Imprecise copies – it’s statistics that makes the cells different

Under certain conditions, a population of reproducing cells can spontaneously divide into two groups with distinctly different functions. The researchers have since long been looking for the reasons of such a spectacular process but the mechanisms found so far were complicated and did not explain all observed cases. It were only theoretical calculations and computer simulations carried out by scientists from the Institute of Physical Chemistry of the Polish Academy of Sciences (IPC PAS) in Warsaw that provided the simplest explanation. “We discovered a statistical law that is responsible for cell differentiation,” says Dr Anna Ochab-Marcinek from the IPC PAS. The new statistical mechanism will possibly allow to rationalize one of the sources of bacteria’s resistance to antibiotics and help understand why monozygotic twins and cloned organisms are not their identical copies. A paper describing the discovery has just appeared in the “Proceedings of the National Academy of Sciences”, a prestigious scientific journal published by the US National Academy of Sciences.

Already in the middle of the past century it has been noticed in laboratory studies that an Escherichia coli population could divide into two groups with one of them showing expression of a specific gene, e.g., the gene responsible for production of an enzyme to digest a specific type of sugar, whereas in the other group the same gene remained inactive. The effect is known in science as population bimodality. The observation was intriguing, as all the cells had the same DNA and were kept under the same conditions. Moreover, despite the lack of changes in the gene set, subsequent cell generations were able to inherit new functions. The researchers from the IPC PAS set themselves the task of discovering the simplest possible mechanism that is responsible for such an unexpected behaviour of cells. For that purpose, they carried out theoretical calculations followed by a verification with a series of Monte Carlo simulations. The theoretical and computational work involved the most important chemical reactions that take place in a living cell.

The genetic information in cells is contained in the DNA structure, the proteins, however, are synthesised based on the sequences in the messenger RNA (mRNA). To produce a protein encoded in a gene, the information must be first transferred from DNA to mRNA. The transfer process (transcription) is controlled by molecules called transcription factors. After attachment to DNA, these molecules may repress (then they are called repressors) or promote (activators) the gene translation. “A cell is a bag with a plenty of various molecules, moving randomly due to thermal motions. So, it may happen that after cell division one daughter cell will include more transcription factors than the other,” describes Dr Anna Ochab-Marcinek from the IPC PAS. Using computer simulations, the researchers analysed, how a different number of repressors or activators affects the cell population.

The computer simulations carried out at the Institute of Physical Chemistry of the PAS mapped fluctuating concentrations of proteins produced by each cell during the development of population. As the number of molecules of a specific type in a cell is relatively low, the cell divisions result in an unequal distribution of repressors or activators among the daughter cells. As a result, the cell population growth leads to appearance of cells that produce a significantly more protein than other cells or do not produce it at all.

The dependence between the production rate of a specific protein and the number of repressors or activators in a cell is not proportional. The effect is referred to as a nonlinearity as the plot showing how the number of protein molecules depends on the number of transcription factors (the so called transfer function) is not a straight line. The researchers from the IPC PAS have shown that the nonlinearity is responsible for formation of two distinct groups in the population: in one of them the gene is active, whereas in the other – it is not.

The division of a cell population into two groups is of significant evolutional importance. The differentiation increases the survival chance for a part of the population, if any changes unfavourably affecting one of the groups would occur in the environment. “It is known that bacteria mutate and become more resistant to drugs. We have shown the simplest mechanism by which the very nature of bacteria and the underlying laws of statistics increase the survival probability of at least a part of the population, even if no mutations have occurred,” says Dr Ochab-Marcinek.

The researchers from the IPC PAS have also introduced a simple method of geometric construction that can be used to predict when a specific cell population can develop a cell differentiation. The method consists in plotting of a straight line that intersects the axes of the coordinate system at points corresponding to the measured burst frequency of the transcription factor production in a population and the magnitude of these bursts. If the straight line intersects the gene response curve – known from the laboratory measurements – then the cell population starts to develop bimodality. With such a simple geometrical operation one can easily explain the results of earlier experiments performed by other research groups, for instance the appearance of bimodality in population only at specific antibiotic concentrations.

“As the mechanism we discovered is the simplest among all possible ones, we suppose that, unavoidably, it is very common in cells,” says Dr Marcin Tabaka, a co-discoverer of the phenomenon. “The statistical law we discovered describes how a random disorder inside individual cells transforms into an order leading to a differentiation of population that is of benefit for its survival,” sums up Dr Ochab-Marcinek.

The project has been completed under a TEAM Programme of the Foundation for Polish Science, co-founded by the EU European Regional Development Fund (TEAM/2008-2/2). 

The Institute of Physical Chemistry of the Polish Academy of Sciences ( was established in 1955 as one of the first chemical institutes of the PAS. The Institute's scientific profile is strongly related to the newest global trends in the development of physical chemistry and chemical physics. Scientific research is conducted in nine scientific departments. CHEMIPAN R&D Laboratories operating as part of the Institute implement, produce and commercialise specialist chemical compounds to be used, in particular, in agriculture and pharmacy. The Institute publishes approximately 300 original research papers annually.

Full bibliographic information

Bimodal gene expression in noncooperative regulatory systems; Anna Ochab-Marcinek, Marcin Tabaka; Proceedings of the National Academy of Sciences of the United States of America; doi: 10.1073/pnas.1008965107
Attached files
  • PDF file
  • The statistical law, discovered by scientists from the Institute of Physical Chemistry of the Polish Academy of Sciences (IPC PAS) in Warsaw, describes how a random disorder inside individual cells transforms into an order leading to a differentiation of population. Above: Dr Anna Ochab-Marcinek, one of the co-discoverers. (Source: IPC PAS, Grzegorz Krzyżewski)

Other content in...