Coherent feed-forward loops exist extensively in realistic biological regulatory systems, and are common signaling motifs. Here, we study the characteristics and the propagation mechanism of the output noise in a coherent feed-forward transcriptional regulatory loop that can be divided into a main road and branch. Using the linear noise approximation, we derive analytical formulae for the total noise of the full loop, the noise of the branch, and the noise of the main road, which are verified by the Gillespie algorithm. Importantly, we find that (i) compared with the branch motif or the main road motif, the full motif can effectively attenuate the output noise level; (ii) there is a transition point of system state such that the noise of the main road is dominated when the underlying system is below this point, whereas the noise of the branch is dominated when the system is beyond the point. The entire analysis reveals the mechanism of how the noise is generated and propagated in a simple yet representative signaling module.

Neurons can detect weak target signals from complex background signals through stochastic resonance (SR) and vibrational resonance (VR) mechanisms. However, random phase variation of rapidly fluctuating background signals is generally ignored in classical VR or SR studies. Here, the rapidly fluctuating background signals are modeled by bounded noise with random rapidly fluctuating phase derived from Wiener process. Then, the influences of bounded noise on the weak signal detection are discussed in the FitzHugh-Nagumo (FHN) neuron. Numerical results reveal the occurrence of bounded noise-induced single-and biresonance as well as a transition between them. Randomness in phase can enhance the adaptability of neurons, but at the cost of signal detection performance so that neurons can work in more complex environments with a wider frequency range. More interestingly, bounded noise with appropriate parameters can not only optimize information transmission but also simultaneously reduce energy consumption. Finally, the potential mechanism of bounded noise is explained.

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A set–reset latch is a basic building block of computers and can be used to store state information. Here, by testing the influence of the two logical input signals on the reliable set–reset latch logic operation in the bistable system, we found that there are two types of input signals, namely, suprathreshold and subthreshold signals. For the suprathreshold signals, reliable set–reset logic operation can be achieved without any driving forces and exhibits certain anti-interference ability; for the subthreshold signals, a single harmonic could induce correct set–reset latch logic operation but with a narrow optimal parameter region. The introduction of biharmonic-induced set–reset latch logic operation (logical vibrational resonance) could greatly expand the parameter region. Explanations for the above results were provided by taking the logical inputs as the dynamic bias to analyze the dynamic changes in the system. Finally, the results were further verified by circuit simulation and actual hardware circuit.

It was demonstrated recently that logical chaotic resonance (LCR) can be observed in a bistable system. In other words, the system can operate robustly as a specific logic gate in an optimal window of chaotic signal intensity. Here, we report that the size of the optimal window of chaotic signal intensity can be remarkably extended by exploiting the constructive interaction of chaotic signal and periodic force, as well as coupling, in a coupled bistable system. In addition, medium-frequency periodic force and an increasing system size can also lead to an improvement in the response speed of logic devices. The results are corroborated by circuit experiments. Taken together, a reliable and rapid-response logic operation can be realized based on periodic force- and array-enhanced LCR.

The essence of logical stochastic resonance is the dynamic manipulation of potential wells. The effect of time delay on the depth of potential wells and the width of a bistable region can be inferred by logic operations in the bistable system with time delay. In a time-delayed synthetic gene network, time delay in the synthesis process can increase the depth of the potential wells, while that in the degradation process, it can reduce the depth of the potential wells, which will result in a decrease in the width of the bistable region (the reason for time delay to induce logic operations without external driving force) and the instability of the system (oscillation). These two opposite effects imply stretching and folding, leading to complex dynamical behaviors of the system, including period, chaos, bubble, chaotic bubble, forward and reverse period doubling bifurcation, intermittency, and coexisting attractors.