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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?


Notes

  • 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

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The distinction between Lamarckism or not doesn’t make sense for single-cell organisms: the cells acquire features all the time and pass those on to their daughter cells – literally Lamarckism. (Disclaimer: Lamarck of course neither thought of single-cell organisms nor did he imagine a feasible mechanism by which his theory could be made to work.) –  Konrad Rudolph Jul 23 '12 at 20:20
    
Thanks @KonradRudolph, but to clarify from a naive modelers perspective: if I was making a model of the interaction of single-cell organisms learning and evolution then it would be reasonable to have the organism pass on its learned strategy (which would hypothetically be encoded in something like the levels of various proteins) to its offspring? –  Artem Kaznatcheev Jul 23 '12 at 21:59
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It does, by necessity: the mother cell splits off into two daughter cells which each “inherit” some of the material from the mother cell. Since there is no “erasing” step going on during mitosis, this means that daughter cells inherit the proteins of the parent. Now, whether this information is sustained across generations is a different question: proteins in particular have a half-life so after some time all this learned “information” is gone unless it’s encoded in the genome or as epigenetic information. –  Konrad Rudolph Jul 24 '12 at 12:16
    
Thanks for the explanation @KonradRudolph, if you have more insights I'd love to hear them on G+. I might ask a separate question about how to best model how the proteins are distributed among the daughter cells. –  Artem Kaznatcheev Jul 24 '12 at 15:24
    
@KonradRudolph: Looks like you've more or less answered the question; would you mind turning your comments into an actual answer? –  Ilmari Karonen Aug 31 '12 at 14:35
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This phenomenon is well known and can be observed in several species. In fact, if you look at the time it takes for E. coli to change its transcription program in order to react to the environment (signal->transcription->translation), you will find it can be longer than its ~20 minute doubling time. You can indeed think of it as a form of Lamarckism. However, it is part of a field that has been booming in the last ~10 years, known as epigenetics.

Epigenetics is a field of research that deals with hereditary information that is passed by non-genetic mechanisms, i.e. not in the DNA sequence. This includes several mechanisms including passing of proteins/RNA, chemical modifications of DNA (methylation) and chromatin (histone modification). It turns out that epigenetic effects can be observed in virtually all species (including human) and affected phenotypes can be significant (leading to disease, for example).

This is a very interesting field of research and is very wide, so I would recommend reading a bit. Specifically regarding protein/RNA passing, I believe this is somewhat less deeply studied, perhaps due to the fact that the effect decreases exponentially (due to dilution), can be limited by protein/RNA stability and some measurement difficulties. However, I think I recall mathematical treatment of this in Prof. Uri Alon's book. You can also catch his systems biology course online on youtube, which I think touches on some of this material.

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Just to clarify: The most well-known examples of epigenetics are chromatin (DNA/histone) modifications, but there are several other mechanisms that can pass hereditary information, often along several generations. Any such mechanism is considered epigenetic. Passing protein/RNA is one such mechanism and it is certainly being studied by epigenetics researchers. –  Bitwise Oct 23 '12 at 3:21
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I would say not, though you might find occasional cases where it is important.

Lamarckism could certainly apply to single celled organisms, but it would still tend to be associated with DNA. As originally described by Lamarck, the traits cited would be retained through the offspring's lifetime, potentially being passed on to later generations.

Protein half lives vary quite a bit, but usually in bacteria they are about an hour and can change faster than that. The changes accorded to Lamarckism should at least persistant for most of a lifetime. If this is Lamarckism then all embryonic stem cells have Larmarckian inheritance... at least for a few hours.

On the other hand... This is Lamarckism in the sense that historically Lamarck was sometimes observing physiological adaptation. One of his classic examples was how a blacksmith's muscles would become large from working hard. The Blacksmith's children who also did this work would also become muscular. That has little to do with inheritance though.

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