Journal Papers


  1. Gemma Fernández-Mendoza G, Abraham Méndez-Fernández, Hugo J. Alves-Figueiredo, Gerardo García-Rivas and Moisés Santillán (2023) Exploring the Mechanisms Underlying Stroke Volume Variability Reduction in a Murine Model of Heart Failure with Reduced Ejection Fraction, PLOS ONE, 18(10): e0292687. DOI: 10.1371/journal.pone.0292687
  2. Ángel J. Zamora-Ramírez and Moisés Santillán (2023) Effects of fission and mitophagy on mitochondrial functionality under accelerated damage conditions: A mathematical modeling approach, Frontiers in Applied Mathematics and Statistics, 9: 1082928. DOI: 10.3389/fams.2023.1082928
  3. González-Ayala, Antonio Calvo-Hernández and Moisés Santillán (2023) Thermodynamic performance of coupled enzymatic reactions: a chemical kinetics model for analyzing cotransporters, ion pumps, and ATP synthases, Biophysical Chemistry, 293: 106932. DOI: 10.1016/j.bpc.2022.106932


  1. Moisés Santillán (2022) Systems Biology, Elsevier Reference Collection in Life Sciences, DOI: 10.1016/B978-0-12-822563-9.00087-1
  2. Diego A. Castro-López, Luis E. González-de-la-Vara, Moisés Santillán and Agustino Martínez-Antonio (2022) A molecular dynamic model of tryptophan overproduction in Escherichia coli, Fermentation, 8(10): 560. DOI: 10.3390/fermentation8100560
  3. Humberto Reyes-Pardo, Daniel P. Sánchez-Herrera, and Moisés Santillán (2022) On the effects of diabetes mellitus on the mechanical properties of DRG sensory neurons and their possible relation with diabetic neuropathy, Physical Biology, 19(4): 046002. DOI: 10.1088/1478-3975/ac6722
  4. Marc R. Roussel, Moisés Santillán (2022) Biochemical Problems, Mathematical Solutions, AIMS Mathematics, 7(4): 5662-5669. DOI: 10.3934/math.2022313
  5. J. Pantoja-Hernández, Víctor F. Breña-Medina, M. Santillán (2021) Hybrid reaction-diffusion and clock-and-wavefront model for the arrest of oscillations in the somitogenesis segmentation clock. Chaos 31(6): 063107 DOI: 10.1063/5.0045460. Paper highlited as noteworthy by the journal editors. Press release:
  6. J. Pantoja-Hernández and M. Santillán (2021) Segmentation-clock synchronization in circular-lattice networks of embryonic presomitic-mesoderm cells. AIMS Mathematics  6(6): 5817-5836 DOI: 10.3934/math.2021344


  1. J. A. Arias-Del-Angel, J. M. Santana-Solano, M. Santillán, R. G. Manning-Cela (2020) Motility patterns of Trypanosoma cruzi trypomastigotes correlate with the efficiency of parasite invasion in vitro. Scientific Reports 10: 15894 DOI: 10.1038/s41598-020-72604-4
  2. J. A. Arias-Del-Angel, R. G. Manning-Cela, M. Santillán (2020) Dynamics of mammalian cell infection by T. cruzi trypomastigotes. Frontiers in Microbiology 11: 559660 DOI: 10.3389/fmicb.2020.559660
  3. J. G. Guerrero and M. Santillán (2020) Crosstalk between the circadian clock and the mTORC1 pathway. Journal of Theoretical Biology 501: 110360 DOI: 10.1016/j.jtbi.2020.110360
  4. O. A. Gallardo Navarro and M. Santillán (2019)  Three-way interactions in an artificial community of bacterial strains directly isolated from the environment and their effect on the system population dynamics, Frontiers in Microbiology 10: 2555 DOI: 10.3389/fmicb.2019.02555
  5. L. Sánchez-Gómez, A. Guerrero-Hernández, and M. Santillán (2019)  Polymerization of sarcoplasmic-reticulum calcium-binding proteins might explain observed reticulum kinetics-on-demand behavior, Journal of Theoretical Biology 482: 109986 DOI: 10.1016/j.jtbi.2019.08.017
  6. A. Vázquez-Jiménez, M. Santillán, and J. Rodríguez-González (2019) Characterization of intrinsic and extrinsic noise effects in positively regulated genes, Journal of Biological Systems 27(3): 383-398 DOI: 10.1142/S0218339019500165
  7. L. Diambra and M. Santillán (2019) Editorial: Emergent Effects of Noise in Biology: From Gene Expression to Cell Motility, Frontiers in Physics 7: 83 DOI: 10.3389/fphy.2019.00083
  8. D. I. Ororzco-Gómez, J. E. Sosa-Hernández, O. A. Gallardo-Navarro, J. Santana-Solano, and M. Santillán (2019) Bistable behavior and medium-dependent post-translational regulation of the tryptophanase operon regulatory pathway in Escherichia coli. Scientific Reports 9(1): 5451 DOI: 10.1038/s41598-019-41856-0
  9. O. Díaz-Hernández, E. Ramírez-Álvarez, A. Flores-Rosas, C. Enríquez-Flores, M. Santillán, P. Padilla-Longoria, and G. Escalera-Santos (2019) Amplitude death induced by intrinsic noise in a system of three coupled stochastic Brusselators, Journal of Computational and Nonlinear Dynamics 14(4): 041004 DOI: 10.1115/1.4042322


  1. J. González-Ayala, M. Santillán, I. Reyes-Ramírez, M. Jesús-Santos, A. Calvo-Hernández, and J. M. Mateos-Roco (2018) Optimization and Stability of Heat Engines: The Role of Entropy Evolution, Entropy 20(11): 865 DOI: 10.3390/e20110865
  2. 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 98: 032142 DOI: 10.1103/PhysRevE.98.032142
  3. M. Santillán (2018) Synchronization dynamics of two mutually coupled 555-IC based electronic oscillators, Revista Mexicana de Física 64: 107-115 DOI: 10.31349/RevMexFis.64.107
  4. 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
  5. 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
  6. 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
  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, DOI:10.1007/BF02451604
  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


  1. M. Santillán (2007) Complex dynamic behaviour in simple gene regulatory networks, AIP Conference Proceedings 885: 161-184, DOI: 10.1063/1.2563191