Rational design of a genetic finite state machine: Combining biology, engineering, and mathematics for bio-computer research

[EN] The recent success of biological engineering is due to a tremendous amount of research effort and the increasing number of market opportunities. Indeed, this has been partially possible due to the contribution of advanced mathematical tools and the application of engineering principles in genetic-circuit development. In this work, we use a rationally designed genetic circuit to show how models can support research and motivate students to apply mathematics in their future careers. A genetic four-state machine is analyzed using three frameworks: Deterministic and stochastic modeling through di erential and master equations, and a spatial approach via a cellular automaton. Each theoretical framework sheds light on the problem in a complementary way. It helps in understanding basic concepts of modeling and engineering, such as noise, robustness, and reaction¿di usion systems. The designed automaton could be part of a more complex system of modules conforming future bio-computers and it is a paradigmatic example of how models can assist teachers in multidisciplinary education.D.F. was supported by an internal grant from Palacky University Olomouc (no. IGA_PrF_2020_028) and J.A.C. by MEC, grant number MTM2016-75963-P.Fuente, D.; Garibo I Orts, Ó.; Conejero, JA.; Urchueguía Schölzel, JF. (2020). Rational design of a genetic finite state machine: Combining biology, engineering, and mathematics for bio-computer research. Mathematics. 8(8):1-20. https://doi.org/10.3390/math8081362S12088Khalil, A. S., & Collins, J. J. (2010). Synthetic biology: applications come of age. Nature Reviews Genetics, 11(5), 367-379. doi:10.1038/nrg2775Jullesson, D., David, F., Pfleger, B., & Nielsen, J. (2015). Impact of synthetic biology and metabolic engineering on industrial production of fine chemicals. 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Cell Systems, 7(3), 231-244. doi:10.1016/j.cels.2018.08.007Britton, N. F., Bulai, I. M., Saussure, S., Holst, N., & Venturino, E. (2019). Can aphids be controlled by fungus? A mathematical model. Applied Mathematics and Nonlinear Sciences, 4(1), 79-92. doi:10.2478/amns.2019.1.00009Rojas, C., & Belmonte-Beitia, J. (2018). Optimal control problems for differential equations applied to tumor growth: state of the art. Applied Mathematics and Nonlinear Sciences, 3(2), 375-402. doi:10.21042/amns.2018.2.00029Tsimring, L. S. (2014). Noise in biology. Reports on Progress in Physics, 77(2), 026601. doi:10.1088/0034-4885/77/2/026601Székely, T., & Burrage, K. (2014). Stochastic simulation in systems biology. Computational and Structural Biotechnology Journal, 12(20-21), 14-25. doi:10.1016/j.csbj.2014.10.003Bessonov, N., Bocharov, G., Meyerhans, A., Popov, V., & Volpert, V. (2020). Nonlocal Reaction–Diffusion Model of Viral Evolution: Emergence of Virus Strains. 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Efficiency improvement of a ground coupled heat pump system from energy management

The installed capacity of an air conditioning system is usually higher than the average cooling or heating demand along the year. So, most of the time, the system is working under its actual capacity. In this contribution, we study the way to improve the efficiency of a ground coupled heat pump air conditioning system by adapting its produced thermal energy to the actual thermal demand. For this purpose, an air conditioning system composed by a ground coupled heat pump and a central fan coil linked to an office located in a cooling dominated area was simulated, and a new management strategy aiming to diminish electrical consumption was developed under the basic constraint that comfort requirements are kept. This strategy takes advantage of the possibility of managing the air flow in the fan, the water mass flows in the internal and external hydraulic systems, and the set point temperature in the heat pump to achieve this objective. The electrical consumption of the system is calculated for the new management strategy and compared with the results obtained for a conventional one, resulting in estimated energy savings around 30%This work has been supported by the Spanish Government under projects "Modelado y simulacion de sistemas energeticos complejos" (2005 Ramon y Cajal program), "Modelado, simulacion y validacion experimental de la transferencia de calor en el entorno de la edificacion" (ENE2008-0059/CON). A. Sala is grateful to the financial support of grants DPI2008-06731-c02-01 (Spanish Government), and Generalitat Valenciana Prometeo/2008/088.Pardo García, N.; Montero Reguera, ÁE.; Sala Piqueras, A.; Martos Torres, J.; Urchueguía Schölzel, JF. (2011). Efficiency improvement of a ground coupled heat pump system from energy management. Applied Thermal Engineering. 31(2):391-398. https://doi.org/10.1016/j.applthermaleng.2010.09.016S39139831

Large scale evaluation of differences between network-based and pairwise sequence-alignment-based methods of dendrogram reconstruction

[EN] Dendrograms are a way to represent relationships between organisms. Nowadays, these are inferred based on the comparison of genes or protein sequences by taking into account their differences and similarities. The genetic material of choice for the sequence alignments (all the genes or sets of genes) results in distinct inferred dendrograms. In this work, we evaluate differences between dendrograms reconstructed with different methodologies and for different sets of organisms chosen at random from a much larger set. A statistical analysis is performed to estimate fluctuations between the results obtained from the different methodologies that allows us to validate a systematic approach, based on the comparison of the organisms' metabolic networks for inferring dendrograms. This has the advantage that it allows the comparison of organisms very far away in the evolutionary tree even if they have no known ortholog gene in common. Our results show that dendrograms built using information from metabolic networks are similar to the standard sequence-based dendrograms and can be a complement to them.All authors received funding from the European Union Seventh Framework Program (FP7/2007-2013) under grant agreement number 308518 (CyanoFactory) (https://ec.europa.eu/research/fp7/index_en.cfm).The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.Gamermann, D.; Montagud, A.; Conejero, JA.; Fernández De Córdoba, P.; Urchueguía Schölzel, JF. (2019). Large scale evaluation of differences between network-based and pairwise sequence-alignment-based methods of dendrogram reconstruction. PLoS ONE. 14(9):1-13. https://doi.org/10.1371/journal.pone.0221631S113149Robinson, D. F., & Foulds, L. R. (1981). Comparison of phylogenetic trees. Mathematical Biosciences, 53(1-2), 131-147. doi:10.1016/0025-5564(81)90043-2Day, W. H. E. (1985). 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Cladistics, 27(4), 417-427. doi:10.1111/j.1096-0031.2010.00337.xWu, M., & Eisen, J. A. (2008). A simple, fast, and accurate method of phylogenomic inference. Genome Biology, 9(10), R151. doi:10.1186/gb-2008-9-10-r151Wu, D., Hugenholtz, P., Mavromatis, K., Pukall, R., Dalin, E., Ivanova, N. N., … Eisen, J. A. (2009). A phylogeny-driven genomic encyclopaedia of Bacteria and Archaea. Nature, 462(7276), 1056-1060. doi:10.1038/nature08656Mai, H., Lam, T.-W., & Ting, H.-F. (2017). A simple and economical method for improving whole genome alignment. BMC Genomics, 18(S4). doi:10.1186/s12864-017-3734-2Feng, B., Lin, Y., Zhou, L., Guo, Y., Friedman, R., Xia, R., … Tang, J. (2017). Reconstructing Yeasts Phylogenies and Ancestors from Whole Genome Data. Scientific Reports, 7(1). doi:10.1038/s41598-017-15484-5Rokas, A., Williams, B. L., King, N., & Carroll, S. B. (2003). Genome-scale approaches to resolving incongruence in molecular phylogenies. Nature, 425(6960), 798-804. doi:10.1038/nature02053JEFFROY, O., BRINKMANN, H., DELSUC, F., & PHILIPPE, H. (2006). Phylogenomics: the beginning of incongruence? Trends in Genetics, 22(4), 225-231. doi:10.1016/j.tig.2006.02.003Gamermann, D., Montagud, A., Conejero, J. A., Urchueguía, J. F., & de Córdoba, P. F. (2014). New Approach for Phylogenetic Tree Recovery Based on Genome-Scale Metabolic Networks. Journal of Computational Biology, 21(7), 508-519. doi:10.1089/cmb.2013.0150Jeong, H., Tombor, B., Albert, R., Oltvai, Z. N., & Barabási, A.-L. (2000). The large-scale organization of metabolic networks. Nature, 407(6804), 651-654. doi:10.1038/35036627Clemente, J. C., Satou, K., & Valiente, G. (2007). Phylogenetic reconstruction from non-genomic data. Bioinformatics, 23(2), e110-e115. doi:10.1093/bioinformatics/btl307Deyasi, K., Banerjee, A., & Deb, B. (2015). Phylogeny of metabolic networks: A spectral graph theoretical approach. 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Light distribution and spectral composition within cultures of micro-algae: Quantitative modelling of the light field in photobioreactors

[EN] Light, being the fundamental energy source to sustain life on Earth, is the external factor with the strongest impact on photosynthetic microorganisms. Moreover, when considering biotechnological applications such as the production of energy carriers and commodities in photobioreactors, light supply within the reactor volume is one of the main limiting factors for an efficient system. Thus, the prediction of light availability and its spectral distribution is of fundamental importance for the productivity of photo-biological processes. The light field model here presented is able to predict the intensity and spectral distribution of light throughout the reactor volume. The input data for the algorithm are chlorophyll-specific absorption and scattering spectra at different irradiance values for a given organism, the depth of the photobioreactor, the cell-density and also the intensity and emission spectrum of the light source. Although in the form exposed here the model is optimized for photosynthetic microorganism cultures inside flat-type photobioreactors, the theoretical framework is easily extensible to other geometries. Our calculation scheme has been applied to model the light field inside Synechocystis sp. PCC 6803 wild-type and Olive antenna mutant cultures at different cell-density concentrations exposed to LED lamps of different colours, delivering results with reasonable accuracy, despite the data uncertainties. To achieve this, Synechocystis experimental attenuation profiles for different light sources were estimated by means of the Beer- Lambert law, whereby the corresponding downward irradiance attenuation coefficients were obtained through inherent optical properties at any wavelength within the photosynthetically active radiation band. In summary, the model is a general tool to predict light availability inside photosynthetic microorganism cultures and to optimize light supply, in respect to both intensity and spectral distribution, in technological applications. This knowledge is crucial for industrialscale optimisation of light distribution within photobioreactors and a fundamental parameter for unravelling the nature of many photosynthetic processes.This project has received funding from the European Union's Seventh Programme for Research, Technological Development and Demonstration under grant agreement No 308518 CyanoFactory, to Javier Urchueguia's and Matthias Rogner's respective research groups and from the grant Contratos Predoctorales FPI 2013 of the Universitat Politecnica de Valencia to the first one. We would also like to thank David Lea-Smith and Dariusz Stramski for their fruitful and selfless contribution. We kindly acknowledge the experimental support of Saori Fuse for the cultivation of cyanobacteria.Fuente-Herraiz, D.; Keller, J.; Conejero, JA.; Roegner, M.; Rexroth, S.; Urchueguía Schölzel, JF. (2017). Light distribution and spectral composition within cultures of micro-algae: Quantitative modelling of the light field in photobioreactors. Algal Research. 23:166-177. https://doi.org/10.1016/j.algal.2017.01.004S1661772

New approach for phylogenetic tree recovery based on genome-scale metabolic networks

[EN] A wide range of applications and research has been done with genome-scale metabolic models. In this work, we describe an innovative methodology for comparing metabolic networks constructed from genome-scale metabolic models and how to apply this comparison in order to infer evolutionary distances between different organisms. Our methodology allows a quantification of the metabolic differences between different species from a broad range of families and even kingdoms. This quantification is then applied in order to reconstruct phylogenetic trees for sets of various organisms.The research leading to these results has received funding from the European Union Seventh Framework Program (FP7/2007-2013) under grant agreement number 308518 (CyanoFactory).Gamermann, D.; Montagud Aquino, A.; Conejero Casares, JA.; Urchueguía Schölzel, JF.; Fernández De Córdoba Castellá, PJ. (2014). New approach for phylogenetic tree recovery based on genome-scale metabolic networks. Journal of Computational Biology. 21(7):508-519. https://doi.org/10.1089/cmb.2013.0150S50851921

A transfer matrix method for the analysis of fractal quantum potentials

The scattering properties of quantum particles on fractal potentials at different stages of fractal growth are obtained by means of the transfer matrix method. This approach can be easily adopted for project assignments in introductory quantum mechanics for undergraduates. The reflection coefficients for both the fractal potential and the finite periodic potential are calculated and compared. It is shown that the reflection coefficient for the fractal has a self-similar structure associated with the fractal distribution of the potential

In situ optimization methodology for the water circulation pumps frequency of ground source heat pump systems: Analysis for multistage heat pump units

[EN] In order to optimize the global energy performance of a ground source heat pump system, special attention needs to be paid to the auxiliaries as they stand for a considerable part of the total energy consumption. A new in situ experimental methodology based on the frequency variation of the water circulation pumps in order to optimize the energy performance of the system was previously published by the authors for a ground source heat pump system using a single stage heat pump with ON/OFF regulation. The original single stage heat pump was recently replaced with a multistage unit consisting of two compressors of the same capacity working in tandem. A new experimental campaign was carried out and a new study was performed in order to adapt the in situ optimization methodology to the performance of the tandem compressors unit, and, by extension, to the multistage case. This paper presents the in situ optimization methodology for the water circulation pumps frequency adapted for multistage ground source heat pump systems. Results show that energy savings up to 32% can be obtained by applying this optimization methodology.This work was supported by the "Programa de Ayudas de Investigacion y Desarrollo (PAID)" of the Universitat Politecnica de Valencia. This work was also supported by the European FP7 project "Advanced ground source heat pump systems for heating and cooling in Mediterranean climate" (GROUND-MED).Cervera Vázquez, J.; Montagud Montalvá, CI.; Corberán Salvador, JM. (2015). In situ optimization methodology for the water circulation pumps frequency of ground source heat pump systems: Analysis for multistage heat pump units. Energy and Buildings. 88:238-247. https://doi.org/10.1016/j.enbuild.2014.12.008S2382478

A modular synthetic device to calibrate promoters

In this contribution, a design of a synthetic calibration genetic circuit to characterize the relative strength of different sensing promoters is proposed and its specifications and performance are analyzed via an effective mathematical model. Our calibrator device possesses certain novel and useful features like modularity (and thus the possibility of being used in many different biological contexts), simplicity, being based on a single cell, high sensitivity and fast response. To uncover the critical model parameters and the corresponding parameter domain at which the calibrator performance will be optimal, a sensitivity analysis of the model parameters was carried out over a given range of sensing protein concentrations (acting as input). Our analysis suggests that the half saturation constants for repression, sensing and difference in binding cooperativity (Hill coefficients) for repression are the key to the performance of the proposed device. They furthermore are determinant for the sensing speed of the device, showing that it is possible to produce detectable differences in the repression protein concentrations and in turn in the corresponding fluorescence in less than two hours. This analysis paves the way for the design, experimental construction and validation of a new family of functional genetic circuits for the purpose of calibrating promoters.Comment: 24 pages, 11 figure

Polarization instabilities in a two-photon laser

We describe the operating characteristics of a new type of quantum oscillator that is based on a two-photon stimulated emission process. This two-photon laser consists of spin-polarized and laser-driven $^{39}$K atoms placed in a high-finesse transverse-mode-degenerate optical resonator, and produces a beam with a power of $\sim$0.2 $\mu$W at a wavelength of 770 nm. We observe complex dynamical instabilities of the state of polarization of the two-photon laser, which are made possible by the atomic Zeeman degeneracy. We conjecture that the laser could emit polarization-entangled twin beams if this degeneracy is lifted.Comment: Accepted by Physical Review Letters. REVTeX 4 pages, 4 EPS figure