Chunhua Zeng

Delay and noise induced regime shift and enhanced stability in gene expression dynamics

A quantitative model of autoregulatory gene expression involving a single gene with time delays and cross-correlated noise sources is investigated. The probability density and mean first passage time (MFPT) of the protein concentration are obtained. The impacts of multiplicative (σM) and additive (σA) noise intensities, cross-correlation intensity λ between two noises, time delays τ in the degradation process and θ in the synthesis process and time delay β in both processes on the probability density and MFPT of the regime shifts between high and low protein concentration states are discussed, respectively. These results indicate that (i) the regime shifts from a high (or low) protein concentration state to a low (or high) one can be induced by σM, λ and θ (or σA and β); (ii) the MFPT as a function of the noise intensity σM or σA exhibits one maximum value in the case of λ > 0 or θ > 0, this maximum is a signature of the noises enhanced stability phenomenon for high protein concentration state; and (iii) τ and β can weaken the stability of high protein concentration state but, in contrast, λ and θ can enhance it in the gene expression dynamics.

Noises-induced toggle switch and stability in a gene regulation network

It is well-known that noises are inevitable in gene regulatory networks due to the low-copy numbers of molecules and environmental fluctuations. In this paper, we investigate the stationary probability distribution (SPD) between both low (OFF state) and high (ON state) protein levels and mean first passage time (MFPT) in an abstract model of the Myc/E2F/miR-17-92 network presented by Aguda et al., PNAS 105, 19678 (2008), where the gene expression is assumed to be disturbed simultaneously by intrinsic and extrinsic noises that were correlated. Our results show that (i) the OFF state is enhanced by the extrinsic noise (D), while the ON state is enhanced by the intrinsic noise (Q) or cross-correlation between two noises (λ); (ii) for the cases of negative or no cross-correlation (λ⩽0.0), the increase of the noise intensity (D or Q) leads to a decline of the MFPT and enhances the probability of toggle switch to the OFF state; (iii) but for the case of positive cross-correlation (λ>0.0), the MFPT as a function of the noise intensity (D or Q) exhibits a maximum, this maximum for MFPT identifies the characteristic of noise enhanced stability of the ON state and (iv) the cross-correlation between two noises can enhance stability of the ON state.

Effects of correlated noise in a tumor cell growth model in the presence of immune response

The effects of correlated noises in a tumor cell growth model in the presence of immune response under the simultaneous action of correlated multiplicative and additive white noise and a weak periodic signal are investigated. The analytical expression of the signal-to-noise ratio (SNR) for the model is obtained by using the theory of SNR in the adiabatic limit. Based on the numerical computations, it is found that (i) a maximum appears in the curve of SNR as a function of cross-correlation intensity λ in the region of λ> 0, i.e. this is a resonant peak, and (ii) for the case of λ>0, the curve of SNR as a function of additive noise intensity α exhibits a minimum first and then a maximum, that is to say, it exhibits suppression first and resonance later. But for the case of λ≤0, the resonant peak of the SNR-α curve disappears.

Delay-induced state transition and resonance in periodically driven tumor model with immune surveillance

The phenomenon of stochastic resonance (SR) in a tumor growth model under the presence of immune surveillance is investigated. Time delay and cross-correlation between multiplicative and additive noises are considered in the system. The signal-to-noise ratio (SNR) is calculated when periodic signal is introduced multiplicatively. Our results show that: (i) the time delay can accelerate the transition from the state of stable tumor to that of extinction, however the correlation between two noises can accelerate the transition from the state of extinction to that of stable tumor; (ii) the time delay and correlation between two noises can lead to a transition between SR and double SR in the curve of SNR as a function of additive noise intensity, however for the curve of SNR as a function of multiplicative noise intensity, the time delay can cause the SR phenomenon to disappear, and the cross-correlation between two noises can lead to a transition from SR to stochastic reverse-resonance. Finally, we compare the SR phenomenon for the multiplicative periodic signal with that for additive periodic signal in the tumor growth model with immune surveillance.

Entropic noises-induced resonance in a geometrically confined system

We consider the motion of Brownian particles through a narrow tube of varying cross-section in a geometrically confined system subjected to a sinusoidal oscillating force. The varying cross-section of the confinement results in an effective purely entropic potential in reduced dimension. Besides an additive Langevin force, one external additive and another multiplicative noise are acting along the x-direction. We demonstrate that the presence of a periodic input may give rise to a maximum and a minimum of the spectral amplification at corresponding optimal values of the noise strength, and therefore to the appearance of the purely entropic stochastic resonance and reverse-resonance phenomena. Furthermore, we show that the cross-correlation between two noises leads to a decrease of the spectral amplification, i.e., we observe the cross-correlation between two noises weakening the resonance. Mechanisms for the cross-correlation weakening the resonance are explained from the point of view of the effective purely entropic potential.

First-principles calculations of NO and NO2 adsorption on a spinel ZnGaAlO4(100) surface

Density functional theory (DFT) has been used to investigate the properties of NO and NO2 adsorption on a ZnGaAlO4(100) surface. The calculation results show that the minimum surface energy is 2.3073 J m−2. The configuration of NO adsorbed on the surface is more stable through an N-down orientation due to the strong hybridization between d states and the NO-π orbital. In particular, NO approaches Zn via its N side with an adsorption energy of −23.50 kcal mol−1, while the comparable value is −44.19 kcal mol−1 for NO2 adsorbed at Zn, suggesting a higher degree of adsorption stability. In addition, substitution of Al with Ga is responsible for the most stable mode of NO2 adsorption with a binding energy of −53.40 kcal mol−1. This demonstrates that the process of desorption of NO2 is thermodynamically feasible. NO2 adsorbed on the surface is activated, showing that the adsorption can directly lead to a dissociation of NO2. Moreover, the process of dissociation of NO2 adsorbed at Ga is favored due to a lower energy barrier of activation.

Facilitated transport and efficiency optimization in a cross-correlated noise ratchet

We study the energetic efficiency of a Brownian particle moving in a spatially symmetric potential with temporally symmetric unbiased fluctuations, which is driven by cross-correlated multiplicative and additive noise. The analytical expressions of the current and efficiency at the quasi-steady state limit are presented. Based on the current and efficiency, it is found that: (i) there exists an optimal value of the temperatures and driving force, at which the current takes its maximum, which means that these parameters can facilitate the transport of Brownian particles; (ii) the efficiency shows a resonant-like phenomenon as a function of the temperatures, the load and the driving force, which implies that these parameters can induce optimized efficiency of energy transformation at finite values; and (iii) the efficiency optimization increases with the increase of the cross-correlation between two noises, i.e. the cross-correlation between two noises can enhance the efficiency optimization.

The relaxation time of processes in a FitzHugh–Nagumo neural system with time delay

In this paper, we study the relaxation time (RT) of the steady-state correlation function in a FitzHugh–Nagumo neural system under the presence of multiplicative and additive white noises and time delay. The noise correlation parameter λ can produce a critical behavior in the RT as functions of the multiplicative noise intensity D, the additive noise intensity Q and the time delay τ. That is, the RT decreases as the noise intensities D and Q increase, and increases as the time delay τ increases below the critical value of λ. However, above the critical value, the RT first increases, reaches a maximum, and then decreases as D, Q and τ increase, i.e. a noise intensity D or Q and a time delay τ exist, at which the time scales of the relaxation process are at their largest. In addition, the additive noise intensity Q can also produce a critical behavior in the RT as a function of λ. The noise correlation parameter λ first increases the RT of processes, then decreases it below the critical value of Q. Above the critical value, λ increases it.