×

Fractional diffusion on the human proteome as an alternative to the multi-organ damage of SARS-CoV-2. (English) Zbl 1445.92136

Summary: The coronavirus 2019 (COVID-19) respiratory disease is caused by the novel coronavirus SARS-CoV-2 (severe acute respiratory syndrome coronavirus 2), which uses the enzyme ACE2 to enter human cells. This disease is characterized by important damage at a multi-organ level, partially due to the abundant expression of ACE2 in practically all human tissues. However, not every organ in which ACE2 is abundant is affected by SARS-CoV-2, which suggests the existence of other multi-organ routes for transmitting the perturbations produced by the virus. We consider here diffusive processes through the protein-protein interaction (PPI) network of proteins targeted by SARS-CoV-2 as an alternative route. We found a subdiffusive regime that allows the propagation of virus perturbations through the PPI network at a significant rate. By following the main subdiffusive routes across the PPI network, we identify proteins mainly expressed in the heart, cerebral cortex, thymus, testis, lymph node, kidney, among others of the organs reported to be affected by COVID-19.
©2020 American Institute of Physics

MSC:

92C50 Medical applications (general)
92-10 Mathematical modeling or simulation for problems pertaining to biology
26A33 Fractional derivatives and integrals
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Gorbalenya, A.; Baker, S.; Baric, R., The species severe acute respiratory syndrome-related coronavirus: Classifying 2019-nCoV and naming it SARS-CoV-2, Nat. Microbiol., 5, 536-544 (2020) · doi:10.1038/s41564-020-0695-z
[2] Zhou, P.; Yang, X. L.; Wang, X. G.; Hu, B.; Zhang, L.; Zhang, W.; Si, H. R.; Zhu, Y.; Li, B.; Huang, C. L.; Chen, H. D., A pneumonia outbreak associated with a new coronavirus of probable bat origin, Nature, 579, 270-273 (2020) · doi:10.1038/s41586-020-2012-7
[3] Wu, F.; Zhao, S.; Yu, B.; Chen, Y. M.; Wang, W.; Song, Z. G.; Hu, Y.; Tao, Z. W.; Tian, J. H.; Pei, Y. Y.; Yuan, M. L., A new coronavirus associated with human respiratory disease in china, Nature, 579, 265-269 (2020) · doi:10.1038/s41586-020-2008-3
[4] Jiang, F.; Deng, L.; Zhang, L.; Cai, Y.; Cheung, C. W.; Xia, Z., Review of the clinical characteristics of coronavirus disease 2019 (COVID-19), J. Gen. Intern. Med., 35, 1545-1549 (2020) · doi:10.1007/s11606-020-05762-w
[5] Zhang, B.; Zhou, X.; Qiu, Y.; Feng, F.; Feng, J.; Jia, Y.; Zhu, H.; Hu, K.; Liu, J.; Liu, Z.; Wang, S.; Gong, Y.; Zhou, C.; Zhu, T.; Cheng, Y.; Liu, Z.; Deng, H.; Tao, F.; Ren, Y.; Cheng, B.; Gao, L.; Wu, X.; Yu, L.; Huang, Z.; Mao, Z.; Song, Q.; Zhu, B.; Wang, J., medRxiv · doi:10.1101/2020.02.26.20028191
[6] Zhou, M.; Zhang, X.; Qu, J., Coronavirus disease 2019 (COVID-19): A clinical update, Front. Med., 14, 126-135 (2020) · doi:10.1007/s11684-020-0767-8
[7] Zaim, S.; Chong, J. H.; Sankaranarayanan, V.; Harky, A., COVID-19 and multi-organ response, Curr. Probl. Cardiol., 45, 100618 (2020) · doi:10.1016/j.cpcardiol.2020.100618
[8] Chan, J. F.; Kok, K. H.; Zhu, Z.; Chu, H.; To, K. K.; Yuan, S.; Yuen, K. Y., Genomic characterization of the 2019 novel human-pathogenic coronavirus isolated from a patient with atypical pneumonia after visiting Wuhan, Emerg. Microb. Infect., 9, 221-236 (2020) · doi:10.1080/22221751.2020.1719902
[9] Li, W.; Moore, M. J.; Vasilieva, N.; Sui, J.; Wong, S. K.; Berne, M. A.; Somasundaran, M.; Sullivan, J. L.; Luzuriaga, K.; Greenough, T. C.; Choe, H.; Farzan, M., Angiotensin-converting enzyme 2 is a functional receptor for the SARS coronavirus, Nature, 426, 450-454 (2003) · doi:10.1038/nature02145
[10] Hoffmann, M.; Kleine-Weber, H.; Schroeder, S.; Krueger, N.; Herrler, T.; Erichsen, S.; Schiergens, T. S.; herrler, G.; Wu, N.-H.; Nitsche, A.; Müller, M. A.; Drosten, C.; Pöhlmann, S., SARS-CoV-2 cell entry depends on ACE2 and TMPRSS2 and is blocked by a clinically proven protease inhibitor, Cell, 181, 272-280 (2020) · doi:10.1016/j.cell.2020.02.052
[11] Chai, X., Hu, L., Zhang, Y., Han, W., Lu, Z., Ke, A., Zhou, J., Shi, G., Fang, N., Fan, J., Cai, J., Fan, J., and Lan, F., “Specific ACE2 expression in cholangiocytes may cause liver damage after 2019-nCoV infection,” bioRxiv (2020).
[12] Zhao, Y.; Zhao, Z.; Wang, Y.; Zhou, Y.; Ma, Y.; Zuo, W., bioRxiv · doi:10.1101/2020.01.26.919985
[13] Hamming, I.; Timens, W.; Bulthuis, M. L.; Lely, A. T.; Navis, G. J.; van Goor, H., Tissue distribution of ACE2 protein, the functional receptor for SARS coronavirus. A first step in understanding SARS pathogenesis, J. Pathol., 203, 631-637 (2004) · doi:10.1002/path.1570
[14] Gordon, D. E.; Jang, G. M.; Bouhaddou, M.; Xu, J.; Obernier, K.; O’meara, M. J.; Guo, J. Z.; Swaney, D. L.; Tummino, T. A.; Huttenhain, R.; Kaake, R. M., A SARS-CoV-2-human protein-protein interaction map reveals drug targets and potential drug-repurposing, Nature, 583, 459 (2020) · doi:10.1038/s41586-020-2286-9
[15] Gysi, D. M.; Valle, I. D.; Zitnik, M.; Ameli, A.; Gan, X.; Varol, O.; Sanchez, H.; Baron, R. M.; Ghiassian, D.; Loscalzo, J.; Barabási, A. L.
[16] Maslov, S.; Sneppen, K., Specificity and stability in topology of protein networks, Science, 296, 910-913 (2002) · doi:10.1126/science.1065103
[17] Antal, M. A.; Bode, C.; Csermely, P., Perturbation waves in proteins and protein networks: Applications of percolation and game theories in signaling and drug design, Curr. Prot. Pept. Sci., 10, 161-72 (2009) · doi:10.2174/138920309787847617
[18] Santolini, M.; Barabási, A. L., Predicting perturbation patterns from the topology of biological networks, Proc. Natl. Acad. Sci. U.S.A., 115, E6375-E6383 (2018) · doi:10.1073/pnas.1720589115
[19] Stöcker, B. K.; Köster, J.; Zamir, E.; Rahmann, S., Modeling and simulating networks of interdependent protein interactions, Integr. Biol., 10, 290-305 (2018) · doi:10.1039/C8IB00012C
[20] Barabási, A. L.; Gulbahce, N.; Loscalzo, J., Network medicine: A network-based approach to human disease, Nat. Rev. Genet., 12, 56-68 (2011) · doi:10.1038/nrg2918
[21] Taylor, I. W.; Wrana, J. L., Protein interaction networks in medicine and disease, Proteomics, 12, 1706-1716 (2012) · doi:10.1002/pmic.201100594
[22] Furlong, L. I., Human diseases through the lens of network biology, Trends Genet., 29, 150-159 (2013) · doi:10.1016/j.tig.2012.11.004
[23] Batada, N. N.; Shepp, L. A.; Siegmund, D. O., Stochastic model of protein-protein interaction: Why signaling proteins need to be colocalized, Proc. Natl. Acad. Sci. U.S.A., 101, 6445-6449 (2004) · doi:10.1073/pnas.0401314101
[24] Zacharias, M., Accounting for conformational changes during protein-protein docking, Curr. Opin. Struct. Biol., 20, 180-186 (2010) · doi:10.1016/j.sbi.2010.02.001
[25] Chen, L.; Zhang, Y. H.; Zhang, Z.; Huang, T.; Cai, Y. D., Inferring novel tumor suppressor genes with a protein-protein interaction network and network diffusion algorithms, Mol. Ther. Meth. Clin. Devel., 21, 57-67 (2018) · doi:10.1016/j.omtm.2018.06.007
[26] Stojmirović, A.; Yu, Y. K., Information flow in interaction networks, J. Comput. Biol., 14, 1115-1143 (2007) · doi:10.1089/cmb.2007.0069
[27] Guigas, G.; Weiss, M., Sampling the cell with anomalous diffusion—The discovery of slowness, Biophys. J., 94, 90-94 (2008) · doi:10.1529/biophysj.107.117044
[28] Basak, S.; Sengupta, S.; Chattopadhyay, K., Understanding biochemical processes in the presence of sub-diffusive behavior of biomolecules in solution and living cells, Biophys. Rev., 11, 851-872 (2019) · doi:10.1007/s12551-019-00580-9
[29] Woringer, M.; Darzacq, X., Protein motion in the nucleus: From anomalous diffusion to weak interactions, Biochem. Soc. Trans., 46, 945-956 (2018) · doi:10.1042/BST20170310
[30] Sposini, V.; Chechkin, A. V.; Seno, F.; Pagnini, G.; Metzler, R., Random diffusivity from stochastic equations: Comparison of two models of Brownian yet non-Gaussian diffusion, New J. Phys., 20, 043044 (2018) · doi:10.1088/1367-2630/aab696
[31] Weiss, M.; Hashimoto, H.; Nilsson, T., Anomalous protein diffusion in living cells as seen by fluorescence correlation spectroscopy, Biophys. J., 84, 4043-4052 (2003) · doi:10.1016/S0006-3495(03)75130-3
[32] Weiss, M.; Elsner, M.; Kartberg, F.; Nilsson, T., Anomalous subdiffusion is a measure for cytoplasmic crowding in living cell, Biophys. J., 87, 3518-3524 (2004) · doi:10.1529/biophysj.104.044263
[33] Szymanski, J.; Weiss, M., Elucidating the origin of anomalous diffusion in crowded fluids, Phys. Rev. Lett., 103, 038102 (2009) · doi:10.1103/PhysRevLett.103.038102
[34] Weiss, M.; Nilsson, T., In a mirror dimly: Tracing the movements of molecules in living cells, Trends Cell Biol., 14, 267-273 (2004) · doi:10.1016/j.tcb.2004.03.012
[35] Gupta, S.; Biehl, R.; Sill, C.; Allgaier, J.; Sharp, M.; Ohl, M.; Richter, D., Protein entrapment in polymeric mesh: Diffusion in crowded environment with fast process on short scales, Macromolecules, 49, 1941-1949 (2016) · doi:10.1021/acs.macromol.5b02281
[36] Barkai, E.; Metzler, R.; Klafter, J., From continuous time random walks to fractional Fokker-Planck equation, Phys. Rev. E, 61, 132-138 (2000) · doi:10.1103/PhysRevE.61.132
[37] Shorten, P. R.; Sneyd, J., A mathematical analysis of obstructed diffusion within skeletal muscle, Biophys. J., 96, 4764-4778 (2009) · doi:10.1016/j.bpj.2009.02.060
[38] Mainardi, F., Fractional Calculus and Waves in Linear Viscoelasticity. An Introduction to Mathematical Models (2010), Imperial College Press · Zbl 1210.26004
[39] Cao, Y., Li, Y., Ren, W., and Chen, Y., “Distributed coordination algorithms for multiple fractional-order systems,” in 2008 47th IEEE Conference on Decision and Control (IEEE, 2008), pp. 2920-2925.
[40] Cao, Y.; Li, Y.; Ren, W.; Chen, Y., Distributed coordination of networked fractional-order systems, IEEE Trans. Syst. Man Cybern. B, 40, 362-370 (2009) · doi:10.1109/TSMCB.2009.2024647
[41] Lu, J., Shen, J., Cao, J., and Kurths, J., “Consensus of networked multi-agent systems with delays and fractional-order dynamics,” in Consensus and Synchronization in Complex Networks (Springer, Berlin, 2013), pp. 69-110.
[42] Metzler, R.; Klafter, J., The random walk’s guide to anomalous diffusion: A fractional dynamics approach, Phys. Rep., 339, 1-77 (2000) · Zbl 0984.82032 · doi:10.1016/S0370-1573(00)00070-3
[43] Riascos, A. P.; Mateos, J. L., Long-range navigation on complex networks using Lévy random walks, Phys. Rev. E, 86, 056110 (2012) · doi:10.1103/PhysRevE.86.056110
[44] Riascos, A. P.; Mateos, J. L., Fractional dynamics on networks: Emergence of anomalous diffusion and Lévy flights, Phys. Rev. E, 90, 032809 (2014) · doi:10.1103/PhysRevE.90.032809
[45] Michelitsch, T.; Riascos, A. P.; Collet, B.; Nowakowski, A.; Nicolleau, F., Fractional Dynamics on Networks and Lattices (2019), John Wiley and Sons, Inc.
[46] Benzi, M., Bertaccini, D., Durastante, F., and Simunec, I., “Nonlocal network dynamics via fractional graph Laplacians,” J. Compl. Net. (in press) (2020). · Zbl 1461.90020
[47] Coifman, R. R.; Lafon, S., Diffusion maps, Appl. Comput. Harm. Anal., 21, 5-30 (2006) · Zbl 1095.68094 · doi:10.1016/j.acha.2006.04.006
[48] Lonsdale, J.; Thomas, J.; Salvatore, M.; Phillips, R.; Lo, E.; Shad, S.; Hasz, R.; Walters, G.; Garcia, F.; Young, N.; Foster, B., The genotype-tissue expression (GTEx) project, Nat. Genet., 45, 580-585 (2013) · doi:10.1038/ng.2653
[49] Uhlén, M.; Fagerberg, L.; Hallström, B. M.; Lindskog, C.; Oksvold, P.; Mardinoglu, A.; Sivertsson, Å.; Kampf, C.; Sjöstedt, E.; Asplund, A.; Olsson, I.; Edlund, K.; Lundberg, E.; Navani, S.; Al-Khalili Szigyarto, C.; Odeberg, J.; Djureinovic, D.; Ottosson Takanen, J.; Hober, S.; Alm, T.; Edqvist, P.-H.; Berling, H.; Tegel, H.; Mulder, J.; Rockberg, J.; Nilsson, P.; Schwenk, J. M.; Hamsten, M.; von Feilitzen, K.; Forsberg, M.; Persson, L.; Johansson, F.; Zwahlen, M.; von Heijne, G.; Nielsen, J.; Pontén, F., Tissue-based map of the human proteome, Science, 347, 1260419 (2015) · doi:10.1126/science.1260419
[50] A promoter-level mammalian expression atlas, Nature, 507, 462-470 (2014) · doi:10.1038/nature13182
[51] Sun, W.; Li, Y.; Li, C.; Chen, Y., Convergence speed of a fractional order consensus algorithm over undirected scale-free networks, Asian J. Control, 13, 936-46 (2011) · Zbl 1263.93013 · doi:10.1002/asjc.390
[52] Piñero, J.; Ramírez-Anguita, J. M.; Saüch-Pitarch, J.; Ronzano, F.; Centeno, E.; Sanz, F.; Furlong, L. I., The DisGeNET knowledge platform for disease genomics: 2019 update, Nucleic Acids Res., 48, D845-D855 (2020) · doi:10.1093/nar/gkz1021
[53] Akhmerov, A.; Marbán, E., COVID-19 and the heart, Circulation Res., 126, 1443-1455 (2020) · doi:10.1161/CIRCRESAHA.120.317055
[54] Inciardi, R. M.; Lupi, L.; Zaccone, G.; Italia, L.; Raffo, M.; Tomasoni, D.; Cani, D. S.; Cerini, M.; Farina, D.; Gavazzi, E.; Maroldi, R., JAMA Cardiol., 5, 7, 819-824 (2020) · doi:10.1001/jamacardio.2020.1096
[55] Zheng, Y.; Ma, Y.; Zhang, J.; Xie, X., COVID-19 and the cardiovascular system, Nat. Rev. Cardiol., 17, 259-260 (2020) · doi:10.1038/s41569-020-0360-5
[56] Clerkin, K. J.; Fried, J. A.; Raikhelkar, J.; Sayer, G.; Griffin, J. M.; Masoumi, A.; Jain, S. S.; Burkhoff, D.; Kumaraiah, D.; Rabbani, L.; Schwartz, A., Coronavirus disease 2019 (COVID-19) and cardiovascular disease, Circulation, 141, 1648-1655 (2020) · doi:10.1161/CIRCULATIONAHA.120.046941
[57] Maya, W. D.; Du Plessis, S. S.; Velilla, P. A., SARS-CoV-2 and the testis: Similarity to other viruses and routes of infection, Reproduct. BioMed. Online, 40, 763-764 (2020) · doi:10.1016/j.rbmo.2020.04.009
[58] Chen, F.; Lou, D., Urology (2020) · doi:10.1016/j.urology.2020.04.069
[59] Wang, S.; Zhou, X.; Zhang, T.; Wang, Z., The need for urogenital tract monitoring in COVID-19, Nat. Rev. Urol., 17, 314-315 (2020) · doi:10.1038/s41585-020-0319-7
[60] Fan, C.; Li, K.; Ding, Y.; Lu, W. L.; Wang, J., medRxiv · doi:10.1101/2020.02.12.20022418
[61] Saavedra, J. M., COVID-19, angiotensin receptor blockers, and the brain, Cell. Mol. Neurobiol., 40, 667-674 (2020) · doi:10.1007/s10571-020-00861-y
[62] Lushina, N.; Kuo, J. S.; Shaikh, H. A., Radiology (2020) · doi:10.1148/radiol.2020201623
[63] Zhou, B.; She, J.; Wang, Y.; Ma, X., A case of coronavirus disease 2019 with concomitant acute cerebral infarction and deep vein thrombosis, Front. Neurol., 11, 296 (2020) · doi:10.3389/fneur.2020.00296
[64] Ronco, C.; Reis, T., Kidney involvement in COVID-19 and rationale for extracorporeal therapies, Nat. Rev. Nephrol., 16, 308-310 (2020) · doi:10.1038/s41581-020-0284-7
[65] Fanelli, V.; Fiorentino, M.; Cantaluppi, V.; Gesualdo, L.; Stallone, G.; Ronco, C.; Castellano, G., Acute kidney injury in SARS-CoV-2 infected patients, Critical Care, 24, 155 (2020) · doi:10.1186/s13054-020-02872-z
[66] Li, Z.; Wu, M.; Yao, J.; Guo, J.; Liao, X.; Song, S.; Li, J.; Duan, G.; Zhou, Y.; Wu, X.; Zhou, Z., medRxiv · doi:10.1101/2020.02.08.20021212
[67] Ruggiero, A.; Attinà, G.; Chiaretti, A., Acta Paediatr., 69, 1690 (2020) · doi:10.1111/apa.15328
[68] Feng, Z.; Diao, B.; Wang, R.; Wang, G.; Wang, C.; Tan, Y.; Liu, L.; Wang, C.; Liu, Y.; Liu, Y.; Yuan, Z., medRxiv · doi:10.1101/2020.03.27.20045427
[69] Pal, R., COVID-19, hypothalamo-pituitary-adrenal axis and clinical implications, Endocrine, 68, 251-252 (2020) · doi:10.1007/s12020-020-02325-1
[70] Estrada, E., Estrada-Rodriguez, G., and Gimperlin, H., “Metaplex networks: Influence of the exo-endo structure of complex systems on diffusion,” SIAM Rev. (in press). · Zbl 1458.92034
[71] Estrada, E., Path Laplacian matrices: Introduction and application to the analysis of consensus in networks, Lin. Algebra Appl., 436, 3373-3391 (2012) · Zbl 1241.05077 · doi:10.1016/j.laa.2011.11.032
[72] Estrada, E.; Hameed, E.; Hatano, N.; Langer, M., Path Laplacian operators and superdiffusive processes on graphs. I. One-dimensional case, Lin. Algebra Appl., 523, 307-334 (2017) · Zbl 06766348 · doi:10.1016/j.laa.2017.02.027
[73] Estrada, E.; Hameed, E.; Langer, M.; Puchalska, A., Path Laplacian operators and superdiffusive processes on graphs. II. Two-dimensional lattice, Lin. Algebra Appl., 555, 373-397 (2018) · Zbl 06914735 · doi:10.1016/j.laa.2018.06.026
[74] Asllani, M.; Carletti, T.; Di Patti, F.; Fanelli, D.; Piazza, F., Hopping in the crowd to unveil network topology, Phys. Rev. Lett., 120, 158301 (2018) · doi:10.1103/PhysRevLett.120.158301
[75] Qiu, M., Wu, D., Ning, W., Zhang, J., Shu, T., Huang, C., Chen, R., Huang, M., Xu, J., Yang, Q., and Li, R., Postmortem tissue proteomics reveals the pathogenesis of multiorgan injuries of COVID-19 (2020).
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.