologists, who are notoriously math-averse). Mathematical prowess unfortunately is not a shortcut, substitute, or alternative to understanding biology—you really do have to understand the structure and temporal dynamics of the physical system at scales ranging from the molecular to the anatomical.
If you do want to understand the immune system, you could try Janeway. I started this subject after years of prior bio classes, so I don’t know how it would land with your background. Also, Janeway’s going to cover it in a lot more depth than a survey course. You’ll get rich details about things like protein structure that aren’t always as useful for understanding the major processes of an adaptive response. Another fun option is Immune, by Phillip Dettmer. I’m sure there are also MOOCs and such!
The number of MHC class I loci. As the number of loci increases, the organism gains an ability to respond to a greater diversity of pathogens and avert evasion of an immune response. At the same time, with each new locus, any T cells that respond to self peptides bound to the new MHC class I molecule must be removed to maintain self tolerance. There is an optimal balance of MHC class I diversity and T cell count. In the case of humans, the optimal number of MHC class I loci appears to be 3.
!!! This got me so excited.
This is a knowledge gap I’ve always been missing about how the immune system works.
I love it and would love to get some sources I can read up on how immunity works, described in Mathy terms that I as a non biology person can understand.
I’m glad it excites you! Please bear in mind it’s just a hypothesis, from a biomedical engineering graduate student enrolled in his first immunology survey class :)
As a fellow mathy person, I’ll say that one of the most important things to bear in mind is that, like all biology, formal mathematical modeling only allows us to predict the immune system’s behavior in bits and pieces.
This is partly due to the shortcomings of current methods. For example, we don’t really have a good way to continuously monitor the course of a particular infection in vivo. Instead, we have to give a bunch of inbred mice the same infection, sacrifice them at intervals, take tissue samples, stain them for things like cell count or quantity and location of protein, and try to make sense of the jumble.
An analogy might be trying to infer the “dynamics of an action movie” by taking still frames at roughly the same time points from all six Die Hard movies and looking at specific metrics, like whether or not there was a weapon in the shot.
It’s also because biological behavior at the level of the cell, especially that of the immune system, is so heterogeneous and dynamically interconnected. We understand that processes like feedback loops are important, and we can also gather the “data still frames” I just described to inform us about the causes and effects of these processes.
For example, the adaptive immune response is to some extent a product of a positive feedback loop, in which activating cytokines and attracting chemokines cause an influx of immune cells to a site of infection. We can empirically determine how long that takes to happen in a particular infection, in a particular model organism, under particular treatment conditions. Sometimes, we can generalize, to give an estimate of how long a primary adaptive immune response takes to develop across many diseases.
But my experience thus far is that understanding immunity, or any other biological process, really depends on having a deep awareness of an immense number of different types of biological structures, and how they interact. In conjunction with knowledge of lots of factoids about norms and patterns (i.e. how long cell type X takes to reach 60-90% confluence in medium Y at temperature Z), you can make more and more useful predictions about what will happen if you intervene in a certain way.
Math is useful for understanding and using what models we do have, as well as potentially for producing more of them. It improves your reasoning and helps avoid this being the limiting factor in your progress (as it can be for some biologists, who are notoriously math-averse). Mathematical prowess unfortunately is not a shortcut, substitute, or alternative to understanding biology—you really do have to understand the structure and temporal dynamics of the physical system at scales ranging from the molecular to the anatomical.
If you do want to understand the immune system, you could try Janeway. I started this subject after years of prior bio classes, so I don’t know how it would land with your background. Also, Janeway’s going to cover it in a lot more depth than a survey course. You’ll get rich details about things like protein structure that aren’t always as useful for understanding the major processes of an adaptive response. Another fun option is Immune, by Phillip Dettmer. I’m sure there are also MOOCs and such!
Ty! Ty!
I have an audible credit lying around that I’m not using, so I’m going to get started on Immune.
Thanks for the detailed response and the caveats. I’ll keep them in mind!