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Modeling DNA thermal denaturation at the mesoscopic level
1. | Dep. Ingegneria Civile Informatica Edile Ambientale e Matematica Applicata, University of Messina, Contrada Di Dio, Vill. S. Agata, 98166 Messina, Italy |
2. | Faculty of Mathematics, Informatics and Mechanics, Institute of Applied Mathematics and Mechanics, University of Warsaw, ul. Banacha 2, 02-097 Warszawa |
References:
[1] |
A. E. Allahverdyan, Z. H. S. Gevorkian, C.-K. Hu and Th. M. Nieuwenhuizeni, How absorption influences DNA denaturation, Phys. Rev. E, 79 (2009), 031903, 15 pp.
doi: 10.1103/PhysRevE.79.031903. |
[2] |
L. Arlotti, E. De Angelis, L. Fermo, M. Lachowicz and N. Bellomo, On a class of integro-differential equations modeling complex systems with nonlinear interactions, Appl. Math. Letters, 25 (2012), 490-495.
doi: 10.1016/j.aml.2011.09.043. |
[3] |
A. Bar, A. Kabakcioglu and D. Mukamel, Macroscopic loop formation in circular DNA denaturation, Phys. Rev. E, 85 (2012), 051919. |
[4] |
A. Bar, A. Kabakcioglu and D. Mukamel, Constrained thermal denaturation of DNA underfixed linking number, Cent. Eur. J. Phys., 10 (2012), 582-586. |
[5] |
S. Behnia, A. Akhshani, M. Panahi, A. Mobaraki and M. Ghaderian, Multifractal analysis of thermal denaturation based on the Peyrard-Bishop-Dauxois model, Phys. Rev. E, 84 (2011), 1-8.
doi: 10.1103/PhysRevE.84.031918. |
[6] |
S. Behnia, A. Akhshani, M. Panahi, A. Mobaraki and M. Ghaderian, Multifractal properties of denaturation process based on Peyrard-Bishop model, Phys. Letters A, 376 (2012), 2538-2547.
doi: 10.1016/j.physleta.2012.05.062. |
[7] |
N. Bellomo and B. Carbonaro, Review: Toward a mathematical theory of living systems focusingon developmental biology and evolution: A review and perspectives, Phys. Life Reviews, 8 (2011), 1-18. |
[8] |
N. Bellomo, A. Bellouquid, J. Nieto and J. Soler, On the asymptotic theory form microscopic to macroscopic growing tissue models: an overview with perspectives, Math. Models Meth. Appl. Sci., 22 (2012), 37 pp.
doi: 10.1142/S0218202512005885. |
[9] |
V. Coscia, L. Fermo and N. Bellomo, On the mathematical theory of living systems II: The interplay between mathematics and system biology, Comp. Math. Appl., 62 (2011), 3902-3911.
doi: 10.1016/j.camwa.2011.09.043. |
[10] |
T. Dauxois and M. Peyrad, Entropy-driven transition in a one-dimensional system, Phys. Rev. E, 51 (1995), 4027-4040.
doi: 10.1103/PhysRevE.51.4027. |
[11] |
T. Dauxois, M. Peyrad and B. Bishop, Dynamics and thermodynamics of a nonlinear model for DNA denaturation, Phys. Rev. E, 47 (1993), 684-697.
doi: 10.1103/PhysRevE.47.684. |
[12] |
R. Durrett, Probability Models for DNA Sequence Evolution, Springer, 2002.
doi: 10.1007/978-1-4757-6285-3. |
[13] |
A. A. Evans and A. J. Levine, High-energy deformation of filaments with internal structureand localized torque-induced melting of DNA, Phys. Rev. E, 85 (2012), 1-9. |
[14] |
M. E. Fisher, Effect of excluded volume on phase transitions in biopolymers, J. Chem. Phys., 45 (1966), 1469-1473.
doi: 10.1063/1.1727787. |
[15] |
R. M. Grey, Toeplitz and Circulant Matrices: A Review,, NOW the essence of knowledge, ().
doi: 10.1561/0100000006. |
[16] |
A. Hanke, M. G. Ochoa and R. Metzler, Denaturation Transition of Stretched DNA, Phys. Rev. Lett., 100 (2008), 1-4.
doi: 10.1103/PhysRevLett.100.018106. |
[17] |
Y. Kafri, D. Mukamel and L. Peliti, Why is the DNA denaturation transition first order, Phys. Review Letters, 85 (2000), 4988-4991.
doi: 10.1103/PhysRevLett.85.4988. |
[18] |
G. Kalosakas and S. Ares, Dependence on temperature and guanine-cytosine content of bubble length distributions in DNA, Chem. Phys., 130 (2009), 1-7.
doi: 10.1063/1.3149859. |
[19] |
J. Y. Kim, J. H. Jeon and W. Sung, A breathing wormlike chain model on DNA denaturation and bubble:Effects of stacking interactions, J. Chem. Phys., 128 (2008), 1-6.
doi: 10.1063/1.2827471. |
[20] |
, Lab Manual: Measuring DNA Melting Curves,, 2013. Available from: , ().
|
[21] |
M. Lachowicz, Microscopic, mesoscopic and macroscopic descriptions of complex systems, Probabilistic Engineering Mechanics, 26 (2010), 54-60.
doi: 10.1016/j.probengmech.2010.06.007. |
[22] |
M. Lachowicz and A. Quartarone, A general framework for modeling tumor-immune system competition at the mesoscopic level, Appl. Math. Letters, 25 (2012), 2118-2122.
doi: 10.1016/j.aml.2012.04.021. |
[23] |
M. Lachowicz, Individually-based Markov processes modeling nonlinear systems in mathematical biology, Nonlinear Analysis Real World Appl., 12 (2011), 2396-2407.
doi: 10.1016/j.nonrwa.2011.02.014. |
[24] |
M. Lachowicz and D. Wrzosek, Nonlocal bilinear equations. Equilibrium solutions and diffusive limit, Math. Models Methods Appl. Sci., 11 (2001), 1393-1409.
doi: 10.1142/S0218202501001380. |
[25] |
M. Lachowicz and T. V. Ryabukha, Equilibrium solutions for microscopic stochastic systems in population dynamics, Math. Biosci. Engin., 10 (2013), 777-786.
doi: 10.3934/mbe.2013.10.777. |
[26] |
M. Peyrard, Nonlinear dynamics and statistical physics of DNA, Nonlinearity, 17 (2004), R1-R40.
doi: 10.1088/0951-7715/17/2/R01. |
[27] |
M. Peyrard, S. Cuesta-López and G. James, Modelling DNA at the mesoscale: A challenge for nonlinear science?, Nonlinearity, 21 (2008), T91-T100.
doi: 10.1088/0951-7715/21/6/T02. |
[28] |
M. Peyrard and B. Bishop, Statistical Mechanics of a Nonlinear Model for DNA Denaturation, Phys. Rev. Lett., 62 (1989), 1-70.
doi: 10.1103/PhysRevLett.62.2755. |
[29] |
D. Poland and H. A. Scheraga, Theory of Helix-Coil Transitions in Biopolymers: Statistical Mechanical Theory of Order-Disorder Transitions in Biological Macromolecules, Academic, New York, 1970. |
[30] |
S. J. Rahi, M. P. Hertzberg and M. Kardar, Melting of persistent double-stranded polymers, Phys. Rev. E, 78 (2008), 1-8.
doi: 10.1103/PhysRevE.78.051910. |
[31] |
S. J. Rahi, M. P. Hertzberg and M. Kardar, Denaturation of circular DNA: Supercoil mechanism, Phys. Rev. E, 84 (2008), 1-8. |
[32] |
R.G. Rutledge and D. Stewart, Critical evaluation of methods used to determine amplification efficiency refutes the exponential character of real-time PCR, BMC Molecular Biology, 9 (2008), 96-108.
doi: 10.1186/1471-2199-9-96. |
[33] |
R. G. Rutledge and D. Stewart, A kinetic-based sigmoidal model for the polymerase chain reaction and its applications to high-capacity absolute quantitative real-time PCR, BMC Molecular Biology, 8 (2008), 47-75.
doi: 10.1186/1472-6750-8-47. |
[34] |
P. Sadhukhan and S. M. Bhattacharjee, Entanglement entropy of a quantum unbinding transition and entropy of DNA,, preprint, ().
|
[35] |
N. Theodorakopoulos, Bubbles, Clusters and denaturation in genomic DNA: modeling, parametrization efficient computation, Journal of Nonlinear Mathematical Physics, 18 (2011), 429-447.
doi: 10.1142/S1402925111001611. |
[36] |
C. J. Thompson, Mathematical Statistical Mechanics, Princeton University, 1979. |
[37] |
J. D. Watson and F. H. C. Crick, A Structure for Deoxyribose Nucleic Acid, Nature, 171 (1953), 737-738. |
[38] |
K. A. Velizhanin, C. C. Chien, Y. Dubi and M. Zwolak, Bubbles, Driving denaturation: Nanoscalethermal transport as a probe of DNA melting, Phys. Rev. E, 83 (2011), 1-4. |
show all references
References:
[1] |
A. E. Allahverdyan, Z. H. S. Gevorkian, C.-K. Hu and Th. M. Nieuwenhuizeni, How absorption influences DNA denaturation, Phys. Rev. E, 79 (2009), 031903, 15 pp.
doi: 10.1103/PhysRevE.79.031903. |
[2] |
L. Arlotti, E. De Angelis, L. Fermo, M. Lachowicz and N. Bellomo, On a class of integro-differential equations modeling complex systems with nonlinear interactions, Appl. Math. Letters, 25 (2012), 490-495.
doi: 10.1016/j.aml.2011.09.043. |
[3] |
A. Bar, A. Kabakcioglu and D. Mukamel, Macroscopic loop formation in circular DNA denaturation, Phys. Rev. E, 85 (2012), 051919. |
[4] |
A. Bar, A. Kabakcioglu and D. Mukamel, Constrained thermal denaturation of DNA underfixed linking number, Cent. Eur. J. Phys., 10 (2012), 582-586. |
[5] |
S. Behnia, A. Akhshani, M. Panahi, A. Mobaraki and M. Ghaderian, Multifractal analysis of thermal denaturation based on the Peyrard-Bishop-Dauxois model, Phys. Rev. E, 84 (2011), 1-8.
doi: 10.1103/PhysRevE.84.031918. |
[6] |
S. Behnia, A. Akhshani, M. Panahi, A. Mobaraki and M. Ghaderian, Multifractal properties of denaturation process based on Peyrard-Bishop model, Phys. Letters A, 376 (2012), 2538-2547.
doi: 10.1016/j.physleta.2012.05.062. |
[7] |
N. Bellomo and B. Carbonaro, Review: Toward a mathematical theory of living systems focusingon developmental biology and evolution: A review and perspectives, Phys. Life Reviews, 8 (2011), 1-18. |
[8] |
N. Bellomo, A. Bellouquid, J. Nieto and J. Soler, On the asymptotic theory form microscopic to macroscopic growing tissue models: an overview with perspectives, Math. Models Meth. Appl. Sci., 22 (2012), 37 pp.
doi: 10.1142/S0218202512005885. |
[9] |
V. Coscia, L. Fermo and N. Bellomo, On the mathematical theory of living systems II: The interplay between mathematics and system biology, Comp. Math. Appl., 62 (2011), 3902-3911.
doi: 10.1016/j.camwa.2011.09.043. |
[10] |
T. Dauxois and M. Peyrad, Entropy-driven transition in a one-dimensional system, Phys. Rev. E, 51 (1995), 4027-4040.
doi: 10.1103/PhysRevE.51.4027. |
[11] |
T. Dauxois, M. Peyrad and B. Bishop, Dynamics and thermodynamics of a nonlinear model for DNA denaturation, Phys. Rev. E, 47 (1993), 684-697.
doi: 10.1103/PhysRevE.47.684. |
[12] |
R. Durrett, Probability Models for DNA Sequence Evolution, Springer, 2002.
doi: 10.1007/978-1-4757-6285-3. |
[13] |
A. A. Evans and A. J. Levine, High-energy deformation of filaments with internal structureand localized torque-induced melting of DNA, Phys. Rev. E, 85 (2012), 1-9. |
[14] |
M. E. Fisher, Effect of excluded volume on phase transitions in biopolymers, J. Chem. Phys., 45 (1966), 1469-1473.
doi: 10.1063/1.1727787. |
[15] |
R. M. Grey, Toeplitz and Circulant Matrices: A Review,, NOW the essence of knowledge, ().
doi: 10.1561/0100000006. |
[16] |
A. Hanke, M. G. Ochoa and R. Metzler, Denaturation Transition of Stretched DNA, Phys. Rev. Lett., 100 (2008), 1-4.
doi: 10.1103/PhysRevLett.100.018106. |
[17] |
Y. Kafri, D. Mukamel and L. Peliti, Why is the DNA denaturation transition first order, Phys. Review Letters, 85 (2000), 4988-4991.
doi: 10.1103/PhysRevLett.85.4988. |
[18] |
G. Kalosakas and S. Ares, Dependence on temperature and guanine-cytosine content of bubble length distributions in DNA, Chem. Phys., 130 (2009), 1-7.
doi: 10.1063/1.3149859. |
[19] |
J. Y. Kim, J. H. Jeon and W. Sung, A breathing wormlike chain model on DNA denaturation and bubble:Effects of stacking interactions, J. Chem. Phys., 128 (2008), 1-6.
doi: 10.1063/1.2827471. |
[20] |
, Lab Manual: Measuring DNA Melting Curves,, 2013. Available from: , ().
|
[21] |
M. Lachowicz, Microscopic, mesoscopic and macroscopic descriptions of complex systems, Probabilistic Engineering Mechanics, 26 (2010), 54-60.
doi: 10.1016/j.probengmech.2010.06.007. |
[22] |
M. Lachowicz and A. Quartarone, A general framework for modeling tumor-immune system competition at the mesoscopic level, Appl. Math. Letters, 25 (2012), 2118-2122.
doi: 10.1016/j.aml.2012.04.021. |
[23] |
M. Lachowicz, Individually-based Markov processes modeling nonlinear systems in mathematical biology, Nonlinear Analysis Real World Appl., 12 (2011), 2396-2407.
doi: 10.1016/j.nonrwa.2011.02.014. |
[24] |
M. Lachowicz and D. Wrzosek, Nonlocal bilinear equations. Equilibrium solutions and diffusive limit, Math. Models Methods Appl. Sci., 11 (2001), 1393-1409.
doi: 10.1142/S0218202501001380. |
[25] |
M. Lachowicz and T. V. Ryabukha, Equilibrium solutions for microscopic stochastic systems in population dynamics, Math. Biosci. Engin., 10 (2013), 777-786.
doi: 10.3934/mbe.2013.10.777. |
[26] |
M. Peyrard, Nonlinear dynamics and statistical physics of DNA, Nonlinearity, 17 (2004), R1-R40.
doi: 10.1088/0951-7715/17/2/R01. |
[27] |
M. Peyrard, S. Cuesta-López and G. James, Modelling DNA at the mesoscale: A challenge for nonlinear science?, Nonlinearity, 21 (2008), T91-T100.
doi: 10.1088/0951-7715/21/6/T02. |
[28] |
M. Peyrard and B. Bishop, Statistical Mechanics of a Nonlinear Model for DNA Denaturation, Phys. Rev. Lett., 62 (1989), 1-70.
doi: 10.1103/PhysRevLett.62.2755. |
[29] |
D. Poland and H. A. Scheraga, Theory of Helix-Coil Transitions in Biopolymers: Statistical Mechanical Theory of Order-Disorder Transitions in Biological Macromolecules, Academic, New York, 1970. |
[30] |
S. J. Rahi, M. P. Hertzberg and M. Kardar, Melting of persistent double-stranded polymers, Phys. Rev. E, 78 (2008), 1-8.
doi: 10.1103/PhysRevE.78.051910. |
[31] |
S. J. Rahi, M. P. Hertzberg and M. Kardar, Denaturation of circular DNA: Supercoil mechanism, Phys. Rev. E, 84 (2008), 1-8. |
[32] |
R.G. Rutledge and D. Stewart, Critical evaluation of methods used to determine amplification efficiency refutes the exponential character of real-time PCR, BMC Molecular Biology, 9 (2008), 96-108.
doi: 10.1186/1471-2199-9-96. |
[33] |
R. G. Rutledge and D. Stewart, A kinetic-based sigmoidal model for the polymerase chain reaction and its applications to high-capacity absolute quantitative real-time PCR, BMC Molecular Biology, 8 (2008), 47-75.
doi: 10.1186/1472-6750-8-47. |
[34] |
P. Sadhukhan and S. M. Bhattacharjee, Entanglement entropy of a quantum unbinding transition and entropy of DNA,, preprint, ().
|
[35] |
N. Theodorakopoulos, Bubbles, Clusters and denaturation in genomic DNA: modeling, parametrization efficient computation, Journal of Nonlinear Mathematical Physics, 18 (2011), 429-447.
doi: 10.1142/S1402925111001611. |
[36] |
C. J. Thompson, Mathematical Statistical Mechanics, Princeton University, 1979. |
[37] |
J. D. Watson and F. H. C. Crick, A Structure for Deoxyribose Nucleic Acid, Nature, 171 (1953), 737-738. |
[38] |
K. A. Velizhanin, C. C. Chien, Y. Dubi and M. Zwolak, Bubbles, Driving denaturation: Nanoscalethermal transport as a probe of DNA melting, Phys. Rev. E, 83 (2011), 1-4. |
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