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"What you leave behind
is not what is engraved
in stone monuments,
but what is woven
into the lives of others"

Pericles

A life is not important except
in the impact it has on other lives.

From Jackie Robinson's tombstone

Dream like you'll live forever ...
Love like you've never been hurt ....
Work like you don't need the money ...
and .....
Dance like nobody is watching!

Satchel Paige

Age is a question of mind and matter..
If you don't mind, it doesn't matter!

Mark Twain

Hans G. Othmer
School of Mathematics
270A Vincent Hall
University of Minnesota
Minneapolis, MN 55455
USA

E-mail: othmer@umn.edu
Office: (612) 624-8325
Fax: (612) 626-2017
Department: (612) 625-9845

Some Pictures
Links to Papers

Pictures


Spiral wave of cAMP computed from the Dictyostelium signalling model (cf. Dallon and Othmer (1997)).	Superposition of the cAMP wave (dark blue) and the cell streams.

Papers and Notes -- old and new

Instability and dynamic pattern in cellular networks, J Theor Biol, 32, 507-537, (1971) (with L.E. Scriven). pdf file
On the significance of finite propagation speeds in multicomponent reacting systems, J. Chem. Phys.., 6, 460-470, (1976) . pdf file
Current problems in pattern formation, Lects. Math. Life Sci., 9, 57-85, (1977). pdf file
The Effects of Cell Density and Metabolite Flux on Cellular Dynamics, J. Math. Biol., 5, 169-200, (1978) (with John Aldridge). pdf file
The dynamics of feedback control circuits in biochemical pathways, Prog. Theor. Biol., 5, 1-62, (1978) (with J. Tyson). pdf file
Scale-invariance in reaction-diffusion models of spatial pattern formation, PNAS, 7, 4180-4184, (1980) (with E. Pate). pdf file
Synchronized and differentiated modes of cellular dynamics, In Dyn. Syner. Sys., 191-204, (1980). pdf file
The interaction of structure and dynamics in chemical reaction networks , in Modelling of Chemical Reaction Systems, (K.H. Ebert, P. Deuflhard, W. Jager, eds.), Springer-Verlag: Heidelberg (1981). pdf file
A graph-theoretic analysis of chemical reaction networks, Class Notes -- Rutgers University, (1979). pdf file
Models of dispersal in biological systems, J. Math. Biol., 26, 263-298 (1988) (with S. Dunbar and W. Alt) . pdf file
On the resonance structure in a forced excitable system, SIAM JAM , 50, 1373-1418 (1990) (with J. Alexander and E. Doedel)) . pdf file
Oscillations and waves in a model in InsP_3 controlled calcium dynamics, Experimental and Theoretical Advances in Biological Pattern Formation,, 277-300, (1993) (with Y. Tang). pdf file
A G-protein-based model for cAMP dynamics in Dictyostelium discoideum, Math Biosciences, 120, 25-76, (1994) (with Y. Tang). pdf file
Pattern formation in generalized Turing systems, J Math Biol, 120, 25-76, (1994) (with R. Dillon and P. Maini). pdf file
Frequency encoding in excitable systems with applications to calcium oscillations, PNAS, 98, 75-110, (1996) (with Y. Tang). pdf file
Excitation, oscillations and wave propagation in a G-protein-based model of signal transduction in Dictyostelium discoideum, Phil Trans Roy Soc, 349, 179-195, (1995) (with Y. Tang). pdf file
Resonance in excitable systems under step-function forcing. II. Subharmonic solutions and persistence, Physica D, 92, 7869-7873, (1996) (with M. Xie and M. Watanabe). pdf file
Simplification and analysis of models of calcium dynamics based on IP₃ sensitive calcium channel kinetics, Biophys. Jour., 70, 246-263, (1996) (with Y. Tang). pdf file
Aggregation, Blowup and Collapse: The ABC's of taxis in reinforced random walks, SIAM J. Applied Math., 57, 1044-1081 (1997), (with Angela Stevens). pdf file
A discrete cell model with adaptive signaling for aggregation of Dictyostelium discoideum, Phil. Trans. Roy. Soc. (Lon.), 352, 391-418, (1997) (with J. Dallon). pdf file
A discrete cell model with adaptive signalling, In Dynamics of Cell and Tissue Motion, W. Alt, A. Deutsch and G. Dunn, eds. Birkhauser-Verlag, (1997), 195-197, (with J. Dallon).
Scalable implicit methods for reaction-diffusion equations in two and three space dimensions, In Proc. of the Copper Mountain Conference on Iterative Methods, 1-7, (1996).
Signal transduction and second messenger systems, In Case Studies in Mathematical Modeling -- Ecology, Physiology,and Cell Biology, H. G. Othmer, F. R. Adler, M. A. Lewis and J. C. Dallon, eds, 99-126, (1996).
A model of excitation and adaptation in bacterial chemotaxis, PNAS, 94, 7263-7268, (1997), (with P. Spiro and J. S. Parkinson). pdf file
Oscillatory cAMP signaling in the development of Dictyostelium discoideum, Comments on Theoretical Biology, 5, 175-282, (1998), (with P. Schaap). pdf file
A continuum analysis of the chemotactic signal seen by Dictyostelium discoideum, J. Theor. Biol., 194, 461-483, (1998). (with J. Dallon) pdf file
Pattern formation in a cellular slime mold, In Numerical Methods for Bifurcation Problems and Large-Scale Dynamical Systems, E. Doedel and L. S. Tuckerman, (eds.), IMA Proceedings, 119, 359-383, (2000), (with B. Lilly and J. C. Dallon). pdf file
A mathematical model for outgrowth and spatial patterning of the vertebrate limb bud, J. Theor. Biol., 197, 295-330, (1999), (with R. Dillon). pdf file
Stripe formation in juvenile Pomacanthus explained by a generalized Turing mechanism with chemotaxis, PNAS, 96, 5549-5554, (1999), (with K. J. Painter and P. K. Maini). pdf file
Subharmonic resonance and chaos in forced excitable systems, J. Math. Biol., 39, 139-171, (1999), (with M. Xie). pdf file
The effect of heterogeneously-distributed RYR channels on calcium dynamics in cardiac myocytes, Bull. Math. Biol., 61, 651-681, (1999). (with P. Spiro). pdf file
Development and applications of a model for cellular response to multiple chemotactic cues, J. Math. Biol., 41, 285-314 (2000), (with K. J. Painter and P. K. Maini). pdf file
A chemotactic model for the advance and retreat of the primitive streak in avian development, Bull. Math. Biol, 62, 501-525, (2000), (with K. J. Painter and P. K. Maini). pdf file
The diffusion limit of transport equations derived from a velocity jump process, SIAM JAM, 61, 751-775, (2000), (with Thomas Hillen) pdf file
Discrete and continuum models of primitive streak formation, in Mathematical Models for Biological Pattern Formation, P. K. Maini and H. G. Othmer, (eds.), 11-35,( 2001), (with S. Schnell, K. J. Painter and P. K. Maini).pdf file
A model for individual and collective cell movement in Dictyostelium discoideum, PNAS, 97, 10446-10453, (2000), (with E. Palsson). pdf file
The diffusion limit of transport equations II: Chemotaxis equations, SIAM JAM, 62, 1222-1250, (2002), (with Thomas Hillen). pdf file
Localization in lattice and continuum models of reinforced random walks, Appld Math Letters, 16, #3, 375-381, (2003), (with Kevin Painter and Dirk Horstmann). pdf file
The topology of the regulatory interactions predict the expression pattern of the segment polarity genes in Drosophila melanogaster, J. Theor. Biol., 223,1-18, (2003), (with Reka Albert). pdf file
Aggregation under local reinforcement: From lattice to continuum, Eur. J. Appld. Math, 15, 545-576, (2004), (with D. Horstmann and K. Painter) . pdf file
Short- and long-range effects of Sonic hedgehog in limb development, PNAS, 100, 10152-10157, (2003), (with C. Gadgil and R. Dillon). pdf file
From individual to collective behavior in bacterial chemotaxis, SIAM JAM, 65, 361-391 , (2004), (with R. Erban). pdf file
Application of coarse integration to bacterial chemotaxis, Multiscale Modeling and Simulation, 4, 307-327, (2005), (with S.Setayeshgar, C. W. Gear and I. G. Kevrekidis). pdf file
A continuum model of motility in amoeboid cells, Bull. Math. Biol., 66, 167-193, (2004), (with M. Gracheva). pdf file
Mathematical modeling of tumor-induced angiogenesis, J. Math. Biol., 49, 111-187, (2004), (with N. Mantzaris and S. Webb). pdf file
Dynamic receptor team formation can explain the high signal transduction gain in E. coli, Biophys. J., 86, 2650-2659, (2004), (with R. Albert and Y. Chiu). pdf file
A stochastic analysis of first-order reaction networks, Bull. Math. Biol., 67, 901-946, (2005), (with C. Gadgil and C. H. Lee). pdf file
How cellular movement determines the collective force generated by the Dictyostelium discoideum slug, J. Theor. Biol, 231 , 203-222, (2004), (with J. Dallon). pdf file
From signal transduction to spatial pattern formation in E. coli: A paradigm for multi-scale modeling in biology, Multiscale Modeling and Simulation, 3 , 362-394, (2005), (with R. Erban). pdf file
Wave propagation and blocking in inhomogeneous media, Discrete and Continuous Dynamical Systems, 13, 843-876, (2005), (with D. G. Aronson and N. V. Mantzaris). pdf file
Facilitated transport of a Dpp/Scw heterodimer by Sog/Tsg leads to robust patterning of the Drosophila blastoderm embryo, Cell, 120, 873-886, (2005), (with O. Shimmi, D. Umulis and M. O Connor). pdf file
An equation-free computational approach for extracting population-level behavior from individual-based models of biological dispersal, Physica D, 215 , 1-24, (2006), (with R. Erban and I. G. Kevrekidis). pdf file
A model for a G-protein-mediated mechanism for synaptic channel modulation, Mathematical Biosciences, 200 ,188-213, (2006), (with G. Soto). pdf file
Shaping BMP morphogen gradients in the Drosophila embryo and pupal wings, Development, 133, (2), 183-93, (2006), (with M. O'Connor, D. Umulis, and S. Blair). pdf file
Taxis equations for amoeboid cells, J. Math. Biol., 54, 847-885, (2007), (with R. Erban). pdf file
Macroscopic taxis equations from cell-based models, Oberwolfach Reports, 6, 2, (2006), (with R. Erban). pdf file
A theoretical approach to actin filament dynamics, J. Stat. Phys.,128, (1), 111-138 , (2007), (with J. Hu and T. Matzavinos). pdf file
Robust, bistable, Bmp-dependent patterning of the Drosophila blastoderm embryo, PNAS, 103, 11613-11618, (2006), (with D. Umulis, M. Serpe and M. B. O'Connor). pdf file Supporting online material pdf file
A stochastic analysis of actin polymerization in the presence of twinfilin and gelsolin, J. Theor. Biol., 249 , 723-736, (2007), (with A. Matzavinos). pdf file
A hybrid model for tumor spheroid growth in vitro I: Theoretical development and early results , Math. Models Methods in Appl Sci, 17,1773-1798, (2007), (with Y. Kim and M. Stolarska). pdf file
Robustness of embryonic spatial patterning in Drosophila melanogaster , Curr Topics in Dev Bio, 81, 65-111, (2008), (with D. Umulis and M. B. O'Connor). pdf file
The dynamics of SQUIDs and coupled pendula, In Numerical Continuation Methods for Dynamical Systems, B. Krauskopf, et al., eds, Springer, (2007), pp 155-176 (with D. Aronson). pdf file
The variety of cytosolic calcium responses and possible roles of PLC and PKC, Phys. Biol., 4, 4, 325-343, (2007) (with M. Kang) pdf file
The BMP binding protein Crossveinless 2 is a short-range, concentration-dependent, biphasic modulator of BMP signaling in Drosophila , Developmental Cell, 14, 940-953, (2008), (with M. Serpe, D. Umulis, A. Ralston, J. Chen, D. Olson, A. Avanesov, M. B. O'Connor, and S. Blair). pdf file
Multiscale models of taxis-driven patterning in bacterial populations, SIAM JAM, 70, 1, 133-167, (2009) (with C. Xue). pdf file
From individual to collective behavior of unicellular organisms: Recent results and open problems, In Multiscale Phenomena in Biology, R. M. Sinclair and K. M. Sriefel, eds , AIP Conf. Proc. vol 1167, 3-14, (2009) (with R. Erban and C. Xue). pdf file
Multiscale models of cell and tissue dynamics, Phil. Trans. Roy. Soc. A, 367, 3525-3553, (2009), (with M. Stolarska and Y. J. Kim). pdf file
The intersection of theory and application in elucidating pattern formation in developmental biology, Math. Mod. Nat. Phenom., 4, 4, 3-79 (2009), (with K. Painter, D. Umulis, and C. Xue). pdf file
Spatio-temporal characteristics of calcium dynamics in astrocytes , Chaos, 19, DOI: 10.1063/1.3206698, 21 pp, (2009), (with M. Kang). pdf file Copyright 2009 American Institute of Physics. This article may be downloaded for personal use only . Any other use requires prior permission of the author and the American Institute of Physics. Also at http://link.aip.org/link/?CHA/19/037116
A multi-time-scale analysis of chemical reaction networks: I. Deterministic systems, J. Math. Biol., 60, 387-450, (2010), (with C. H. Lee). pdf file
Organism-scale modeling of early Drosophila patterning via bone morphogenetic proteins, Dev. Cell., do:10.1016/jdevcel.2010.01.006, (2010), (with David M. Umulis, Osamu Shimmi, and Michael B. O’Connor) pdf file
The role of the microenvironment in tumor growth and invasion, Prog. Biophys. Mol. Biol., 106, 353-379, (2011), (with Y. J. Kim and M. Stolarska) pdf file
A theoretical analysis of filament length fluctuations in actin and other polymers, J. Math. Biol., 63, 101-149, DOI 10.1007/s00285-010-0400-6, (2011), (with J. Hu ) pdf file
A new method for choosing the computational cell in stochastic reaction-diffusion systems, J. Math. Biol., DOI 10.1007/s00285-011-0469-6, 83pp, (2012), (with H-W. Kang and L. Zheng ) pdf file
Models of low Reynolds number swimmers, in Natural Locomotion in Fluids and on Surfaces, (S. Childress, et al., eds), Springer , (2012), (with Q. Wang and J. Hu ) pdf file
The mathematical analysis of biological aggregation and dispersal: progress, problems and perspectives, In Dispersal, individual movement and spatial ecology: A mathematical perspective (M. Lewis, P. Maini and S. Petrovskii, eds.), 79-127, (2013) (with C. Xue) pdf file
Radial and spiral stream formation in Proteus mirabilis colonies, PLoS Comp Biol, 7, 1-11, (2011), (with C. Xue and E. Budrene) pdf file
The effect of the signaling scheme on the robustness of pattern formation in development, J. R. Soc. Interface Focus, DOI: 10.1098/rsfs.2011.0116, (2012), (with H. Kang and L. Zheng) pdf file
A trimer of dimers- based model for the chemotactic signal transduction network in bacterial chemotaxis, Bull. Math. Biol., DOI 10.1007/s11538-012-9756-7, 46pp, (2012), (with X. Xin) pdf file
A new conceptual paradigm for the hemodynamics of salt-sensitive hypertension: a mathematical modeling approach, J. Physiol., doi:10.1113/jphysiol.2012.228619, 46pp, (2012), (with V.A. Averina, G.D. Fink, and J. W. Osborn) pdf file
Scale invariance of morphogen-mediated patterning by flux optimization, In Proc of the 2012 5th Int Conf on Biomedical Engineering and Informatics, 1030-1035, (2012), (with D. Umulis) pdf file
The importance of geometry in mathematical models of developing systems, Current Opinion in Genetics and Development, 22, # 6, pp 547–552, (2012), (with D. Umulis) pdf file
A hybrid model of tumor-stromal interactions in breast cancer, Bull. Math. Biol, 75, , 1304--1350, (2013), (with Y.J. Kim) pdf file
A continuum model of actin waves in Dictyostelium discoideum, PLoS One, 8, DOI:10.1371/journal.pone.0064272, 24pp, (2013), (with V. Khamviwath and J. Hu ) pdf file
Excitation and adaptation in bacteria -- a model signal transduction system that controls taxis and spatial pattern formation, Int. J. Mol. Sci. 14, 9205-9248, (2013), (with X. Xin and C. Xue ) pdf file
Mechanisms of scaling in pattern formation, Development 140, 4830-4843, (2013), (with D. Umulis ) pdf file
Stochastic analysis of reaction-diffusion processes, Bull. Math. Biol, 76, , 854-894, (2014), (with J. Hu and H. K. Kang) pdf file
The role of mathematical models in understanding pattern formation in developmental biology, Bull. Math. Biol. DOI 10.1007/s11538-014-0019-7, 1-29, (2014), (with D. Umulis ) pdf file
Hybrid models of cell and tissue dynamics in tumor growth, Math. Bio. & Eng.. 12, 1141-56, (2014), (with Y. J. Kim ) pdf file
A mathematical model of salt-sensitive hypertension:the neurogenic hypothesis, J. Physiol. 14, 3065-3076, (2015), (with V. Averina, G. Fink and J. Osborn ) pdf file
Constant-complexity stochastic simulation algorithm with optimal binning, J. Chem. Phys.. 143, doi: 10.1063/1.4928635, 11pp, (2015), (with K. Sanft) pdf file
Computational analysis of amoeboid swimming at low Reynolds number, J. Math. Biol., 72, 1893-1926, (2015), (with Q. Wang) pdf file
The performance of discrete models of low Reynolds number swimmers, Math. Biosci. & Eng.., 12, 1303-1320, (2015), (with Q. Wang) pdf file
A multi-time-scale analysis of chemical reaction networks: II Stochastic systems, J. Math. Biol. 73, 1081-1129 (2016) (with X. Kan and C.H. Lee) ) pdf file
A model for direction sensing in Dictyostelium Discoideum : Ras activity and symmetry breaking driven by a G$_{\beta\gamma}$- mediated G$_{\alpha2}$-Ric8 -- dependent signal transduction network , PLoS Comp. Biol., DOI:10.137, 40 pp, (2016) (with Y. Cheng) ) pdf file
Progress and perspectives in signal transduction, actin dynamics, and movement at the cell and tissue level -- lessons from Dictyostelium, Interface Focus 6, 1-16 (2016), (with T. Bretschneider and K. Weijer) pdf file
Cell-based, continuum and hybrid models of tissue dynamics, Lecture Notes in Mathematics, 2167, 1-72, (2016) pdf file
The role of the tumor microenvironment in glioblastoma: A mathematical model, IEEE Transactions on Biomedical Engineering, PP-99, 1-9, (2016) (with Y.J. Kim and H. Jeon) pdf file
Improving parameter inference from FRAP data: an analysis motivated by pattern formation in the Drosophila wing disc, Bull. Math. Biol. 79, 448-497 (2017) (with Lin Lin). pdf file
Analysis of a model microswimmer with applications to blebbing cells and mini-robots, J. Math. Biol., 65 pp, (2018), (with Q. Wang). pdf file
Getting in shape and swimming: the role of cortical forces and membrane heterogeneity in eukaryotic cells, J. Math. Biol., (2018), (with H. Wu and M. Ponce de Leon). pdf file
Eukaryotic cell motility from crawlers to swimmers, WIREs Comp. Mol. Sci., https://doi.org/10.1002/wcms.1376 24 pp (2018). pdf file
A model for the Hippo pathway in the Drosophila wing disc, Biophys. J., 115, 737-747, (2018).(with Jia Gou and Lin Lin) pdf file
A Primer on Reaction-Diffusion Models in Embryonic Development, Ency. Life Sciences, 16pp, DOI: 10.1002/9780470015902.a0026599, (2018). (with Matthew Thompson and David Umulis) pdf file
Noise-induced mixing and multimodality in reaction networks, Eur. J. Applied Math., 25pp, DOI:10.1017/S0956792518000517 (2018). (with Tomislav Plesa and Radek Erban) pdf file
A stochastic model for actin waves in eukaryotic cells , 48pp, bioRxiv, doi: https://doi.org/10.1101/2019.12.31.892034, (2019). (with Jifeng Hu and Varunyu Khamviwath) pdf file
Synergistic Effects of Bortezomib-OV Therapy and Anti-Invasive Strategies in Glioblastoma: A Mathematical Model, Cancers , 11 , 28pp, DOI::10.3390/cancers11020215, (2019). (with Yangjin Kim, Junho Lee, Donggu Lee ) pdf file
Growth control in the Drosophila wing disk, WIRES Systems Biology and Medicine , e14781 , 28pp, DOI::10.1002/wsbm.1478, (2020). (with Jia Gou and Jay Stotsky ) pdf file
The status of the QSSA approximation in stochastic simulations of reaction networks, 2018 MATRIX Annal, 137-147, (2020). (with A.V.P Bobadilla, B.J. Bartmanski, and R. Grima) pdf file
Visualizing mesoderm and neural crest cell dynamics during chick head morphogenesis, , Developmental Biology, 461, 184-196, (2020). (with M. C. McKinney et al.) pdf file
The Roles of Signaling in Cytoskeletal Changes, Random Movement, Direction-Sensing and Polarization of Eukaryotic Cells, , Cells, 9, (2020), https://doi.org/10.3390/cells9061437xs. (with Y. Cheng and B. Felix) pdf file
A phosphoinositide-based model of actin waves in frustrated phagocytosis, J. Theor. Biol., 527, (2021), https://doi.org/10.1016/j.jtbi.2021.110764. (with M. Ponce de Leon and B. Felix) pdf file
A random walk approach to transport in tissues and complex media: from microscale descriptions to macroscale models, Bull. Math. Biol., 83, (2021), https://doi.org/10.1007/s11538-021-00917-0. (with J. Stotsky and J. Gou) pdf file
The discrete-time Kermack-McKendrick model: A versatile and computationally attractive framework for modeling epidemics, PNAS, (2021), https://doi.org/10.1073/pnas.2106332118, (with O. Diekmann, R. Planque, and M. C. J. Bootsmaa) pdf file
How surrogates for cortical forces determine cell shape, Int. J. Nonlin. Mech., 140, (2022), https://doi.org/10.1016/j.ijnonlinmec.2022.103907. (with J. Stotsky) pdf file
The effects of internal forces and membrane heterogeneity on three-dimensional cell shapes, J. of Math. Biol., 86:1, (2023), https://doi.org/10.1007/s00285-022-01836-x. (with Jay Stotsky) pdf file
The interaction of mechanics and the Hippo pathway in Drosophila melanogaster, Cancers, 15, (2023), https://doi.org/10.3390/cancers15194840. (with Jia Gou and Tianhao Zhang) pdf file

Last Update Oct 8, 2023

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Papers and Notes -- old and new

Hans Othmer's
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