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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.


Standard deviation versus average number of molecules. Using the same data set and parameters as for Fig. 1, the relationship between the average and standard deviation was plotted for all chemical species. The solid line is for reference.
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f2-1_25: Standard deviation versus average number of molecules. Using the same data set and parameters as for Fig. 1, the relationship between the average and standard deviation was plotted for all chemical species. The solid line is for reference.

Mentions: The width of the distribution for each chemical, shown in Fig. 1, looks almost independent of its average. This suggests a connection between the fluctuations and the averages of the chemicals. We therefore plotted the standard deviation of each chemical as a function of the average n̄i in Fig. 2, and indeed found a linear relationship between the standard deviation (not the variance) and the average number of molecules. This can be understood by considering the steady growth and cascade structure of the catalytic reactions. Take two chemicals i and j, one of which (j) catalyzes the synthesis of the other in the cascade. During the steady growth phase of a cell, the synthesis and conversion of chemical i should be balanced, i.e., nj × A−ni× B=0, where A and B are average concentrations of other chemicals involved in the catalytic reaction. The average concentration then satisfies n̄j /n̄i = A/B. Taking into account that the relation remains satisfied as ni, nj, ... increase while the cell grows, it is natural to assume that the relationship holds for the fluctuations of the average as well: . Hence the variance is expected to be proportional to the square of the mean, yielding the linear relationship between the mean and the standard deviation.


Ubiquity of log-normal distributions in intra-cellular reaction dynamics
Standard deviation versus average number of molecules. Using the same data set and parameters as for Fig. 1, the relationship between the average and standard deviation was plotted for all chemical species. The solid line is for reference.
© Copyright Policy
Related In: Results  -  Collection

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

f2-1_25: Standard deviation versus average number of molecules. Using the same data set and parameters as for Fig. 1, the relationship between the average and standard deviation was plotted for all chemical species. The solid line is for reference.
Mentions: The width of the distribution for each chemical, shown in Fig. 1, looks almost independent of its average. This suggests a connection between the fluctuations and the averages of the chemicals. We therefore plotted the standard deviation of each chemical as a function of the average n̄i in Fig. 2, and indeed found a linear relationship between the standard deviation (not the variance) and the average number of molecules. This can be understood by considering the steady growth and cascade structure of the catalytic reactions. Take two chemicals i and j, one of which (j) catalyzes the synthesis of the other in the cascade. During the steady growth phase of a cell, the synthesis and conversion of chemical i should be balanced, i.e., nj × A−ni× B=0, where A and B are average concentrations of other chemicals involved in the catalytic reaction. The average concentration then satisfies n̄j /n̄i = A/B. Taking into account that the relation remains satisfied as ni, nj, ... increase while the cell grows, it is natural to assume that the relationship holds for the fluctuations of the average as well: . Hence the variance is expected to be proportional to the square of the mean, yielding the linear relationship between the mean and the standard deviation.

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.