Exact(6)
This control system, which is a simple regulation motif [ 26], only contains two elements: the positive regulator FlhDC, and its target operon fliL ([Additional file 1: supplemental figure S3b]).
In this section, we will illustrate that the Kalman filter, a well-established optimal estimation algorithm, can be applied for stochastic modeling of a simple regulation (two-gene network).
The noise in Figure 13(b) can be regarded to be as intrinsic only, indicating that a simple regulation can behave as a low-pass filter (removes high-frequency signals which are noise components in this example) [32].
Hence we obtain a simple regulation event, namely, "IL-4 regulation," which means "IL-4" is the theme of "regulation".
First, the evolution of the repressor Y (t) is identical to the one obtained in the previous section for a simple regulation, because eq. (4) coincides with eq. (1).
In the case of a simple regulation with periodic square pulses, the model equation (1) is easily worked out and from that calculation one deduces the observables ⟨ Y⟩ T, Ymax and Ymin as: (2) 〈 Y 〉 T = κ τ τ + σ Y max = κ 1 − e − α τ 1 − e − α Y min = κ e α τ − 1 e α − 1 Fig. 3 shows an example of these functions when the inter-pulse σ is varied, for a fixed pulse duration τ.
Similar(53)
On the other hand, if the signal and transcription factor behave in opposite ways (one is an activator while the other one is a repressor), it is an incoherent simple regulation (Fig. 2B).
When they act in the same way (both of them are either activators or repressors), it is called a coherent simple regulation (Fig. 2A).
Figure 4(a) shows an example of cascaded simple regulation blocks.
A two-gene network (or simple regulation) can be regarded as a fundamental unit that serves as a basic building block for constructing elaborate networks.
We conclude from elementary calculations that a pulsatile activation of the simple regulation schemes (1) or (3) provides a way to adjust the variations of Y in a range of values which can be controlled by tuning the temporal pattern of the pulses.
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