Hans Othmer's

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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@math.umn.edu Office: (612) 624-8325 Fax: (612) 626-2017 Department: (612) 625-9845 |

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. |

**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 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

**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

**A G-protein-based model for cAMP dynamics in**Math Biosciences,*Dictyostelium discoideum,***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**Phil Trans Roy Soc,*Dictyostelium discoideum,***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 IP**Biophys. Jour.,_{3}sensitive calcium channel kinetics,**70**, 246-263, (1996) (with Y. Tang).

**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**Phil. Trans. Roy. Soc. (Lon.),*Dictyostelium discoideum*,**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**Comments on Theoretical Biology,*Dictyostelium discoideum*,**5**, 175-282, (1998), (with P. Schaap). pdf file

**A continuum analysis of the chemotactic signal seen by**J. Theor. Biol.,*Dictyostelium discoideum*,**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**PNAS,*Pomacanthus*explained by a generalized Turing mechanism with chemotaxis,**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**PNAS,*Dictyostelium discoideum*,**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**, J. Theor. Biol.,*Drosophila melanogaster***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**PNAS,*Sonic hedgehog*in limb development,**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**Biophys. J.,*E. coli*,**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**J. Theor. Biol,*Dictyostelium discoideum*slug,**231**, 203-222, (2004), (with J. Dallon). pdf file

**From signal transduction to spatial pattern formation in**Multiscale Modeling and Simulation,*E. coli*: A paradigm for multi-scale modeling in biology,**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**Cell,*Drosophila*blastoderm embryo,**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**Development,*Drosophila*embryo and pupal wings,**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**PNAS,*Drosophila*blastoderm embryo,**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**Math. Models Methods in Appl Sci,*in vitro*I: Theoretical development and early results ,**17**,1773-1798, (2007), (with Y. Kim and M. Stolarska). pdf file

**Robustness of embryonic spatial patterning in**Curr Topics in Dev Bio,*Drosophila melanogaster ,***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**Developmental Cell,*Drosophila*,**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**, Dev. Cell., do:10.1016/jdevcel.2010.01.006, (2010), (with David M. Umulis, Osamu Shimmi, and Michael B. O’Connor) pdf file*Drosophila*patterning via bone morphogenetic proteins

**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**PLoS Comp Biol, 7, 1-11, (2011), (with C. Xue and E. Budrene) pdf file*Proteus mirabilis*colonies,

**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

**The performance of discrete models of low Reynolds number swimmers,**Math. Bio. & Eng..**12**, 1301-20, (2014), (with Q. Wang ) 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., DOI 10.1007/s00285-015-0925-9, 34 pp, (2105), (with Q. Wang) pdf file

**A multi-time-scale analysis of chemical reaction networks: II Stochastic systems,**J. Math. Biol. to appear, 35pp, (2016) (with X. Kan and C.H. Lee) ) pdf file

**A Model for Direction Sensing in {\em Dictyostelium Discoideum}: Ras Activity and Symmetry Breaking Driven by a G$_{\beta\gamma}$- Mediated G$_{\alpha2}$-Ric8 -- Dependent Signal Transduction Network ,**PLoS Comp. Biol., to appear, 45 pp, (2016) (with Y. Cheng) ) pdf file

**Last Update April 19, 2016**