ncRNA-mediated bistability in the synthesis of hundreds of distinct mRNAs and proteins

The kinetics of gene expression can be bistable due to the feedback between the mRNA and protein formation. In eukaryotic cells, the interplay between mRNAs and proteins can be influenced by non-coding RNAs. Some of these RNAs, e.g., microRNAs, may target hundreds of distinct mRNAs. The model presented here shows how a non-coding RNA can be used as a mediator in order to involve numerous mRNAs and proteins into a bistable network.     

Oscillatory kinetics of gene expression: Protein conversion and slow mRNA transport

The negative feedback between mRNA and regulatory-protein production may result in oscillations in the kinetics of gene expression if the mRNA-protein interplay includes protein conversion. Using a mean-field kinetic model, we show that such oscillations can be amplified due to limitations of the mRNA transport between the nucleus and cytoplasm. This effect may be dramatic for the mRNA population in the nucleus. The article is published in the original.     

Quantenfeldtheorie wechselwirkender Vielteilchensysteme zur semiklassischen Beschreibung von kollektiver Bewegung mit großen Amplituden

By using path integral methods a collective quantum field theory of interacting many-body systems is developed, the classical limit of which is given by the time-dependent mean-field approximation. In this way the mean-field approximation is embedded into the full quantum mechanics and the quantum corrections to the “classical” mean-field approximation can be systematically evaluated. By including the dominant quantum corrections to the mean-field approximation a semiclassical theory of large amplitude collective motions in many-body-systems, which show a highly nonlinear dynamic and are not accessible to perturbation theoretical methods, is derived. The semiclassical theory is developed explicitly for bound states and decay processes like nuclear fission. In the case of bound states this leads to the quantization of the time-dependent Hartree-Fock-Theory, which is demonstrated for a uniform nuclear rotation.     

利用随机共振在强噪声下提取信息信号

已有利用随机共振在强噪声下提取单一频率信号的若干报道，但单一频率信号所携带的信息量为零.本实验研究表明：在调幅波和白噪声的协同作用下，非线性双稳系统的输出不仅可以呈现随机共振现象，而且经检波、滤波后能提取出调制信号(信息信号)；与直接经电子学系统检波、线性滤波后所提取的调制信号相比，前者所获调制信号的信噪比更高.给出了绝热近似条件下，调制信号信噪比的解析表达式. 关键词： 随机共振 信噪比 调制信号 噪声     

Deterministic chaos and noise in optical bistability

The time-dependent solutions of the mean-field Maxwell-Bloch equations for optical bistability are studied numerically for the deterministic equations and the stochastic equations with additional noise sources. From the solutions of the deterministic equations, a discrete map is constructed showing that the periodic and chaotic solutions form a Feigenbaum scenarium. Inclusion of noise sources leads to a finite lifetime of the states in the upper bistable branch and to destabilization of higher periodic solutions.     

Stochastic resonance in a locally excited system of bistable oscillators

Stochastic resonance is studied in a one-dimensional array of overdamped bistable oscillators in the presence of a local subthreshold periodic perturbation. The system can be treated as an ensemble of pseudospins tending to align parallel which are driven dynamically by an external periodic magnetic field. The oscillators are subjected to a dynamic white noise as well as to a static topological disorder. The latter is quantified by the fraction of randomly added long-range connections among ensemble elements. In the low connectivity regime the system displays an optimal global stochastic resonance response if a small-world network is formed. In the mean-field regime we explain strong changes in the dynamic disorder strength provoking a maximal stochastic resonance response via the variation of fraction of long-range connections by taking into account the ferromagnetic-paramagnetic phase transition of the pseudospins. The system size analysis shows only quantitative power-law type changes on increasing number of pseudospins.     

A generic 3D kinetic model of gene expression

Recent experiments show that mRNAs and proteins can be localized both in prokaryotic and eukaryotic cells. To describe such situations, I present a 3D mean-field kinetic model aimed primarily at gene expression in prokaryotic cells, including the formation of mRNA, its translation into protein, and slow diffusion of these species. Under steady-state conditions, the mRNA and protein spatial distribution is described by simple exponential functions. The protein concentration near the gene transcribed into mRNA is shown to depend on the protein and mRNA diffusion coefficients and degradation rate constants.     

Damping of giant resonances in a stochastic two-level model

We derive a theory for small amplitude motion about states in thermal equilibrium. This motion couples mean-field oscillations and occupation number relaxations. The theory contains the effects of two-body collisions treated beyond the Markov approximation. The damping of collective modes is studied in a stochastic two-level model. The widths of giant resonances in finite nuclei are estimated using sum rules.     

Noise-intensity fluctuation in Langevin model and its higher-order Fokker-Planck equation

In this paper, we investigate a Langevin model subjected to stochastic intensity noise (SIN), which incorporates temporal fluctuations in noise-intensity. We derive a higher-order Fokker-Planck equation (HFPE) of the system, taking into account the effect of SIN by the adiabatic elimination technique. Stationary distributions of the HFPE are calculated by using the perturbation expansion. We investigate the effect of SIN in three cases: (a) parabolic and quartic bistable potentials with additive noise, (b) a quartic potential with multiplicative noise, and (c) a stochastic gene expression model. We find that the existence of noise-intensity fluctuations induces an intriguing phenomenon of a bimodal-to-trimodal transition in probability distributions. These results are validated with Monte Carlo simulations.     

Dynamic phase transition in the kinetic spin-1 Blume-Capel model: Phase diagrams in the temperature and crystal-field interaction plane

Within a mean-field approach, the stationary states of the kinetic spin-1 Blume-Capel model in the presence of a time-dependent oscillating external magnetic field is studied. The Glauber-type stochastic dynamics is used to describe the time evolution of the system and obtain the mean-field dynamic equation of motion. The dynamic phase-transition points are calculated and phase diagrams are presented in the temperature and crystal-field interaction plane. According to the values of the magnetic field amplitude, three fundamental types of phase diagrams are found: One exhibits a dynamic tricritical point, while the other two exhibit a dynamic zero-temperature critical point. The text was submitted by the authors in English.     

A semi-analytic method for computing the long-time order parameter dynamics in mean-field coupled overdamped oscillators with colored noises

The order parameter dynamics of a mean-field model is frequently investigated in macroscopic cumulant dynamics, from which a bifurcation can be predicted qualitatively. In this Letter, for quantitatively investigating the long-time order parameter dynamics, a semi-analytic method is proposed based on approximate nonlinear Fokker-Planck equations. Applying the new method to the mean-field model of periodically driven overdamped bistable oscillators with colored noise, we exhibit the bifurcation behavior and the nonlinear stochastic resonance of the order parameter by tuning noise intensity or coupling coefficient, and the accuracy of the new method are verified by direct simulation. Our observations disclose some new properties about the order parameter dynamics of the mean-field model. For example, the periodic signal shifts the critical coupling coefficient to a larger value, while the nonzero correlation time of the colored noise shifts it to a lower value. Our observation also discloses that there is no quantitatively corresponding relation between the resonant peak and the critical bifurcation parameter of the Gaussian moment system.     

First passage times and minimum actions for a stochastic minimal bistable system

Bistability is an ubiquitous phenomenon in biological systems, and always plays important roles in cell division, differentiation, cancer onset, apoptosis and so on. However, stochastic fluctuations in bistable systems are still hard to understand. To address this issue, we propose a chemical master equation model for a minimal bistable system, which underlies generally bistable systems. For this master equation model, we mainly focus on the mean first passage times (MFPTs) by respectively using Gillespie algorithm and an approximation method of the large deviation theory, and does on minimum actions along optimal transition paths from OFF to ON states by the large deviation theory. Further, we find that for this stochastic system the MFPTs have different change tendencies compared to the corresponding minimum actions. Our results of this minimal stochastic model can also well understand more general bistable systems.