MATHEMATICS OF SELF-ORGANISATION IN CELL SYSTEMS
 
 
 
by Steffen Härting
by Moritz Mercker
by Moritz Mercker
by Steffen Härting
Publications since 2008

Journal articles

2017
Y. Li, A. Marciniak-Czochra, I. Takagi, B. Wu, "Steady states of FitzHugh-Nagumo system with non-diffusive activator and diffusive inhibitor.", Tohoku J. Math., Accepted
P. Gwiazda, A. Marciniak-Czochra, H. Thieme, "Measures under the flat norm as ordered normed vector space", Positivity, Accepted, doi:10.1007/s11117-017-0503-z
W. Wang, T. Stiehl, S. Raffel, V. T. Hoang, I. Hoffmann, L. Poisa-Beiro, B. R. Saeed, R. Blume, L. Manta, V. Eckstein, T. Bochtler, P. Wuchter, M. Essers, A. Jauch, A. Trumpp, A. Marciniak-Czochra, A. D. Ho, C. Lutz, "Reduced hematopoietic stem cells frequency predicts outcome in acute myeloid leukemia", Haematologica May 2017, doi:10.3324/haematol.2016.163584
M. V. Barbarossa, M. Pollner, G. Röst, "Stability switches induced by immune system boosting in an SIRS model with discrete and distributed delay", SIAM J. Appl. Math, accepted.
A. Marciniak-Czochra, G. Karch, K. Suzuki, "Instability of Turing patterns in recation-diffusion-ODE systems", J. Math. Biol. 74: 583-618
S. Härting, A. Marciniak-Czochra, I. Takagi, "Stable patterns with jump discontinuity in systems with Turing instability and hysteresis, Disc. Cont. Dyn. Sys. A. 37: 757-800
2016
D. Wollny, S. Zhao, I. Everlien, X. Lun, J. Brunken, D. Brne, F. Ziebell, I. Tabansky, W. Weichert, A. Marciniak-Czochra, A. Martin-Villalba, "Single cell analysis uncovers clonal acinar cell heterogeneity in the adult pancreas", Dev. Cell 39: 289-301
Y. Li, A. Marciniak-Czochra, I. Takagi, B. Wu, "Bifurcation Analysis of a Diffusion- ODE Model with Turing Instability and Hysteresis", Hiroshima Mathematical Journal, accepted.
T. Stiehl, C. Lutz, A. Marciniak-Czochra, "Emergence of heterogeneity in acute leukemias", Biology Direct 11(51), doi:10.1186/s13062-016-0154-1
M. Mercker, F. Brinkmann, A. Marciniak-Czochra, T. Richter, "Beyond Turing: Mechanochemical pattern formation in biological tissues", Biology Direct 11(22), doi:10.1186/s13062-016-0124-7 (link)
J.-E. Busse, P. Gwiazda, A. Marciniak-Czochra, "Mass concentration in a non-local model of clonal selection", J. Math. Biol., doi:10.1007/s00285-016-0979-3
A. Marciniak-Czochra, A. Mikelic, "Shadow limits via the renormalization group method and the center manifold method", Vietnam J. Mathematics. A special issue in honour of Prof. Willi Jäger 1-23, doi:10.1007/s10013-016-0199-6.
M. V. Barbarossa, C. Kuttler, "Mathematical modeling of bacteria communication in continuous cultures", MDPI Appl. Scie. Special Issue on Dynamical Models of Biology and Medicine A 6(5):149
A. Marciniak-Czochra, G. Karch, K. Suzuki, J. Zienkiewicz, "Diffusion-driven blowup in reaction-diffusion-ODE systems", J. Diff. Integral Eq. 29(7/8): 715-730.
P. Gwiazda, K. Kropielnicka, A. Marciniak-Czochra, "The Escalator Boxcar Train method for a system of aged-structured equations", Appl. Math. J. Networks and Heterogeneous Media, to appear.
2015
M. Mercker, A. Köthe, A. Marciniak-Czochra, "Mechanochemical symmetry breaking in Hydra aggregates", Biophysical J. 108(9): 2396-2407, link
A. Marciniak-Czochra, M. Nakayama, I. Takagi, "Pattern formation in a diffusion-ODE model with hysteresis", J. Diff. Integral Eq. 28: 655-694.
T. Stiehl, N. Baran, A. D. Ho, A. Marciniak-Czochra, "Cell division patterns in acute myeloid leukemia stem-like cells determine clinical course: a model to predict patient survival", Cancer Research 75: 940-949, published online, DOI:10.1158/0008-5472
A. Marciniak-Czochra, A. Mikelic, "A rigorous derivation of the equation for the clampled Biot-Kirchhoff-Love poroelastic plate", Arch. Rat. Mech. Anal. 215: 1035-1062.
M. Mercker, A. Marciniak-Czochra, "Bud neck scaffolding as a possible driving force during ESCRT-induced membrane budding", Biophysical J. 108: 833-843, link
T. Carraro, C. Goll, A. Marciniak-Czochra, "Effective interface conditions for the forced infiltration of an unconfined fluid into a porous medium using homogenization", Computer Meth. Appl. Mech. Eng. 292: 195-220, DOI: 10.1016/j.cma.2014.10.050
2014
S. Härting, A. Marciniak-Czochra, "Spike patterns in a reaction-diffusion-ode model with Turing instability", Math. Meth. Appl. Sci. 37: 1377-1391
T. Stiehl, N. Baran, N., A. D. Ho, A. Marciniak-Czochra, "Clonal selection and therapy resistance in acute leukemias: Mathematical modelling explains different proliferation patterns at diagnosis and relapse", J. Royal Society Interface 11: 20140079, link
T. Walenda, T. Stiehl, H. Braun, J. Fröbel, A. D. Ho, T. Schroeder, T. Goecke, U. Germing, U., A. Marciniak-Czochra, W. Wagner, "Feedback Signals in Myelodysplastic Syndromes: Increased Self-Renewal of the Malignant Clone Suppresses Normal Hematopoiesis", PLOS Comp. Biol. 10.1371/journal.pcbi.1003599
F. Ziebell, A. Martin-Villalba, A. Marciniak-Czochra, "Mathematical modelling of adult hippocampal neurogenesis: effect of altered stem cell dynamics on cell counts and BrdU-labelled cells", J. Royal Society Interface 11:20140144, link
O. Wolkenhauer, C. Auffray, O. Brass, J. Clairambault, A. Deutsch, D. Drasdo, F. Gervasio, L. Preziosi, P. Maini, A. Marciniak-Czochra, C. Kossow, L. Kuepfer, K. Rateitschak, I. Ramis-Conde, B. Ribba, A. Schuppert, R. Smallwood, G. Stamatakos, F. Winter, H. Byrne, "The Role of Multiscale Modelling in Systems Medicine", Genome Medicine 6:21, DOI: 10.1186/gm538
P. Gwiazda, J. Jabłoński, A. Marciniak-Czochra, A. Ulikowska, "Analysis of particle methods for structured population models with nonlocal boundary term in the framework of bounded Lipschitz distance", Num. Meth. Partial Diff. Eq. 30(6): 1797-1820, DOI: 10.1002/num.21879
J. Kawka, A. Marciniak-Czochra, S. Pfister, S. Pleier, D. Sturm, "Revealing the role of SGK1 in the dynamics of medulloblastoma using mathematical models", J. Theor. Biol. 10.1016/j.jtbi.2014.03.028
A. Marciniak-Czochra, A. Mikelic, "A nonlinear effective slip interface law for transport phenomena between a fracture flow and a porous medium", Discrete Cont. Dyn. Systems - Series S 7: 1065-1077
T. Stiehl, A. D. Ho, A. Marciniak-Czochra, "The impact of CD34+ cell dose on engraftment after Stem Cell Transplantations: personalized estimates based on mathematical modeling", Bone Marrow Transplantation 49: 30-37
M. Mohr, M. V. Barbarossa, C. Kuttler, "Predator-prey interactions, age structures and delay equations", Math. Mod. Natural Phenomena 9(1): 92-107
M. Stock, J. Baer, M. Mercker, "Trischen-wax and wane of a Wadden Sea island", Wadden Sea Ecosystem 33: 63-98
2013
M. Mercker, A. Marciniak-Czochra, T. Richter, D. Hartmann, "Modeling and computing of the deformation dynamics of inhomogeneous biological surface", SIAM J. Appl. Math. 73: 1768-1792
M. Mercker, D. Hartmann, A. Marciniak-Czochra, "A mechanochemical model for embryonic pattern formation: Coupling tissue mechanics and morphogen expression", PLOS One DOI: 10.1371/journal.pone.0082617
T. Carraro, C. Goll, A. Marciniak-Czochra, A. Mikelic, "Pressure jump interface law for the Stokes-Darcy coupling: Confirmation by direct numerical simulations", J. Fluid Mechanics 732: 510-536
P. Getto, A. Marciniak-Czochra, Y. Nakata, M. Vivanco, "Global dynamics of two-compartment models for cell production systems with regulatory mechanisms", Math. Biosci. 245: 258-268
A. Marciniak-Czochra, G. Karch, K. Suzuki, "Unstable patterns in reaction-diffusion model of early carcinogenesis", J. Math. Pures Appl. 99: 509-543, link
F. Clément, P. Michel, D. Monniaux, T. Stiehl, "Coupled Somatic Cell Kinetics and Germ Cell Growth: Multiscale Model-Based Insight on Ovarian Follicular Development", Multiscale Model. Simul. 11(3): 719-746
M. Mercker, J. Baer, "Predator-prey interactions as possible explanation for recent declines of seabird breeding populations - the example of the Wadden Sea island Trischen", Vogelwelt 134: 115-128, link
2012
P. Gwiazda, G. Jamróz, A. Marciniak-Czochra, "Models of discrete and continuous cell differentiation in the framework of transport equation", SIAM J. Math. Anal. 44:1103-1133
A. Marciniak-Czochra, A. Mikelic, "Effective pressure interface law for transport phenomena between an unconfined fluid and a porous medium using homogenization", SIAM Multiscale Model. Sim. 10: 285-305
T. Stiehl, A. Mariniak-Czochra, "Mathematical modelling of leukemogenesis and cancer stem cell dynamics", Math. Mod. Natural Phenomena 7: 166-202
A. Marciniak-Czochra, "Strong two-scale convergence and corrector result for the receptor-based model of the intercellular communication", IMA J. Appl. Math., DOI:10.1093/imamat/hxs052
Y. Golovaty, A. Marciniak-Czochra, M. Ptashnyk, "Stability of nonconstant stationary solutions in a reaction-diffusion equation coupled to the system of ordinary differential equations", Comm. Pure Appl. Anal. 11: 229-241
Y. Nakata, P. Getto, A. Marciniak-Czochra, T. Alarcon, "Stability analysis of multi-compartment models for cell production systems", J. Biol. Dynamics 6, Supp 1: 2-18
D. Trucu, M. Chaplain, A. Marciniak-Czochra, "Three-scale convergence for processes in complex heterogeneous media", Applicable Analysis 91: 1352-1373
M. Mercker, M. Ptashnyk, J. Kühnle, D. Hartmann, M. Weiss, W. Jäger, "A multiscale approach to curvature modulated sorting in biological membranes", J. Theor. Biol. 301: 67-82
J. A. Carrillo, R. Colombo, P. Gwiazda, A. Ulikowska, "Structured populations, cell growth and measure valued balance laws", J. Differential Equations 252(4):3245-3277
2011
M. Doumic, A. Marciniak-Czochra, B. Perthame, J. Zubelli, "Structured population model of stem cell differentiation", SIAM J. Appl. Math. 71: 1918-1940
T. Alarcon, P. Getto, A. Marciniak-Czochra, M. Vivanco, "A model for stem cell population dynamics with regulated maturation delay", Discrete Cont. Dyn. Systems B. Suppl.: 32-43
T. Stiehl, A. Marciniak-Czochra, "Characterization of stem cells using mathematical models of multistage cell lineages", Math. Comp. Models 53: 1505-1517
D. Cholewa, T. Stiehl, G. Bokermann, S. Joussen, C. Koch, T. Walenda, N. Pallua, A. Marciniak-Czochra, C. V. Suschek, W. Wagner, "Expansion of mesenchymal stromal cells is affected by serum supplements and passaging: Comprehensive insights from a cell automaton model", Cell Transplantation, published online, DOI:10.3727/096368910X557218
M. Mercker, T. Richter, T. Hartmann, "Sorting mechanism and communication in phase separating coupled monolayers", J. Phys. Chem. B. 115(40): 11739-11745, published online, DOI:10.1021/jp204127g
M. Chaplain, M. Lachowicz, Z. Szymańska, D. Wrzosek, "Mathematical modelling of cancer invasion: The importance of cell-cell adhesion and cell-matrix adhesion", Math. Models Methods Appl. Sci. 21: 719-743
2010
A. Marciniak-Czochra, M. Ptashnyk, "Boundedness of solutions of a haptotaxis model", Math. Models Methods Appl. Sci 20: 449-476
P. Gwiazda, A. Marciniak-Czochra, "Structured population models in metric spaces", J. Hyp. Diff. Eq. 7: 733-773
P. Gwiazda, T. Lorenz, A. Marciniak-Czochra, "A nonlinear structured population model: Lipschitz continuity of measure valued solutions with respect to model ingredients", J. Differential Equations 248: 2703-2735
G. Jamróz, "Elliptic equations, multivalued x-dependent graphs and Orlicz spaces", Nonlinear Analysis: TMA 73(8): 2666-2679
A. Ito, M. Gokieli, M. Niezgódka, Z. Szymańska, "Local existence and uniqueness to approximate system of 1D tumor invasion model", Nonlinear Anal. RWA. 11: 3555-3566
2009
A. Marciniak-Czochra, T. Stiehl, W. Wagner, "Modeling of replicative senescence in hematopoietic development", Aging 1: 723-732
A. Marciniak-Czochra, T. Stiehl, A. D. Ho, W. Jäger, W. Wagner, "Modeling asymmetric cell division in hematopietic stem cells regulation of self-renewal is essential for efficient repopulation", Stem Cells Dev. 18: 377-385
Z. Szymańska, J. Urbański, A. Marciniak-Czochra, "Mathematical modelling of the influence of heat shock proteins on cancer invasion of tissue", J. Math. Biol. 58: 819-844
M. Mercker, K. Kollath-Leiss, S. Allgaier, N. Weiland, K. Kempken, "The BEM46-like protein appears to be assential for hyphal development upon ascospore germination in Neurospora crassa and is targeted to the endoplasmic reticulum", Current Genetics 55(2): 151
Z. Szymańska, M. Żylicz, "Mathematical modeling of heat shock protein synthesis in response to temperature change", J. Theor. Biol. 259: 562-569
Z. Szymańska, C. Morales-Rodrigo, M. Lachowicz, M. Chaplain, "Mathematical modelling of cancer invasion of tissue: The role and effect of nonlocal interactions", Math. Models Methods Appl. Sci. 19: 257-281
M. Bodnar, U. Foryś, Z. Szymańska, "Model of AIDS-related tumour with time delay", Applicationes Mathematicae 36: 263-278
U. Foryś, Z. Szymańska, "Heterotrophic-autorophic organisms models", Applicationes Mathematicae 36: 279-294
2008
A. Marciniak-Czochra, M. Ptashnyk, "Derivation of a macroscopic receptorbased model using homogenisation techniques", SIAM J. Mat. Anal. 40: 215-237
A. Marciniak-Czochra, M. Kimmel, "Reaction-diffusion model of early carcinogenesis: The effects of influx of mutated cells", Math. Mod. Natural Phenomena 7: 90-114
P. Getto, M. Kimmel, A. Marciniak-Czochra, "Modelling and analysis of dynamics of viral infection of cells and of interferon resistance",J. Math. Anal. Appl. 344: 821-850
R. Kowalczyk, Z. Szymańska, "On the global existence of solutions to an aggregation model", J. Math. Anal. Appl. 343: 379-398

Proceedings and book chapters

P. Getto, A. Marciniak-Czochra, "Mathematical modelling as a tool to understand cell self-renewal and differentiation", in "Mammary Stem Cells: Methods and Protocols", M. d. M. Vivanco, "Methods in Molecular Biology" Volume 1293, Springer, 2014
A. Marciniak-Czochra, "Reaction-diffusion-ODE models of pattern formation", in "Evolutionary Equations with Applications in Natural Science", J. Banasiak, "Lecture Notes in Mathematics", Springer, 2014
T. Stiehl, A. D. Ho, A. Marciniak-Czochra, "Assessing hematopoietic (stem-) cell behavior during regenerative pressure", in: "Systems Biology of Blood", S. Corey, M. Kimmel, J. Leonard, "Advances in Experimental Medicine and Biology" Volume 844, Springer, New York, 2014
A. Köthe, A. Marciniak-Czochra, "Multistability and hysteresis-based mechanism of pattern formation in biology", in "Pattern Formation in Morphogenesis-problems and their Mathematical Formalization", V. Capasso, M. Gromov, N. Morozova (Eds.), Springer "Proceedings in Mathematics" 15: 153-173, 2013
A. Marciniak-Czochra, T. Stiehl, "Mathematical models of hematopoietic reconstitution after stem cell transplantation", in "Model Based Parameter Estimation: Theory and Applications" H. G. Bock, T. Carraro, W. Jäger, S. Körkel, R. Rannacher, J. P. Schlöder (Eds.), "Contributions in Mathematical and Computational Sciences" Volume 3, Springer Verlag, 2013
A. Marciniak-Czochra, "Reaction-diffusion models of pattern formation in developmental biology", in: "Mathematics and Life Sciences", A. Antoniouk, E. V. N. Melnik, De Gruyter, Germany, 189-212, 2012
A. Marciniak-Czochra, "Mathematical models of stem cells renewal and differentiation", Oberwolfach Reports, 2, 2009
A. Marciniak-Czochra, M. Ptashnyk, "Effects of logistic proliferation in the model of cancer invasion", Proceedings of the XIII National Conference Application of Mathematics in Biology and Medicine, Leszno, September 17-19, 2008

Popular science

A. Marciniak-Czochra, M. Mercker, "Modelling the experimental impossible: Dance of the molecules", Ruperto Carola, Forschungsmagazin 3, 132-139, 2013