I was reading through the Karr et al. (2012) whole-cell computational model. One of the things they did was to induce single-gene disruptions in their model. They observed several to be fatal, but:
In some cases (Figure 6B, fifth column), the time required for the levels of specific proteins to fall to lethal levels was greater than one generation (Figures 6C and 6D).
As far as I understand this is because when a single-cell divides, daughters get not only get a copy of the mother DNA, but also have their initial levels of proteins and RNA set to those of their mother (or similar, with some statistical fluctuation).
To me this screams of Lamarkism: if an organism during its lifetime came in contact with an environment that caused a greater expression of some protein that in had at birth, its children will also have a higher initial expression of the same protein. In other words, the trait of "level of this protein" seems to be being passed down in a Lamarkian way. Is my understanding correct, or am I missing the point?
If my understanding is correct, then what are some standard methods to account for this short-term Lamarkism in mathematical models of evolution?
I am primarily interested in mathematical (or other formal) treatments of this. I have a background in mathematics and some work in mathematical modeling for population biology and evolutionary game theory. I have no background in biochemistry or microbiology. I would appreciate answers or references that cater to this awkward background but I am not adverse to plowing through some microbio if it is for something awesome.
Similar partial arguments can be made for non-single-cell and sexual organism by considering hormone expressions of the mother during pregnancy, as in this answer. I am satisfied with an explanation for asexual single-cell organisms, but bonus points if it can also say something about non-single-cell and/or sexual organisms.
Follow up question on modeling the mechanism behind this: Macromolecule levels in daughter cells after fission