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 spatiotemporal models and tools for application to cell and developmental biology.
Doppler Effect Goes Nonlinear
Modulated Amplitude Waves
Publications of Lutz Brusch
2017

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] 
A predictive 3D multiscale model of biliary fluid dynamics in the liver lobule
Cell Systems, 4, 3, 277–290.e9, 2017 [DOI] 
pSSAlib: The partialpropensity stochastic chemical network simulator
PLoS Computational Biology, 13, 12, e1005865, 2017 [DOI]
2016

Accelerated cell divisions drive the outgrowth of the regenerating spinal cord in axolotls
eLife, 5, e20357, 2016 [DOI]
2015

Mathematical modelling of fluid transport and its regulation at multiple scales
BioSystems, 130, 110, 2015 [DOI] 
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] 
Cellular dynamics underlying regeneration of appropriate segment number during axolotl tail regeneration
BMC Developmental Biology, 15, 1, 48, 2015 [DOI]
2014

Mathematical modeling of regenerative processes
Curr. Top. Dev. Biol., 108, 283317, 2014 [DOI] 
Chevron formation of the zebrafish muscle segments
J. Exp. Biol., 217, 21, 38703882, 2014 [DOI] 
Morpheus: a userfriendly modeling environment for multiscale and multicellular systems biology
Bioinformatics, 30, 13311332, 2014 [DOI]
2013

Transdifferentiation of pancreatic cells by loss of contactmediated signaling
BMC Syst. Biol., 7, 77, 2013 [DOI] 
Phosphorylation of the Smo tail is controlled by membrane localization and is dispensable for clustering
J. Cell Sci., 126, 20, 46844697, 2013 [DOI]
2012

On the role of lateral stabilization during early patterning in the pancreas
J. R. Soc. Interface, 10, 20120766, 2012 [DOI] 
A latticegas cellular automaton model for in vitro sprouting angiogenesis
Acta Phys. Pol. B, 5, 1, 99115, 2012 [DOI] 
A general theoretical framework to infer endosomal network dynamics from quantitative image analysis
Curr. Biol., 22, 15, 1381  1390, 2012 [DOI]
2011

Predicting Pancreas Cell Fate Decisions and Reprogramming with a Hierarchical MultiAttractor Model
PLoS ONE volume 6, issue 3, e14752, 2011 [DOI]
2010

Parameter estimation with a novel gradientbased optimization method for biological latticegas cellular automaton models
J. Math. Biol., 63, 1, 173200, 2010 [DOI] 
LigandSpecific cFos Expression Emerges from the Spatiotemporal Control of ErbB Network Dynamics
Cell, 141, 884896, 2010 [DOI] 
Coveragemaximization in networks under resource constraints
Phys. Rev. E, 81, 061124, 2010 [DOI] 
Modeling discrete combinatorial systems as alphabetic bipartite networks: Theory and applications
Phys. Rev. E, 81, 036103, 2010 [DOI] 
A model for cyst lumen expansion and size regulation via fluid secretion
Journal of Theoretical Biology, 264, 10771088, 2010 [DOI] 
Prediction of traveling front behavior in a latticegas cellular automaton model for tumor invasion
Computers and Mathematics with Applications, 59, 23262339, 2010 [DOI] 
From cellular automaton rules to an effective macroscopic meanfield description
Acta Physica Polonica B Proceedings Supplement, 3, 399416, 2010 [PDF]
2009

Biosimulation of drug metabolismA yeast based model
European Journal of Pharmaceutical Sciences, 36, 157170, 2009 [DOI]
2008

The coherence of the vesicle theory of protein secretion
J. Theor. Biol., 252, 370373, 2008 [DOI] 
Protein domains of GTPases on membranes: do they rely on Turing's mechanism?
In: Mathematical Modeling of Biological Systems, Volume I.
Birkhauser, Boston, 3346, 2008 [DOI] 
Membrane identity and GTPase cascades regulated by toggle and cutout switches
Mol. Syst. Biol., 4, 206, 2008 [DOI] 
Coverage Maximization in Small World Network Under Bandwidth Constraint
In: SIGCOMM 2008 Conference on Applications, Technologies, Architectures, and Protocols for Computer Communications
ACM, 481482, 2008
2007

Biosimulation in Drug Development
WileyVCH, Weinheim, 3764, 2007
2006

Ethanol production with microorganisms. Process control and modelling
In: Proceedings of the 18th ECMI modelling week
Lappeenrannan teknillinen yliopisto, Lappeenranta, 923, 2006 
Characterization of Travelling Front Behaviour in a Lattice Gas Cellular Automaton Model of Glioma Invasion
Math. Mod. Meth. Appl. Sci., 15, 17791794, 2006 
Towards in vivo computing: Quatitative analysis of an artificial gene regulatory network behaving as a RS flipflop and simulating the system in silico
In: BioInspired Models of Network, Information and Computing Systems
IEEE, 17, 2006 [DOI]
2005

Spiral instabilities in periodically forced extended oscillatory media
In: EQUADIFF 2003International Conference on Differential equations
World Scientific, Singapore, 777782, 2005 [DOI] 
Design and analysis of a bioinspired search algorithm for peertopeer networks
In: SelfStar Properties in Complex Information Systems
SpringerVerlag, Heidelberg, 3460, 2005 [DOI]
2004

Model evaluation for glycolytic oscillations in yeast biotransformations of xenobiotics
Biophys. Chem., 109, 413426, 2004 [DOI] 
Comment on "Antispiral Waves in ReactionDiffusion Systems" [3] (multiple letters)
Phys. Rev. Lett., 92, 898011898021, 2004 [DOI] 
Mechanism for spiral wave breakup in excitable and oscillatory media.
Phys. Rev. Lett., 92, 119801, 2004 [DOI] 
Breakup of spiral waves caused by radial dynamics: Eckhaus and finite wave number instabilities
New J. Phys., 6, 5, 2004 [DOI] 
Antispiral waves as sources in oscillatory reactiondiffusion media
J Phys Chem B, 108, 1473314740, 2004 [DOI]
2003

Doppler Effect of Nonlinear Waves and Superspirals in Oscillatory Media
Phys Rev Lett, 91, 10830211083024, 2003 [DOI] 
Nonlinear analysis of the Eckhaus instability: Modulated amplitude waves and phase chaos with nonzero average phase gradient
Phys D Nonlinear Phenom, 174, 152167, 2003 [DOI] 
Antispiral and superspiral waves
Wiss. Z. TU Dresden, 52, 5558, 2003 
Modelling thinfilm dewetting on structured substrates and templates: Bifurcation analysis and numerical simulations
Eur. Phys. J. E, 11, 255271, 2003 [DOI]
2002

FoldHopf bursting in a model for calcium signal transduction
Z. Phys. Chem., 216, 487497, 2002 [DOI] 
Dewetting of thin films on heterogeneous substrates: Pinning versus coarsening
Phys. Rev.~E, 66, 15, 2002 [DOI]
2001

Modulated amplitude waves and defect formation in the onedimensional complex GinzburgLandau equation
Phys D Nonlinear Phenom, 160, 127148, 2001 [DOI]
2000

Modulated amplitude waves and the transition from phase to defect chaos
Phys Rev Lett, 85, 8689, 2000 [DOI]
1999
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 GinzburgLandau equation), as scientists now report in
Physical Review Letters.
The authors theoretically studied wave sources that oscillate
backandforth 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 welldefined set of modulations,
socalled
modulated amplitude waves (MAWs), exists and forces all (initially)
different
modulations to evolve to MAWshape and MAWproperties. Hence almost all
information imprinted by the source's motion into the initial
modulation is
deleted by selforganising 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 GinzburgLandau equation)
has been used to study moving wave sources. Figure 1 of the paper shows selforganising superspiral waves in a chemical reaction (d) and our simulations (e,f). Standard spirals are shown in (ac).
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 crosssection 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, comoving 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 GinzburgLandau 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, selforganised distortions of a background wave that travel with constant shape and speed on top of this background wave, and have the general form (z=xvt 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 twoparameter 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 spatiotemporal 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 saddlenode (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 BelousovZhapotinsky 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 filebased 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 @
insatlse.fr .
The MAW construction kit may also be suited for education in pattern
formation.