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Ubiquity of log-normal distributions in intra-cellular reaction dynamics

View Article: PubMed Central - PubMed

ABSTRACT

The discovery of two fundamental laws concerning cellular dynamics with recursive growth is reported. Firstly, the chemical abundances measured over many cells were found to obey a log-normal distribution and secondly, the relationship between the average and standard deviation of the abundances was found to be linear. The ubiquity of these laws was explored both theoretically and experimentally. By means of a model with a catalytic reaction network, the laws were shown to exist near a critical state with efficient self-reproduction. Additionally, by measuring distributions of fluorescent proteins in bacteria cells, the ubiquity of log-normal distribution of protein abundances was confirmed. Relevance of these findings to cellular function and biological plasticity is briefly discussed.

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The number distribution of the proteins measured by fluorescence intensity, normalized by the cell volume. Distributions were obtained from three Escherichia coli cell populations containing different reporter plasmids (see text). Note that, although the IPTG induction changes the average fluorescence intensity, both the distributions (with and without the induction) can be fitted to log-normal distributions well.
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f3-1_25: The number distribution of the proteins measured by fluorescence intensity, normalized by the cell volume. Distributions were obtained from three Escherichia coli cell populations containing different reporter plasmids (see text). Note that, although the IPTG induction changes the average fluorescence intensity, both the distributions (with and without the induction) can be fitted to log-normal distributions well.

Mentions: In Fig. 3, we plotted the distributions of the emitted fluorescence intensity from Escherichia coli cells with reporter plasmids containing either EGFP (enhanced green fluorescent protein) under the control of the tetA promoter without repression, or dsRed.t4 (monomeric red fluorescent protein) under the control of the trc promoter with and without IPTG induction18. In general, the fluorescence intensity (the abundance of the protein) increased with the cell size. To avoid the effect of variation in cell size, which may also obey log-normal distribution, we normalized the fluorescence intensity with the volume of each cell. Here we adopted the forward-scatter (FS) signal from the flow cytometry to estimate cell volume. Infact, by plotting data of the fluorescence intensity versus FS signal, the two were proportional in general. (The data points were distributed around the proportionality line between the two, as was generally observed in the plot of fluorescence intensity made by flow cytometry). Thus, we normalized the fluorescence intensity by dividing it with the FS signal. Fig. 3 is the distribution of this normalized fluorescence intensity. Note that all these data fit well with log-normal, rather than Gaussian, distributions, even though each of the expressions is controlled by a different condition of the promoter.


Ubiquity of log-normal distributions in intra-cellular reaction dynamics
The number distribution of the proteins measured by fluorescence intensity, normalized by the cell volume. Distributions were obtained from three Escherichia coli cell populations containing different reporter plasmids (see text). Note that, although the IPTG induction changes the average fluorescence intensity, both the distributions (with and without the induction) can be fitted to log-normal distributions well.
© Copyright Policy
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC5036630&req=5

f3-1_25: The number distribution of the proteins measured by fluorescence intensity, normalized by the cell volume. Distributions were obtained from three Escherichia coli cell populations containing different reporter plasmids (see text). Note that, although the IPTG induction changes the average fluorescence intensity, both the distributions (with and without the induction) can be fitted to log-normal distributions well.
Mentions: In Fig. 3, we plotted the distributions of the emitted fluorescence intensity from Escherichia coli cells with reporter plasmids containing either EGFP (enhanced green fluorescent protein) under the control of the tetA promoter without repression, or dsRed.t4 (monomeric red fluorescent protein) under the control of the trc promoter with and without IPTG induction18. In general, the fluorescence intensity (the abundance of the protein) increased with the cell size. To avoid the effect of variation in cell size, which may also obey log-normal distribution, we normalized the fluorescence intensity with the volume of each cell. Here we adopted the forward-scatter (FS) signal from the flow cytometry to estimate cell volume. Infact, by plotting data of the fluorescence intensity versus FS signal, the two were proportional in general. (The data points were distributed around the proportionality line between the two, as was generally observed in the plot of fluorescence intensity made by flow cytometry). Thus, we normalized the fluorescence intensity by dividing it with the FS signal. Fig. 3 is the distribution of this normalized fluorescence intensity. Note that all these data fit well with log-normal, rather than Gaussian, distributions, even though each of the expressions is controlled by a different condition of the promoter.

View Article: PubMed Central - PubMed

ABSTRACT

The discovery of two fundamental laws concerning cellular dynamics with recursive growth is reported. Firstly, the chemical abundances measured over many cells were found to obey a log-normal distribution and secondly, the relationship between the average and standard deviation of the abundances was found to be linear. The ubiquity of these laws was explored both theoretically and experimentally. By means of a model with a catalytic reaction network, the laws were shown to exist near a critical state with efficient self-reproduction. Additionally, by measuring distributions of fluorescent proteins in bacteria cells, the ubiquity of log-normal distribution of protein abundances was confirmed. Relevance of these findings to cellular function and biological plasticity is briefly discussed.

No MeSH data available.


Related in: MedlinePlus