TY - JOUR AU - Turner, T. E. AU - Schnell, S. AU - Burrage, K. PY - 2004 DA - 2004// TI - Stochastic approaches for modelling in vivo reactions JO - Computational Biology and Chemistry VL - 28 UR - https://doi.org/10.1016/j.compbiolchem.2004.05.001 DO - 10.1016/j.compbiolchem.2004.05.001 ID - Turner2004 ER - TY - BOOK AU - Klipp, E. AU - Herwig, R. AU - Kowald, A. AU - Wierling, C. AU - Lehrach, H. PY - 2005 DA - 2005// TI - Systems biology in practice UR - https://doi.org/10.1002/3527603603 DO - 10.1002/3527603603 ID - Klipp2005 ER - TY - BOOK AU - Wilkinson, D. PY - 2006 DA - 2006// TI - Stochastic Modelling for Systems Biology ID - Wilkinson2006 ER - TY - JOUR AU - Villà, J. AU - Warshel, A. PY - 2001 DA - 2001// TI - Energetics and Dynamics of Enzymatic Reactions JO - J Phys Chem B VL - 105 UR - https://doi.org/10.1021/jp011048h DO - 10.1021/jp011048h ID - Villà2001 ER - TY - JOUR AU - McAdams, H. AU - Arkin, A. PY - 1997 DA - 1997// TI - Stochastic mechanisms in gene expression JO - Proceedings of the National Academy of Sciences VL - 94 UR - https://doi.org/10.1073/pnas.94.3.814 DO - 10.1073/pnas.94.3.814 ID - McAdams1997 ER - TY - JOUR AU - Hasty, J. AU - Pradines, J. AU - Dolnik, M. AU - Collins, J. PY - 2000 DA - 2000// TI - Noise-based switches and amplifiers for gene expression JO - Proceedings of the National Academy of Sciences VL - 97 UR - https://doi.org/10.1073/pnas.040411297 DO - 10.1073/pnas.040411297 ID - Hasty2000 ER - TY - CHAP AU - Thattai, M. AU - van Oudenaarden, A. PY - 2001 DA - 2001// TI - Intrinsic noise in gene regulatory networks BT - Proceedings of the National Academy of Sciences ID - Thattai2001 ER - TY - JOUR AU - Ozbudak, E. AU - Thattai, M. AU - Kurtser, I. AU - Grossman, A. AU - van Oudenaarden, A. PY - 2002 DA - 2002// TI - Regulation of noise in the expression of a single gene JO - Nature Genetics VL - 31 UR - https://doi.org/10.1038/ng869 DO - 10.1038/ng869 ID - Ozbudak2002 ER - TY - JOUR AU - Isaacs, F. AU - Hasty, J. AU - Cantor, C. AU - Collins, J. PY - 2003 DA - 2003// TI - Prediction and measurement of an autoregulatory genetic module JO - Proceedings of the National Academy of Sciences VL - 100 UR - https://doi.org/10.1073/pnas.1332628100 DO - 10.1073/pnas.1332628100 ID - Isaacs2003 ER - TY - JOUR AU - Thattai, M. AU - van Oudenaarden, A. PY - 2004 DA - 2004// TI - Stochastic Gene Expression in Fluctuating Environments JO - Genetics VL - 167 UR - https://doi.org/10.1534/genetics.167.1.523 DO - 10.1534/genetics.167.1.523 ID - Thattai2004 ER - TY - JOUR AU - Tian, T. AU - Burrage, K. PY - 2004 DA - 2004// TI - Bistability and switching in the lysis/lysogeny genetic regulatory network of bacteriophage [lambda] JO - Journal of Theoretical Biology VL - 227 UR - https://doi.org/10.1016/j.jtbi.2003.11.003 DO - 10.1016/j.jtbi.2003.11.003 ID - Tian2004 ER - TY - JOUR AU - Bratsun, D. AU - Volfson, D. AU - Tsimring, L. S. AU - Hasty, J. PY - 2005 DA - 2005// TI - Delay-induced stochastic oscillations in gene regulation JO - Proceedings of the National Academy of Sciences of the United States of America VL - 102 UR - https://doi.org/10.1073/pnas.0503858102 DO - 10.1073/pnas.0503858102 ID - Bratsun2005 ER - TY - JOUR AU - Kaern, M. AU - Elston, T. AU - Blake, W. AU - Collins, J. PY - 2005 DA - 2005// TI - Stochasticity in gene expression: from theories to phenotypes JO - Nat Rev Genet VL - 6 UR - https://doi.org/10.1038/nrg1615 DO - 10.1038/nrg1615 ID - Kaern2005 ER - TY - JOUR AU - Komili, S. AU - Silver, P. PY - 2008 DA - 2008// TI - Coupling and coordination in gene expression processes: a systems biology view JO - Nature Reviews Genetics VL - 9 UR - https://doi.org/10.1038/nrg2223 DO - 10.1038/nrg2223 ID - Komili2008 ER - TY - JOUR AU - Halley, J. AU - Winkler, D. AU - Burden, F. PY - 2008 DA - 2008// TI - Toward a Rosetta stone for the stem cell genome: Stochastic gene expression, network architecture, and external influences JO - Stem Cell Research VL - 1 UR - https://doi.org/10.1016/j.scr.2008.03.001 DO - 10.1016/j.scr.2008.03.001 ID - Halley2008 ER - TY - JOUR AU - Kurtz, T. G. PY - 1972 DA - 1972// TI - The Relationship between Stochastic and Deterministic Models for Chemical Reactions JO - The Journal of Chemical Physics VL - 57 UR - https://doi.org/10.1063/1.1678692 DO - 10.1063/1.1678692 ID - Kurtz1972 ER - TY - JOUR AU - Gillespie, D. T. PY - 1977 DA - 1977// TI - Exact stochastic simulation of coupled chemical reactions JO - The Journal of Physical Chemistry VL - 81 UR - https://doi.org/10.1021/j100540a008 DO - 10.1021/j100540a008 ID - Gillespie1977 ER - TY - JOUR AU - Gillespie, D. T. PY - 2007 DA - 2007// TI - Stochastic simulation of chemical kinetics JO - Annual review of physical chemistry VL - 58 UR - https://doi.org/10.1146/annurev.physchem.58.032806.104637 DO - 10.1146/annurev.physchem.58.032806.104637 ID - Gillespie2007 ER - TY - JOUR AU - Gibson, M. A. AU - Bruck, J. PY - 2000 DA - 2000// TI - Efficient Exact Stochastic Simulation of Chemical Systems with Many Species and Many Channels JO - The Journal of Physical Chemistry A VL - 104 UR - https://doi.org/10.1021/jp993732q DO - 10.1021/jp993732q ID - Gibson2000 ER - TY - JOUR AU - Gillespie, D. T. PY - 2001 DA - 2001// TI - Approximate accelerated stochastic simulation of chemically reacting systems JO - The Journal of Chemical Physics VL - 115 UR - https://doi.org/10.1063/1.1378322 DO - 10.1063/1.1378322 ID - Gillespie2001 ER - TY - JOUR AU - Cao, Y. AU - Gillespie, D. T. AU - Petzold, L. R. PY - 2006 DA - 2006// TI - Efficient step size selection for the tau-leaping simulation method JO - The Journal of Chemical Physics VL - 124 UR - https://doi.org/10.1063/1.2159468 DO - 10.1063/1.2159468 ID - Cao2006 ER - TY - JOUR AU - Tian, T. AU - Burrage, K. PY - 2004 DA - 2004// TI - Binomial leap methods for simulating stochastic chemical kinetics JO - The Journal of Chemical Physics VL - 121 UR - https://doi.org/10.1063/1.1810475 DO - 10.1063/1.1810475 ID - Tian2004 ER - TY - JOUR AU - Chatterjee, A. AU - Vlachos, D. G. AU - Katsoulakis, M. A. PY - 2005 DA - 2005// TI - Binomial distribution based tau-leap accelerated stochastic simulation JO - The Journal of Chemical Physics VL - 122 UR - https://doi.org/10.1063/1.1833357 DO - 10.1063/1.1833357 ID - Chatterjee2005 ER - TY - JOUR AU - Auger, A. AU - Chatelain, P. AU - Koumoutsakos, P. PY - 2006 DA - 2006// TI - R-leaping: Accelerating the stochastic simulation algorithm by reaction leaps JO - The Journal of Chemical Physics VL - 125 UR - https://doi.org/10.1063/1.2218339 DO - 10.1063/1.2218339 ID - Auger2006 ER - TY - JOUR AU - Monk, N. A. PY - 2003 DA - 2003// TI - Oscillatory expression of Hes1, p53, and NF-kappaB driven by transcriptional time delays JO - Curr Biol VL - 13 UR - https://doi.org/10.1016/S0960-9822(03)00494-9 DO - 10.1016/S0960-9822(03)00494-9 ID - Monk2003 ER - TY - JOUR AU - Yildirim, N. AU - Mackey, M. C. PY - 2003 DA - 2003// TI - Feedback Regulation in the Lactose Operon: A Mathematical Modeling Study and Comparison with Experimental Data JO - Biophys J VL - 84 UR - https://doi.org/10.1016/S0006-3495(03)70013-7 DO - 10.1016/S0006-3495(03)70013-7 ID - Yildirim2003 ER - TY - JOUR AU - Barrio, M. AU - Burrage, K. AU - Leier, A. AU - Tian, T. PY - 2006 DA - 2006// TI - Oscillatory Regulation of Hes1: Discrete Stochastic Delay Modelling and Simulation JO - PLoS Comput Biol VL - 2 UR - https://doi.org/10.1371/journal.pcbi.0020117 DO - 10.1371/journal.pcbi.0020117 ID - Barrio2006 ER - TY - JOUR AU - Leier, A. AU - Marquez-Lago, T. T. AU - Burrage, K. PY - 2008 DA - 2008// TI - Generalized binomial tau-leap method for biochemical kinetics incorporating both delay and intrinsic noise JO - The Journal of Chemical Physics VL - 128 UR - https://doi.org/10.1063/1.2919124 DO - 10.1063/1.2919124 ID - Leier2008 ER - TY - JOUR AU - Anderson, D. F. PY - 2007 DA - 2007// TI - A modified next reaction method for simulating chemical systems with time dependent propensities and delays JO - The Journal of Chemical Physics VL - 127 UR - https://doi.org/10.1063/1.2799998 DO - 10.1063/1.2799998 ID - Anderson2007 ER - TY - BOOK AU - Hairer, E. AU - Norsett, S. P. AU - Wanner, G. PY - 2002 DA - 2002// TI - Solving Ordinary, Differential Equations II. Stiff and Differential-Algebraic Problems PB - Springer-Verlag CY - Second Revised Editio edition ID - Hairer2002 ER - TY - JOUR AU - Abdulle, A. AU - Medovikov, A. PY - 2001 DA - 2001// TI - Second order Chebyshev methods based on orthogonal polynomials JO - Numerische Mathematik VL - 90 UR - https://doi.org/10.1007/s002110100292 DO - 10.1007/s002110100292 ID - Abdulle2001 ER - TY - CHAP AU - Abdulle, A. AU - Cirilli, S. PY - 2008 DA - 2008// TI - S-ROCK: Chebyshev Methods for Stiff Stochastic Differential Equations BT - SIAM J Sci Comput ID - Abdulle2008 ER - TY - JOUR AU - Hernandez, D. AU - Spigler, R. PY - 1993 DA - 1993// TI - Convergence and stability of implicit runge-kutta methods for systems with multiplicative noise JO - BIT Numerical Mathematics VL - 33 UR - https://doi.org/10.1007/BF01990541 DO - 10.1007/BF01990541 ID - Hernandez1993 ER - TY - JOUR AU - Schlögl, F. PY - 1972 DA - 1972// TI - Chemical reaction models for non-equilibrium phase transitions JO - Zeitschrift für Physik A Hadrons and Nuclei VL - 253 ID - Schlögl1972 ER - TY - BOOK AU - Øksendal, B. PY - 2005 DA - 2005// TI - Stochastic Differential Equations: An Introduction with Applications (Universitext) ID - Øksendal2005 ER - TY - JOUR AU - Burrage, K. AU - Burrage, P. M. PY - 1996 DA - 1996// TI - High strong order explicit Runge-Kutta methods for stochastic ordinary differential equations JO - Applied Numer Maths VL - 22 UR - https://doi.org/10.1016/S0168-9274(96)00027-X DO - 10.1016/S0168-9274(96)00027-X ID - Burrage1996 ER - TY - JOUR AU - Li, T. PY - 2007 DA - 2007// TI - Analysis of Explicit Tau-Leaping Schemes for Simulating Chemically Reacting Systems JO - Multiscale Modeling and Simulation VL - 6 UR - https://doi.org/10.1137/06066792X DO - 10.1137/06066792X ID - Li2007 ER - TY - JOUR AU - Cao, Y. AU - Petzold, L. R. AU - Rathinam, M. AU - Gillespie, D. T. PY - 2004 DA - 2004// TI - The numerical stability of leaping methods for stochastic simulation of chemically reacting systems JO - J Chem Phys VL - 121 UR - https://doi.org/10.1063/1.1823412 DO - 10.1063/1.1823412 ID - Cao2004 ER - TY - JOUR AU - de Lomana, A. L. G. AU - Gómez-Garrido, A. AU - Sportouch, D. AU - Villà-Freixa, J. PY - 2008 DA - 2008// TI - Optimal Experimental Design in the Modelling of Pattern Formation JO - LNCS VL - 5101 ID - de Lomana2008 ER - TY - BOOK AU - van Kampen, N. G. PY - 2007 DA - 2007// TI - Stochastic Processes in Physics and Chemistry ID - van Kampen2007 ER - TY - JOUR AU - Huang, C. Y. AU - Ferrell, J. E. PY - 1996 DA - 1996// TI - Ultrasensitivity in the mitogen-activated protein kinase cascade JO - Proceedings of the National Academy of Sciences of the United States of America VL - 93 UR - https://doi.org/10.1073/pnas.93.19.10078 DO - 10.1073/pnas.93.19.10078 ID - Huang1996 ER - TY - JOUR AU - Novère, N. L. AU - Bornstein, B. J. AU - Broicher, A. AU - Courtot, M. AU - Donizelli, M. AU - Li, L. AU - Sauro, H. M. AU - Schilstra, M. J. AU - Shapiro, B. E. AU - Snoep, J. L. AU - Hucka, M. PY - 2006 DA - 2006// TI - BioModels Database: a free, centralized database of curated, published, quantitative kinetic models of biochemical and cellular systems JO - Nucleic Acids Research VL - 92 UR - https://doi.org/10.1093/nar/gkj092 DO - 10.1093/nar/gkj092 ID - Novère2006 ER - TY - JOUR AU - Matsumoto, M. AU - Nishimura, T. PY - 1998 DA - 1998// TI - Mersenne Twister: A 623-dimensionally equidistributed uniform pseudorandom number generator JO - ACM Transactions on Modeling and Computer Simulation VL - 8 UR - https://doi.org/10.1145/272991.272995 DO - 10.1145/272991.272995 ID - Matsumoto1998 ER -