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During his doctorate, Professor Hernández-Lemus worked in theoretical chemical physics and non-equilibrium statistical physics. In particular, he developed an irreversible thermodynamics formalism to study molecular systems in the critical point far from equilibrium. In the context of this formalism, by extending ideas from measure theory and mathematical statistical mechanics, he was able to derive correlation functions for non-equilibrium systems without using equilibrium closures (such as the Ornstein-Zernike). This work was the first fully-analytical study, free from adjustable parameters, to describe appropriately (both quantitatively and qualitatively) the critical co-solution transition for a binary mixture with its associated transport processes [Hernández-Lemus, E. García-Colín, L.S., Non-equilibrium critical behavior: An extended irreversible thermodynamics approach, Jou. of Non-Equil. Thermodyn., 31, 4, 397-417, (2006)].
Within biological physics and computational systems biology, current research includes the development of a non-equilibrium thermodynamics theoretical framework to study whole genome transcriptional regulation in eukaryotes (humans in particular) [Hernández-Lemus, E., Non-Equilibrium Thermodynamics of Gene Expression and Transcriptional Regulation, Jou. of Non-Equil. Thermodyn., 34, 4, 371-394, (2009)].
This theoretical framework has been used to analyze transcriptional bursts and their relation with anomalous gene expression in cancer [Hernández-Lemus, E., Correa-Rodríguez, M.D., Non-equilibrium hyperbolic transport in transcriptional regulation, PLoS ONE 6, 7, e21558 (2011)] and their role in specific genes at the coupling between metabolic disruption and cancer [Baca-López, K., Hidalgo-Miranda, A., Mayorga, M., Gutiérrez-Nájera, N.,Hernández-Lemus, E., The role of master regulators in the metabolic/ transcriptional coupling in breast carcinomas, PLoS ONE 7, 8, e42678, (2012)].
Aside from individual developments, Professor Hernández-Lemus has been also involved in the statistical and computational design of high-end experimental projects such as the Mexican Genome Project (Mexican Genome Diversity and Genomic Medicine Project) [Silva-Zolezzi I, et al., Analysis of genomic diversity in Mexican Mestizo populations to develop genomic medicine in Mexico. PNAS 106, 21, 8611- 8616, (2009)] and the sequencing of the genome of diffuse large B-cell lymphoma cells [Lohr, J., et al., Discovery and Prioritization of Somatic Mutations in DLBCL by Whole Exome Sequencing, PNAS 109, 10, 3879-3884, (2012)].
Dr. Hernández- Lemus is also a strong advocate for OpenScience/OpenAccess [He is Academic Editor at PLoS ONE and Review Editor at Frontiers in Physiology] and has devoted special efforts to spread the role of theoretical physics (specially statistical mechanics and complex systems) in the biomedical research community within his country.