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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.

No MeSH data available.


The distribution of the fluorescence intensity normalized by the cell volume, plotted (a) with a logarithmic scale and (b) with a normal scale. Data were obtained from a population of isogenic bacterial cells with an expression of GFP-GS fusion protein in the chromosome. It is clear that the distribution with the logarithmic scale is symmetric and close to a Gaussian form.
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f4-1_25: The distribution of the fluorescence intensity normalized by the cell volume, plotted (a) with a logarithmic scale and (b) with a normal scale. Data were obtained from a population of isogenic bacterial cells with an expression of GFP-GS fusion protein in the chromosome. It is clear that the distribution with the logarithmic scale is symmetric and close to a Gaussian form.

Mentions: To clarify the existence of a larger tail for greater abundances of proteins, in Fig. 4, we plotted the distribution of protein abundances both in a logarithmic scale and in a normal scale. The abundances of fluorescent protein expressed from the chromosome was also found to obey the log-normal distribution, as shown in Fig. 4. Here, the data was obtained from Escherichia coli cells with an expression of glutamine synthetase (GS) fused to GFP in the chromosome, whose expression is controlled by an upstream tetA promoter. In Fig. 4, the distribution of fluorescence intensity, again normalized by cell volume, is plotted. As can be seen, when using the logarithmic scale (a), the distribution is roughly symmetrical and close to Gaussian, while when using the normal scale (b), the distribution has a larger tail on the side of greater abundances. The fact that a log-normal distribution was also observed when genes were located on the genome indicates that the nature of the log-normal distribution was not due to a variation in plasmid copy number. We also examined several other cases using different reporter genes both on the plasmids and on the genome, and obtained similar results supporting the universality of log-normal distributions. It is furthermore interesting to note that the abundances of fluorescent proteins, reported in the literature so far, have been often plotted with a logarithmic scale7.


Ubiquity of log-normal distributions in intra-cellular reaction dynamics
The distribution of the fluorescence intensity normalized by the cell volume, plotted (a) with a logarithmic scale and (b) with a normal scale. Data were obtained from a population of isogenic bacterial cells with an expression of GFP-GS fusion protein in the chromosome. It is clear that the distribution with the logarithmic scale is symmetric and close to a Gaussian form.
© Copyright Policy
Related In: Results  -  Collection

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

f4-1_25: The distribution of the fluorescence intensity normalized by the cell volume, plotted (a) with a logarithmic scale and (b) with a normal scale. Data were obtained from a population of isogenic bacterial cells with an expression of GFP-GS fusion protein in the chromosome. It is clear that the distribution with the logarithmic scale is symmetric and close to a Gaussian form.
Mentions: To clarify the existence of a larger tail for greater abundances of proteins, in Fig. 4, we plotted the distribution of protein abundances both in a logarithmic scale and in a normal scale. The abundances of fluorescent protein expressed from the chromosome was also found to obey the log-normal distribution, as shown in Fig. 4. Here, the data was obtained from Escherichia coli cells with an expression of glutamine synthetase (GS) fused to GFP in the chromosome, whose expression is controlled by an upstream tetA promoter. In Fig. 4, the distribution of fluorescence intensity, again normalized by cell volume, is plotted. As can be seen, when using the logarithmic scale (a), the distribution is roughly symmetrical and close to Gaussian, while when using the normal scale (b), the distribution has a larger tail on the side of greater abundances. The fact that a log-normal distribution was also observed when genes were located on the genome indicates that the nature of the log-normal distribution was not due to a variation in plasmid copy number. We also examined several other cases using different reporter genes both on the plasmids and on the genome, and obtained similar results supporting the universality of log-normal distributions. It is furthermore interesting to note that the abundances of fluorescent proteins, reported in the literature so far, have been often plotted with a logarithmic scale7.

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.