Abstract
Gene transcription is a noisy process, and cell division cycle is an important source of gene transcription noise. In this work, we develop a mathematical approach by coupling transcription kinetics with cell division cycles to delineate how they are combined to regulate transcription output and noise. In view of gene dosage, a cell cycle is divided into an early stage and a late stage . The analytical forms for the mean and the noise of mRNA numbers are given in each stage. The analysis based on these formulas predicts precisely the fold change r* of mRNA numbers from to measured in a mouse embryonic stem cell line. When transcription follows similar kinetics in both stages, r* buffers against DNA dosage variation and r* ∈ (1, 2). Numerical simulations suggest that increasing cell cycle durations up-regulates transcription with less noise, whereas rapid stage transitions induce highly noisy transcription. A minimization of the transcription noise is observed when transcription homeostasis is attained by varying a single kinetic rate. When the transcription level scales with cellular volume, either by reducing the transcription burst frequency or by increasing the burst size in , the noise shows only a minor variation over a wide range of cell cycle stage durations. The reduction level in the burst frequency is nearly a constant, whereas the increase in the burst size is conceivably sensitive, when responding to a large random variation of the cell cycle durations and the gene duplication time.
Highlights
Are expressed by linear combinations of related probabilities
We recall that I, M, and U specify the promoter state, the mRNA copy number of the gene, and the cell cycle stage of a single cell in an isogenic cell population, respectively
Suppose that the gene is OFF and the cell resides on S1 stage with m copies of mRNA molecules at time t + h for an infinitesimal time increment h > 0
Summary
+ 2ν2P2(2, m − 1, t) + (m + 1)δ2P2(2, m + 1, t). P1(i, m, t) =Prob I(t) = i, M (t) = m, U (t) = 1 , i = 0, 1; m = 0, 1, 2, · · · , (6) P2(i, m, t) =Prob I(t) = i, M (t) = m, U (t) = 2 , i = 0, 1, 2; m = 0, 1, 2, · · · , (7). P2(n, t) = P2(0, n, t) + P2(1, n, t) + P2(2, n, t) is the probability that the cell resides on S2 stage with n transcripts. P1(m, t) = P1(0, m, t) + P1(1, m, t), P2(m, t) = P2(0, m, t) + P2(1, m, t) + P2(2, m, t) we can express P1(k, t) and P2(k, t) in (8) as the sums of the basic probabilities defined in (6)-(7). We the help of these simplification, we verify the first equation of (9). The second equation of (9) can be obtained by a similar calculation. After expressing P1(k, t) and P2(k, t) in (10) as the sums of the basic probabilities defined in (6)-(7), we differentiate ω1(t) in (10). The second equation can be verified by a similar procedure
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