Finite Number Effect

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What is it

The most recognized source of stochasticity in cellular protein production is the finite number effect. The finite number effect states that variability, manifested in the difference in protein production in genetically identical cells, will increase as the size of the system decreases. The size of the system refers to the protein concentration of the cell (the amount of transcriptional machinery that the cell has to work with).


Graphs A and B in Figure 1 are simulations of the abundance of a reporter protein measured over time (Collins et. al., 2003[1]). Graph A details results in a system of a high number of expressed protein and mRNA molecules (3000 and 10000 respectively). Graph B details the same simulation, however the number of expressed proteins and mRNA molecules was decreased to 30 and 100 molecules respectively (100-fold difference.) The histogram on the right of each graph depicts the probability of a population expressing a respective abundance of protein. Broad distributions of populations in the histograms coupled with larger fluctuations in protein abundance, in graph b, demonstrates the finite number effect.

Figure 1

Protein level effects (vs determinisitic equations).png

Figure 1 was obtained at permission pending

A representative example is useful when demonstrating the finite number effect. Consider a cell where 10 protein molecules sit in the nucleus and 1000 in the cytoplasm. The removal of a molecule from the nucleus results in a 10% change in nuclear concentration, however the removal of a molecule from the cytoplasm results in only a 0.1% change. Thus broader population heterogeneity can be achieved when the size of the system is relatively small because of a small system's susceptibility to concentration changes as a result of stochastic events.

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