Journal Papers


  1. J. González-Ayala, M. Santillán, I. Reyes-Ramírez, and A. Calvo-Hernández (2018) Link between optimization and local stability of a low dissipation heat engine: dynamic and energetic behaviors, Physical Review E In Press
  2. M. Santillán (2018) Synchronization dynamics of two mutually coupled 555-IC based electronic oscillators, Revista Mexicana de Física 64: 107-115
  3. A. Vázquez-Jiménez, M. Santillán, and J. Rodríguez-González (2017) How the extrinsic noise in gene expression can be controlled? IFAC-PapersOnline 50: 15092-15096 DOI: 10.1016/j.ifacol.2017.08.2236
  4. I. Reyes-Ramírez, J. González-Ayala, A. Calvo-Hernández, and , M. Santillán  (2017) Local stability analysis of a low dissipation heat engine working at maximum power output, Physical Review E 96: 042128 DOI: 10.1103/PhysRevE.96.042128
  5. J. E. Sosa-Hernández, M. Santillán, and J. Santana-Solano (2017) Motility of Escherichia coli in a quasi-two-dimensional porous medium, Physical Review E 95: 032404 DOI: 10.1103/PhysRevE.95.032404


  1. M. Santillán (2016) Periodic forcing of a 555-IC based electronic oscillator in the strong coupling limit, International Journal of Bifurcation and Chaos 26: 1630007 DOI: 10.1142/S021812741630007X
  2. E. Sosa-Hernández, G. Ballestero-Rodea, J. A. Arias-del-Angel, D. Dévora-Canales, R. Manning-Cela, J. Santana-Solano, and M. Santillán (2015) Experimental and mathematical-modeling characterization of Trypanosoma cruzi epimastigote motility, PLoS ONE 10: e0142478 DOI: 10.1371/journal.pone.0142478
  3. N. C. Pérez-Rosas, N. L. Gómez-Viquez, A. Dagnino-Acosta, M. Santillán, and A. Guerrero-Hernández (2015) Kinetics on demand is a simple mathematical solution that fits recorded caffeine-induced luminal SR Ca2+ changes in smooth muscle cells, PLoS ONE 10: e0138195 DOI: 10.1371/journal.pone.0138195
  4. R. Zapién-Campos, G. Olmedo-Alvarez and M. Santillán (2015) Antagonistic interactions are sufficient to explain self-assemblage of bacterial communities in a homogeneous environment: a computational modeling approach, Frontiers in Microbiology 6: 489 DOI: 10.3389/fmicb.2015.00489
  5. M. C. Mackey, M. Santillán, M. Tyran-Kamińska, and E. S. Zeron (2015) The utility of simple mathematical models in understanding gene regulatory dynamics, In Silico Biol. 12: 22-53 DOI: 10.3233/ISB-140463


  1. R. S. Pérez-Alfaro, M. Santillán, E. Galán-Vázquez, and A. Martínez-Antonio (2014) Regulatory switches for hierarchichal use of carbon sources in E. coli, Network Biology 4: 95-108 URL:
  2. M. Reséndiz-Antonio and M. Santillán (2014) On the dynamical vs. thermodynamical performance of a beta-type Stirling engine, Phys. A 409: 162-174 DOI: 10.1016/j.physa.2014.04.040
  3. E. Salazar-Cavazos and M. Santillán (2014) Optimal performance of the tryptophan operon of E. coli: a stochastic, dynamical, mathematical-modeling approach, Bull. Math. Biol. 76: 314-334 DOI: 10.1007/s11538-013-9920-8
  4. M. C. Mackey and M. Santillán (2013) Andrew Fielding Huxley (1917-2012), Notices of the AMS 576: 576-584 DOI: 10.1090/noti998
  5. M. Santillán and H. Qian (2013) Stochastic thermodynamics across scales: emergent inter-attractoral discrete Markov jump process and its underlying continuous diffusion, Physica A 392: 123-135 DOI: 10.1016/j.physa.2012.08.019
  6. R.-A. Pérez-Gutiérrez, V. López-Ramírez, A. Islas, L. D. Alcaraz, I. Hernandez-González, B. C. Luna Olivera, M. Santillán, L. Eguiarte, V. Souza, M. Travisano, and G. Olmedo-Alvarez (2013) Antagonism influences assembly of a Bacillus guild in a local community and is depicted as a food-chain network, ISME J. 7: 487-497 DOI: 10.1038/ismej.2012.119


  1. A. Martínez-Antonio, D. A. Velázquez-Ramírez, J. Sánchez-Mondragón, and M. Santillán (2012) Hierarchical dynamics of a transcription factor network in E. coli, Molec. Biosys. 8: 2932-2936 DOI: 10.1039/c2mb25236h
  2. C. Zamora-Chimal, M. Santillán, and J. Rodríguez-González (2012) Influence of the feedback loops in the trp operon of B. subtilis on the system dynamic response and noise amplitude, J. Theor. Biol. 317: 119-131. DOI: 10.1016/j.jtbi.2012.06.014
  3. L. U. Aguilera, B. E. Galindo, D. Sánchez, and M. Santillán (2012) What is the core oscillator in the speract-activated pathway of the Strongylocentrotus purpuratus sperm flagellum? Biophys J. 102: 2481-2488. DOI: 10.1016/j.bpj.2012.03.075
  4. E. Zavala-López and M. Santillán (2012) An analysis of overall network architecture reveals an infinite-period bifurcation underlying oscillation arrest in the segmentation clock, Math. Model. Nat. Phenom. 7: 95-106. DOI: 10.1051/mmnp/20127605
  5. G. Ballesteros-Rodea, M. Santillán, M. Cruz-Aguilar, et al. (2012) The alternative products of Trypanosoma cruzi LYT1 have different localization patterns, Vet. Mex. 43: 29-43.
  6. G. Ballesteros-Rodea, M. Santillán, S. Martínez-Calvillo and R. G. Manning-Cela (2012) Flagellar motility of Trypanosoma cruzi epimastigotes, J. Biomed. Biotechnol. 2012: 520380. DOI: 10.1155/2012/520380
  7. M. Santillán (2011) Dynamic stability and thermodynamic characterization in an enzymatic reaction at the single molecule level, Phys. A 390: 4038-4044. DOI: 10.1016/j.physa.2011.05.032
  8. M. Santillán and H. Qian (2011) Irreversible thermodynamics in multiscale stochastic dynamical systems, Phys. Rev. E 83: 041130. DOI: 10.1103/PhysRevE.83.041130
  9. E. S. Zeron and M. Santillán (2011) Numerical solution of the chemical master equation: uniqueness and stability of the stationary distribution for chemical networks, and mRNA bursting in a gene network with negative feedback, Meth. Enzymol. 487 C: 149-171. DOI: 10.1016/B978-0-12-381270-4.00006-8


  1. O. Díaz-Hernández and M. Santillán (2010) Bistable behavior of the lac operon in E. coli when induced with a mixture of lactose and TMG, Frontiers in Physiology 1: 22, DOI: 10.3389/fphys.2010.00022
  2. O. Díaz-Hernández, R. Páez-Hernández, and M. Santillán (2010) Thermodynamic performance vs. dynamic stability in an enzymatic reaction model, Physica A 389: 3476-3483, DOI: 10.1016/j.physa.2010.04.006
  3. E. S. Zeron and M. Santillán (2010) Distributions for negative-feedback-regulated stochastic gene expression: dimension reduction and numerical solution of the chemical master equation, J. Theor. Biol. 264: 377-385, DOI: 10.1016/j.jtbi.2010.02.004
  4. A. Hernández-Valdez, M. Santillán, and E. S. Zeron (2010) Cycling expression and cooperative operator interaction in the trp operon of Escherichia coli, J. Theor. Biol. 263: 340-352, DOI: 10.1016/j.jtbi.2009.12.005
  5. M. Santillán and M. C. Mackey (2008) Dynamic stability vs thermodynamic performance in a simple model for a Brownian motor, Phys. Rev. E. 78: 061122, DOI: 10.1103/PhysRevE.78.061122
  6. M. Santillán (2008) Reflections on the origin, meaning, and future of Systems Biology, Math. Model. Nat. Phenom. 3: 98-101. DOI: 10.1051/mmnp:2008057
  7. M. Santillán (2008) On the use of Hill functions in mathematical models of gene regulatory networks, Math. Model. Nat. Phenom. 3: 85-97, DOI: 10.1051/mmnp:2008056
  8. M. Santillán, E. S. Zeron, and J. L. del Río-Correa (2008) A formal derivation of the Gibbs entropy for classical systems following the Schrödinger quantum mechanical approach, Eur. J. Phys. 29: 629-638, DOI: 10.1088/0143-0807/29/3/022
  9. M. Santillán and M. C. Mackey (2008) Quantitative approaches to the study of bistability in the lac operon of Escherichia coli, J. Roy. Soc. Interface 5 Suppl. 1: S29-S39, DOI: 10.1098/rsif.2008.0086.focus
  10. R. Páez-Hernández and M. Santillán (2008) Comparison of the energetic properties and the dynamical stability in a mathematical model of the stretch reflex, Physica A 387: 3574-3582, DOI: 10.1016/j.physa.2008.02.046
  11. L. Guzmán-Vargas and M. Santillán (2008) Comparative analysis of the complex transcription-factor gene regulatory networks of E. coli and S. cerevisiae, BMC Systems Biology 2: 13, DOI: 10.1186/1752-0509-2-13
  12. M. Santillán and M. C. Mackey (2008) A Proposed Mechanism for the Interaction of the Segmentation Clock and the Determination Front in Somitogenesis, PLoS ONE 3: e1561, DOI: 10.1371/journal.pone.0001561
  13. M. Santillán (2008) Bistable behaviour in a model of the lac operon in Escherichia coli with variable growth rate, Biophys. J. 94: 2065-2081, DOI: 10.1529/biophysj.107.118026


  1. J. G. Rodríguez-González, M. Santillán, A. C. Fowler, and M. C. Mackey (2007) The segmentation clock in mice: interaction between the Wnt and Notch signalling pathways, J. Theor. Biol. 248: 37-47, DOI: 10.1016/j.jtbi.2007.05.003
  2. M. Santillán, M. C. Mackey, and E. S. Zeron (2007) Origin of bistability in the lac operon, Biophys. J. 92: 3830-3842, DOI: 10.1529/biophysj.106.101717
  3. R. Páez-Hernández, F. Angulo-Brown, and M. Santillán (2006) Dynamic robustness and thermodynamic optimization in a non-endoreversible Curzon-Ahlborn engine, J. Non-equilib. Thermodyn. 31: 173-188, DOI: 10.1515/JNETDY.2006.008
  4. M. Santillán and E. S. Zeron (2006) Analytical study of the multiplicity of regulatory mechanisms in the tryptophan operon, Bull. Math. Biol. 68: 343-359, DOI: 10.1007/s11538-005-9025-0
  5. M. C. Mackey and M. Santillán (2005) Mathematics, biology, and physics: interactions and interdependence, Notices of the AMS 52: 832-846
  6. M. Santillán and M. C. Mackey (2005) Dynamic behaviour of the B12 riboswitch, Phys. Biol. 2: 29-35,DOI: 10.1088/1478-3967/2/1/004
  7. M. Santillán and E. S. Zeron (2004) Dynamic influence of feedback enzyme inhibition and transcription attenuation on the tryptophan operon response to nutritional shifts, J. Theor. Biol. 231: 287-298, DOI: 10.1016/j.jtbi.2004.06.023
  8. N. Yildrim, M. Santillán, Daisuke Horike, and M. C. Mackey (2004) Dynamics and bistability in a reduced model of the lac operon, Chaos 14: 279-292, DOI: 10.1063/1.1689451
  9. M. C. Mackey, M. Santillán, and N. Yildrim (2004) Modeling operon dynamics: the tryptophan and lactose operons as paradigms, CR Biologies 327: 211-224, DOI: 10.1016/j.crvi.2003.11.009
  10. M. Santillán and M. C. Mackey (2004) Influence of catabolite repression and inducer exclusion on the bistable behavior of the lac operon, Biophys J. 86: 1282-1292, DOI:10.1016/S0006-3495(04)74202-2
  11. M. Santillán and M. C. Mackey (2004) Why the lysogenic state of phage lambda is so stable: A mathematical modeling approach, Biophys J. 86: 75-84, DOI:10.1016/S0006-3495(04)74085-0


  1. M. Santillán (2003) Allometric scaling law in a simple oxygen exchanging system: possible implications on the biological allometric scaling laws, J. Theor. Biol. 223: 249-257, DOI: 10.1016/S0022-5193(03)00097-3
  2. M. Santillán, R. Hernández-Pérez, and R. Delgado-Lezama (2003) A numeric study of the noise-induced tremor in a mathematical model of the stretch reflex, J. Theor. Biol. 222: 99-115, DOI: 10.1016/S0022-5193(03)00016-X
  3. F. Angulo-Brown, L. A. Arias-Hernández, and M. Santillán (2002) On some connections between first order irreversible thermodynamics and finite-time thermodynamics, Rev. Mex. Fis. 48 Suppl. 1: 182-192
  4. M. Santillán, G. Maya, and F. Angulo-Brown (2001) Local stability analysis of an endoreversible Curxon-Ahlborn-Novikov engine working in a maximum-power-like regime, J. Phys. D: Appl. Phys. 34: 2068-2072, DOI: 10.1088/0022-3727/34/13/318
  5. M. Santillán, and M. C. Mackey (2001) Dynamic behaviour in mathematical models of the tryptophan operon, Chaos 11: (1) 261-268, DOI:10.1063/1.1336806
  6. M. Santillán and M. C. Mackey (2001) Dynamic regulation of the tryptophan operon: A modeling study and comparison with experimental data, Proc. Natl. Acad. Sci. USA 98: (4) 1364-1369, DOI: 10.1073/pnas.98.4.1364
  7. M. Santillán, F. Angulo-Brown, and O. Chavoya-Aceves (2001) Formalization of common power and efficiency definitions for energy-converting intracellular biochemical processes, Rev. Mex. Fis. 47: 158-161
  8. M. Santillán, J. M. Mahaffy, J. Bélair, and M. C. Mackey (2000) Regulation of Platelet Production: The Normal Response to Perturbation and Cyclical Platelet Disease. J. Theor. Biol. 206: 585-603, DOI:10.1006/jtbi.2000.2149


  1. M. Santillán (1999) A Thermodynamic Optimization Analysis of a Possible Relation between the Parameters that Determine the Energetics of Muscle Contraction in Steady State, J. Theor Biol. 199:105-112, DOI:10.1006/jtbi.1999.0946
  2. M. Santillán (1998) The optimum weight of a baseball bat, Rev. Mex. Fis. 44: 529-532
  3. G. Ares de Parga and M. Santillán (1998) A variational approach to some properties of endorreversible heat engines, Rev. Mex. Fis. 44: 373-376
  4. M. Santillán, G. Ares de Parga, and F. Angulo-Brown (1998) Black body radiation and the maximum entropy production regime, Eur. J. Phys. 19: 361-369, DOI: 10.1088/0143-0807/19/4/008
  5. M. Santillán and F. Angulo-Brown (1997) A thermodynamic approach to the compromise between power and efficiency in muscle contraction, J. Theor. Biol. 189: 391-398,DOI:10.1006/jtbi.1997.0526
  6. M. Santillán, L. A. Arias-Hernández and F. Angulo-Brown (1997) Some optimization criteria for biological systems in linear irreversible thermodynamics, Il Nuovo Cimento 19D: 99-109
  7. G. Ortega-Pierres, A. Alarcón, et al. (1996) Impact of new methodologies in the study of parasites, Gac. Med. Mex. 132: 475-517
  8. F. Angulo-Brown, M. Santillán, and E. Calleja Quevedo (1995) Thermodynamic optimality in some biochemical reactions, Il Nuovo Cimento 17D: 85-89
  9. E. Frixione, L. Ruiz, M. Santillán, L. V. de Vargas, J. M. Tejero, and A. H. Undeen (1992) Dynamics of polar filamet discharge and sporoplasm expulsion by microsporidian spores, Cell Motil. Cytoskel. 22: 38-50, DOI: 10.1002/cm.970220105