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TU Dresden
Dept. for Innovative
Methods of Computing

Lutz Brusch

Lutz Brusch received his PhD from the Max Planck Institute for the Physics of Complex Systems in Dresden. As a postdoc, he worked on pattern formation, yeast metabolism and cellular signal transduction at the Centre de Bioingénierie Gilbert Durand in Toulouse and the Riken Omics Science Center in Yokohama. He is now heading the independent junior research group SpaceSys with a focus on the development of spatio-temporal models and tools for application to cell and developmental biology.


Former Projects:

Doppler Effect Goes Nonlinear
Modulated Amplitude Waves


Publications of Lutz Brusch

  • K. B. Hoffmann, A. Voss-Böhme, J. C. Rink, L. Brusch
    A dynamically diluted alignment model reveals the impact of cell turnover on the plasticity of tissue polarity patterns
    Journal of The Royal Society Interface, 14 (135), 20170466, 2017 [DOI]

  • K. Meyer, O. Ostrenko, G. Bourantas, H. Morales-Navarrete, N. Porat-Shliom, F. Segovia-Miranda, H. Nonaka, A. Ghaemi, J.-M. Verbavatz, L. Brusch, I. Sbalzarini, Y. Kalaidzidis, R. Weigert, M. Zerial
    A predictive 3D multi-scale model of biliary fluid dynamics in the liver lobule
    Cell Systems, 4, 3, 277–290.e9, 2017 [DOI]

  • O. Ostrenko, P. Incardona, R. Ramaswamy, L. Brusch, I. F. Sbalzarini
    pSSAlib: The partial-propensity stochastic chemical network simulator
    PLoS Computational Biology, 13, 12, e1005865, 2017 [DOI]

  • F. Rost, A. R. Albors, V. Mazurov, L. Brusch, A. Deutsch, E. M. Tanaka, O. Chara
    Accelerated cell divisions drive the outgrowth of the regenerating spinal cord in axolotls
    eLife, 5, e20357, 2016 [DOI]

  • O. Chara, L. Brusch
    Mathematical modelling of fluid transport and its regulation at multiple scales
    BioSystems, 130, 1-10, 2015 [DOI]

  • L. Foret, L. Brusch, F. Jülicher
    Theory of cargo and membrane trafficking. In Stahl and Bradshaw (Eds.)
    Encyclopedia of Cell Biology, Elsevier, Vol.4: Systems Cell Biology, 56–62, 2015 [DOI]

  • C. Vincent, F. Rost, W. Masselink, L. Brusch, E. Tanaka
    Cellular dynamics underlying regeneration of appropriate segment number during axolotl tail regeneration
    BMC Developmental Biology, 15, 1, 48, 2015 [DOI]

  • O. Chara, E. M. Tanaka, L. Brusch
    Mathematical modeling of regenerative processes
    Curr. Top. Dev. Biol., 108, 283-317, 2014 [DOI]

  • F. Rost, C. Eugster, C. Schröter, A.C. Oates, L. Brusch
    Chevron formation of the zebrafish muscle segments
    J. Exp. Biol., 217, 21, 3870-3882, 2014 [DOI]

  • J. Starruß, W. de Back, L. Brusch, A. Deutsch
    Morpheus: a user-friendly modeling environment for multiscale and multicellular systems biology
    Bioinformatics, 30, 1331-1332, 2014 [DOI]

  • W. de Back, R. Zimm, L. Brusch
    Transdifferentiation of pancreatic cells by loss of contact-mediated signaling
    BMC Syst. Biol., 7, 77, 2013 [DOI]

  • A.P. Kupinski, I. Raabe, M. Michel, D. Ail, L. Brusch, T. Weidemann, C. Bökel
    Phosphorylation of the Smo tail is controlled by membrane localization and is dispensable for clustering
    J. Cell Sci., 126, 20, 4684-4697, 2013 [DOI]

  • W. de Back, J.X. Zhou, L. Brusch
    On the role of lateral stabilization during early patterning in the pancreas
    J. R. Soc. Interface, 10, 20120766, 2012 [DOI]

  • C. Mente, I. Prade, L. Brusch, G. Breier, A. Deutsch
    A lattice-gas cellular automaton model for in vitro sprouting angiogenesis
    Acta Phys. Pol. B, 5, 1, 99-115, 2012 [DOI]

  • L. Foret, J.E. Dawson, R. Villaseñor, C. Collinet, A. Deutsch, L. Brusch, M. Zerial, Y. Kalaidzidis,
    F. Jülicher

    A general theoretical framework to infer endosomal network dynamics from quantitative image analysis
    Curr. Biol., 22, 15, 1381 - 1390, 2012 [DOI]

  • J.X. Zhou, L. Brusch, S. Huang
    Predicting Pancreas Cell Fate Decisions and Reprogramming with a Hierarchical Multi-Attractor Model
    PLoS ONE volume 6, issue 3, e14752, 2011 [DOI]

  • C. Mente, I. Prade, L. Brusch, G. Breier & A. Deutsch
    Parameter estimation with a novel gradient-based optimization method for biological lattice-gas cellular automaton models
    J. Math. Biol., 63, 1, 173-200, 2010 [DOI]

  • T. Nakakuki, M. R. Birtwistle, Y. Saeki, N. Yumoto, K. Ide, T. Nagashima, L. Brusch, B. A. Ogunnaike, M. Okada-Hatakeyama, B. N. Kholodenko
    Ligand-Specific c-Fos Expression Emerges from the Spatiotemporal Control of ErbB Network Dynamics
    Cell, 141, 884-896, 2010 [DOI]

  • S. Nandi, L. Brusch, A. Deutsch, N. Ganguly
    Coverage-maximization in networks under resource constraints
    Phys. Rev. E, 81, 061124, 2010 [DOI]

  • M. Choudhury, N. Ganguly, A. Maiti, A. Mukherjee, L. Brusch, A. Deutsch, F. Peruani
    Modeling discrete combinatorial systems as alphabetic bipartite networks: Theory and applications
    Phys. Rev. E, 81, 036103, 2010 [DOI]

  • E. Gin, E. M. Tanaka, L. Brusch
    A model for cyst lumen expansion and size regulation via fluid secretion
    Journal of Theoretical Biology, 264, 1077-1088, 2010 [DOI]

  • H. Hatzikirou, L. Brusch, C. Schaller, M. Simon, A. Deutsch
    Prediction of traveling front behavior in a lattice-gas cellular automaton model for tumor invasion
    Computers and Mathematics with Applications, 59, 2326-2339, 2010 [DOI]

  • H. Hatzikirou, L. Brusch, A. Deutsch
    From cellular automaton rules to an effective macroscopic mean-field description
    Acta Physica Polonica B Proceedings Supplement, 3, 399-416, 2010 [PDF]

  • I. Pieper, K. Wechler, M. Katzberg, L. Brusch, P. G. Sørensen, F. Mensonides, M. Bertau
    Biosimulation of drug metabolism--A yeast based model
    European Journal of Pharmaceutical Sciences, 36, 157-170, 2009 [DOI]

  • L. Brusch, A. Deutsch
    The coherence of the vesicle theory of protein secretion
    J. Theor. Biol., 252, 370-373, 2008 [DOI]

  • L. Brusch, P. del Conte-Zerial, Y. Kalaidzidis, J. Rink, B. Habermann, M. Zerial, A. Deutsch
    Protein domains of GTPases on membranes: do they rely on Turing's mechanism?
    In: Mathematical Modeling of Biological Systems, Volume I.
    Birkhauser, Boston, 33-46, 2008 [DOI]

  • P. del Conte-Zerial, L. Brusch, J. Rink, C. Collinet, Y. Kalaidzidis, M. Zerial, A. Deutsch
    Membrane identity and GTPase cascades regulated by toggle and cut-out switches
    Mol. Syst. Biol., 4, 206, 2008 [DOI]

  • S. Nandi, L. Brusch, A. Pal, N. Ganguly
    Coverage Maximization in Small World Network Under Bandwidth Constraint
    In: SIGCOMM 2008 Conference on Applications, Technologies, Architectures, and Protocols for Computer Communications
    ACM, 481-482, 2008

  • M. Bertau, J. Smolinski, L. Brusch, U. Kummer, F. Mensonides
    Biosimulation in Drug Development
    Wiley-VCH, Weinheim, 37-64, 2007

  • A. Bianchi, I. Pakarinen, J. Bajars, P. P. Caro, P. Grydgaard, J. Parrott, L. Brusch
    Ethanol production with micro-organisms. Process control and modelling
    In: Proceedings of the 18th ECMI modelling week
    Lappeenrannan teknillinen yliopisto, Lappeenranta, 9-23, 2006

  • H. Hatzikirou, L. Brusch, A. Deutsch, C. Schaller, M. Simon
    Characterization of Travelling Front Behaviour in a Lattice Gas Cellular Automaton Model of Glioma Invasion
    Math. Mod. Meth. Appl. Sci., 15, 1779-1794, 2006

  • S. Hayat, K. Ostermann, L. Brusch, W. Pompe, G. Rödel
    Towards in vivo computing: Quatitative analysis of an artificial gene regulatory network behaving as a RS flip-flop and simulating the system in silico
    In: Bio-Inspired Models of Network, Information and Computing Systems
    IEEE, 1-7, 2006 [DOI]

  • L. Brusch, H. K. Park, M. Bär, A. Torcini
    Spiral instabilities in periodically forced extended oscillatory media
    In: EQUADIFF 2003-International Conference on Differential equations
    World Scientific, Singapore, 777-782, 2005 [DOI]

  • N. Ganguly, L. Brusch, A. Deutsch
    Design and analysis of a bio-inspired search algorithm for peer-to-peer networks
    In: Self-Star Properties in Complex Information Systems
    Springer-Verlag, Heidelberg, 3460, 2005 [DOI]

  • L. Brusch, G. Cuniberti, M. Bertau
    Model evaluation for glycolytic oscillations in yeast biotransformations of xenobiotics
    Biophys. Chem., 109, 413-426, 2004 [DOI]

  • L. Brusch, E. M. Nicola, M. Bär, Y. Gong, D. J. Christini
    Comment on "Antispiral Waves in Reaction-Diffusion Systems" [3] (multiple letters)
    Phys. Rev. Lett., 92, 898011-898021, 2004 [DOI]

  • M. Bär, L. Brusch, M. Or-Guil
    Mechanism for spiral wave breakup in excitable and oscillatory media.
    Phys. Rev. Lett., 92, 119801, 2004 [DOI]

  • M. Bär, L. Brusch
    Breakup of spiral waves caused by radial dynamics: Eckhaus and finite wave number instabilities
    New J. Phys., 6, 5, 2004 [DOI]

  • E. Nicola, L. Brusch, M. Bär
    Antispiral waves as sources in oscillatory reaction-diffusion media
    J Phys Chem B, 108, 14733-14740, 2004 [DOI]

  • L. Brusch, A. Torcini, M. Bär
    Doppler Effect of Nonlinear Waves and Superspirals in Oscillatory Media
    Phys Rev Lett, 91, 1083021-1083024, 2003 [DOI]

  • L. Brusch, A. Torcini, M. Bär
    Nonlinear analysis of the Eckhaus instability: Modulated amplitude waves and phase chaos with nonzero average phase gradient
    Phys D Nonlinear Phenom, 174, 152-167, 2003 [DOI]

  • L. Brusch
    Antispiral and superspiral waves
    Wiss. Z. TU Dresden, 52, 55-58, 2003

  • U. Thiele, L. Brusch, M. Bestehorn, M. Bär
    Modelling thin-film dewetting on structured substrates and templates: Bifurcation analysis and numerical simulations
    Eur. Phys. J. E, 11, 255-271, 2003 [DOI]

  • L. Brusch, W. Lorenz, M. Or-Guil, M. Bär, U. Kummer
    Fold-Hopf bursting in a model for calcium signal transduction
    Z. Phys. Chem., 216, 487-497, 2002 [DOI]

  • L. Brusch, H. Kühne, U. Thiele, M. Bär
    Dewetting of thin films on heterogeneous substrates: Pinning versus coarsening
    Phys. Rev.~E, 66, 1-5, 2002 [DOI]

  • L. Brusch, A. Torcini, M. Van Hecke, M. G. Zimmermann, M. Bär
    Modulated amplitude waves and defect formation in the one-dimensional complex Ginzburg-Landau equation
    Phys D Nonlinear Phenom, 160, 127-148, 2001 [DOI]

  • L. Brusch, M. G. Zimmermann, M. Van Hecke, M. Bär, A. Torcini
    Modulated amplitude waves and the transition from phase to defect chaos
    Phys Rev Lett, 85, 86-89, 2000 [DOI]

  • G. Diener, L. Brusch
    A new simple version of the replica method
    J. Phys. A, 32, 585-593, 1999 [DOI]

  • G. Diener, L. Brusch
    Simplified replica treatment of various random-energy and random-field models with confinement potential
    Phys. Rev. E, 60, 3573-3579, 1999 [DOI]

Former Projects

Doppler Effect Goes Nonlinear

Bats are lucky as the Doppler effect guards them through the night. Their echo navigation system also reliably detects insect prey who's motion modulates the frequency of the reflected sound wave, according to the Doppler effect. Thanks to the essentially linear propagation of sound the signal can be received uncorrupted and information like the prey's speed can be retrieved. The case changes dramatically when transferred to a nonlinear medium (here described by the complex Ginzburg-Landau equation), as scientists now report in Physical Review Letters.
The authors theoretically studied wave sources that oscillate back-and-forth or rotate along a circle much like flies in the gathering around a lantern. As expected, the emitted waves got modulated by the source's motion but this modulation was not conserved as the waves propagated through the nonlinear medium. The authors applied methods like bifurcation analysis from dynamical systems theory to prove that the nonlinear medium does not support arbitrary forms of modulation. Instead a well-defined set of modulations, so-called modulated amplitude waves (MAWs), exists and forces all (initially) different modulations to evolve to MAW-shape and MAW-properties. Hence almost all information imprinted by the source's motion into the initial modulation is deleted by self-organising processes in the nonlinear medium. Because of this authority, MAWs are called attractors and they have been found in numerous experiments of fluid dynamics including recent work on hydrothermal waves by Garnier et al. [Phys. Rev. Lett. 88, 134501 (2002)] . Furthermore the authors demonstrate that superspiral waves that were observed by Qi Ouyang and coworkers [Phys. Rev. Lett. 85, 1650 (2000)] in a chemical reaction are also governed by MAWs. As verified in this example from chemistry, there are only two units of information that a MAW can transmit: its average frequency and the period of its modulation, the former is fixed by the mechanism of wave emission and the latter resembles the period of the source's motion. Everything else including the radius of the source's circular trajectory and its speed remain a secret to the observer of the modulated wave in a nonlinear medium.
Bats would certainly have less fun hunting in this unfavorable environment.

The standard model of nonlinear oscillatory media (the complex Ginzburg-Landau equation)

has been used to study moving wave sources. Figure 1 of the paper shows self-organising superspiral waves in a chemical reaction (d) and our simulations (e,f). Standard spirals are shown in (a-c).

We combined the panels (e) and (f) in the following figure where the actual spiral wave rotates at the bottom and the upper sheet shows the local amplitude of the emitted wave. This amplitude itself possesses a spiral wave that rotates with different speed and thereby modulates the bottom spiral (elongated and compressed waves). The vertical cross-section shows the spatial profile (white) of the modulation which is approaching the independently predicted MAW (blue) away from the center. The source (wave tip in the lower sheet) rotates autonomously around a small circle (a few pixels only).

Currently, we conduct simulations for an animation of the above picture where both spirals rotate and send out their waves. Moreover, co-moving profiles of the modulation and the MAW will illustrate the discovered nonlinear version of the Doppler effect.

As a guide to the eye, we show a simpler animation of recently observed antispiral waves. We may also combine both, superspiral and antispiral, effects etc...

Modulated Amplitude Waves

Modulated amplitude waves (MAWs) are a class of solutions of the complex Ginzburg-Landau equation (CGLE). The equation is a universal model of nonlinear oscillatory media near the supercritical onset of oscillations (or wave propagation). The two coefficients c1 and c3 describe the medium's properties.

MAWs are coherent structures, self-organised distortions of a background wave that travel with constant shape and speed on top of this background wave, and have the general form (z=x-vt is the coordinate in the MAW's rest frame)

Inserting this ansatz into the CGLE (consider one dimension x only) yields three coupled nonlinear ordinary differential equations (ODEs) of first order for the unknown functions a(z) and phi(z). Limit cycles in these ODEs correspond to MAWs. The limit cycles originate in Hopf bifurcations from fixed points which represent the unperturbed background wave.
MAWs form a two-parameter family which is conveniently parameterized by the average phase gradient q (when phi is periodic, it's local phase gradient does not contribute to the average) and the spatial period P of the modulation (equal to the period of the limit cycle).
M. Bär, L. Brusch, M. van Hecke, M. Zimmermann and A. Torcini showed (see [Phys. Rev. Lett. 85, 86 (2000)], [Physica D 160, 127 (2001)], [Physica D 174, 152 (2003)]) that MAWs are responsible for many features of spatio-temporal chaos in the CGLE. You may view a movie (12Mb, by Alessandro Torcini, dashed lines are max and min of MAW at SN, the central peak near x=200 approaches the profile of the MAW at SN including the long tail, once it becomes larger it forms a defect |A|=0 near x=130) of defect formation in simulations at c3=2 and c1=0.65 near the L3 transition from phase turbulence to amplitude turbulence. In particular they vanish in a saddle-node (of limit cycles) bifurcation and the typical dynamics around such a bifurcation (triangle) are shown below. The dependence of this bifurcation on the MAW parameters and CGLE coefficients is easy to obtain with the MAW construction kit which also computes the shape and all properties of the MAW.

Recently, superspiral waves in the Belousov-Zhapotinsky reaction (see [Phys. Rev. Lett. 85, 1650 (2000)] by Qi Ouyang and coworkers) and hydrothermal waves (see [Phys. Rev. Lett. 88, 134501 (2002)] by Nicolas Garnier et al.) have been linked to MAWs (see the preprint). There are many more phenomena that wait to be explained in terms of coherent structures.

MAW Construction Kit

Download the MAW construction kit to study MAWs in the framework of the CGLE. The MAW construction kit works together with the excellent bifurcation analysis software AUTO by Eusebius Doedel.

There are two equivalent versions available:
- The first is based on files (r.maw...) which store the instructions for AUTO97. If you like the flexibility of adjusting all the numerical parameters then this is your choice. Download it now. Install AUTO97 and unpack (gunzip, tar) the kit which also has an example MAW (file q.maw) and a README. Follow the steps in the README file to compute your MAWs.
- The second version is a Python script that controls the computations in the background and produces the MAWs and bifurcation diagrams (well, some of them) that you ask it for. Download will be available soon. You need the enhanced version AUTO2000 and to unpack (gunzip, tar) the script. The included README will guide you further.

Creating a file-based version for AUTO2000 should be a simple exercise. After some reformatting you could even run the MAW construction kit under WINDOWs with XPP but I strongly recomment using the Linux/unix plateform (where XPP is running as well).
If you have problems or suggestions, send email to brusch @ . The MAW construction kit may also be suited for education in pattern formation.