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1. | Interdisciplinary Center for Applied Mathematics, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061-0531, United States |
2. | Department of Mathematics, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061-0123 |
References:
[1] |
R. Albert and H. Othmer, The topology of the regulatory interactions predicts the expression pattern of the segment polarity genes in drosophila melanogaster, J. Theoret. Biol., 223 (2003), 1-18.
doi: 10.1016/S0022-5193(03)00035-3. |
[2] |
E. Aurell and K. Sneppen, Epigenetics as a first exit problem, Phys. Rev. Lett., 88 (2002), 048101.
doi: 10.1103/PhysRevLett.88.048101. |
[3] |
M. Cohn and K. Horibata, Inhibition by glucose of the induced synthesis of the $\beta$-galactoside-enzyme system of escherichia coli. analysis of maintenance, J. Bacteriol., 78 (1959), 601-612. |
[4] |
C. Conradi, J. Stelling and J. Raisch, Structure discrimination of continuous models for biochemical reaction networks via finite state machines, Proc. IEEE Int. Symposium on Intelligent Control (Mexico City, Mexico), 2001, 138-143. |
[5] | |
[6] |
R. Edwards, H. T. Siegelmann, K. Aziza and L. Glass, Symbolic dynamics and computation in model gene networks, Chaos, 11 (2001), 160-169.
doi: 10.1063/1.1336498. |
[7] |
N. Friedman, M. Linial and I. Nachman, Using bayesian networks to analyze expression data, Journal of Computational Biology, 7 (2000), 601-620.
doi: 10.1089/106652700750050961. |
[8] |
F. Jacob and J. Monod, Genetic regulatory mechanisms in the synthesis of proteins, J. Mol. Biol., 3 (1961), 318-356.
doi: 10.1016/S0022-2836(61)80072-7. |
[9] |
S. A. Kauffman, Metabolic stability and epigenesis in randomly constructed genetic nets, Journal of Theoretical Biology, 22 (1969), 437-467.
doi: 10.1016/0022-5193(69)90015-0. |
[10] |
R. Laubenbacher and A. Jarrah, Dvd - discrete visualizer of dynamics., , ().
|
[11] |
L. Mendoza and I. Xenarios, A method for the generation of standardized qualitative dynamical systems of regulatory networks, Theoretical Biology and Medical Modelling, 3 (2006), 13+.
doi: 10.1186/1742-4682-3-13. |
[12] |
A. Novick and M. Weiner, Enzyme induction as an all-or-none phenomenon, Proc. Natl. Acad. Sci. USA, 43 (1957), 553-66.
doi: 10.1073/pnas.43.7.553. |
[13] |
M. Ptashne, "A Genetic Switch Phage Lambda Revisited," 3rd ed., Cold Spring Harbor Laboritory Press, 2004. |
[14] |
M. Santillán and M. C. Mackey, Why the lysogenic state of phage lambda is so stable: A mathematical modeling approach, Biophys. J., 86 (2004), 75-84.
doi: 10.1016/S0006-3495(04)74085-0. |
[15] |
T. Tian and K. Burrage, Stochastic models for regulatory networks of the genetic toggle switch, Proc. Natl. Acad. Sci. USA, 103 (2006), 8372-8377.
doi: 10.1073/pnas.0507818103. |
[16] |
P. Wong, S. Gladney and J. D. Keasling, Mathematical model of the lac operon: Inducer exclusion, catabolite repression, and diauxic growth on glucose and lactose, Biotechnology progress, 13 (1997), 132-143.
doi: 10.1021/bp970003o. |
[17] |
N. Yildirim and M. C. Mackey, Feedback regulation in the lactose operon: A mathematical modeling study and comparison with experimental data, Biophys. J., 84 (2003), 2841-2851.
doi: 10.1016/S0006-3495(03)70013-7. |
show all references
References:
[1] |
R. Albert and H. Othmer, The topology of the regulatory interactions predicts the expression pattern of the segment polarity genes in drosophila melanogaster, J. Theoret. Biol., 223 (2003), 1-18.
doi: 10.1016/S0022-5193(03)00035-3. |
[2] |
E. Aurell and K. Sneppen, Epigenetics as a first exit problem, Phys. Rev. Lett., 88 (2002), 048101.
doi: 10.1103/PhysRevLett.88.048101. |
[3] |
M. Cohn and K. Horibata, Inhibition by glucose of the induced synthesis of the $\beta$-galactoside-enzyme system of escherichia coli. analysis of maintenance, J. Bacteriol., 78 (1959), 601-612. |
[4] |
C. Conradi, J. Stelling and J. Raisch, Structure discrimination of continuous models for biochemical reaction networks via finite state machines, Proc. IEEE Int. Symposium on Intelligent Control (Mexico City, Mexico), 2001, 138-143. |
[5] | |
[6] |
R. Edwards, H. T. Siegelmann, K. Aziza and L. Glass, Symbolic dynamics and computation in model gene networks, Chaos, 11 (2001), 160-169.
doi: 10.1063/1.1336498. |
[7] |
N. Friedman, M. Linial and I. Nachman, Using bayesian networks to analyze expression data, Journal of Computational Biology, 7 (2000), 601-620.
doi: 10.1089/106652700750050961. |
[8] |
F. Jacob and J. Monod, Genetic regulatory mechanisms in the synthesis of proteins, J. Mol. Biol., 3 (1961), 318-356.
doi: 10.1016/S0022-2836(61)80072-7. |
[9] |
S. A. Kauffman, Metabolic stability and epigenesis in randomly constructed genetic nets, Journal of Theoretical Biology, 22 (1969), 437-467.
doi: 10.1016/0022-5193(69)90015-0. |
[10] |
R. Laubenbacher and A. Jarrah, Dvd - discrete visualizer of dynamics., , ().
|
[11] |
L. Mendoza and I. Xenarios, A method for the generation of standardized qualitative dynamical systems of regulatory networks, Theoretical Biology and Medical Modelling, 3 (2006), 13+.
doi: 10.1186/1742-4682-3-13. |
[12] |
A. Novick and M. Weiner, Enzyme induction as an all-or-none phenomenon, Proc. Natl. Acad. Sci. USA, 43 (1957), 553-66.
doi: 10.1073/pnas.43.7.553. |
[13] |
M. Ptashne, "A Genetic Switch Phage Lambda Revisited," 3rd ed., Cold Spring Harbor Laboritory Press, 2004. |
[14] |
M. Santillán and M. C. Mackey, Why the lysogenic state of phage lambda is so stable: A mathematical modeling approach, Biophys. J., 86 (2004), 75-84.
doi: 10.1016/S0006-3495(04)74085-0. |
[15] |
T. Tian and K. Burrage, Stochastic models for regulatory networks of the genetic toggle switch, Proc. Natl. Acad. Sci. USA, 103 (2006), 8372-8377.
doi: 10.1073/pnas.0507818103. |
[16] |
P. Wong, S. Gladney and J. D. Keasling, Mathematical model of the lac operon: Inducer exclusion, catabolite repression, and diauxic growth on glucose and lactose, Biotechnology progress, 13 (1997), 132-143.
doi: 10.1021/bp970003o. |
[17] |
N. Yildirim and M. C. Mackey, Feedback regulation in the lactose operon: A mathematical modeling study and comparison with experimental data, Biophys. J., 84 (2003), 2841-2851.
doi: 10.1016/S0006-3495(03)70013-7. |
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