last minor edit. all other flaws will survive for now.

_posts/2024-01-12-Two-fun-inferences-about-neutralizing-antibodies-and-viral-infection.md

@@ -16,7 +16,7 @@ Dose response models capture the probability of infection as a function of dose.
 
 The simplest dose response model is exponential, based on the Poisson distribution, where the probability of infection is the probability that at least one viral infectious unit sucessfully initiates infection, $1-\exp(-rD)$, where $r\in(0,1)$ is the average probability of causing an infection per infectious unit and $D$ is the number of infectious units---aka the dose. A better model which accounts for heterogeneities in response across people to a measured dose is the beta-Poisson model, which assumes that the rate $r$ is itself beta-distributed. For a detailed discussion of the meaning of the beta-Poisson model in the context of parameter inference, see [Schmidt *et al* 2013](https://pubmed.ncbi.nlm.nih.gov/23311599/).
 
-I kept saying "infectious unit" above because there are different definitions. One intuitively might thing we count the number of viral particles and talk about infectiousness per virion, but that is rarely measured because it's hard and [not often clear that it's the right thing biologically anyway](https://www.nature.com/articles/d41586-019-01880-6). More common is to use a reference standard, like the cell culture infectious dose that causes $50\%$ of cell culture plates using a standarized assay get infected when exposed to virus. This measure, abbreviated CCID50, is much more commonly measured in the lab and used. 
+I kept saying "infectious unit" above because there are different definitions. One intuitively might thing we count the number of viral particles and talk about infectiousness per virion, but that is rarely measured because it's hard and [not often clear that it's the right thing biologically anyway](https://www.nature.com/articles/d41586-019-01880-6). More common is to use a reference standard, like the cell culture infectious dose that causes 50% of cell culture plates using a standarized assay get infected when exposed to virus. This measure, abbreviated CCID50, is much more commonly measured in the lab and used. 
 
 ## Back to polio
 
@@ -68,7 +68,7 @@ To confirm this is right, it would be nice to look at published cell culture tit
 
 **So anyway, here's what really cool.**  In humans, we estimate $\gamma=0.46$ which is definitely less than 1 (and more importantly, definitely less than whatever we exactly see in a cell culture system).  This means that poliovirus neutralization in the human body--specifically for gut infection measured by stool sampling---is *sub-diffusive*. As in, the ability of neutralizing antibodies to find virus is less efficient than in a cell culture system, and not just proportionally so, but with decreasing efficiency as antibody levels in the blood get higher. 
 
-This is super cool and it also should be super obvious, like so many things in hindsight. Why? Antibodies have to find the virus, but our tissues are really crowded. So diffusion is slower than in simple solution. Moreover, poliovirus replication primarily starts in the gut---on a two-dimensional(ish) surface[^1] that antibodies need to be trafficked to from serum and cellular media through crowded tissue. It's probably possible to figure out something about the subdiffusive dynamics of antibody and virion mixing just from the exponents and a physical model that can be measured independently. That might be fun to try some day. 
+This is super cool and it also should be super obvious, like so many things in hindsight. Why? Antibodies have to find the virus, but our tissues are really crowded. So diffusion is slower than in simple solution. Moreover, poliovirus replication primarily starts in the gut---on a two-dimensional(ish) surface[^1] that antibodies need to be trafficked to from serum and cellular media through crowded tissue. It's probably possible to figure out something that can be measured independently about the subdiffusive dynamics of antibody and virion mixing just from the exponents and a physical model. That might be fun to try some day. 
 
 But until then, it's cool to see that looking at the probability a person gets a detectible infection, composed of bazillions of replicating viruses, from a small dose, can tell us non-trivial stuff about biophysics inside our tissues. Pretty cool!