Large-scale on-off switching of genetic activity mediated by the folding-unfolding transition in a giant DNA molecule: An hypothesis

We present a model to describe the on-off switching of transcriptional activity in a genetic assembly by considering the intrinsic characteristics of a giant genomic DNA molecule which can undergo a discrete structural transition between coiled and compact states. We propose a model in which the transition in the higher-order structure of DNA plays an essential role in regulating stable on-off switching and/or the oscillation of a large number of genes under the fluctuations in a living cell, where such a structural transition is caused by environmental factors. This model explains the rapid and broad transcriptional response in a genetic assembly as well as its robustness against fluctuations.

Figure 1

(a) Structural transition of a giant DNA chain. Brightness distributions of fluorescence microscopy images and schematic representations of a DNA molecule (T4, 166 kbp) in a coiled (left) and a compact (right) state are shown. Due to the blurring effect, the bright molecules appear to be much larger than their actual sizes. Based on the measurement of the Brownian motion of individual DNA molecules, it has been confirmed that the volume ratio between the coiled and compact states is on the order of ${10}^4–{10}^5$ [14]. Scale bars are $5\mu \text{m}$. (b) Change in transcriptional activity depending on the structural transition of DNA (BAC, 106 kbp), modified based on the report by Luckel et al. [17]. The transcriptional activities are on and off in the coiled and compact states, respectively.

Figure 2

Free-energy profile of a DNA molecule. The profile has two minima; $\eta =0$ and 1, which correspond to the coiled and compact states. The energy barriers of the transition from a coiled to a compact state and from a compact to a coiled state are $\Delta F-\gamma \left(c-c_0\right)$ and $\Delta F+\gamma \left(c-c_0\right)$, respectively. The right figure schematically shows the time change in potential profiles.

Figure 3

Schematic representations of the transition probabilities of $n_k$. (a) Transition probabilities when DNA is in a coiled state. Each transition probability of the number of $k\text{th}$ product molecules is given by Eqs. (6, 7, 8), respectively. (b) Transition probabilities when DNA is in a compact state. Each probability of the number of $k\text{th}$ product molecules is given by Eqs. (9, 10), respectively. It is noted that the probability of increase in the numbers of $k\text{th}$ product (shown with dotted lines) is zero because the transcriptional activity of a compacted DNA molecule is completely suppressed.

Figure 4

Results of the numerical simulation based on Eqs. (4, 5, 6, 7, 8, 9, 10) with the initial conditions $\eta =1$ and $n_k=3$ for all $k$. The values of the parameters are as follows: $A_1=0.01$, $A_2=0.05$, $B_1=0.001$, $B_2=0.003$, $K=1$, $V=1$, $\Delta F/k_{\text{B}}T=25000$, $\gamma /k_{\text{B}}T=100$, and $c_0=500$. (a) Change in each $n_k$ over time. We show representative profiles for $k=1$–3. (b) Change in the nonspecific parameter $c$ over time. (c) Change in the order parameter $\eta$ over time, which represents the time change in the structure of a DNA molecule; $\eta =0$ and 1 correspond to the coiled and compact states, respectively.