One of the major challenges in single-cell data analysis is the determination of cellular developmental trajectories using single-cell data.Although substantial studies have been conducted in recent years,more effecti...One of the major challenges in single-cell data analysis is the determination of cellular developmental trajectories using single-cell data.Although substantial studies have been conducted in recent years,more effective methods are still strongly needed to infer the developmental processes accurately.This work devises a new method,named DTFLOW,for determining the pseudotemporal trajectories with multiple branches.DTFLOW consists of two major steps:a new method called Bhattacharyya kernel feature decomposition(BKFD)to reduce the data dimensions,and a novel approach named Reverse Searching on k-nearest neighbor graph(RSKG)to identify the multi-branching processes of cellular differentiation.In BKFD,we first establish a stationary distribution for each cell to represent the transition of cellular developmental states based on the random walk with restart algorithm,and then propose a new distance metric for calculating pseudotime of single cells by introducing the Bhattacharyya kernel matrix.The effectiveness of DTFLOW is rigorously examined by using four single-cell datasets.We compare the efficiency of DTFLOW with the published state-of-the-art methods.Simulation results suggest that DTFLOW has superior accuracy and strong robustness properties for constructing pseudotime trajectories.The Python source code of DTFLOW can be freely accessed at https://github.com/statway/DTFLOW.展开更多
Gene expression is a complex biochemical process, involving many specific processes such as transcription, translation, switching between promoter states, and regulation. All these biochemical processes inevitably lea...Gene expression is a complex biochemical process, involving many specific processes such as transcription, translation, switching between promoter states, and regulation. All these biochemical processes inevitably lead to fluctuations in mRNA and protein abundances. This noise has been identified as an important factor underlying the observed phenotypic variability of genetically identical cells in homogeneous environments. Quantifying the contributions of different sources of noise using stochastic models of gene expression is an important step towards understanding fundamental cellular processes and cell-to-cell variability in expression levels. In this paper, we review progresses in quantitative study of simple gene expression systems, including some results that we have not published. We analytically show how specific processes associated with gene expression affect expression levels. In particular, we derive the analytical decomposition of expression noise, which is important for understanding the roles of the factorial noise in controlling phenotypic variability. We also introduce a new index （called attribute factor） to quantify expression noise, which has more advantages than the commonly-used noise indices such as noise intensity and Fano factor.展开更多
Stochasticity in gene expression can result in fluctuations in gene product levels. Recent experiments indicated that feedback regulation plays an important role in controlling the noise in gene expression.A quantitat...Stochasticity in gene expression can result in fluctuations in gene product levels. Recent experiments indicated that feedback regulation plays an important role in controlling the noise in gene expression.A quantitative understanding of the feedback effect on gene expression requires analysis of the corresponding stochastic model. However, for stochastic models of gene expression with general regulation functions, exact analytical results for gene product distributions have not been given so far. Here, we propose a technique to solve a generalized ON-OFF model of stochastic gene expression with arbitrary(positive or negative, linear or nonlinear) feedbacks including posttranscriptional or posttranslational regulation. The obtained results, which generalize results obtained previously, provide new insights into the role of feedback in regulating gene expression. The proposed analytical framework can easily be extended to analysis of more complex models of stochastic gene expression.展开更多
In biological development, morphogens are locally produced and spread to other regions in organs, forming gradients that control the inter-related pattern and growth of developing organs. Mechanisms of morphogen trans...In biological development, morphogens are locally produced and spread to other regions in organs, forming gradients that control the inter-related pattern and growth of developing organs. Mechanisms of morphogen transport were built and investigated by numerical simulations in [A. D. Lander, Q. Nie and F. Y. M. Wan, Do morphogen gradients arise by diffusion？ Developmental Cell 2 （2002） 785-796]. In that paper, model C, which considers endocytosis, exocytosis and receptor synthesis and degradation, is in a one-dimensional spatial region and couples a partial differential equation with ordinary differential equations. Here, this model is promoted to an arbitrary dimension bounded region. We prove existence, uniqueness and non-negativity of a global solution for this advanced model, of its steady-state solution and linear stability of steady state by operator semigroup, the Schauder theorem and local perturbation method. Our results improve previous results for this model in a one dimension region.展开更多
基金the National Natural Science Foundation of China(Grant Nos.11571368,11931019,11775314,and 11871238)the Fundamental Research Funds for the Central Universities,China(Grant No.2662019QD031).
文摘One of the major challenges in single-cell data analysis is the determination of cellular developmental trajectories using single-cell data.Although substantial studies have been conducted in recent years,more effective methods are still strongly needed to infer the developmental processes accurately.This work devises a new method,named DTFLOW,for determining the pseudotemporal trajectories with multiple branches.DTFLOW consists of two major steps:a new method called Bhattacharyya kernel feature decomposition(BKFD)to reduce the data dimensions,and a novel approach named Reverse Searching on k-nearest neighbor graph(RSKG)to identify the multi-branching processes of cellular differentiation.In BKFD,we first establish a stationary distribution for each cell to represent the transition of cellular developmental states based on the random walk with restart algorithm,and then propose a new distance metric for calculating pseudotime of single cells by introducing the Bhattacharyya kernel matrix.The effectiveness of DTFLOW is rigorously examined by using four single-cell datasets.We compare the efficiency of DTFLOW with the published state-of-the-art methods.Simulation results suggest that DTFLOW has superior accuracy and strong robustness properties for constructing pseudotime trajectories.The Python source code of DTFLOW can be freely accessed at https://github.com/statway/DTFLOW.
文摘Gene expression is a complex biochemical process, involving many specific processes such as transcription, translation, switching between promoter states, and regulation. All these biochemical processes inevitably lead to fluctuations in mRNA and protein abundances. This noise has been identified as an important factor underlying the observed phenotypic variability of genetically identical cells in homogeneous environments. Quantifying the contributions of different sources of noise using stochastic models of gene expression is an important step towards understanding fundamental cellular processes and cell-to-cell variability in expression levels. In this paper, we review progresses in quantitative study of simple gene expression systems, including some results that we have not published. We analytically show how specific processes associated with gene expression affect expression levels. In particular, we derive the analytical decomposition of expression noise, which is important for understanding the roles of the factorial noise in controlling phenotypic variability. We also introduce a new index （called attribute factor） to quantify expression noise, which has more advantages than the commonly-used noise indices such as noise intensity and Fano factor.
基金supported by National Natural Science Foundation of China (Grant Nos. 11931019, 11775314 and 91530320)
文摘Stochasticity in gene expression can result in fluctuations in gene product levels. Recent experiments indicated that feedback regulation plays an important role in controlling the noise in gene expression.A quantitative understanding of the feedback effect on gene expression requires analysis of the corresponding stochastic model. However, for stochastic models of gene expression with general regulation functions, exact analytical results for gene product distributions have not been given so far. Here, we propose a technique to solve a generalized ON-OFF model of stochastic gene expression with arbitrary(positive or negative, linear or nonlinear) feedbacks including posttranscriptional or posttranslational regulation. The obtained results, which generalize results obtained previously, provide new insights into the role of feedback in regulating gene expression. The proposed analytical framework can easily be extended to analysis of more complex models of stochastic gene expression.
文摘In biological development, morphogens are locally produced and spread to other regions in organs, forming gradients that control the inter-related pattern and growth of developing organs. Mechanisms of morphogen transport were built and investigated by numerical simulations in [A. D. Lander, Q. Nie and F. Y. M. Wan, Do morphogen gradients arise by diffusion？ Developmental Cell 2 （2002） 785-796]. In that paper, model C, which considers endocytosis, exocytosis and receptor synthesis and degradation, is in a one-dimensional spatial region and couples a partial differential equation with ordinary differential equations. Here, this model is promoted to an arbitrary dimension bounded region. We prove existence, uniqueness and non-negativity of a global solution for this advanced model, of its steady-state solution and linear stability of steady state by operator semigroup, the Schauder theorem and local perturbation method. Our results improve previous results for this model in a one dimension region.
