BACKGROUND: The high dimensionality of data in single cell transcriptomics (scRNAseq) requires investigators to choose subsets of genes ("feature selection") for downstream analysis (e.g., unsupervised cell clustering). The evaluation of different approaches to feature selection is hampered by the fact that, as we show here, the difficulty of feature selection can vary greatly, depending on the dataset being analyzed. RESULTS: For routine cell type identification, even randomly chosen features can perform well, but for cell type differences that are subtle, both number of features and selection strategy matter strongly. We present a simple feature selection method grounded in an analytical model that allows for interpretable delineation of how many and which features to choose, facilitating identification of biologically meaningful rare cell types. We compare this method to default methods in scanpy and Seurat, as well as SCTransform, showing how greater accuracy can often be achieved with surprisingly few, well-chosen features. CONCLUSIONS: Feature selection is a critical step in scRNAseq for downstream analyses. We explore the pitfalls that can arise from incautious feature selection and present a statistical method to facilitate improved outcomes.

BACKGROUND: Many approaches have been developed to overcome technical noise in single cell RNA-sequencing (scRNAseq). As researchers dig deeper into data-looking for rare cell types, subtleties of cell states, and details of gene regulatory networks-there is a growing need for algorithms with controllable accuracy and fewer ad hoc parameters and thresholds. Impeding this goal is the fact that an appropriate null distribution for scRNAseq cannot simply be extracted from data in which ground truth about biological variation is unknown (i.e., usually). RESULTS: We approach this problem analytically, assuming that scRNAseq data reflect only cell heterogeneity (what we seek to characterize), transcriptional noise (temporal fluctuations randomly distributed across cells), and sampling error (i.e., Poisson noise). We analyze scRNAseq data without normalization-a step that skews distributions, particularly for sparse data-and calculate p values associated with key statistics. We develop an improved method for selecting features for cell clustering and identifying gene-gene correlations, both positive and negative. Using simulated data, we show that this method, which we call BigSur (Basic Informatics and Gene Statistics from Unnormalized Reads), captures even weak yet significant correlation structures in scRNAseq data. Applying BigSur to data from a clonal human melanoma cell line, we identify thousands of correlations that, when clustered without supervision into gene communities, align with known cellular components and biological processes, and highlight potentially novel cell biological relationships. CONCLUSIONS: New insights into functionally relevant gene regulatory networks can be obtained using a statistically grounded approach to the identification of gene-gene correlations.

Single-cell RNA sequencing trades read-depth for dimensionality, often leading to loss of critical signaling gene information that is typically present in bulk data sets. We introduce DURIAN (Deconvolution and mUltitask-Regression-based ImputAtioN), an integrative method for recovery of gene expression in single-cell data. Through systematic benchmarking, we demonstrate the accuracy, robustness and empirical convergence of DURIAN using both synthetic and published data sets. We show that use of DURIAN improves single-cell clustering, low-dimensional embedding, and recovery of intercellular signaling networks. Our study resolves several inconsistent results of cell-cell communication analysis using single-cell or bulk data independently. The method has broad application in biomarker discovery and cell signaling analysis using single-cell transcriptomics data sets.

The human cerebral cortex undergoes profound structural and functional dynamic variations across the lifespan, whereas the underlying molecular mechanisms remain unclear. Here, with a novel method transcriptome-connectome correlation analysis (TCA), which integrates the brain functional magnetic resonance images and region-specific transcriptomes, we identify age-specific cortex (ASC) gene signatures for adolescence, early adulthood and late adulthood. The ASC gene signatures are significantly correlated with the cortical thickness (P-value <2.00e-3) and myelination (P-value <1.00e-3), two key brain structural features that vary in accordance with brain development. In addition to the molecular underpinning of age-related brain functions, the ASC gene signatures allow delineation of the molecular mechanisms of neuropsychiatric disorders, such as the regulation between ARNT2 and its target gene ETF1 involved in Schizophrenia. We further validate the ASC gene signatures with published gene sets associated with the adult cortex, and confirm the robustness of TCA on other brain image datasets. Availability: All scripts are written in R. Scripts for the TCA method and related statistics result can be freely accessed at https://github.com/Soulnature/TCA. Additional data related to this paper may be requested from the authors.

MOTIVATION: Single-cell sequencing assay for transposase-accessible chromatin (scATAC-seq) provides new opportunities to dissect epigenomic heterogeneity and elucidate transcriptional regulatory mechanisms. However, computational modeling of scATAC-seq data is challenging due to its high dimension, extreme sparsity, complex dependencies and high sensitivity to confounding factors from various sources. RESULTS: Here, we propose a new deep generative model framework, named SAILER, for analyzing scATAC-seq data. SAILER aims to learn a low-dimensional nonlinear latent representation of each cell that defines its intrinsic chromatin state, invariant to extrinsic confounding factors like read depth and batch effects. SAILER adopts the conventional encoder-decoder framework to learn the latent representation but imposes additional constraints to ensure the independence of the learned representations from the confounding factors. Experimental results on both simulated and real scATAC-seq datasets demonstrate that SAILER learns better and biologically more meaningful representations of cells than other methods. Its noise-free cell embeddings bring in significant benefits in downstream analyses: clustering and imputation based on SAILER result in 6.9% and 18.5% improvements over existing methods, respectively. Moreover, because no matrix factorization is involved, SAILER can easily scale to process millions of cells. We implemented SAILER into a software package, freely available to all for large-scale scATAC-seq data analysis. AVAILABILITY AND IMPLEMENTATION: The software is publicly available at https://github.com/uci-cbcl/SAILER. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

During early mammalian embryo development, a small number of cells make robust fate decisions at particular spatial locations in a tight time window to form inner cell mass (ICM), and later epiblast (Epi) and primitive endoderm (PE). While recent single-cell transcriptomics data allows scrutinization of heterogeneity of individual cells, consistent spatial and temporal mechanisms the early embryo utilize to robustly form the Epi/PE layers from ICM remain elusive. Here we build a multiscale three-dimensional model for mammalian embryo to recapitulate the observed patterning process from zygote to late blastocyst. By integrating the spatiotemporal information reconstructed from multiple single-cell transcriptomic datasets, the data-informed modeling analysis suggests two major processes critical to the formation of Epi/PE layers: a selective cell-cell adhesion mechanism (via EphA4/EphrinB2) for fate-location coordination and a temporal attenuation mechanism of cell signaling (via Fgf). Spatial imaging data and distinct subsets of single-cell gene expression data are then used to validate the predictions. Together, our study provides a multiscale framework that incorporates single-cell gene expression datasets to analyze gene regulations, cell-cell communications, and physical interactions among cells in complex geometries at single-cell resolution, with direct application to late-stage development of embryogenesis.

The vertebrate hindbrain is segmented into rhombomeres (r) initially defined by distinct domains of gene expression. Previous studies have shown that noise-induced gene regulation and cell sorting are critical for the sharpening of rhombomere boundaries, which start out rough in the forming neural plate (NP) and sharpen over time. However, the mechanisms controlling simultaneous formation of multiple rhombomeres and accuracy in their sizes are unclear. We have developed a stochastic multiscale cell-based model that explicitly incorporates dynamic morphogenetic changes (i.e. convergent-extension of the NP), multiple morphogens, and gene regulatory networks to investigate the formation of rhombomeres and their corresponding boundaries in the zebrafish hindbrain. During pattern initiation, the short-range signal, fibroblast growth factor (FGF), works together with the longer-range morphogen, retinoic acid (RA), to specify all of these boundaries and maintain accurately sized segments with sharp boundaries. At later stages of patterning, we show a nonlinear change in the shape of rhombomeres with rapid left-right narrowing of the NP followed by slower dynamics. Rapid initial convergence improves boundary sharpness and segment size by regulating cell sorting and cell fate both independently and coordinately. Overall, multiple morphogens and tissue dynamics synergize to regulate the sizes and boundaries of multiple segments during development.

Unraveling molecular regulatory networks underlying disease progression is critically important for understanding disease mechanisms and identifying drug targets. The existing methods for inferring gene regulatory networks (GRNs) rely mainly on time-course gene expression data. However, most available omics data from cross-sectional studies of cancer patients often lack sufficient temporal information, leading to a key challenge for GRN inference. Through quantifying the latent progression using random walks-based manifold distance, we propose a latent-temporal progression-based Bayesian method, PROB, for inferring GRNs from the cross-sectional transcriptomic data of tumor samples. The robustness of PROB to the measurement variabilities in the data is mathematically proved and numerically verified. Performance evaluation on real data indicates that PROB outperforms other methods in both pseudotime inference and GRN inference. Applications to bladder cancer and breast cancer demonstrate that our method is effective to identify key regulators of cancer progression or drug targets. The identified ACSS1 is experimentally validated to promote epithelial-to-mesenchymal transition of bladder cancer cells, and the predicted FOXM1-targets interactions are verified and are predictive of relapse in breast cancer. Our study suggests new effective ways to clinical transcriptomic data modeling for characterizing cancer progression and facilitates the translation of regulatory network-based approaches into precision medicine.

Identifying essential genes in comparison states (EGS) is vital to understanding cell differentiation, performing drug discovery, and identifying disease causes. Here, we present a machine learning method termed Prediction of Essential Genes in Comparison States (PreEGS). To capture the alteration of the network in comparison states, PreEGS extracts topological and gene expression features of each gene in a five-dimensional vector. PreEGS also recruits a positive sample expansion method to address the problem of unbalanced positive and negative samples, which is often encountered in practical applications. Different classifiers are applied to the simulated datasets, and the PreEGS based on the random forests model (PreEGSRF) was chosen for optimal performance. PreEGSRF was then compared with six other methods, including three machine learning methods, to predict EGS in a specific state. On real datasets with four gene regulatory networks, PreEGSRF predicted five essential genes related to leukemia and five enriched KEGG pathways. Four of the predicted essential genes and all predicted pathways were consistent with previous studies and highly correlated with leukemia. With high prediction accuracy and generalization ability, PreEGSRF is broadly applicable for the discovery of disease-causing genes, driver genes for cell fate decisions, and complex biomarkers of biological systems.

Differential network analysis has become an important approach in identifying driver genes in development and disease. However, most studies capture only local features of the underlying gene-regulatory network topology. These approaches are vulnerable to noise and other changes which mask driver-gene activity. Therefore, methods are urgently needed which can separate the impact of true regulatory elements from stochastic changes and downstream effects. We propose the differential network flow (DNF) method to identify key regulators of progression in development or disease. Given the network representation of consecutive biological states, DNF quantifies the essentiality of each node by differences in the distribution of network flow, which are capable of capturing comprehensive topological differences from local to global feature domains. DNF achieves more accurate driver-gene identification than other state-of-the-art methods when applied to four human datasets from The Cancer Genome Atlas and three single-cell RNA-seq datasets of murine neural and hematopoietic differentiation. Furthermore, we predict key regulators of crosstalk between separate networks underlying both neuronal differentiation and the progression of neurodegenerative disease, among which APP is predicted as a driver gene of neural stem cell differentiation. Our method is a new approach for quantifying the essentiality of genes across networks of different biological states.

Motivation: Single-cell RNA-sequencing (scRNA-seq) offers unprecedented resolution for studying cellular decision-making processes. Robust inference of cell state transition paths and probabilities is an important yet challenging step in the analysis of these data. Results: Here we present scEpath, an algorithm that calculates energy landscapes and probabilistic directed graphs in order to reconstruct developmental trajectories. We quantify the energy landscape using 'single-cell energy' and distance-based measures, and find that the combination of these enables robust inference of the transition probabilities and lineage relationships between cell states. We also identify marker genes and gene expression patterns associated with cell state transitions. Our approach produces pseudotemporal orderings that are-in combination-more robust and accurate than current methods, and offers higher resolution dynamics of the cell state transitions, leading to new insight into key transition events during differentiation and development. Moreover, scEpath is robust to variation in the size of the input gene set, and is broadly unsupervised, requiring few parameters to be set by the user. Applications of scEpath led to the identification of a cell-cell communication network implicated in early human embryo development, and novel transcription factors important for myoblast differentiation. scEpath allows us to identify common and specific temporal dynamics and transcriptional factor programs along branched lineages, as well as the transition probabilities that control cell fates. Availability and implementation: A MATLAB package of scEpath is available at https://github.com/sqjin/scEpath. Supplementary information: Supplementary data are available at Bioinformatics online.

The mammalian skin epidermis is a stratified epithelium composed of multiple layers of epithelial cells that exist in appropriate sizes and proportions, and with distinct boundaries separating each other. How the epidermis develops from a single layer of committed precursor cells to form a complex multilayered structure of multiple cell types remains elusive. Here, we construct stochastic, three-dimensional, and multiscale models consisting of a lineage of multiple cell types to study the control of epidermal development. Symmetric and asymmetric cell divisions, stochastic cell fate transitions within the lineage, extracellular morphogens, cell-to-cell adhesion forces, and cell signaling are included in model. A GPU algorithm was developed and implemented to accelerate the simulations. These simulations show that a balance between cell proliferation and differentiation during lineage progression is crucial for the development and maintenance of the epidermal tissue. We also find that selective intercellular adhesion is critical to sharpening the boundary between layers and to the formation of a highly ordered structure. The long-range action of a morphogen provides additional feedback regulations, enhancing the robustness of overall layer formation. Our model is built upon previous experimental findings revealing the role of Ovol transcription factors in regulating epidermal development. Direct comparisons of experimental and simulation perturbations show remarkable consistency. Taken together, our results highlight the major determinants of a well-stratified epidermis: balanced proliferation and differentiation, and a combination of both short- (symmetric/asymmetric division and selective cell adhesion) and long-range (morphogen) regulations. These underlying principles have broad implications for other developmental or regenerative processes leading to the formation of multilayered tissue structures, as well as for pathological processes such as epidermal wound healing.

How does pattern formation occur accurately when confronted with tissue growth and stochastic fluctuations (noise) in gene expression? Dorso-ventral (D-V) patterning of the mandibular arch specifies upper versus lower jaw skeletal elements through a combination of Bone morphogenetic protein (Bmp), Endothelin-1 (Edn1), and Notch signaling, and this system is highly robust. We combine NanoString experiments of early D-V gene expression with live imaging of arch development in zebrafish to construct a computational model of the D-V mandibular patterning network. The model recapitulates published genetic perturbations in arch development. Patterning is most sensitive to changes in Bmp signaling, and the temporal order of gene expression modulates the response of the patterning network to noise. Thus, our integrated systems biology approach reveals non-intuitive features of the complex signaling system crucial for craniofacial development, including novel insights into roles of gene expression timing and stochasticity in signaling and gene regulation.

An efficient and reliable network alignment serves to find the mapping with maximum similarity between different networks, which is a way to improve our understanding of biology system and biological process. To build such network alignment is a foremost challenging task in computational biology because it involves the bipartite graph matching problem, which is an NP-hard problem. In this work, we propose a novel global biomolecular network alignment method named NFMA. Based on the minimum cost maximum flow problem (MCMFP) of network flow model, NFMA introduces opposite numbers to address the maximum cost problem so that the new model can get the alignment with maximum similarity. Furthermore, based on the existing method used to describe topological structure in undirected network, we present a new measure to identify topological information in directed network, which enables NFMA to extend to alignment in directed network. We conduct three experiments on classical yeast protein-protein interaction networks (PINs) and human PINs. We compare NFMA with other 7 eminent algorithms, and prove that NFMA can obtain an efficient and meaningful alignment which takes both biological similarity and topological similarity into consideration, and the time efficiency of NFMA is also outstanding in that it only takes approximately 250 seconds to get an accurate alignment when aligning two large networks.

A critical event in mammalian embryo development is construction of an inner cell mass surrounded by a trophoectoderm (a shell of cells that later form extraembryonic structures). We utilize multi-scale, stochastic modeling to investigate the design principles responsible for robust establishment of these structures. This investigation makes three predictions, each supported by our quantitative imaging. First, stochasticity in the expression of critical genes promotes cell plasticity and has a critical role in accurately organizing the developing mouse blastocyst. Second, asymmetry in the levels of noise variation (expression fluctuation) of Cdx2 and Oct4 provides a means to gain the benefits of noise-mediated plasticity while ameliorating the potentially detrimental effects of stochasticity. Finally, by controlling the timing and pace of cell fate specification, the embryo temporally modulates plasticity and creates a time window during which each cell can continually read its environment and adjusts its fate. These results suggest noise has a crucial role in maintaining cellular plasticity and organizing the blastocyst.

A fundamental question in biology is how sharp boundaries of gene expression form precisely in spite of biological variation/noise. Numerous mechanisms position gene expression domains across fields of cells (e.g. morphogens), but how these domains are refined remains unclear. In some cases, domain boundaries sharpen through differential adhesion-mediated cell sorting. However, boundaries can also sharpen through cellular plasticity, with cell fate changes driven by up- or down-regulation of gene expression. In this context, we have argued that noise in gene expression can help cells transition to the correct fate. Here we investigate the efficacy of cell sorting, gene expression plasticity, and their combination in boundary sharpening using multi-scale, stochastic models. We focus on the formation of hindbrain segments (rhombomeres) in the developing zebrafish as an example, but the mechanisms investigated apply broadly to many tissues. Our results indicate that neither sorting nor plasticity is sufficient on its own to sharpen transition regions between different rhombomeres. Rather the two have complementary strengths and weaknesses, which synergize when combined to sharpen gene expression boundaries.

Survival information potential (SIP) is defined by the survival distribution function instead of the probability density function (PDF) of a random variable. SIP can be used as a risk function equipped with learning error compensation ability while this SIP based risk function does not involve the estimation of PDF. This is desirable for a robust learning application in view of the error compensation ability. The learning error compensation scheme provided by SIP requires rank information of learning errors. The accuracy of error compensation desires a large number of input data but is computationally expensive. It is shown that the error compensation can be approximated by an error-related distribution. Based on this approximation, a dictionary based error compensation scheme is proposed to obtain a fixed-budget recursive online learning method. This proposed method is compared with several well-known online learning methods including least-mean-square method, least absolute deviation method, affine projection algorithm, recursive least-mean-square method, and sliding window based SIP method. Simulation results validate the outstanding smooth and consistent convergence performance of the proposed method particularly in α-stable-noise environments.

Mating of budding yeast cells is a model system for studying cell-cell interactions. Haploid yeast cells secrete mating pheromones that are sensed by the partner which responds by growing a mating projection toward the source. The two projections meet and fuse to form the diploid. Successful mating relies on precise coordination of dynamic extracellular signals, signaling pathways, and cell shape changes in a noisy background. It remains elusive how cells mate accurately and efficiently in a natural multi-cell environment. Here we present the first stochastic model of multiple mating cells whose morphologies are driven by pheromone gradients and intracellular signals. Our novel computational framework encompassed a moving boundary method for modeling both a-cells and α-cells and their cell shape changes, the extracellular diffusion of mating pheromones dynamically coupled with cell polarization, and both external and internal noise. Quantification of mating efficiency was developed and tested for different model parameters. Computer simulations revealed important robustness strategies for mating in the presence of noise. These strategies included the polarized secretion of pheromone, the presence of the α-factor protease Bar1, and the regulation of sensing sensitivity; all were consistent with data in the literature. In addition, we investigated mating discrimination, the ability of an a-cell to distinguish between α-cells either making or not making α-factor, and mating competition, in which multiple a-cells compete to mate with one α-cell. Our simulations were consistent with previous experimental results. Moreover, we performed a combination of simulations and experiments to estimate the diffusion rate of the pheromone a-factor. In summary, we constructed a framework for simulating yeast mating with multiple cells in a noisy environment, and used this framework to reproduce mating behaviors and to identify strategies for robust cell-cell interactions.

It is challenging to obtain reliable and optimal mapping between networks for alignment algorithms when both nodal and topological structures are taken into consideration due to the underlying NP-hard problem. Here, we introduce an adaptive hybrid algorithm that combines the classical Hungarian algorithm and the Greedy algorithm (HGA) for the global alignment of biomolecular networks. With this hybrid algorithm, every pair of nodes with one in each network is first aligned based on node information (e.g., their sequence attributes) and then followed by an adaptive and convergent iteration procedure for aligning the topological connections in the networks. For four well-studied protein interaction networks, i.e., C.elegans, yeast, D.melanogaster, and human, applications of HGA lead to improved alignments in acceptable running time. The mapping between yeast and human PINs obtained by the new algorithm has the largest value of common gene ontology (GO) terms compared to those obtained by other existing algorithms, while it still has lower Mean normalized entropy (MNE) and good performances on several other measures. Overall, the adaptive HGA is effective and capable of providing good mappings between aligned networks in which the biological properties of both the nodes and the connections are important.

The epithelium of the small intestinal crypt, which has a vital role in protecting the underlying tissue from the harsh intestinal environment, is completely renewed every 4-5 days by a small pool of stem cells at the base of each crypt. How is this renewal controlled and homeostasis maintained, particularly given the rapid nature of this process? Here, based on the recent observations from in vitro "mini gut" studies, we use a hybrid stochastic model of the crypt to investigate how exogenous niche signaling (from Wnt and BMP) combines with auto-regulation to promote homeostasis. This model builds on the sub-cellular element method to account for the three-dimensional structure of the crypt, external regulation by Wnt and BMP, internal regulation by Notch signaling, as well as regulation by internally generated diffusible signals. Results show that Paneth cell derived Wnt signals, which have been observed experimentally to sustain crypts in cultured organs, have a dramatically different influence on niche dynamics than does mesenchyme derived Wnt. While this signaling can indeed act as a redundant backup to the exogenous gradient, it introduces a positive feedback that destabilizes the niche and causes its uncontrolled expansion. We find that in this setting, BMP has a critical role in constraining this expansion, consistent with observations that its removal leads to crypt fission. Further results also point to a new hypothesis for the role of Ephrin mediated motility of Paneth cells, specifically that it is required to constrain niche expansion and maintain the crypt's spatial structure. Combined, these provide an alternative view of crypt homeostasis where the niche is in a constant state of expansion and the spatial structure of the crypt arises as a balance between this expansion and the action of various sources of negative regulation that hold it in check.

Reversible epithelial-to-mesenchymal transition (EMT) is central to tissue development, epithelial stemness, and cancer metastasis. While many regulatory elements have been identified to induce EMT, the complex process underlying such cellular plasticity remains poorly understood. Utilizing a systems biology approach integrating modeling and experiments, we found multiple intermediate states contributing to EMT and that the robustness of the transitions is modulated by transcriptional factor Ovol2. In particular, we obtained evidence for a mutual inhibition relationship between Ovol2 and EMT inducer Zeb1, and observed that adding this regulation generates a novel four-state system consisting of two distinct intermediate phenotypes that differ in differentiation propensities and are favored in different environmental conditions. We identified epithelial cells that naturally exist in an intermediate state with bidirectional differentiation potential, and found the balance between EMT-promoting and -inhibiting factors to be critical in achieving and selecting between intermediate states. Our analysis suggests a new design principle in controlling cellular plasticity through multiple intermediate cell fates and underscores the critical involvement of Ovol2 and its associated molecular regulations.

In this paper, we present a novel technique, based on compressive sensing principles, for reconstruction and enhancement of multi-dimensional image data. Our method is a major improvement and generalization of the multi-scale sparsity based tomographic denoising (MSBTD) algorithm we recently introduced for reducing speckle noise. Our new technique exhibits several advantages over MSBTD, including its capability to simultaneously reduce noise and interpolate missing data. Unlike MSBTD, our new method does not require an a priori high-quality image from the target imaging subject and thus offers the potential to shorten clinical imaging sessions. This novel image restoration method, which we termed sparsity based simultaneous denoising and interpolation (SBSDI), utilizes sparse representation dictionaries constructed from previously collected datasets. We tested the SBSDI algorithm on retinal spectral domain optical coherence tomography images captured in the clinic. Experiments showed that the SBSDI algorithm qualitatively and quantitatively outperforms other state-of-the-art methods.

The phosphorylation of a substrate at multiple sites is a common protein modification that can give rise to important structural and electrostatic changes. Scaffold proteins can enhance protein phosphorylation by facilitating an interaction between a protein kinase enzyme and its target substrate. In this work we consider a simple mathematical model of a scaffold protein and show that under specific conditions, the presence of the scaffold can substantially raise the likelihood that the resulting system will exhibit bistable behavior. This phenomenon is especially pronounced when the enzymatic reactions have sufficiently large K(M), compared to the concentration of the target substrate. We also find for a closely related model that bistable systems tend to have a specific kinetic conformation. Using deficiency theory and other methods, we provide a number of necessary conditions for bistability, such as the presence of multiple phosphorylation sites and the dependence of the scaffold binding/unbinding rates on the number of phosphorylated sites.

Feedback modules, which appear ubiquitously in biological regulations, are often subject to disturbances from the input, leading to fluctuations in the output. Thus, the question becomes how a feedback system can produce a faithful response with a noisy input. We employed multiple time scale analysis, Fluctuation Dissipation Theorem, linear stability, and numerical simulations to investigate a module with one positive feedback loop driven by an external stimulus, and we obtained a critical quantity in noise attenuation, termed as "signed activation time". We then studied the signed activation time for a system of two positive feedback loops, a system of one positive feedback loop and one negative feedback loop, and six other existing biological models consisting of multiple components along with positive and negative feedback loops. An inverse relationship is found between the noise amplification rate and the signed activation time, defined as the difference between the deactivation and activation time scales of the noise-free system, normalized by the frequency of noises presented in the input. Thus, the combination of fast activation and slow deactivation provides the best noise attenuation, and it can be attained in a single positive feedback loop system. An additional positive feedback loop often leads to a marked decrease in activation time, decrease or slight increase of deactivation time and allows larger kinetic rate variations for slow deactivation and fast activation. On the other hand, a negative feedback loop may increase the activation and deactivation times. The negative relationship between the noise amplification rate and the signed activation time also holds for the six other biological models with multiple components and feedback loops. This principle may be applicable to other feedback systems.