TY  - JOUR
A1  - Beta, Carsten
A1  - Gov, Nir S.
A1  - Yochelis, Arik
T1  - Why a Large-Scale Mode Can Be Essential for Understanding Intracellular Actin Waves
JF  - Cells
N2  - During the last decade, intracellular actin waves have attracted much attention due to their essential role in various cellular functions, ranging from motility to cytokinesis. Experimental methods have advanced significantly and can capture the dynamics of actin waves over a large range of spatio-temporal scales. However, the corresponding coarse-grained theory mostly avoids the full complexity of this multi-scale phenomenon. In this perspective, we focus on a minimal continuum model of activator–inhibitor type and highlight the qualitative role of mass conservation, which is typically overlooked. Specifically, our interest is to connect between the mathematical mechanisms of pattern formation in the presence of a large-scale mode, due to mass conservation, and distinct behaviors of actin waves.
KW  - nonlinear waves
KW  - actin polymerization
KW  - bifurcation theory
KW  - mass conservation
KW  - spatial localization
KW  - pattern formation
KW  - activator–inhibitor models
Y1  - 2020
U6  - https://doi.org/10.3390/cells9061533
SN  - 2073-4409
VL  - 9
IS  - 6
PB  - MDPI
CY  - Basel
ER  - 
TY  - JOUR
A1  - Straube, Arthur V.
A1  - Pikovskij, Arkadij
T1  - Pattern formation induced by time-dependent advection
JF  - Mathematical modelling of natural phenomena
N2  - We study pattern-forming instabilities in reaction-advection-diffusion systems. We develop an approach based on Lyapunov-Bloch exponents to figure out the impact of a spatially periodic mixing flow on the stability of a spatially homogeneous state. We deal with the flows periodic in space that may have arbitrary time dependence. We propose a discrete in time model, where reaction, advection, and diffusion act as successive operators, and show that a mixing advection can lead to a pattern-forming instability in a two-component system where only one of the species is advected. Physically, this can be explained as crossing a threshold of Turing instability due to effective increase of one of the diffusion constants.
KW  - pattern formation
KW  - reaction-advection-diffusion equation
Y1  - 2011
U6  - https://doi.org/10.1051/mmnp/20116107
SN  - 0973-5348
VL  - 6
IS  - 1
SP  - 138
EP  - 148
PB  - EDP Sciences
CY  - Les Ulis
ER  - 
TY  - JOUR
A1  - Stich, Michael
A1  - Beta, Carsten
T1  - Standing waves in a complex Ginzburg-Landau equation with time-delay  feedback
JF  - Discrete and continuous dynamical systems : a journal bridging mathematics and sciences
N2  - Standing waves are studied as solutions of a complex Ginsburg-Landau equation subjected to local and global time-delay feedback terms. The onset of standing waves is studied at the instability of the homogeneous periodic solution with respect to spatially periodic perturbations. The solution of this spatiotemporal wave pattern is given and is compared to the homogeneous periodic solution.
KW  - pattern formation
KW  - reaction-diffusion system
KW  - control
Y1  - 2011
SN  - 1078-0947
SN  - 1553-5231
IS  - 1
SP  - 1329
EP  - 1334
PB  - American Institute of Mathematical Sciences
CY  - Springfield
ER  -