{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,21]],"date-time":"2026-01-21T13:48:25Z","timestamp":1769003305838,"version":"3.49.0"},"update-to":[{"DOI":"10.1371\/journal.pcbi.1010019","type":"new_version","label":"New version","source":"publisher","updated":{"date-parts":[[2022,4,14]],"date-time":"2022-04-14T00:00:00Z","timestamp":1649894400000}}],"reference-count":75,"publisher":"Public Library of Science (PLoS)","issue":"4","license":[{"start":{"date-parts":[[2022,4,4]],"date-time":"2022-04-04T00:00:00Z","timestamp":1649030400000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100014440","name":"Ministerio de Ciencia, Innovaci\u00f3n y Universidades","doi-asserted-by":"publisher","award":["PGC2018-097257-B-C31"],"award-info":[{"award-number":["PGC2018-097257-B-C31"]}],"id":[{"id":"10.13039\/100014440","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100014440","name":"Ministerio de Ciencia, Innovaci\u00f3n y Universidades","doi-asserted-by":"publisher","award":["PID2019-106099RB-C44\/AEI\/10.13039\/501100011033"],"award-info":[{"award-number":["PID2019-106099RB-C44\/AEI\/10.13039\/501100011033"]}],"id":[{"id":"10.13039\/100014440","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100010067","name":"Gobierno de Arag\u00f3n","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100010067","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["www.ploscompbiol.org"],"crossmark-restriction":false},"short-container-title":["PLoS Comput Biol"],"abstract":"<jats:p>Microfluidic capacities for both recreating and monitoring cell cultures have opened the door to the use of Data Science and Machine Learning tools for understanding and simulating tumor evolution under controlled conditions. In this work, we show how these techniques could be applied to study Glioblastoma, the deadliest and most frequent primary brain tumor. In particular, we study Glioblastoma invasion using the recent concept of Physically-Guided Neural Networks with Internal Variables (PGNNIV), able to combine data obtained from microfluidic devices and some physical knowledge governing the tumor evolution. The physics is introduced in the network structure by means of a nonlinear advection-diffusion-reaction partial differential equation that models the Glioblastoma evolution. On the other hand, multilayer perceptrons combined with a nodal deconvolution technique are used for learning the <jats:italic>go or grow<\/jats:italic> metabolic behavior which characterises the Glioblastoma invasion. The PGNNIV is here trained using synthetic data obtained from <jats:italic>in silico<\/jats:italic> tests created under different oxygenation conditions, using a previously validated model. The unravelling capacity of PGNNIV enables discovering complex metabolic processes in a non-parametric way, thus giving explanatory capacity to the networks, and, as a consequence, surpassing the predictive power of any parametric approach and for any kind of stimulus. Besides, the possibility of working, for a particular tumor, with different boundary and initial conditions, permits the use of PGNNIV for defining virtual therapies and for drug design, thus making the first steps towards <jats:italic>in silico<\/jats:italic> personalised medicine.<\/jats:p>","DOI":"10.1371\/journal.pcbi.1010019","type":"journal-article","created":{"date-parts":[[2022,4,4]],"date-time":"2022-04-04T17:33:31Z","timestamp":1649093611000},"page":"e1010019","update-policy":"https:\/\/doi.org\/10.1371\/journal.pcbi.corrections_policy","source":"Crossref","is-referenced-by-count":10,"title":["Understanding glioblastoma invasion using physically-guided neural networks with internal variables"],"prefix":"10.1371","volume":"18","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2564-6038","authenticated-orcid":true,"given":"Jacobo","family":"Ayensa-Jim\u00e9nez","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0088-7222","authenticated-orcid":true,"given":"Mohamed H.","family":"Doweidar","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8371-3820","authenticated-orcid":true,"given":"Jose A.","family":"Sanz-Herrera","sequence":"additional","affiliation":[]},{"given":"Manuel","family":"Doblare","sequence":"additional","affiliation":[]}],"member":"340","published-online":{"date-parts":[[2022,4,4]]},"reference":[{"key":"pcbi.1010019.ref001","unstructured":"Organization WH, et al. WHO report on cancer: setting priorities, investing wisely and providing care for all. 2020;."},{"issue":"suppl_2","key":"pcbi.1010019.ref002","first-page":"ii1","article-title":"CBTRUS statistical report: Primary brain and central nervous system tumors diagnosed in the United States in 2006-2010","volume":"15","author":"QT Ostrom","year":"2013","journal-title":"Neuro-oncology"},{"issue":"11","key":"pcbi.1010019.ref003","doi-asserted-by":"crossref","first-page":"e78943","DOI":"10.1371\/journal.pone.0078943","article-title":"Radiotherapy plus concomitant adjuvant temozolomide for glioblastoma: Japanese mono-institutional results","volume":"8","author":"T Oike","year":"2013","journal-title":"PLoS One"},{"issue":"1","key":"pcbi.1010019.ref004","doi-asserted-by":"crossref","first-page":"102","DOI":"10.14694\/EdBook_AM.2012.32.48","article-title":"Glioblastoma: biology, genetics, and behavior","volume":"32","author":"DJ Brat","year":"2012","journal-title":"American Society of Clinical Oncology Educational Book"},{"issue":"5","key":"pcbi.1010019.ref005","doi-asserted-by":"crossref","DOI":"10.1615\/CritRevOncog.2014011777","article-title":"Glioblastoma heterogeneity and cancer cell plasticity","volume":"19","author":"D Friedmann-Morvinski","year":"2014","journal-title":"Critical Reviews\u2122 in Oncogenesis"},{"issue":"21","key":"pcbi.1010019.ref006","doi-asserted-by":"crossref","first-page":"2683","DOI":"10.1101\/gad.1596707","article-title":"Malignant astrocytic glioma: genetics, biology, and paths to treatment","volume":"21","author":"FB Furnari","year":"2007","journal-title":"Genes & development"},{"issue":"12","key":"pcbi.1010019.ref007","doi-asserted-by":"crossref","first-page":"1575","DOI":"10.1093\/neuonc\/nou147","article-title":"Targeting adaptive glioblastoma: an overview of proliferation and invasion","volume":"16","author":"Q Xie","year":"2014","journal-title":"Neuro-oncology"},{"issue":"9","key":"pcbi.1010019.ref008","doi-asserted-by":"crossref","first-page":"1219","DOI":"10.1093\/neuonc\/now024","article-title":"Glycolysis and the pentose phosphate pathway are differentially associated with the dichotomous regulation of glioblastoma cell migration versus proliferation","volume":"18","author":"A Kathagen-Buhmann","year":"2016","journal-title":"Neuro-oncology"},{"key":"pcbi.1010019.ref009","article-title":"Cell movements: from molecules to motility","author":"D Bray","year":"2000","journal-title":"Garland Science"},{"issue":"7491","key":"pcbi.1010019.ref010","doi-asserted-by":"crossref","first-page":"181","DOI":"10.1038\/nature13118","article-title":"The present and future role of microfluidics in biomedical research","volume":"507","author":"EK Sackmann","year":"2014","journal-title":"Nature"},{"issue":"6","key":"pcbi.1010019.ref011","doi-asserted-by":"crossref","first-page":"1205","DOI":"10.1002\/bit.21851","article-title":"Epidermal growth factor promotes breast cancer cell chemotaxis in CXCL12 gradients","volume":"100","author":"B Mosadegh","year":"2008","journal-title":"Biotechnology and bioengineering"},{"issue":"10","key":"pcbi.1010019.ref012","doi-asserted-by":"crossref","first-page":"1934","DOI":"10.1039\/C6LC00236F","article-title":"Microfluidic co-culture platform to quantify chemotaxis of primary stem cells","volume":"16","author":"Z Tat\u00e1rov\u00e1","year":"2016","journal-title":"Lab on a Chip"},{"issue":"7","key":"pcbi.1010019.ref013","doi-asserted-by":"crossref","first-page":"1247","DOI":"10.1038\/nprot.2012.051","article-title":"Microfluidic assay for simultaneous culture of multiple cell types on surfaces or within hydrogels","volume":"7","author":"Y Shin","year":"2012","journal-title":"Nature protocols"},{"issue":"11","key":"pcbi.1010019.ref014","doi-asserted-by":"crossref","first-page":"2364","DOI":"10.1039\/C5LC00234F","article-title":"Micromilling: a method for ultra-rapid prototyping of plastic microfluidic devices","volume":"15","author":"DJ Guckenberger","year":"2015","journal-title":"Lab on a Chip"},{"key":"pcbi.1010019.ref015","doi-asserted-by":"crossref","first-page":"14","DOI":"10.1016\/j.mee.2019.01.004","article-title":"Microfluidic platforms for cell cultures and investigations","volume":"208","author":"ML Coluccio","year":"2019","journal-title":"Microelectronic Engineering"},{"issue":"3","key":"pcbi.1010019.ref016","doi-asserted-by":"crossref","first-page":"310","DOI":"10.1016\/j.tibtech.2018.08.005","article-title":"Deep learning with microfluidics for biotechnology","volume":"37","author":"J Riordon","year":"2019","journal-title":"Trends in biotechnology"},{"issue":"6","key":"pcbi.1010019.ref017","doi-asserted-by":"crossref","first-page":"1893","DOI":"10.1016\/j.matt.2020.08.034","article-title":"Intelligent Microfluidics: The Convergence of Machine Learning and Microfluidics in Materials Science and Biomedicine","volume":"3","author":"EA Galan","year":"2020","journal-title":"Matter"},{"issue":"3","key":"pcbi.1010019.ref018","first-page":"1","article-title":"Application of microfluidic devices for glioblastoma study: current status and future directions","volume":"22","author":"X Cai","year":"2020","journal-title":"Biomedical Microdevices"},{"issue":"4","key":"pcbi.1010019.ref019","doi-asserted-by":"crossref","first-page":"511","DOI":"10.1111\/j.1365-2184.2009.00613.x","article-title":"Virtual glioblastoma: growth, migration and treatment in a three-dimensional mathematical model","volume":"42","author":"SE Eikenberry","year":"2009","journal-title":"Cell proliferation"},{"issue":"1","key":"pcbi.1010019.ref020","doi-asserted-by":"crossref","first-page":"49","DOI":"10.1093\/imammb\/dqq011","article-title":"\u2018Go or grow\u2019: the key to the emergence of invasion in tumour progression?","volume":"29","author":"H Hatzikirou","year":"2012","journal-title":"Mathematical medicine and biology: a journal of the IMA"},{"issue":"4","key":"pcbi.1010019.ref021","doi-asserted-by":"crossref","first-page":"397","DOI":"10.1038\/labinvest.3700070","article-title":"Vaso-occlusive and prothrombotic mechanisms associated with tumor hypoxia, necrosis, and accelerated growth in glioblastoma","volume":"84","author":"DJ Brat","year":"2004","journal-title":"Laboratory Investigation"},{"issue":"3","key":"pcbi.1010019.ref022","doi-asserted-by":"crossref","first-page":"920","DOI":"10.1158\/0008-5472.CAN-03-2073","article-title":"Pseudopalisades in glioblastoma are hypoxic, express extracellular matrix proteases, and are formed by an actively migrating cell population","volume":"64","author":"DJ Brat","year":"2004","journal-title":"Cancer research"},{"issue":"24","key":"pcbi.1010019.ref023","doi-asserted-by":"crossref","first-page":"5928","DOI":"10.1158\/1078-0432.CCR-10-1360","article-title":"Hypoxia and hypoxia-inducible factors: master regulators of metastasis","volume":"16","author":"X Lu","year":"2010","journal-title":"Clinical cancer research"},{"issue":"6","key":"pcbi.1010019.ref024","doi-asserted-by":"crossref","first-page":"1239","DOI":"10.1111\/j.1582-4934.2011.01258.x","article-title":"Why is the partial oxygen pressure of human tissues a crucial parameter? Small molecules and hypoxia","volume":"15","author":"A Carreau","year":"2011","journal-title":"Journal of cellular and molecular medicine"},{"issue":"11","key":"pcbi.1010019.ref025","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1038\/s41419-020-03150-0","article-title":"The HIF1\u03b1\/HIF2\u03b1-miR210-3p network regulates glioblastoma cell proliferation, dedifferentiation and chemoresistance through EGF under hypoxic conditions","volume":"11","author":"P Wang","year":"2020","journal-title":"Cell death & disease"},{"issue":"1","key":"pcbi.1010019.ref026","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1038\/srep36086","article-title":"Development and characterization of a microfluidic model of the tumour microenvironment","volume":"6","author":"JM Ayuso","year":"2016","journal-title":"Scientific reports"},{"issue":"4","key":"pcbi.1010019.ref027","first-page":"503","article-title":"Glioblastoma on a microfluidic chip: Generating pseudopalisades and enhancing aggressiveness through blood vessel obstruction events","volume":"19","author":"JM Ayuso","year":"2017","journal-title":"Neuro-oncology"},{"issue":"1","key":"pcbi.1010019.ref028","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1038\/s41598-020-78215-3","article-title":"Mathematical formulation and parametric analysis of in vitro cell models in microfluidic devices: application to different stages of glioblastoma evolution","volume":"10","author":"J Ayensa-Jim\u00e9nez","year":"2020","journal-title":"Scientific Reports"},{"key":"pcbi.1010019.ref029","doi-asserted-by":"crossref","first-page":"104547","DOI":"10.1016\/j.compbiomed.2021.104547","article-title":"Predicting cell behaviour parameters from glioblastoma on a chip images. A deep learning approach","author":"M P\u00e9rez-Aliacar","year":"2021","journal-title":"Computers in Biology and Medicine"},{"key":"pcbi.1010019.ref030","doi-asserted-by":"crossref","unstructured":"Ayensa-Jim\u00e9nez J, Doweidar MH, Sanz-Herrera JA, Doblar\u00e9 M. Identification of state functions by physically-guided neural networks with physically-meaningful internal layers. arXiv preprint arXiv:201108567. 2020;.","DOI":"10.1016\/j.cma.2021.113816"},{"key":"pcbi.1010019.ref031","unstructured":"Ayensa-Jim\u00e9nez J, Doweidar MH, Sanz-Herrera JA, Doblar\u00e9 M. On the application of Physically-Guided Neural Networks with Internal Variables to Continuum Problems. arXiv preprint arXiv:201111376. 2020;."},{"key":"pcbi.1010019.ref032","doi-asserted-by":"crossref","first-page":"686","DOI":"10.1016\/j.jcp.2018.10.045","article-title":"Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations","volume":"378","author":"M Raissi","year":"2019","journal-title":"Journal of Computational Physics"},{"issue":"12","key":"pcbi.1010019.ref033","doi-asserted-by":"crossref","first-page":"e1008462","DOI":"10.1371\/journal.pcbi.1008462","article-title":"Biologically-informed neural networks guide mechanistic modeling from sparse experimental data","volume":"16","author":"JH Lagergren","year":"2020","journal-title":"PLoS computational biology"},{"issue":"11","key":"pcbi.1010019.ref034","doi-asserted-by":"crossref","first-page":"118101","DOI":"10.1103\/PhysRevLett.98.118101","article-title":"Migration and proliferation dichotomy in tumor-cell invasion","volume":"98","author":"S Fedotov","year":"2007","journal-title":"Physical Review Letters"},{"issue":"6","key":"pcbi.1010019.ref035","doi-asserted-by":"crossref","first-page":"e1002556","DOI":"10.1371\/journal.pcbi.1002556","article-title":"The impact of phenotypic switching on glioblastoma growth and invasion","volume":"8","author":"P Gerlee","year":"2012","journal-title":"PLoS computational biology"},{"issue":"3","key":"pcbi.1010019.ref036","doi-asserted-by":"crossref","first-page":"1778","DOI":"10.1137\/17M1146257","article-title":"Traveling waves of a go-or-grow model of glioma growth","volume":"78","author":"TL Stepien","year":"2018","journal-title":"SIAM Journal on Applied Mathematics"},{"issue":"1","key":"pcbi.1010019.ref037","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1016\/S0025-5564(02)00096-2","article-title":"Analysis of logistic growth models","volume":"179","author":"A Tsoularis","year":"2002","journal-title":"Mathematical biosciences"},{"issue":"17","key":"pcbi.1010019.ref038","doi-asserted-by":"crossref","first-page":"2725","DOI":"10.1016\/j.febslet.2013.06.009","article-title":"The origins of enzyme kinetics","volume":"587","author":"A Cornish-Bowden","year":"2013","journal-title":"FEBS letters"},{"issue":"3","key":"pcbi.1010019.ref039","doi-asserted-by":"crossref","first-page":"260","DOI":"10.1086\/394439","article-title":"On the rate of oxygen consumption by tissues and lower organisms as a function of oxygen tension","volume":"8","author":"PS Tang","year":"1933","journal-title":"The Quarterly Review of Biology"},{"issue":"535","key":"pcbi.1010019.ref040","doi-asserted-by":"crossref","first-page":"515","DOI":"10.1259\/0007-1285-45-535-515","article-title":"Oxygen diffusion and the distribution of cellular radiosensitivity in tumours","volume":"45","author":"IF Tannock","year":"1972","journal-title":"The British journal of radiology"},{"issue":"17","key":"pcbi.1010019.ref041","doi-asserted-by":"crossref","first-page":"2829","DOI":"10.1088\/0031-9155\/48\/17\/307","article-title":"Theoretical simulation of tumour oxygenation and results from acute and chronic hypoxia","volume":"48","author":"A Da\u015fu","year":"2003","journal-title":"Physics in Medicine & Biology"},{"issue":"4540","key":"pcbi.1010019.ref042","doi-asserted-by":"crossref","first-page":"978","DOI":"10.1038\/178978a0","article-title":"Role of oxygen in modifying the radiosensitivity of E. coli B","volume":"178","author":"T Alper","year":"1956","journal-title":"Nature"},{"key":"pcbi.1010019.ref043","doi-asserted-by":"crossref","first-page":"16","DOI":"10.1016\/j.bios.2013.07.031","article-title":"Real-time and non-invasive impedimetric monitoring of cell proliferation and chemosensitivity in a perfusion 3D cell culture microfluidic chip","volume":"51","author":"KF Lei","year":"2014","journal-title":"Biosensors and Bioelectronics"},{"issue":"2","key":"pcbi.1010019.ref044","doi-asserted-by":"crossref","first-page":"97","DOI":"10.1007\/s13206-015-9202-7","article-title":"Based cell culture microfluidic system","volume":"9","author":"FF Tao","year":"2015","journal-title":"BioChip Journal"},{"issue":"1","key":"pcbi.1010019.ref045","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1186\/1741-7007-10-29","article-title":"Advances in establishment and analysis of three-dimensional tumor spheroid-based functional assays for target validation and drug evaluation","volume":"10","author":"M Vinci","year":"2012","journal-title":"BMC biology"},{"issue":"4695","key":"pcbi.1010019.ref046","doi-asserted-by":"crossref","first-page":"1296","DOI":"10.1038\/1841296b0","article-title":"Non-inverted versus inverted plots in enzyme kinetics","volume":"184","author":"B Hofstee","year":"1959","journal-title":"Nature"},{"issue":"3","key":"pcbi.1010019.ref047","doi-asserted-by":"crossref","first-page":"658","DOI":"10.1021\/ja01318a036","article-title":"The determination of enzyme dissociation constants","volume":"56","author":"H Lineweaver","year":"1934","journal-title":"Journal of the American chemical society"},{"issue":"10","key":"pcbi.1010019.ref048","doi-asserted-by":"crossref","first-page":"e0139515","DOI":"10.1371\/journal.pone.0139515","article-title":"Study of the chemotactic response of multicellular spheroids in a microfluidic device","volume":"10","author":"JM Ayuso","year":"2015","journal-title":"PloS one"},{"issue":"4","key":"pcbi.1010019.ref049","doi-asserted-by":"crossref","first-page":"355","DOI":"10.1111\/j.1469-1809.1937.tb02153.x","article-title":"The wave of advance of advantageous genes","volume":"7","author":"RA Fisher","year":"1937","journal-title":"Annals of eugenics"},{"issue":"22","key":"pcbi.1010019.ref050","doi-asserted-by":"crossref","first-page":"4855","DOI":"10.1039\/c2lc40306d","article-title":"A novel microfluidic platform for high-resolution imaging of a three-dimensional cell culture under a controlled hypoxic environment","volume":"12","author":"K Funamoto","year":"2012","journal-title":"Lab on a chip"},{"issue":"4","key":"pcbi.1010019.ref051","doi-asserted-by":"crossref","first-page":"45","DOI":"10.3390\/cells6040045","article-title":"The role of hypoxia in glioblastoma invasion","volume":"6","author":"AR Monteiro","year":"2017","journal-title":"Cells"},{"issue":"12","key":"pcbi.1010019.ref052","doi-asserted-by":"crossref","first-page":"e0209574","DOI":"10.1371\/journal.pone.0209574","article-title":"Microfluidic device to attain high spatial and temporal control of oxygen","volume":"13","author":"SF Lam","year":"2018","journal-title":"PLoS One"},{"key":"pcbi.1010019.ref053","doi-asserted-by":"crossref","first-page":"815","DOI":"10.3389\/fphys.2018.00815","article-title":"Every breath you take: non-invasive real-time oxygen biosensing in two-and three-dimensional microfluidic cell models","volume":"9","author":"H Zirath","year":"2018","journal-title":"Frontiers in physiology"},{"issue":"12","key":"pcbi.1010019.ref054","doi-asserted-by":"crossref","first-page":"2603","DOI":"10.1016\/j.camwa.2017.04.006","article-title":"Galerkin finite element method for cancer invasion mathematical model","volume":"73","author":"S Ganesan","year":"2017","journal-title":"Computers & Mathematics with Applications"},{"key":"pcbi.1010019.ref055","volume-title":"Numerical methods for ordinary differential systems: the initial value problem","author":"JD Lambert","year":"1991"},{"key":"pcbi.1010019.ref056","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1007\/BF02551274","article-title":"Approximations by superpositions of a sigmoidal function","volume":"2","author":"G Cybenko","year":"1989","journal-title":"Mathematics of Control, Signals and Systems"},{"issue":"2","key":"pcbi.1010019.ref057","doi-asserted-by":"crossref","first-page":"251","DOI":"10.1016\/0893-6080(91)90009-T","article-title":"Approximation capabilities of multilayer feedforward networks","volume":"4","author":"K Hornik","year":"1991","journal-title":"Neural networks"},{"issue":"1","key":"pcbi.1010019.ref058","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1137\/0911001","article-title":"A method for the spatial discretization of parabolic equations in one space variable","volume":"11","author":"RD Skeel","year":"1990","journal-title":"SIAM journal on scientific and statistical computing"},{"key":"pcbi.1010019.ref059","unstructured":"Kingma DP, Ba J. Adam: A method for stochastic optimization. arXiv preprint arXiv:14126980. 2014;."},{"issue":"2","key":"pcbi.1010019.ref060","doi-asserted-by":"crossref","first-page":"164","DOI":"10.1090\/qam\/10666","article-title":"A method for the solution of certain non-linear problems in least squares","volume":"2","author":"K Levenberg","year":"1944","journal-title":"Quarterly of applied mathematics"},{"issue":"2","key":"pcbi.1010019.ref061","doi-asserted-by":"crossref","first-page":"265","DOI":"10.1242\/jcs.01610","article-title":"Death receptor signaling","volume":"118","author":"I Lavrik","year":"2005","journal-title":"Journal of cell science"},{"issue":"20","key":"pcbi.1010019.ref062","doi-asserted-by":"crossref","first-page":"3589","DOI":"10.1242\/jcs.051011","article-title":"mTOR signaling at a glance","volume":"122","author":"M Laplante","year":"2009","journal-title":"Journal of cell science"},{"issue":"3","key":"pcbi.1010019.ref063","doi-asserted-by":"crossref","first-page":"165","DOI":"10.1038\/nrm1838","article-title":"Cell-signalling dynamics in time and space","volume":"7","author":"BN Kholodenko","year":"2006","journal-title":"Nature reviews Molecular cell biology"},{"issue":"5280","key":"pcbi.1010019.ref064","doi-asserted-by":"crossref","first-page":"100","DOI":"10.1038\/229100a0","article-title":"Thermodynamics, chemical reactions and molecular biology","volume":"229","author":"T Benzinger","year":"1971","journal-title":"Nature"},{"key":"pcbi.1010019.ref065","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511754784","volume-title":"Biological thermodynamics","author":"DT Haynie","year":"2001"},{"key":"pcbi.1010019.ref066","doi-asserted-by":"crossref","DOI":"10.4324\/9780203809075","volume-title":"Molecular driving forces: statistical thermodynamics in biology, chemistry, physics, and nanoscience","author":"K Dill","year":"2010"},{"issue":"12","key":"pcbi.1010019.ref067","doi-asserted-by":"crossref","first-page":"200300","DOI":"10.1098\/rsob.200300","article-title":"Cellular sociology regulates the hierarchical spatial patterning and organization of cells in organisms","volume":"10","author":"S Ganesh","year":"2020","journal-title":"Open Biology"},{"issue":"1","key":"pcbi.1010019.ref068","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1186\/s12964-017-0194-x","article-title":"Crosstalk between glial and glioblastoma cells triggers the \u201cgo-or-grow\u201d phenotype of tumor cells","volume":"15","author":"AI Oliveira","year":"2017","journal-title":"Cell Communication and Signaling"},{"issue":"1","key":"pcbi.1010019.ref069","first-page":"1","article-title":"Crosstalk between microglia and patient-derived glioblastoma cells inhibit invasion in a three-dimensional gelatin hydrogel model","volume":"17","author":"JWE Chen","year":"2020","journal-title":"Journal of neuroinflammation"},{"issue":"2","key":"pcbi.1010019.ref070","doi-asserted-by":"crossref","first-page":"223","DOI":"10.1083\/jcb.200408130","article-title":"Endothelial barrier disruption by VEGF-mediated Src activity potentiates tumor cell extravasation and metastasis","volume":"167","author":"S Weis","year":"2004","journal-title":"The Journal of cell biology"},{"issue":"1","key":"pcbi.1010019.ref071","doi-asserted-by":"crossref","first-page":"C1","DOI":"10.1152\/ajpcell.00238.2015","article-title":"Tumor cell intravasation","volume":"311","author":"SP Chiang","year":"2016","journal-title":"American Journal of Physiology-Cell Physiology"},{"issue":"6801","key":"pcbi.1010019.ref072","doi-asserted-by":"crossref","first-page":"249","DOI":"10.1038\/35025220","article-title":"Angiogenesis in cancer and other diseases","volume":"407","author":"P Carmeliet","year":"2000","journal-title":"nature"},{"issue":"1","key":"pcbi.1010019.ref073","doi-asserted-by":"crossref","first-page":"27","DOI":"10.1016\/j.immuni.2019.06.025","article-title":"Inflammation and cancer: triggers, mechanisms, and consequences","volume":"51","author":"FR Greten","year":"2019","journal-title":"Immunity"},{"issue":"6","key":"pcbi.1010019.ref074","doi-asserted-by":"crossref","first-page":"529","DOI":"10.1097\/00005072-200606000-00001","article-title":"\u2018Pseudopalisading\u2019necrosis in glioblastoma: a familiar morphologic feature that links vascular pathology, hypoxia, and angiogenesis","volume":"65","author":"Y Rong","year":"2006","journal-title":"Journal of Neuropathology & Experimental Neurology"},{"key":"pcbi.1010019.ref075","doi-asserted-by":"crossref","first-page":"161","DOI":"10.1016\/j.copbio.2019.03.004","article-title":"Big data analytics for personalized medicine","volume":"58","author":"D Cirillo","year":"2019","journal-title":"Current opinion in biotechnology"}],"updated-by":[{"DOI":"10.1371\/journal.pcbi.1010019","type":"new_version","label":"New version","source":"publisher","updated":{"date-parts":[[2022,4,14]],"date-time":"2022-04-14T00:00:00Z","timestamp":1649894400000}}],"container-title":["PLOS Computational Biology"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dx.plos.org\/10.1371\/journal.pcbi.1010019","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,4,14]],"date-time":"2022-04-14T17:59:14Z","timestamp":1649959154000},"score":1,"resource":{"primary":{"URL":"https:\/\/dx.plos.org\/10.1371\/journal.pcbi.1010019"}},"subtitle":[],"editor":[{"given":"Inna","family":"Lavrik","sequence":"first","affiliation":[]}],"short-title":[],"issued":{"date-parts":[[2022,4,4]]},"references-count":75,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2022,4,4]]}},"URL":"https:\/\/doi.org\/10.1371\/journal.pcbi.1010019","relation":{"new_version":[{"id-type":"doi","id":"10.1371\/journal.pcbi.1010019","asserted-by":"object"}]},"ISSN":["1553-7358"],"issn-type":[{"value":"1553-7358","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,4,4]]}}}