Noise decomposition of intracellular biochemical signaling networks using nonequivalent reporters.

Experimental measurements of biochemical noise have primarily focused on sources of noise at the gene expression level due to limitations of existing noise decomposition techniques. Here, we introduce a mathematical framework that extends classical extrinsic-intrinsic noise analysis and enables mapping of noise within upstream signaling networks free of such restrictions. The framework applies to systems for which the responses of interest are linearly correlated on average, although the framework can be easily generalized to the nonlinear case. Interestingly, despite the high degree of complexity and nonlinearity of most mammalian signaling networks, three distinct tumor necrosis factor (TNF) signaling network branches displayed linearly correlated responses, in both wild-type and perturbed versions of the network, across multiple orders of magnitude of ligand concentration. Using the noise mapping analysis, we find that the c-Jun N-terminal kinase (JNK) pathway generates higher noise than the NF-κB pathway, whereas the activation of c-Jun adds a greater amount of noise than the activation of ATF-2. In addition, we find that the A20 protein can suppress noise in the activation of ATF-2 by separately inhibiting the TNF receptor complex and JNK pathway through a negative feedback mechanism. These results, easily scalable to larger and more complex networks, pave the way toward assessing how noise propagates through cellular signaling pathways and create a foundation on which we can further investigate the relationship between signaling system architecture and biological noise.

Applying the Kolmogorov-Zurbenko filter followed by random forest models to 7Be observations in Spain (2006-2021).

In this study, we analysed 7Be weekly surface measurements from six Spanish laboratories from 2006 to 2021. The Kolmogorov-Zurbenko filter was applied to the six 7Be time series, and following an iterative process, the original data were divided into two fractions: one related to variations characterized by periods above 33 days (including, among others, the seasonal cycle) and the second noisier fraction related to mechanisms originating from variations with periods below 33 days. Both fractions were independent at the six locations. The second machine-based step using random forest models was applied with the aim of identifying the most influential inputs to the observed 7Be concentrations, and machine learning-inspired regression models were fitted. With respect to seasonal components, the results indicated that the memory of the system was the most influential input, as expected by the large fraction of variance explained by the seasonal cycle, followed by that of humidity and wind-related variables. For the fraction corresponding to periods below 33 d, precipitation-, humidity-, and radiation-related variables were the most influential. This methodology has made it possible to successfully describe the major mechanisms known to be involved in the generation of the surface 7Be concentrations observed in Spain.

Double-edged role of resource competition in gene expression noise and control.

Despite extensive investigation demonstrating that resource competition can significantly alter the deterministic behaviors of synthetic gene circuits, it remains unclear how resource competition contributes to the gene expression noise and how this noise can be controlled. Utilizing a two-gene circuit as a prototypical system, we uncover a surprising double-edged role of resource competition in gene expression noise: competition decreases noise through introducing a resource constraint but generates its own type of noise which we name as "resource competitive noise." Utilization of orthogonal resources enables retainment of the noise reduction conferred by resource constraint while removing the added resource competitive noise. The noise reduction effects are studied using three negative feedback types: negatively competitive regulation (NCR), local, and global controllers, each having four placement architectures in the protein biosynthesis pathway (mRNA or protein inhibition on transcription or translation). Our results show that both local and NCR controllers with mRNA-mediated inhibition are efficacious at reducing noise, with NCR controllers demonstrating a superior noise-reduction capability. We also find that combining feedback controllers with orthogonal resources can improve the local controllers. This work provides deep insights into the origin of stochasticity in gene circuits with resource competition and guidance for developing effective noise control strategies.

Role of integrated noise in pathway-specific signal propagation in feed-forward loops.

Cells impose optimal noise control mechanism in diverse situations to cope with distinct environmental cues. Sometimes, it is desirable for the cell to utilize fluctuations for noise-driven processes. In other cases, noise can be harmful to the cell to show optimal fitness. It is, therefore, important to unravel the noise propagation mechanism inside the cell. Such noise controlling mechanism is accomplished by using gene transcription regulatory networks. One such gene regulatory network is feed-forward loop, having three regulatory nodes S, X and Y. Here, we consider the most abundant type 1 of coherent and incoherent feed-forward loops with both OR and AND logic functions, forming four different architectures. In OR logic function, the functions representing S and X act additively for the regulation of Y, while in AND logic function, the same functions (S and X) act multiplicatively for the regulation of Y. Measurement of susceptibility of the signal at output Y is done using elasticity of each regulation in FFLs. Using susceptibility, we demonstrate the nature of pathway integration by which one-step and two-step pathways get overlapped. The integration type is competitive for motifs having OR gate, while it is noncompetitive for the same with AND gate. The pathway integration property explains the output noise behavior of the motifs properly but cannot infer about the mechanism by which the upstream noise propagates to output. To account this, the total output noise is decomposed, which results in integrated noise as an additional noise source along with pathway-specific noise components. The integrated noise is found to appear as a consequence of integration between the pathways and has different functional characteristics explaining noise amplification and noise attenuation property of coherent and incoherent feed-forward loops, respectively. The noise decomposition also quantifies the contribution of different noise sources toward total noise. Finally, the noise propagation is being tuned as a function of input signal noise and its time scale of fluctuations, which shows considerable intrinsic noise strength and relatively slow relaxation time scale causes a higher degree of noise propagation in FFLs.

Pathway dynamics can delineate the sources of transcriptional noise in gene expression.

Single-cell expression profiling opens up new vistas on cellular processes. Extensive cell-to-cell variability at the transcriptomic and proteomic level has been one of the stand-out observations. Because most experimental analyses are destructive we only have access to snapshot data of cellular states. This loss of temporal information presents significant challenges for inferring dynamics, as well as causes of cell-to-cell variability. In particular, we typically cannot separate dynamic variability from within cells ('intrinsic noise') from variability across the population ('extrinsic noise'). Here, we make this non-identifiability mathematically precise, allowing us to identify new experimental set-ups that can assist in resolving this non-identifiability. We show that multiple generic reporters from the same biochemical pathways (e.g. mRNA and protein) can infer magnitudes of intrinsic and extrinsic transcriptional noise, identifying sources of heterogeneity. Stochastic simulations support our theory, and demonstrate that 'pathway-reporters' compare favourably to the well-known, but often difficult to implement, dual-reporter method.

In biology, seemingly random variation within or between cells can have significant effects on a number of cellular processes, like how cells divide and develop. For example, how often a gene is switched on, or 'expressed', can randomly fluctuate over time. This 'noise' may lead to a cell having slightly more of a particular molecule, causing it to behave differently to other cells in the population. However, it is currently unclear how this random variation is created and controlled in cells, and what effect this has on biological systems as a whole. When a gene is expressed, its sequence typically gets copied in to a molecule called mRNA, which is then processed and used to build the protein encoded by the gene. By measuring the levels of mRNA molecules in individual cells, researchers have been able to investigate how gene expression varies within populations. These experiments are carried out on dead cells at a single point in time, and mathematical models are then applied to detect noise in the molecular data. This approach, however, precludes how noise changes over time, making it difficult to determine the source of cell-to-cell variability. In particular, whether the variation detected is the result of genuine random molecular changes (intrinsic noise), or external factors ­ such as temperature and pH ­ fluctuating in the cells environment (extrinsic noise). Here, Ham et al. have built on previous mathematical models to identify a new approach for investigating the source of molecular noise. They found that for any given gene it is impossible to understand what causes its activity levels to vary just from data on its mRNA levels. Instead, information on other molecules that are affected by expression of the gene (termed 'pathway reporters') can provide a clearer picture of whether molecular variability is the result of intrinsic or extrinsic noise. The mathematical models developed by Ham et al. reveal what can and cannot be learned about noise from gene expression data. Furthermore, pathway-reporters are easier to measure experimentally than other reporters that are typically used to study the origins and effects of cell-to-cell variability. These findings could help researchers design single cell experiments that are better for studying noise, leading to a deeper understanding of how different types of variation impact cell biology.

Optimization scheme of wind energy prediction based on artificial intelligence.

Wind energy, as one of the renewable energies with the most potential for development, has been widely concerned by many countries. However, due to the great volatility and uncertainty of natural wind, wind power also fluctuates, seriously affecting the reliability of wind power system and bringing challenges to large-scale grid connection of wind power. Wind speed prediction is very important to ensure the safety and stability of wind power generation system. In this paper, a new wind speed prediction scheme is proposed. First, improved hybrid mode decomposition is used to decompose the wind speed data into the trend part and the fluctuation part, and the noise is decomposed twice. Then wavelet analysis is used to decompose the trend part and the fluctuation part for the third time. The decomposed data are classified. The long- and short-term memory neural network optimized by the improved particle swarm optimization algorithm is used to train the nonlinear sequence and noise sequence, and the autoregressive moving average model is used to train the linear sequence. Finally, the final prediction results were reconstructed. This paper uses this system to predict the wind speed data of China's Changma wind farm and Spain's Sotavento wind farm. By experimenting with the real data from two different wind farms and comparing with other predictive models, we found that (1) by improving the mode number selection in the variational mode decomposition, the characteristics of wind speed data can be better extracted. (2) According to the different characteristics of component data, the combination method is selected to predict modal components, which makes full use of the advantages of different algorithms and has good prediction effect. (3) The optimization algorithm is used to optimize the neural network, which solves the problem of parameter setting when establishing the prediction model. (4) The combination forecasting model proposed in this paper has clear structure and accurate prediction results. The research work in this paper will help to promote the development of wind energy prediction field, help wind farms formulate wind power regulation strategies, and further promote the construction of green energy structure.

Effects of cell-cycle-dependent expression on random fluctuations in protein levels.

Expression of many genes varies as a cell transitions through different cell-cycle stages. How coupling between stochastic expression and cell cycle impacts cell-to-cell variability (noise) in the level of protein is not well understood. We analyse a model where a stable protein is synthesized in random bursts, and the frequency with which bursts occur varies within the cell cycle. Formulae quantifying the extent of fluctuations in the protein copy number are derived and decomposed into components arising from the cell cycle and stochastic processes. The latter stochastic component represents contributions from bursty expression and errors incurred during partitioning of molecules between daughter cells. These formulae reveal an interesting trade-off: cell-cycle dependencies that amplify the noise contribution from bursty expression also attenuate the contribution from partitioning errors. We investigate the existence of optimum strategies for coupling expression to the cell cycle that minimize the stochastic component. Intriguingly, results show that a zero production rate throughout the cell cycle, with expression only occurring just before cell division, minimizes noise from bursty expression for a fixed mean protein level. By contrast, the optimal strategy in the case of partitioning errors is to make the protein just after cell division. We provide examples of regulatory proteins that are expressed only towards the end of the cell cycle, and argue that such strategies enhance robustness of cell-cycle decisions to the intrinsic stochasticity of gene expression.

Noise Decomposition Principle in a Coherent Feed-Forward Transcriptional Regulatory Loop.

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.