6 ms·

New Statistical Law Discovered

34 points by J3L2404 16y ago

gojomo 16y ago
Bad headline, sure, but interesting result. It suggests even without signalling, and with identical nuclear DNA, cell division can result in daughter cells that each try a different side of a gene-regulation possibility space. If the environment has changed subtly to advantage or disadvantage that gene expression — well, voila, half the offspring are a probe in the better direction. That's why the process reminds me of binary search. And across the billions of sibling cells each trying different levels of each gene? Massively parallel search for the optimal levels of gene expression, without any mutation or genetic exchange. That's an exciting idea, to this layman.
jforman 16y ago
Just in time to vie for "most overhyped scientific headline of 2010." The paper, "Bimodal gene expression in noncooperative regulatory systems" (available at http://www.pnas.org/content/107/51/22096.full http://www.pnas.org/content/107/51/22096.full), addresses the question of how bacterial populations achieve bimodal phenotypic distributions (basically, 1 blue cell goes in, 5 blue cells and 5 pink cells come out in a stable ratio, wtf). This phenomenon has previously been explained by a) cooperativity or b) feedback loops. Cooperativity is a phenomenon in molecular biology where the binding of one protein to, say, DNA will increase the rate of binding of a partner in crime (which can, say, turn a gene on) -- this is a relatively simple regulatory scheme that allows proteins that respond in linear fashion to their environment to produce a non-linear output. Feedback loops are pretty self-explanatory (one thing worth mentioning is that if the feedback loop involves the transcription of a gene, then it is much slower-acting than cooperativity). Cooperativity can explain the bimodal distribution problem because cooperative systems can act as "regulatory switches" where very small fluctuations in environment can result in very different behavior (see http://bioweb.wku.edu/courses/biol566/Images/MCB3-29hemoglobin.JPG http://bioweb.wku.edu/courses/biol566/Images/MCB3-29hemoglob... for a simplistic example of hemoglobin response to oxygen). Thus, one blue cell goes in, 10 cells come out with very slight environmental differences that are on this response-boundary - voila, 5 blue cells, 5 pink cells. Anyway, this paper shows that a cell population can have a bimodal phenotypic distribution without cooperativity, simply by having single proteins that respond in non-linear fashion to their environment. That's...a new statistical law? I don't have the time to fully deconstruct this paper, but after a skim I'm left with the question, "so how does a single protein achieve non-linear response?" This paper seems to provide a mathematical model without giving a good explanation for how it would be achieved in nature. The only answer I can come up with is cooperativity within the protein itself - say, cooperative allosteric regulation. Which would make the theoretical contribution of this paper a lot less exciting.
- tel 16y ago
  I think it was also supposed to be read as "new law based on statistical theory" not "new law of statistical theory".
- carbocation 16y ago
  The overstatement in the headline reminds me about the article posted earlier this year in which someone rediscovered integration: http://care.diabetesjournals.org/content/17/2/152.abstract http://care.diabetesjournals.org/content/17/2/152.abstract
  - gphil 16y ago
    This is funny, I can't believe this made it past a peer review.
  - Confusion 16y ago
    To add insult to injury, the article is cited dozens of times. This is extremely disappointing and worrying. It raises a whole score of questions regarding both the intelligence, the knowledge and the moral fiber of people participating in medical research.
    - shadowfox 16y ago
      Well. You cant really tell that without trawling through the papers themselves. For all you know many of them are refutations. (This is not the first time that someone managed to publish something awkward like that; Academics often flock to this sort of thing like sharks on a blood trail. You can get a lot of leverage by publishing early refutations)
- mikecane 16y ago
  This comment with probably get a downvote but I just have to say it's Comments like yours that make coming here more worthwhile than the links many times! Thank you.
HilbertSpace 16y ago
Commonly in natural processes, a 'concentration' is a 'random walk' with two 'absorbing' states, (1) concentration 0% and (2) concentration 100%. A state is 'absorbing' if when once reach it, then never leave it. So, the work is talking about concentrations of proteins or their mRNA varying due to thermal 'randomness'. Maybe in this case, a decent first-cut mathematical model of what is going on is just a discrete time, discrete state space Markov process. So here each discrete 'step' in time is one generation of a cell. The 'states' record the concentrations. So, could use, say, some of the 'nonlinearity' effects to estimate the probability of moving in one step from one state (of concentrations) to another. But the big, 'global' issue is that the concentrations just keep changing and stop changing only at the absorbing states of 0% or 100%. For something with more detail than this 'global' view, if have those probabilities, then can use some standard work in such Markov processes to say how fast the concentrations reach the 'absorbing' states of 0% or 100%. The literature on Markov processes is enormous. For a start, consider: Erhan Çinlar, 'Introduction to Stochastic Processes', ISBN 0-13-498089-1, Prentice-Hall, Englewood Cliffs, NJ, 1975.
gojomo 16y ago
It's molecular biological binary search!
elptacek 16y ago
"Anna Ochab-Marcinek is one of the co-discoverers of a statistical law that describes how a random disorder inside individual cells transforms into an order leading to a differentiation of population..." ...so we're showing you a picture of her cleavage?
aom 16y ago
> I don't have the time to fully deconstruct this paper, That's why you did not understand it. > but after a skim I'm left with the question, "so how does > a single protein achieve non-linear response?" If you read the paper carefully (also the Supporting Information), you would see the origin of non-linearity. Transcription factors (TFs) bind to the operator and unbind from it. We make an assumption that this process of binding/unbinding is the fastest of all processes in the system. That is why we can describe it in a continuous way (so we do not consider TF single molecules, but their concentration, which is a continuous variable). Under such conditions, the transcription rate is a non-linear function of the the TF concentration. This is explained in the Supporting Information of the paper for the general case of n binding sites. Here I explain it in a more verbose way for the case of 2 binding sites: http://th.if.uj.edu.pl/~ochab/h.pdf http://th.if.uj.edu.pl/~ochab/h.pdf This non-linear function acts as a noise filter: If the TF concentrations across a cell population are not same, but given by a statistical distribution (one may call it "noise"), then the output distribution of transcription rates will be transformed in a counter-intuitive way. For example, a unimodal input distribution (of TFs) can be converted into a bimodal output distribution (of target proteins). So far, no one have found an analytical method of prediction, when the output distribution of proteins in a typical open-loop gene regulatory system will be bimodal. Even in the case of cooperative TF binding. Moreover, no one expected that bimodality can be found also in the case of non-cooperative TF binding. Which is kind of surprising, because the idea itself is simple. We did this. What is especially nice in our work is that the conditions for bimodality can be found without complicated calculations, only using a simple geometric construction that involves quantities that can be experimentally measured. > This paper seems to provide a mathematical model without > giving a good explanation for how it would be achieved in > nature. This is certainly not true. Please see the references, especially Friedman et al. PRL, Cai et al. Nature, Nevozhay et al. PNAS, Dublanche et al. Mol Syst Biol, and Taniguchi et al. Science. Best regards, Anna Ochab-Marcinek
aom 16y ago
> ...so we're showing you a picture of her cleavage? LOL, yes, that was exactly my idea. As I expected, everyone loves this picture. ;-D
- abrown28 16y ago
  If you got it you might as well flaunt it.
aom 16y ago
> Anyway, this paper shows that a cell population can have a bimodal phenotypic distribution without cooperativity, > simply by having single proteins that respond in non-linear fashion to their environment. That's...a new statistical law? What I mean by a "new law" is the formula that describes the conditions for bimodality [of the output distribution resulting from a gamma-distributed input passing a nonlinear filter in the form 1/(1+x)^n or 1/(1+x^n)] in terms of the intersection of two curves (those curves have a well-defined experimental meaning). Maybe, as one of the internauts remarked, this should rather read "a new law based on statistical theory". The language used in the press release was simplified (perhaps over-simplified).
- aom 16y ago
  Actually, this seems to be the error of translation. At least in Polish (the original language of the press release), "a statistical law" (of how cells differentiate) means something different than "a law of statistics". The correct meaning is "a law based on statistical theory".

34 points by J3L2404 16y ago

Bad headline, sure, but interesting result. It suggests even without signalling, and with identical nuclear DNA, cell division can result in daughter cells that each try a different side of a gene-regulation possibility space. If the environment has changed subtly to advantage or disadvantage that gene expression — well, voila, half the offspring are a probe in the better direction. That's why the process reminds me of binary search. And across the billions of sibling cells each trying different levels of each gene? Massively parallel search for the optimal levels of gene expression, without any mutation or genetic exchange. That's an exciting idea, to this layman.

jforman 16y ago

Just in time to vie for "most overhyped scientific headline of 2010." The paper, "Bimodal gene expression in noncooperative regulatory systems" (available at http://www.pnas.org/content/107/51/22096.full http://www.pnas.org/content/107/51/22096.full), addresses the question of how bacterial populations achieve bimodal phenotypic distributions (basically, 1 blue cell goes in, 5 blue cells and 5 pink cells come out in a stable ratio, wtf). This phenomenon has previously been explained by a) cooperativity or b) feedback loops. Cooperativity is a phenomenon in molecular biology where the binding of one protein to, say, DNA will increase the rate of binding of a partner in crime (which can, say, turn a gene on) -- this is a relatively simple regulatory scheme that allows proteins that respond in linear fashion to their environment to produce a non-linear output. Feedback loops are pretty self-explanatory (one thing worth mentioning is that if the feedback loop involves the transcription of a gene, then it is much slower-acting than cooperativity). Cooperativity can explain the bimodal distribution problem because cooperative systems can act as "regulatory switches" where very small fluctuations in environment can result in very different behavior (see http://bioweb.wku.edu/courses/biol566/Images/MCB3-29hemoglobin.JPG http://bioweb.wku.edu/courses/biol566/Images/MCB3-29hemoglob... for a simplistic example of hemoglobin response to oxygen). Thus, one blue cell goes in, 10 cells come out with very slight environmental differences that are on this response-boundary - voila, 5 blue cells, 5 pink cells. Anyway, this paper shows that a cell population can have a bimodal phenotypic distribution without cooperativity, simply by having single proteins that respond in non-linear fashion to their environment. That's...a new statistical law? I don't have the time to fully deconstruct this paper, but after a skim I'm left with the question, "so how does a single protein achieve non-linear response?" This paper seems to provide a mathematical model without giving a good explanation for how it would be achieved in nature. The only answer I can come up with is cooperativity within the protein itself - say, cooperative allosteric regulation. Which would make the theoretical contribution of this paper a lot less exciting.

tel 16y ago
I think it was also supposed to be read as "new law based on statistical theory" not "new law of statistical theory".
carbocation 16y ago
The overstatement in the headline reminds me about the article posted earlier this year in which someone rediscovered integration: http://care.diabetesjournals.org/content/17/2/152.abstract http://care.diabetesjournals.org/content/17/2/152.abstract
- gphil 16y ago
  This is funny, I can't believe this made it past a peer review.
- Confusion 16y ago
  To add insult to injury, the article is cited dozens of times. This is extremely disappointing and worrying. It raises a whole score of questions regarding both the intelligence, the knowledge and the moral fiber of people participating in medical research.
  - shadowfox 16y ago
    Well. You cant really tell that without trawling through the papers themselves. For all you know many of them are refutations. (This is not the first time that someone managed to publish something awkward like that; Academics often flock to this sort of thing like sharks on a blood trail. You can get a lot of leverage by publishing early refutations)
mikecane 16y ago
This comment with probably get a downvote but I just have to say it's Comments like yours that make coming here more worthwhile than the links many times! Thank you.

HilbertSpace 16y ago

Commonly in natural processes, a 'concentration' is a 'random walk' with two 'absorbing' states, (1) concentration 0% and (2) concentration 100%. A state is 'absorbing' if when once reach it, then never leave it. So, the work is talking about concentrations of proteins or their mRNA varying due to thermal 'randomness'. Maybe in this case, a decent first-cut mathematical model of what is going on is just a discrete time, discrete state space Markov process. So here each discrete 'step' in time is one generation of a cell. The 'states' record the concentrations. So, could use, say, some of the 'nonlinearity' effects to estimate the probability of moving in one step from one state (of concentrations) to another. But the big, 'global' issue is that the concentrations just keep changing and stop changing only at the absorbing states of 0% or 100%. For something with more detail than this 'global' view, if have those probabilities, then can use some standard work in such Markov processes to say how fast the concentrations reach the 'absorbing' states of 0% or 100%. The literature on Markov processes is enormous. For a start, consider: Erhan Çinlar, 'Introduction to Stochastic Processes', ISBN 0-13-498089-1, Prentice-Hall, Englewood Cliffs, NJ, 1975.

gojomo 16y ago

It's molecular biological binary search!

elptacek 16y ago

"Anna Ochab-Marcinek is one of the co-discoverers of a statistical law that describes how a random disorder inside individual cells transforms into an order leading to a differentiation of population..." ...so we're showing you a picture of her cleavage?

aom 16y ago

> I don't have the time to fully deconstruct this paper, That's why you did not understand it. > but after a skim I'm left with the question, "so how does > a single protein achieve non-linear response?" If you read the paper carefully (also the Supporting Information), you would see the origin of non-linearity. Transcription factors (TFs) bind to the operator and unbind from it. We make an assumption that this process of binding/unbinding is the fastest of all processes in the system. That is why we can describe it in a continuous way (so we do not consider TF single molecules, but their concentration, which is a continuous variable). Under such conditions, the transcription rate is a non-linear function of the the TF concentration. This is explained in the Supporting Information of the paper for the general case of n binding sites. Here I explain it in a more verbose way for the case of 2 binding sites: http://th.if.uj.edu.pl/~ochab/h.pdf http://th.if.uj.edu.pl/~ochab/h.pdf This non-linear function acts as a noise filter: If the TF concentrations across a cell population are not same, but given by a statistical distribution (one may call it "noise"), then the output distribution of transcription rates will be transformed in a counter-intuitive way. For example, a unimodal input distribution (of TFs) can be converted into a bimodal output distribution (of target proteins). So far, no one have found an analytical method of prediction, when the output distribution of proteins in a typical open-loop gene regulatory system will be bimodal. Even in the case of cooperative TF binding. Moreover, no one expected that bimodality can be found also in the case of non-cooperative TF binding. Which is kind of surprising, because the idea itself is simple. We did this. What is especially nice in our work is that the conditions for bimodality can be found without complicated calculations, only using a simple geometric construction that involves quantities that can be experimentally measured. > This paper seems to provide a mathematical model without > giving a good explanation for how it would be achieved in > nature. This is certainly not true. Please see the references, especially Friedman et al. PRL, Cai et al. Nature, Nevozhay et al. PNAS, Dublanche et al. Mol Syst Biol, and Taniguchi et al. Science. Best regards, Anna Ochab-Marcinek

aom 16y ago

> ...so we're showing you a picture of her cleavage? LOL, yes, that was exactly my idea. As I expected, everyone loves this picture. ;-D

abrown28 16y ago
If you got it you might as well flaunt it.

aom 16y ago

> Anyway, this paper shows that a cell population can have a bimodal phenotypic distribution without cooperativity, > simply by having single proteins that respond in non-linear fashion to their environment. That's...a new statistical law? What I mean by a "new law" is the formula that describes the conditions for bimodality [of the output distribution resulting from a gamma-distributed input passing a nonlinear filter in the form 1/(1+x)^n or 1/(1+x^n)] in terms of the intersection of two curves (those curves have a well-defined experimental meaning). Maybe, as one of the internauts remarked, this should rather read "a new law based on statistical theory". The language used in the press release was simplified (perhaps over-simplified).

aom 16y ago
Actually, this seems to be the error of translation. At least in Polish (the original language of the press release), "a statistical law" (of how cells differentiate) means something different than "a law of statistics". The correct meaning is "a law based on statistical theory".