This paper mainly studies the stochastic character of tumor growth in the presence of immune response and periodically pulsed chemotherapy.First,a stochastic impulsive model describing the interaction and competition ...This paper mainly studies the stochastic character of tumor growth in the presence of immune response and periodically pulsed chemotherapy.First,a stochastic impulsive model describing the interaction and competition among normal cells,tumor cells and immune cells under periodically pulsed chemotherapy is established.Then,sufficient conditions for the extinction,non-persistence in the mean,weak and strong persistence in the mean of tumor cells are obtained.Finally,numerical simulations are performed which not only verify the theoretical results derived but also reveal some specific features.The results show that the growth trend of tumor cells is significantly affected by the intensity of noise and the frequency and dose of drug deliveries.In clinical practice,doctors can reduce the randomness of the environment and increase the intensity of drug input to inhibit the proliferation and growth of tumor cells.展开更多
This paper proposes a high order deep domain decomposition method(HOrderDeepDDM)for solving high-frequency interface problems,which combines high order deep neural network(HOrderDNN)with domain decomposition method(DD...This paper proposes a high order deep domain decomposition method(HOrderDeepDDM)for solving high-frequency interface problems,which combines high order deep neural network(HOrderDNN)with domain decomposition method(DDM).The main idea of HOrderDeepDDM is to divide the computational domain into some sub-domains by DDM,and apply HOrderDNNs to solve the high-frequency problem on each sub-domain.Besides,we consider an adaptive learning rate annealing method to balance the errors inside the sub-domains,on the interface and the boundary during the optimization process.The performance of HOrderDeepDDM is evaluated on high-frequency elliptic and Helmholtz interface problems.The results indicate that:HOrderDeepDDM inherits the ability of DeepDDM to handle discontinuous interface problems and the power of HOrderDNN to approximate high-frequency problems.In detail,HOrderDeepDDMs(p>1)could capture the high-frequency information very well.When compared to the deep domain decomposition method(DeepDDM),HOrderDeepDDMs(p>1)converge faster and achieve much smaller relative errors with the same number of trainable parameters.For example,when solving the high-frequency interface elliptic problems in Section 3.3.1,the minimum relative errors obtained by HOrderDeepDDMs(p=9)are one order of magnitude smaller than that obtained by DeepDDMs when the number of the parameters keeps the same,as shown in Fig.4.展开更多
The determination of cell fate is one of the key questions of developmental biology. Recent experiments showed that feedforward regulation is a novel feature of regulatory networks that controls reversible cellular tr...The determination of cell fate is one of the key questions of developmental biology. Recent experiments showed that feedforward regulation is a novel feature of regulatory networks that controls reversible cellular transitions. However, the underlying mechanism of feedforward regulation-mediated cell fate decision is still unclear. Therefore, using experimental data, we develop a full mathematical model of the molecular network responsible for cell fate selection in budding yeast. To validate our theoretical model, we first investigate the dynamical behaviors of key proteins at the Start transition point and the G1/S transition point; a crucial three-node motif consisting of cyclin (Clnl/2), Substrate/Subunit Inhibitor of cyclin-dependent protein kinase (Sic1) and cyclin B (C165/6) is considered at these points. The rapid switches of these important components between high and low levels at two transition check points are demonstrated reasonably by our model. Many experimental observations about cell fate decision and cell size control are also theoretically reproduced. Interestingly, the feedforward regulation provides a reliable separation between different cell fates. Next, our model reveals that the threshold for the amount of WHiskey OVhi5) removed from the nucleus is higher at the Reentry point in pheromone-arrested cells compared with that at the Start point in cycling cells. Furthermore, we analyze the hysteresis in the cell cycle kinetics in response to changes in pheromone concentration, showing that Cln3 is the primary driver of reentry and Clnl/2 is the secondary driver of reentry. In particular, we demonstrate that the inhibition of C1nl/2 due to the accumulation of Factor ARrest (Far1) directly reinforces arrest. Finally, theoretical work verifies that the three-node coherent feedforward motif created by cell FUSion (Fus3), Farl and STErile (Stel2) ensures the rapid arrest and reversibility of a cellular state. The combination of our theoretical model and the previous experimental data contributes to the understanding of the molecular mechanisms of the cell fate decision at the G1 phase in budding yeast and will stimulate further biological experiments in future.展开更多
This paper proposes a high order deep neural network(HOrderDNN)for solving high frequency partial differential equations(PDEs),which incorporates the idea of“high order”from finite element methods(FEMs)into commonly...This paper proposes a high order deep neural network(HOrderDNN)for solving high frequency partial differential equations(PDEs),which incorporates the idea of“high order”from finite element methods(FEMs)into commonly-used deep neural networks(DNNs)to obtain greater approximation ability.The main idea of HOrderDNN is introducing a nonlinear transformation layer between the input layer and the first hidden layer to form a high order polynomial space with the degree not exceeding p,followed by a normal DNN.The order p can be guided by the regularity of solutions of PDEs.The performance of HOrderDNNis evaluated on high frequency function fitting problems and high frequency Poisson and Helmholtz equations.The results demonstrate that:HOrderDNNs(p>1)can efficiently capture the high frequency information in target functions;and when compared to physics-informed neural network(PINN),HOrderDNNs(p>1)converge faster and achieve much smaller relative errors with same number of trainable parameters.In particular,when solving the high frequency Helmholtz equation in Section 3.5,the relative error of PINN stays around 1 with its depth and width increase,while the relative error can be reduced to around 0.02 as p increases(see Table 5).展开更多
Respiratory syncytial virus(RSV) is the major cause of lower respiratory tract infections in children. Inactivated RSV vaccine was developed in the late 1960’s, but the vaccine-enhanced disease(VED) occurred to vacci...Respiratory syncytial virus(RSV) is the major cause of lower respiratory tract infections in children. Inactivated RSV vaccine was developed in the late 1960’s, but the vaccine-enhanced disease(VED) occurred to vaccinated infants upon subsequent natural RSV infection. The excessive inflammatory immunopathology in the lungs might be involved in the VED, but the underlying mechanisms remain not fully understood. In this study, we utilized UV-inactivated RSV in the prime/boost approach followed by RSV challenge in BALB/c mice to mimic RSV VED. The dynamic virus load,cytokines, histology and transcriptome profiles in lung tissues of mice were investigated from day 1 to day 6 post-infection.Compared to PBS-treated mice, UV-RSV vaccination leads to a Th2 type inflammatory response characterized by enhanced histopathology, reduced Treg cells and increased IL4^(+)CD4 T cells in the lung. Enhanced production of several Th2 type cytokines(IL-4, IL-5, IL-10) and TGF-b, reduction of IL-6 and IL-17 were observed in UV-RSV vaccinated mice. A total of 5582 differentially expressed(DE) genes between PBS-treated or vaccinated mice and na?ve mice were identified by RNA-Seq. Eleven conserved high-influential modules(HMs) were recognized, majorly grouped into regulatory networks related to cell cycle and cell metabolism, signal transduction, immune and inflammatory responses. At an early time post-infection, the vaccinated mice showed obvious decreased expression patterns of DE genes in 11 HMs compared to PBS-treated mice. The extracellular matrix(HM5) and immune responses(HM8) revealed tremendous differences in expression and regulation characteristics of transcripts between PBS-treated and vaccinated mice at both early and late time points. The highly connected genes in HM5 and HM8 networks were further validated by RT-qPCR.These findings reveal the relationship between RSV VED and immune responses, which could benefit the development of novel RSV vaccines.展开更多
Correction to:Virologica Sinica https://doi.org/10.1007/s12250-021-00418-3 The original version of this article,published online on June 17,2021,contained a mistake in Supplementary Table S5.The correct Supplementary ...Correction to:Virologica Sinica https://doi.org/10.1007/s12250-021-00418-3 The original version of this article,published online on June 17,2021,contained a mistake in Supplementary Table S5.The correct Supplementary Table S5 is given below.展开更多
基金supported by the National Natural Science Foundation of China(12071407,11901502)Training plan for young backbone teachers in Henan Province(2019GGJS157)+3 种基金Foundation of Henan Educational Committee under Contract(21A110022)Program for Science&Technology Innovation Talents in Universities of Henan Province(21HASTIT026)Scientific and Technological Key Projects of Henan Province(212102110025)Nanhu Scholars Program for Young Scholars of XYNU。
文摘This paper mainly studies the stochastic character of tumor growth in the presence of immune response and periodically pulsed chemotherapy.First,a stochastic impulsive model describing the interaction and competition among normal cells,tumor cells and immune cells under periodically pulsed chemotherapy is established.Then,sufficient conditions for the extinction,non-persistence in the mean,weak and strong persistence in the mean of tumor cells are obtained.Finally,numerical simulations are performed which not only verify the theoretical results derived but also reveal some specific features.The results show that the growth trend of tumor cells is significantly affected by the intensity of noise and the frequency and dose of drug deliveries.In clinical practice,doctors can reduce the randomness of the environment and increase the intensity of drug input to inhibit the proliferation and growth of tumor cells.
基金supported partly by National Key R&D Program of China(grants Nos.2019YFA0709600 and 2019YFA0709602)National Natural Science Foundation of China(grants Nos.11831016 and 12101609)the Innovation Foundation of Qian Xuesen Laboratory of Space Technology。
文摘This paper proposes a high order deep domain decomposition method(HOrderDeepDDM)for solving high-frequency interface problems,which combines high order deep neural network(HOrderDNN)with domain decomposition method(DDM).The main idea of HOrderDeepDDM is to divide the computational domain into some sub-domains by DDM,and apply HOrderDNNs to solve the high-frequency problem on each sub-domain.Besides,we consider an adaptive learning rate annealing method to balance the errors inside the sub-domains,on the interface and the boundary during the optimization process.The performance of HOrderDeepDDM is evaluated on high-frequency elliptic and Helmholtz interface problems.The results indicate that:HOrderDeepDDM inherits the ability of DeepDDM to handle discontinuous interface problems and the power of HOrderDNN to approximate high-frequency problems.In detail,HOrderDeepDDMs(p>1)could capture the high-frequency information very well.When compared to the deep domain decomposition method(DeepDDM),HOrderDeepDDMs(p>1)converge faster and achieve much smaller relative errors with the same number of trainable parameters.For example,when solving the high-frequency interface elliptic problems in Section 3.3.1,the minimum relative errors obtained by HOrderDeepDDMs(p=9)are one order of magnitude smaller than that obtained by DeepDDMs when the number of the parameters keeps the same,as shown in Fig.4.
基金ACKNOWLEDGMENTS This work was supported by the Major Research Plan of the National Natural Science Foundation of China (No. 91230118 and No.91330113) and the National Natural Science Foundation of China (No.11275259 and No. 61173060).
文摘The determination of cell fate is one of the key questions of developmental biology. Recent experiments showed that feedforward regulation is a novel feature of regulatory networks that controls reversible cellular transitions. However, the underlying mechanism of feedforward regulation-mediated cell fate decision is still unclear. Therefore, using experimental data, we develop a full mathematical model of the molecular network responsible for cell fate selection in budding yeast. To validate our theoretical model, we first investigate the dynamical behaviors of key proteins at the Start transition point and the G1/S transition point; a crucial three-node motif consisting of cyclin (Clnl/2), Substrate/Subunit Inhibitor of cyclin-dependent protein kinase (Sic1) and cyclin B (C165/6) is considered at these points. The rapid switches of these important components between high and low levels at two transition check points are demonstrated reasonably by our model. Many experimental observations about cell fate decision and cell size control are also theoretically reproduced. Interestingly, the feedforward regulation provides a reliable separation between different cell fates. Next, our model reveals that the threshold for the amount of WHiskey OVhi5) removed from the nucleus is higher at the Reentry point in pheromone-arrested cells compared with that at the Start point in cycling cells. Furthermore, we analyze the hysteresis in the cell cycle kinetics in response to changes in pheromone concentration, showing that Cln3 is the primary driver of reentry and Clnl/2 is the secondary driver of reentry. In particular, we demonstrate that the inhibition of C1nl/2 due to the accumulation of Factor ARrest (Far1) directly reinforces arrest. Finally, theoretical work verifies that the three-node coherent feedforward motif created by cell FUSion (Fus3), Farl and STErile (Stel2) ensures the rapid arrest and reversibility of a cellular state. The combination of our theoretical model and the previous experimental data contributes to the understanding of the molecular mechanisms of the cell fate decision at the G1 phase in budding yeast and will stimulate further biological experiments in future.
基金supported partly by National Key R&D Program of China with grants 2019YFA0709600,2019YFA0709602National Natural Science Foundation of China with grants 11831016,12101609the Innovation Foundation of Qian Xuesen Laboratory of Space Technology.
文摘This paper proposes a high order deep neural network(HOrderDNN)for solving high frequency partial differential equations(PDEs),which incorporates the idea of“high order”from finite element methods(FEMs)into commonly-used deep neural networks(DNNs)to obtain greater approximation ability.The main idea of HOrderDNN is introducing a nonlinear transformation layer between the input layer and the first hidden layer to form a high order polynomial space with the degree not exceeding p,followed by a normal DNN.The order p can be guided by the regularity of solutions of PDEs.The performance of HOrderDNNis evaluated on high frequency function fitting problems and high frequency Poisson and Helmholtz equations.The results demonstrate that:HOrderDNNs(p>1)can efficiently capture the high frequency information in target functions;and when compared to physics-informed neural network(PINN),HOrderDNNs(p>1)converge faster and achieve much smaller relative errors with same number of trainable parameters.In particular,when solving the high frequency Helmholtz equation in Section 3.5,the relative error of PINN stays around 1 with its depth and width increase,while the relative error can be reduced to around 0.02 as p increases(see Table 5).
基金This work was supported by the National key R&D program of China(2017YFA0505801)the National Natural Science Foundation of China(11831015)。
文摘Respiratory syncytial virus(RSV) is the major cause of lower respiratory tract infections in children. Inactivated RSV vaccine was developed in the late 1960’s, but the vaccine-enhanced disease(VED) occurred to vaccinated infants upon subsequent natural RSV infection. The excessive inflammatory immunopathology in the lungs might be involved in the VED, but the underlying mechanisms remain not fully understood. In this study, we utilized UV-inactivated RSV in the prime/boost approach followed by RSV challenge in BALB/c mice to mimic RSV VED. The dynamic virus load,cytokines, histology and transcriptome profiles in lung tissues of mice were investigated from day 1 to day 6 post-infection.Compared to PBS-treated mice, UV-RSV vaccination leads to a Th2 type inflammatory response characterized by enhanced histopathology, reduced Treg cells and increased IL4^(+)CD4 T cells in the lung. Enhanced production of several Th2 type cytokines(IL-4, IL-5, IL-10) and TGF-b, reduction of IL-6 and IL-17 were observed in UV-RSV vaccinated mice. A total of 5582 differentially expressed(DE) genes between PBS-treated or vaccinated mice and na?ve mice were identified by RNA-Seq. Eleven conserved high-influential modules(HMs) were recognized, majorly grouped into regulatory networks related to cell cycle and cell metabolism, signal transduction, immune and inflammatory responses. At an early time post-infection, the vaccinated mice showed obvious decreased expression patterns of DE genes in 11 HMs compared to PBS-treated mice. The extracellular matrix(HM5) and immune responses(HM8) revealed tremendous differences in expression and regulation characteristics of transcripts between PBS-treated and vaccinated mice at both early and late time points. The highly connected genes in HM5 and HM8 networks were further validated by RT-qPCR.These findings reveal the relationship between RSV VED and immune responses, which could benefit the development of novel RSV vaccines.
文摘Correction to:Virologica Sinica https://doi.org/10.1007/s12250-021-00418-3 The original version of this article,published online on June 17,2021,contained a mistake in Supplementary Table S5.The correct Supplementary Table S5 is given below.