Recent extensive studies of Escherichia coli (E. coli) chemotaxis have achieved a deep understanding of its mi- croscopic control dynamics. As a result, various quantitatively predictive models have been developed to ...Recent extensive studies of Escherichia coli (E. coli) chemotaxis have achieved a deep understanding of its mi- croscopic control dynamics. As a result, various quantitatively predictive models have been developed to describe the chemotactic behavior of E. coli motion. However, a population-level partial differential equation (PDE) that rationally incorporates such microscopic dynamics is still insufficient. Apart from the traditional Keller-Segel (K-S) equation, many existing population-level models developed from the microscopic dynamics are integro-PDEs. The difficulty comes mainly from cell tumbles which yield a velocity jumping process. Here, we propose a Langevin approximation method that avoids such a difficulty without appreciable loss of precision. The resulting model not only quantitatively repro- duces the results of pathway-based single-cell simulators, but also provides new inside information on the mechanism of E. coli chemotaxis. Our study demonstrates a possible alternative in establishing a simple population-level model that allows for the complex microscopic mechanisms in bacterial chemotaxis.展开更多
Stochastic modeling of biochemical reactions taking place at the cellular level has become the subject of intense research in recent years. Molecular interactions in a single cell exhibit random fluctuations. These fl...Stochastic modeling of biochemical reactions taking place at the cellular level has become the subject of intense research in recent years. Molecular interactions in a single cell exhibit random fluctuations. These fluctuations may be significant when small populations of some reacting species are present and then a stochastic description of the cellular dynamics is required. Often, the biochemically reacting systems encountered in applications consist of many species interacting through many reaction channels. Also, the dynamics of such systems is typically non-linear and presents multiple time-scales. Consequently, the stochastic mathematical models of biochemical systems can be quite complex and their analysis challenging. In this paper, we present a method to reduce a stochastic continuous model of well-stirred biochemical systems, the Chemical Langevin Equation, while preserving the overall behavior of the system. Several tests of our method on models of practical interest gave excellent results.展开更多
The Langevin approach has been applied to model the random open and closing dynamics of ion channels. It has long been known that the gate-based Langevin approach is not sufficiently accurate to reproduce the statisti...The Langevin approach has been applied to model the random open and closing dynamics of ion channels. It has long been known that the gate-based Langevin approach is not sufficiently accurate to reproduce the statistics of stochastic channel dynamics in Hodgkin–Huxley neurons. Here, we introduce a modified gate-based Langevin approach with rescaled noise strength to simulate stochastic channel dynamics. The rescaled independent gate and identical gate Langevin approaches improve the statistical results for the mean membrane voltage, inter-spike interval, and spike amplitude.展开更多
In the framework of classical trajectory model the Langevin random force is included in the mo-tion equations.The phase space distribution of an ensemble of trajectories for the <sup>58</sup>Ni+<sup>...In the framework of classical trajectory model the Langevin random force is included in the mo-tion equations.The phase space distribution of an ensemble of trajectories for the <sup>58</sup>Ni+<sup>58</sup>Ni reaction isgiven in the proximity model and Gross-Kalinowski model,respectively.The fusion probabilities for the<sup>100</sup>Mo+<sup>100</sup>Mo and <sup>86</sup>Kr+<sup>123</sup>Sb reactions are calculated by Monte Carlo sampling of Langevin trajectories.展开更多
An improved isospin dependent Boltzmann Langevin model,in which the inelastic channels and momentum dependent interactions are incorporated,is used to investigate the high-density behavior of nuclear symmetry energy.B...An improved isospin dependent Boltzmann Langevin model,in which the inelastic channels and momentum dependent interactions are incorporated,is used to investigate the high-density behavior of nuclear symmetry energy.By taking several forms of nuclear symmetry energy,we calculate the time evolutions of neutron over proton ratio,π multiplicity and π-/π+ ratio,and the kinetic energy and transverse momentum spectra of π-/π+ ratio in the heavy ion collisions at 400A MeV.It is found that the neutron over proton ratio and π-/π+ ratio are very sensitive to the nuclear symmetry energy,and the π-is more sensitive to the nuclear symmetry energy than the π+.A supersoft symmetry energy results in a larger π-/π+ ratio.展开更多
文摘Recent extensive studies of Escherichia coli (E. coli) chemotaxis have achieved a deep understanding of its mi- croscopic control dynamics. As a result, various quantitatively predictive models have been developed to describe the chemotactic behavior of E. coli motion. However, a population-level partial differential equation (PDE) that rationally incorporates such microscopic dynamics is still insufficient. Apart from the traditional Keller-Segel (K-S) equation, many existing population-level models developed from the microscopic dynamics are integro-PDEs. The difficulty comes mainly from cell tumbles which yield a velocity jumping process. Here, we propose a Langevin approximation method that avoids such a difficulty without appreciable loss of precision. The resulting model not only quantitatively repro- duces the results of pathway-based single-cell simulators, but also provides new inside information on the mechanism of E. coli chemotaxis. Our study demonstrates a possible alternative in establishing a simple population-level model that allows for the complex microscopic mechanisms in bacterial chemotaxis.
文摘Stochastic modeling of biochemical reactions taking place at the cellular level has become the subject of intense research in recent years. Molecular interactions in a single cell exhibit random fluctuations. These fluctuations may be significant when small populations of some reacting species are present and then a stochastic description of the cellular dynamics is required. Often, the biochemically reacting systems encountered in applications consist of many species interacting through many reaction channels. Also, the dynamics of such systems is typically non-linear and presents multiple time-scales. Consequently, the stochastic mathematical models of biochemical systems can be quite complex and their analysis challenging. In this paper, we present a method to reduce a stochastic continuous model of well-stirred biochemical systems, the Chemical Langevin Equation, while preserving the overall behavior of the system. Several tests of our method on models of practical interest gave excellent results.
基金Project supported by the National Natural Science Foundation for Distinguished Young Scholars of China(Grant No.11125419)the National Natural Science Foundation of China(Grant No.10925525)+1 种基金the Funds for the Leading Talents of Fujian ProvinceChina
文摘The Langevin approach has been applied to model the random open and closing dynamics of ion channels. It has long been known that the gate-based Langevin approach is not sufficiently accurate to reproduce the statistics of stochastic channel dynamics in Hodgkin–Huxley neurons. Here, we introduce a modified gate-based Langevin approach with rescaled noise strength to simulate stochastic channel dynamics. The rescaled independent gate and identical gate Langevin approaches improve the statistical results for the mean membrane voltage, inter-spike interval, and spike amplitude.
基金The project supported by the National Natural Science Foundation of China
文摘In the framework of classical trajectory model the Langevin random force is included in the mo-tion equations.The phase space distribution of an ensemble of trajectories for the <sup>58</sup>Ni+<sup>58</sup>Ni reaction isgiven in the proximity model and Gross-Kalinowski model,respectively.The fusion probabilities for the<sup>100</sup>Mo+<sup>100</sup>Mo and <sup>86</sup>Kr+<sup>123</sup>Sb reactions are calculated by Monte Carlo sampling of Langevin trajectories.
基金Supported by National Natural Science Foundation of China(NSFC) projects (Nos.11025524 and 11161130520)National Basic Research Program of China(No.2010CB832903)
文摘An improved isospin dependent Boltzmann Langevin model,in which the inelastic channels and momentum dependent interactions are incorporated,is used to investigate the high-density behavior of nuclear symmetry energy.By taking several forms of nuclear symmetry energy,we calculate the time evolutions of neutron over proton ratio,π multiplicity and π-/π+ ratio,and the kinetic energy and transverse momentum spectra of π-/π+ ratio in the heavy ion collisions at 400A MeV.It is found that the neutron over proton ratio and π-/π+ ratio are very sensitive to the nuclear symmetry energy,and the π-is more sensitive to the nuclear symmetry energy than the π+.A supersoft symmetry energy results in a larger π-/π+ ratio.
