Lutz Brusch

Spatio-temporal pattern formation in cells and tissues

Previous and current research

Feedback regulation is ubiquitous in nature, starting already at the molecular scale and extending all the way up, often linking different spatial scales. Biological systems utilise feedback regulation to let structures and functions self-organise. Such self-organisation often defies our linear-pathway-trained intuition. Mathematical modelling, analysis and computer simulation closely iterated with quantitative experiments can therefore be a fruitful strategy for studying complex regulatory systems.

We have previously applied this theoretical approach in collaboration with experimentalists and found that feedback loops of effector recruitment and activity can couple different Rab GTPases on intracellular organelles in such a way that multistability self-organises (del Conte-Zerial et al., 2008). Therewith, membrane identity is robustly maintained despite of noise and perturbations but can also abruptly switch to a successive identity upon a super-threshold signal. This abrupt switch, as observed for instance in early to late endosome conversion, represents a novel type, termed cut-out switch, which differs from the canonical toggle switch by superposition of negative feedback upon the positive feedback loop and correspondingly novel switch behaviour. Such theoretical insight into biological switches was also applied in the design and analysis of biosynthetic computing circuits (Hayat et al., 2006). Currently, self-organising multistability and switches between different functional states are further explored for pancreas cell differentiation with implications for cell reprogramming in regenerative medicine (Zhou et al., 2011).

More complex spatio-temporal behaviour emerges when regulatory networks couple spatially distributed components. Along this line, a mechanistic model and analysis of ErbB signal transduction and gene regulation revealed that differentiation versus proliferation decisions of cells upon growth factor stimulation arise from spatially distributed signal processing (Nakakuki et al., 2010). We are currently also exploring how feedback regulation and spatio-temporal patterning control tissue morphogenesis and growth (Gin et al., 2010).

Throughout these projects, the mathematical models are inherently nonlinear and only fully disclose their secrets through advanced methods including dynamical systems theory and bifurcation analysis. We continuously develop such analysis methods further, in particular for nonlinear partial differential equation models.

A mechanistic mathematical model of an epithelial cyst (left) gives insight into how intraluminal ion concentration can drive and arrest cyst growth (right, curve shows model simulation compared to experimental data) through an interplay (left) of osmotic fluid transport, ion dilution and stretch-activated cell proliferation.

Future prospects and goals

This theory group, in close collaborations with experimentalists, will further extend and apply systems biology approaches to uncover the regulatory mechanisms that underlie spatio-temporal patterning processes in cells and tissues.

Open questions that inspire our work are

1. Which capabilities does the eukaryotic cell gain from the closed regulatory loop between signal transduction and compartmentalisation/endocytosis?

2. How is hepatocyte polarity established and remodelled in the regenerating liver?

3. What kind of biochemical and/or biophysical signals does a growing, and moreover a regenerating, tissue feed back from the tissue/organ scale down to a single proliferating cell such that a robust organ size emerges?

About

1998-2002: PhD/Postdoctoral work at MPI-PKS, Dresden 2003-2004: Postdoctoral work at Centre de Bioingenierie Gilbert Durand, Toulouse 2004-2007: Postdoctoral work at Center for High Performance Computing, TU Dresden since 2008: Group leader at Center for Information Services and High Performance Computing (ZIH), TU Dresden

Selected publications

Zhou JX, Brusch L, Huang S. Predicting pancreas cell fate decisions and reprogramming with a hierarchical multi-attractor model. PLoS ONE 2011; 6 (3), e14752.

Nakakuki T, Birtwistle MR, Saeki Y, Yumoto N, Ide K, Nagashima T, Brusch L, Ogunnaike BA, Okada-Hatakeyama M, Kholodenko BN. Ligand-specific c-Fos expression emerges from the spatio-temporal control of ErbB network dynamics. Cell 2010; 141: 884-896.

Gin E, Tanaka EM, Brusch L. A model for cyst lumen expansion and size regulation via fluid secretion. J. Theor. Biol. 2010; 264: 1077-1088.

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

Hayat S, Ostermann K, Brusch L, Pompe W, Rödel G. Towards in vivo computing: Quantitative 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 2006; 1-7.

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