Gene expression is a  noisy process. That consists of several random events among which the reinitiation of transcription by RNAP is an important one. The RNAP molecules can bind the gene only after the promoter gets activated by transcription factors. Several transcription factors bind the promoter to put the gene in the active state. The gene turns into the inactive state as the bound transcription factors leave the promoter. During the active period of the gene, many RNAP molecules transcribe the gene to synthesize the mRNA . The binding event of RNAP to the active state of the gene is an probabilistic process and therefore, introduces noise or fluctuations in the protein levels. The binding event of RNAP to the active state of the gene is an probabilistic process and therefore introduces noise in the protein levels. In this paper, we analytically calculate the noise in mRNA and protein levels and also the probability distribution of mRNA numbers exactly with the binding event of RNAP in gene transcription process. The theoretically calculated noise expression of proteins shows excellent agreement with an experimental results. Then , we show that the noise in mRNA level can be sub-Poissonian due to the reinitiation of transcription by RNAP and the mean mRNA level can be increased without increasing the noise. We find that the reinitiation of transcription behaves like the fine-tuned control process to regulate the mRNA/protein level in the cell . We also find the exact distribution of mRNA numbers with the reinitiation of transcription .
Gene expression is a random or noisy process. The process consists of several random events among which the reinitiation of transcription by RNAP is an important one. The RNAP molecules can bind the gene only after the promoter gets activated by transcription factors. Several transcription factors bind the promoter to put the gene in the active state. The gene turns into inactive state as the bound transcription factors leave the promoter. During the active period of the gene, many RNAP molecules transcribe the gene to synthesize the mRNAs . The binding event of RNAP to the active state of the gene is a probabilistic process and therefore, introduces noise or fluctuations in the mRNA and protein levels. In this paper, we analytically calculate the Fano factor in mRNA and protein levels and also the probability distribution of mRNA numbers exactly with the binding event of RNAPs in gene transcription process. The analytically calculated expression of Fano factor of proteins shows excellent agreement with an experimental result. Then we show that the Fano factor in mRNA levels can be sub-Poissonian due to the reinitiation of transcription by RNAP and the mean mRNA level can be increased without increasing the Fano factor. Our study show that the Fano factor can also be reduced keeping mRNA levels fixed. We find that the reinitiation of transcription can behave as a fine-tuned control process to regulate the mRNA/protein level in the cell .
A
random or
R
That
The process
D
the
R
mRNA
mRNAs
R
an
a
R
protein levels. The binding event of RNAP to the active state of the gene is an probabilistic process and therefore introduces noise in the
mRNA and
R
noise
Fano factor
R
RNAP
RNAPs
R
theoretically calculated noise expression of
analytically calculated expression of Fano factor of
R
results. Then ,
result. Then
R
noise in mRNA level
Fano factor in mRNA levels
R
noise.
Fano factor. Our study show that the Fano factor can also be reduced keeping mRNA levels fixed.
R
behaves like the
can behave as a
D
. We also find the exact distribution of mRNA numbers with the reinitiation of transcription