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## A Multi-Algorithm, Multi-Timescale Method for Cell Simulation (2004)

Citations: | 55 - 5 self |

### Citations

3104 |
Numerical Recipes in C: The Art of Scientific Computing
- Press, Teukolsky, et al.
- 1993
(Show Context)
Citation Context ...ons required by the algorithm is seven for starting up, and six or seven during the simulation. The step method Λ for these ODE modules are implemented with a standard adaptive step sizing mechanism =-=(Press et al., 2002). In additi-=-on, time step sizes are constrained by the following condition to ensure that the Stepper does not change variable values too much at once in a single step: ∀j ∈ ˆ Ri : xjɛrel + ɛabs ≥ � δ... |

1045 | Mersenne twister: a 623-dimensionally equidistributed uniform pseudo-random number generator
- Matsumoto, Nishimura
- 1998
(Show Context)
Citation Context ...s θ be the expected time for the reactant of the current Process with the smallest population to change its value by 10 %. If precision precedes efficiency, set ξ = 0. The Mersenne-Twister algorithm=-= (Matsumoto and Nishimura, 1998-=-) has been employed as a pseudo-random number generator. 5 4 Results Two relatively simple models have been constructed to examine the performance of the meta-algorithm. The first is a model of the he... |

779 |
A general method for numerically simulating the stochastic time evolution of coupled chemical reactions
- Gillespie
- 1976
(Show Context)
Citation Context ..., 2002). In addition to those continuous representations, discrete formulation is often used. Stochastic discrete event simulation of coupled chemical reactions was pioneered by Gillespie and others (=-=Gillespie, 1976-=-), and improved by Gibson (Gibson and Bruck, 2000) to work more efficiently. StochSim is a discrete-time stochastic simulation algorithm originally devised as a means of investigating the bacterial ch... |

427 | Efficient exact stochastic simulation of chemical systems with many species and many channels
- Gibson, Bruck
(Show Context)
Citation Context ...epresentations, discrete formulation is often used. Stochastic discrete event simulation of coupled chemical reactions was pioneered by Gillespie and others (Gillespie, 1976), and improved by Gibson (=-=Gibson and Bruck, 2000-=-) to work more efficiently. StochSim is a discrete-time stochastic simulation algorithm originally devised as a means of investigating the bacterial chemotaxis signaling pathway (Morton-Firth and Bray... |

416 |
Numerical Initial Value Problems in Ordinary Differential Equations
- Gear
- 1973
(Show Context)
Citation Context ...on of cellular processes. By far the most widely accepted scheme of describing continuous dynamical systems is representation by differential equations. Apart from standard generic solver algorithms (=-=Gear, 1971-=-), specialized methods are often used for S-System and Generalized Mass-Action (GMA) canonical forms of power-law differential systems in simulations of metabolic and gene regulations (Irvine and Sava... |

241 |
A family of embedded Runge-Kutta formulae
- Dormand, Prince
(Show Context)
Citation Context ...ave been implemented: second-order Fehlberg with a third-order error estimation (Fehlberg 2(3)) (Fehlberg, 1969), and fourth-order Dormand-Prince with a fifth-order error term (DormandPrince 5(4)7M) (=-=Dormand and Prince, 1980). For -=-some integration algorithms including these two, it is possible to derive interpolants by using Hermite polynomial interpolation, the general form of which is: g(x) = � � (j) i j αi,j(x)f i , �... |

181 |
Control, exploitation and tolerance of intracellular noise. Nature
- Rao, Wolf, et al.
- 2002
(Show Context)
Citation Context ... factor in the behavior of the system (Singer, 1953). ODE models isolate the biochemical system into a group of deterministic and continuous reactions, and tacitly ignore fluctuations in the pathway (=-=Rao et al., 2002-=-). With identical parameter settings, the stochastic and deterministic models can produce different results, and stochastic models are generally believed to be more accurate (Marion et. al., 1998; Sri... |

120 | Escherichia coli and Salmonella: Cellular and - Neidhardt - 1996 |

81 |
Predicting temporal fluctuations in an intracellular signaling pathway
- CJ, Bray
- 1998
(Show Context)
Citation Context ...ibson and Bruck, 2000) to work more efficiently. StochSim is a discrete-time stochastic simulation algorithm originally devised as a means of investigating the bacterial chemotaxis signaling pathway (=-=Morton-Firth and Bray, 1998-=-). Simulation methods based on cellular automaton have many applications from reactive gas physics to sociology, and have been found to be very useful for biological simulations (for example, see Weim... |

62 |
Stochastic vs. deterministic modeling of intracellular viral kinetics
- Srivastava, You, et al.
(Show Context)
Citation Context ...002). With identical parameter settings, the stochastic and deterministic models can produce different results, and stochastic models are generally believed to be more accurate (Marion et. al., 1998; =-=Srivastava et al., 2002).-=- Despite its advantages, however, Gillespie’s scheme of exact stochastic simulation has limited utility due to its computational cost which is proportional to the number of molecules. The composite ... |

58 | A cycle of binding and release of the DnaK, DnaJ and GrpE chaperones regulates activity of the E.coli heat shock transcription factor sigma 32. - Gamer, Multhaup, et al. - 1996 |

48 |
Low-order classical Runge-Kutta formulas with stepsize control and their application to some heat transfer problems,” tech. rep
- Fehlberg
- 1969
(Show Context)
Citation Context ...e algorithm. Two instances of embedded explicit Runge-Kutta algorithms with dense output capabilities have been implemented: second-order Fehlberg with a third-order error estimation (Fehlberg 2(3)) (=-=Fehlberg, 1969-=-), and fourth-order Dormand-Prince with a fifth-order error term (DormandPrince 5(4)7M) (Dormand and Prince, 1980). For some integration algorithms including these two, it is possible to derive interp... |

40 |
W.E.: Stochastic kinetic analysis of the escherichia coli stress circuit using σ32-targeted antisense.
- Srivastava, Peterson, et al.
- 2001
(Show Context)
Citation Context ...e of a composite simulation scheme, we set up a pure stochastic model, a pure ODE model and a stochastic/ODE composite model, based on Srivastava’s stochastic petri net model of the E.coli heatshock=-= (Srivastava et al., 2001-=-). Protein folding/unfolding processes have been added to the model, and modeled as differential equations in the ODE and composite models, and using the Gillespie algorithm in the stochastic model (F... |

32 | Some practical Runge-Kutta formulas, - Shampine - 1986 |

29 |
Efficient solution of nonlinear ordinary differential-equations expressed in S-system canonical
- Irvine, Savageau
- 1990
(Show Context)
Citation Context ...hms (Gear, 1971), specialized methods are often used for S-System and Generalized Mass-Action (GMA) canonical forms of power-law differential systems in simulations of metabolic and gene regulations (=-=Irvine and Savageau, 1990-=-). To complement a lack of quantitative kinetic data, an attempt to marry dynamic rate-equation based continuous models and static flux balance from stoichiometry is ongoing (Yugi et al., 2002). In ad... |

23 | Function and regulation of the heat shock proteins. - Gross - 1996 |

14 |
Applications of the theory of stochastic processes to the stud y of irreproducible chemical reactions and nuclea tion processes
- Singer
- 1953
(Show Context)
Citation Context ...down because the steady-state fluctuations in the number of molecules (which is proportional to the square root of the number of molecules) becomes a significant factor in the behavior of the system (=-=Singer, 1953-=-). ODE models isolate the biochemical system into a group of deterministic and continuous reactions, and tacitly ignore fluctuations in the pathway (Rao et al., 2002). With identical parameter setting... |

11 |
Concerning the validity of the stochastic approach to chemical kinetics
- Gillespie
- 1977
(Show Context)
Citation Context ... achieved almost an order of magnitude better performance than the original. 5 Discussion In the limit of large numbers of reactant molecules, stochastic and deterministic simulations are equivalent (=-=Gillespie, 1977-=-). In contrast, if the system has low copy numbers of species, the deterministic law of mass action breaks down because the steady-state fluctuations in the number of molecules (which is proportional ... |

10 | Cellular automata approaches to enzymatic reaction networks.
- Weimar
- 2002
(Show Context)
Citation Context ...1998). Simulation methods based on cellular automaton have many applications from reactive gas physics to sociology, and have been found to be very useful for biological simulations (for example, see =-=Weimar, 2002-=-). Brownian dynamics has proven to be an useful framework of interactions between ligands and binding sites on receptors, enzymes, and transporters (Bartol et al., 1996). Different algorithms have dif... |

9 | Stochastic effects in a model of nematode infection in ruminants - Marion, Renshaw, et al. - 1998 |

7 |
A hybrid static/dynamic simulation algorithm: towards large-scale pathway simulation
- Yugi, Nakayama, et al.
- 2002
(Show Context)
Citation Context ...Irvine and Savageau, 1990). To complement a lack of quantitative kinetic data, an attempt to marry dynamic rate-equation based continuous models and static flux balance from stoichiometry is ongoing (=-=Yugi et al., 2002-=-). In addition to those continuous representations, discrete formulation is often used. Stochastic discrete event simulation of coupled chemical reactions was pioneered by Gillespie and others (Gilles... |

5 |
Computational challenges in cell simulation
- Takahashi, Yugi, et al.
- 2002
(Show Context)
Citation Context ...computational challenges that are distinct from those encountered in problems of other disciplines such as molecular dynamics, or computational physics, and even conventional biochemical simulations (=-=Takahashi et al., 2002-=-). A vast array of molecular processes occur simultaneously in the cell. The involved physical and chemical processes include molecular diffusion, molecular binding, enzymatic catalysis and higher ord... |

4 |
MCELL: generalized Monte Carlo computer simulation of synaptic transmission and chemical signaling
- Bartol, Stiles, et al.
- 1996
(Show Context)
Citation Context ...ological simulations (for example, see Weimar, 2002). Brownian dynamics has proven to be an useful framework of interactions between ligands and binding sites on receptors, enzymes, and transporters (=-=Bartol et al., 1996-=-). Different algorithms have different strengths, and are often suited to different spatial and temporal scales. When constructing models that span multiple scales, one might choose between two princi... |

4 | A family of embedded Runge– Kutta formulae - Dormand, Prince - 1980 |