Exact results for gene-expression models with general waiting-time distributions.

Complex molecular details of transcriptional regulation can be coarse-grained by assuming that reaction waiting times for promoter-state transitions, the mRNA synthesis, and the mRNA degradation follow general distributions. However, how such a generalized two-state model is analytically solved is a long-standing issue. Here we first present analytical formulas of burst-size distributions for this model. Then, we derive an iterative equation for the mRNA moment-generating function, by which mRNA raw and binomial moments of any order can be conveniently calculated. The analytical results obtained in the special cases of phase-type waiting-time distributions not only provide insights into the mechanisms of complex transcriptional regulations but also bring conveniences for experimental data-based statistical inferences.

Analysis of a non-Markov transcription model with nuclear RNA export and RNA nuclear retention.

Transcription involves gene activation, nuclear RNA export (NRE) and RNA nuclear retention (RNR). All these processes are multistep and biochemical. A multistep reaction process can create memories between reaction events, leading to non-Markovian kinetics. This raises an unsolved issue: how does molecular memory affect stochastic transcription in the case that NRE and RNR are simultaneously considered? To address this issue, we analyze a non-Markov model, which considers multistep activation, multistep NRE and multistep RNR can interpret many experimental phenomena. In order to solve this model, we introduce an effective transition rate for each reaction. These effective transition rates, which explicitly decode the effect of molecular memory, can transform the original non-Markov issue into an equivalent Markov one. Based on this technique, we derive analytical results, showing that molecular memory can significantly affect the nuclear and cytoplasmic mRNA mean and noise. In addition to the results providing insights into the role of molecular memory in gene expression, our modeling and analysis provide a paradigm for studying more complex stochastic transcription processes.

Generalized fluctuation-dissipation theorem for non-Markovian reaction networks.

Intracellular biochemical networks often display large fluctuations in the molecule numbers or the concentrations of reactive species, making molecular approaches necessary for system descriptions. For Markovian reaction networks, the fluctuation-dissipation theorem (FDT) has been well established and extensively used in fast evaluation of fluctuations in reactive species. For non-Markovian reaction networks, however, the similar FDT has not been established so far. Here, we present a generalized FDT (gFDT) for a large class of non-Markovian reaction networks where general intrinsic-event waiting-time distributions account for the effect of intrinsic noise and general stochastic reaction delays represent the impact of extrinsic noise from environmental perturbations. The starting point is a generalized chemical master equation (gCME), which describes the probabilistic behavior of an equivalent Markovian reaction network and identifies the structure of the original non-Markovian reaction network in terms of stoichiometries and effective transition rates (extensions of common reaction propensity functions). From this formulation follows directly the solution of the linear noise approximation of the stationary gCME for all the components in the non-Markovian reaction network. While the gFDT can quickly trace noisy sources in non-Markovian reaction networks, example analysis verifies its effectiveness.

SS-RNN: A Strengthened Skip Algorithm for Data Classification Based on Recurrent Neural Networks.

Recurrent neural networks are widely used in time series prediction and classification. However, they have problems such as insufficient memory ability and difficulty in gradient back propagation. To solve these problems, this paper proposes a new algorithm called SS-RNN, which directly uses multiple historical information to predict the current time information. It can enhance the long-term memory ability. At the same time, for the time direction, it can improve the correlation of states at different moments. To include the historical information, we design two different processing methods for the SS-RNN in continuous and discontinuous ways, respectively. For each method, there are two ways for historical information addition: 1) direct addition and 2) adding weight weighting and function mapping to activation function. It provides six pathways so as to fully and deeply explore the effect and influence of historical information on the RNNs. By comparing the average accuracy of real datasets with long short-term memory, Bi-LSTM, gated recurrent units, and MCNN and calculating the main indexes (Accuracy, Precision, Recall, and F1-score), it can be observed that our method can improve the average accuracy and optimize the structure of the recurrent neural network and effectively solve the problems of exploding and vanishing gradients.

Different effects of fast and slow input fluctuations on output in gene regulation.

An important task in the post-gene era is to understand the role of stochasticity in gene regulation. Here, we analyze a cascade model of stochastic gene expression, where the upstream gene stochastically generates proteins that regulate, as transcription factors, stochastic synthesis of the downstream output. We find that in contrast to fast input fluctuations that do not change the behavior of the downstream system qualitatively, slow input fluctuations can induce different modes of the distribution of downstream output and even stochastic focusing or defocusing of the downstream output level, although the regulatory protein follows the same distribution in both cases. This finding is counterintuitive but can have broad biological implications, e.g., slow input rather than fast fluctuations may both increase the survival probability of cells and enhance the sensitivity of intracellular regulation. In addition, we find that input fluctuations can minimize the output noise.

Explicit effect of stochastic reaction delay on gene expression.

Apart from intrinsic stochastic variability, gene expression also involves stochastic reaction delay arising from heterogeneity and fluctuation processes, which can affect the efficiency of reactants (e.g., mRNA or protein) in exploring their environments. In contrast to the former that has been extensively investigated, the impact of the latter on gene expression remains not fully understood. Here, we analyze a non-Markovian model of bursty gene expression with general delay distribution. We analytically find that the effect of stochastic reaction delay is equivalent to the introduction of negative feedback, and stationary protein distribution only depends on the mean of the delay and is independent of its distribution. We numerically show that the stochastic reaction delay always slightly amplifies the mean protein level but remarkably reduces the protein noise (quantified by the ratio of the variance over the squared average). Our analysis indicates that stochastic reaction delay is an important factor affecting gene expression.

3D structure stability of the HIV-1 TAR RNA in ion solutions: A coarse-grained model study.

As an extremely common structural motif, RNA hairpins with bulge loops [e.g., the human immunodeficiency virus type 1 (HIV-1) transactivation response (TAR) RNA] can play essential roles in normal cellular processes by binding to proteins and small ligands, which could be very dependent on their three-dimensional (3D) structures and stability. Although the structures and conformational dynamics of the HIV-1 TAR RNA have been extensively studied, there are few investigations on the thermodynamic stability of the TAR RNA, especially in ion solutions, and the existing studies also have some divergence on the unfolding process of the RNA. Here, we employed our previously developed coarse-grained model with implicit salt to predict the 3D structure, stability, and unfolding pathway for the HIV-1 TAR RNA over a wide range of ion concentrations. As compared with the extensive experimental/theoretical results, the present model can give reliable predictions on the 3D structure stability of the TAR RNA from the sequence. Based on the predictions, our further comprehensive analyses on the stability of the TAR RNA as well as its variants revealed that the unfolding pathway of an RNA hairpin with a bulge loop is mainly determined by the relative stability between different states (folded state, intermediate state, and unfolded state) and the strength of the coaxial stacking between two stems in folded structures, both of which can be apparently modulated by the ion concentrations as well as the sequences.

Analytical results for a generalized model of bursty gene expression with molecular memory.

The activation of a gene is a complex biochemical process and could involve small steps, creating a memory between individual events. However, the effect of this molecular memory was often neglected in previous work. How the molecular memory affects gene expression remains not fully explored. We analyze a stochastic model of bursty gene expression, where the waiting time from inactivation to activation is assumed to follow a nonexponential (in fact, Erlang) distribution. We derive the analytical expression for the gene-product distribution, which explicitly traces the effect of molecule memory. Interestingly, we find that the effect of molecular memory is equivalent to the introduction of feedback. In addition, we analytically show that the stationary distribution is always super-Poissonian, independent of the detail of the waiting-time distribution, and there is the optimal step size that minimizes the Fano factor for any given mean burst size and is a decreasing function of the mean burst size. These analytical results indicate that molecular memory is an unneglectable factor affecting gene expression.

Bayesian quantile regression for nonlinear mixed-effects joint models for longitudinal data in the presence of mismeasured covariate errors.

Quantile regression (QR) models have recently received increasing attention in longitudinal studies where measurements of the same individuals are taken repeatedly over time. When continuous (longitudinal) responses follow a distribution that is quite different from a normal distribution, usual mean regression (MR)-based linear models may fail to produce efficient estimators, whereas QR-based linear models may perform satisfactorily. To the best of our knowledge, there have been very few studies on QR-based nonlinear models for longitudinal data in comparison to MR-based nonlinear models. In this article, we study QR-based nonlinear mixed-effects (NLME) joint models for longitudinal data with non-central location and outliers and/or heavy tails in response, and non-normality and measurement errors in covariate under Bayesian framework. The proposed QR-based modeling method is compared with an MR-based one by an AIDS clinical dataset and through simulation studies. The proposed QR joint modeling approach can be not only applied to AIDS clinical studies, but also may have general applications in other fields as long as relevant technical specifications are met.