Stationary cell size distributions and mean protein chain length distributions of Archaea, Bacteria and Eukaryotes described with an increment model in terms of irreversible thermodynamics

Perturbations of Transcription and Gene Expression-Associated Processes Alter Distribution of Cell Size Values in Saccharomyces cerevisiae

The question of what determines whether cells are big or small has been the focus of many studies because it is thought that such determinants underpin the coupling of cell growth with cell division. In contrast, what determines the overall pattern of how cell size is distributed within a population of wild type or mutant cells has received little attention. Knowing how cell size varies around a characteristic pattern could shed light on the processes that generate such a pattern and provide a criterion to identify its genetic basis. Here, we show that cell size values of wild type Saccharomyces cerevisiae cells fit a gamma distribution, in haploid and diploid cells, and under different growth conditions. To identify genes that influence this pattern, we analyzed the cell size distributions of all single-gene deletion strains in Saccharomyces cerevisiae. We found that yeast strains which deviate the most from the gamma distribution are enriched for those lacking gene products functioning in gene expression, especially those in transcription or transcription-linked processes. We also show that cell size is increased in mutants carrying altered activity substitutions in Rpo21p/Rpb1, the largest subunit of RNA polymerase II (Pol II). Lastly, the size distribution of cells carrying extreme altered activity Pol II substitutions deviated from the expected gamma distribution. Our results are consistent with the idea that genetic defects in widely acting transcription factors or Pol II itself compromise both cell size homeostasis and how the size of individual cells is distributed in a population.

Modelling the growth of plants with a uniform growth logistics

BACKGROUND AND AIMS

The increment model has previously been used to describe the growth of plants in general. Here, we examine how the same logistics enables the development of different superstructures.

METHODS

Data from the literature are analyzed with the increment model. Increments are growth-invariant molecular clusters, treated as heuristic particles. This approach formulates the law of mass action for multi-component systems, describing the general properties of superstructures which are optimized via relaxation processes.

RESULTS

The daily growth patterns of hypocotyls can be reproduced implying predetermined growth invariant model parameters. In various species, the coordinated formation and death of fine roots are modeled successfully. Their biphasic annual growth follows distinct morphological programs but both use the same logistics. In tropical forests, distributions of the diameter in breast height of trees of different species adhere to the same pattern. Beyond structural fluctuations, competition and cooperation within and between the species may drive optimization.

CONCLUSION

All superstructures of plants examined so far could be reproduced with our approach. With genetically encoded growth-invariant model parameters (interaction with the environment included) perfect morphological development runs embedded in the uniform logistics of the increment model.

Origin of lognormal-like distributions with a common width in a growth and division process

Lognormal statistical distributions are observed in a variety of scientific fields. The widths of these distributions in the log scale are often similar, but the underlying mechanism that maintains these widths within a small range has not been well explained. We show that a stochastic process of halving followed by addition can yield a stationary distribution that resembles the universal lognormal distribution with a certain width. The mechanism that we propose here would provide insight into the essence of why lognormal-like distributions in many systems have a common width.

The general growth logistics of cell populations

An increment model based on thermodynamics lays bare that the cell size distributions of archaea, prokaryotes and eukaryotes are optimized and belong to the same universal class. Yet, when a cell absorbs mass or signals are processed, these conditions are disturbed. Relaxation re-installs ideal growth conditions via an exponential process with a rate that slows down with the cell size. In a growing ensemble, a distribution of relaxation modes comes in existence, exactly defined by the universal cell size distribution. The discovery of nano-mechanic acoustic activities in cells led us to assume that in a growing ensemble acoustic signals may contribute significantly to the transmission of essential information about growth-induced disturbances to all cells, initiating that way coordinated relaxation. The frequency increases with the cell number shortening the period between successive signals. The completion of rearrangements occurring at a constant rate is thus progressively impaired, until cellular growth stops, totally. Due to this phenomenon, the so-called "relaxation-frequency-dispersion" cell colonies should exhibit a maximum cell number. In populations with large cell numbers, subsystems, behaving similar-like colonies, should form network-like patterns. Based on these ideas, we formulate equations that describe the growth curves of all cell types, verifying that way the general nature of the growth logistics.