TY - JOUR
AB - The abelian sandpile serves as a model to study self-organized criticality, a phenomenon occurring in biological, physical and social processes. The identity of the abelian group is a fractal composed of self-similar patches, and its limit is subject of extensive collaborative research. Here, we analyze the evolution of the sandpile identity under harmonic fields of different orders. We show that this evolution corresponds to periodic cycles through the abelian group characterized by the smooth transformation and apparent conservation of the patches constituting the identity. The dynamics induced by second and third order harmonics resemble smooth stretchings, respectively translations, of the identity, while the ones induced by fourth order harmonics resemble magnifications and rotations. Starting with order three, the dynamics pass through extended regions of seemingly random configurations which spontaneously reassemble into accentuated patterns. We show that the space of harmonic functions projects to the extended analogue of the sandpile group, thus providing a set of universal coordinates identifying configurations between different domains. Since the original sandpile group is a subgroup of the extended one, this directly implies that it admits a natural renormalization. Furthermore, we show that the harmonic fields can be induced by simple Markov processes, and that the corresponding stochastic dynamics show remarkable robustness over hundreds of periods. Finally, we encode information into seemingly random configurations, and decode this information with an algorithm requiring minimal prior knowledge. Our results suggest that harmonic fields might split the sandpile group into sub-sets showing different critical coefficients, and that it might be possible to extend the fractal structure of the identity beyond the boundaries of its domain.
AU - Lang, Moritz
AU - Shkolnikov, Mikhail
ID - 196
IS - 8
JF - Proceedings of the National Academy of Sciences
TI - Harmonic dynamics of the Abelian sandpile
VL - 116
ER -
TY - JOUR
AB - Tight control over protein degradation is a fundamental requirement for cells to respond rapidly to various stimuli and adapt to a fluctuating environment. Here we develop a versatile, easy-to-handle library of destabilizing tags (degrons) for the precise regulation of protein expression profiles in mammalian cells by modulating target protein half-lives in a predictable manner. Using the well-established tetracycline gene-regulation system as a model, we show that the dynamics of protein expression can be tuned by fusing appropriate degron tags to gene regulators. Next, we apply this degron library to tune a synthetic pulse-generating circuit in mammalian cells. With this toolbox we establish a set of pulse generators with tailored pulse lengths and magnitudes of protein expression. This methodology will prove useful in the functional roles of essential proteins, fine-tuning of gene-expression systems, and enabling a higher complexity in the design of synthetic biological systems in mammalian cells.
AU - Chassin, Hélène
AU - Müller, Marius
AU - Tigges, Marcel
AU - Scheller, Leo
AU - Lang, Moritz
AU - Fussenegger, Martin
ID - 6465
IS - 1
JF - Nature Communications
TI - A modular degron library for synthetic circuits in mammalian cells
VL - 10
ER -
TY - JOUR
AB - The hanging-drop network (HDN) is a technology platform based on a completely open microfluidic network at the bottom of an inverted, surface-patterned substrate. The platform is predominantly used for the formation, culturing, and interaction of self-assembled spherical microtissues (spheroids) under precisely controlled flow conditions. Here, we describe design, fabrication, and operation of microfluidic hanging-drop networks.
AU - Misun, Patrick
AU - Birchler, Axel
AU - Lang, Moritz
AU - Hierlemann, Andreas
AU - Frey, Olivier
ID - 305
JF - Methods in Molecular Biology
TI - Fabrication and operation of microfluidic hanging drop networks
VL - 1771
ER -
TY - JOUR
AB - Temperate bacteriophages integrate in bacterial genomes as prophages and represent an important source of genetic variation for bacterial evolution, frequently transmitting fitness-augmenting genes such as toxins responsible for virulence of major pathogens. However, only a fraction of bacteriophage infections are lysogenic and lead to prophage acquisition, whereas the majority are lytic and kill the infected bacteria. Unless able to discriminate lytic from lysogenic infections, mechanisms of immunity to bacteriophages are expected to act as a double-edged sword and increase the odds of survival at the cost of depriving bacteria of potentially beneficial prophages. We show that although restriction-modification systems as mechanisms of innate immunity prevent both lytic and lysogenic infections indiscriminately in individual bacteria, they increase the number of prophage-acquiring individuals at the population level. We find that this counterintuitive result is a consequence of phage-host population dynamics, in which restriction-modification systems delay infection onset until bacteria reach densities at which the probability of lysogeny increases. These results underscore the importance of population-level dynamics as a key factor modulating costs and benefits of immunity to temperate bacteriophages
AU - Pleska, Maros
AU - Lang, Moritz
AU - Refardt, Dominik
AU - Levin, Bruce
AU - Guet, Calin C
ID - 457
IS - 2
JF - Nature Ecology and Evolution
TI - Phage-host population dynamics promotes prophage acquisition in bacteria with innate immunity
VL - 2
ER -
TY - JOUR
AB - A nonlinear system possesses an invariance with respect to a set of transformations if its output dynamics remain invariant when transforming the input, and adjusting the initial condition accordingly. Most research has focused on invariances with respect to time-independent pointwise transformations like translational-invariance (u(t) -> u(t) + p, p in R) or scale-invariance (u(t) -> pu(t), p in R>0). In this article, we introduce the concept of s0-invariances with respect to continuous input transformations exponentially growing/decaying over time. We show that s0-invariant systems not only encompass linear time-invariant (LTI) systems with transfer functions having an irreducible zero at s0 in R, but also that the input/output relationship of nonlinear s0-invariant systems possesses properties well known from their linear counterparts. Furthermore, we extend the concept of s0-invariances to second- and higher-order s0-invariances, corresponding to invariances with respect to transformations of the time-derivatives of the input, and encompassing LTI systems with zeros of multiplicity two or higher. Finally, we show that nth-order 0-invariant systems realize – under mild conditions – nth-order nonlinear differential operators: when excited by an input of a characteristic functional form, the system’s output converges to a constant value only depending on the nth (nonlinear) derivative of the input.
AU - Lang, Moritz
AU - Sontag, Eduardo
ID - 1007
JF - Automatica
SN - 00051098
TI - Zeros of nonlinear systems with input invariances
VL - 81C
ER -
TY - JOUR
AB - Cell-cell contact formation constitutes an essential step in evolution, leading to the differentiation of specialized cell types. However, remarkably little is known about whether and how the interplay between contact formation and fate specification affects development. Here, we identify a positive feedback loop between cell-cell contact duration, morphogen signaling, and mesendoderm cell-fate specification during zebrafish gastrulation. We show that long-lasting cell-cell contacts enhance the competence of prechordal plate (ppl) progenitor cells to respond to Nodal signaling, required for ppl cell-fate specification. We further show that Nodal signaling promotes ppl cell-cell contact duration, generating a positive feedback loop between ppl cell-cell contact duration and cell-fate specification. Finally, by combining mathematical modeling and experimentation, we show that this feedback determines whether anterior axial mesendoderm cells become ppl or, instead, turn into endoderm. Thus, the interdependent activities of cell-cell signaling and contact formation control fate diversification within the developing embryo.
AU - Barone, Vanessa
AU - Lang, Moritz
AU - Krens, Gabriel
AU - Pradhan, Saurabh
AU - Shamipour, Shayan
AU - Sako, Keisuke
AU - Sikora, Mateusz K
AU - Guet, Calin C
AU - Heisenberg, Carl-Philipp J
ID - 735
IS - 2
JF - Developmental Cell
SN - 15345807
TI - An effective feedback loop between cell-cell contact duration and morphogen signaling determines cell fate
VL - 43
ER -
TY - JOUR
AB - Feedback loops in biological networks, among others, enable differentiation and cell cycle progression, and increase robustness in signal transduction. In natural networks, feedback loops are often complex and intertwined, making it challenging to identify which loops are mainly responsible for an observed behavior. However, minimal synthetic replicas could allow for such identification. Here, we engineered a synthetic permease-inducer-repressor system in Saccharomyces cerevisiae to analyze if a transport-mediated positive feedback loop could be a core mechanism for the switch-like behavior in the regulation of metabolic gene networks such as the S. cerevisiae GAL system or the Escherichia coli lac operon. We characterized the synthetic circuit using deterministic and stochastic mathematical models. Similar to its natural counterparts, our synthetic system shows bistable and hysteretic behavior, and the inducer concentration range for bistability as well as the switching rates between the two stable states depend on the repressor concentration. Our results indicate that a generic permease–inducer–repressor circuit with a single feedback loop is sufficient to explain the experimentally observed bistable behavior of the natural systems. We anticipate that the approach of reimplementing natural systems with orthogonal parts to identify crucial network components is applicable to other natural systems such as signaling pathways.
AU - Gnügge, Robert
AU - Dharmarajan, Lekshmi
AU - Lang, Moritz
AU - Stelling, Jörg
ID - 1008
IS - 10
JF - ACS Synthetic Biology
TI - An orthogonal permease–inducer–repressor feedback loop shows bistability
VL - 5
ER -
TY - JOUR
AB - The increasing complexity of dynamic models in systems and synthetic biology poses computational challenges especially for the identification of model parameters. While modularization of the corresponding optimization problems could help reduce the “curse of dimensionality,” abundant feedback and crosstalk mechanisms prohibit a simple decomposition of most biomolecular networks into subnetworks, or modules. Drawing on ideas from network modularization and multiple-shooting optimization, we present here a modular parameter identification approach that explicitly allows for such interdependencies. Interfaces between our modules are given by the experimentally measured molecular species. This definition allows deriving good (initial) estimates for the inter-module communication directly from the experimental data. Given these estimates, the states and parameter sensitivities of different modules can be integrated independently. To achieve consistency between modules, we iteratively adjust the estimates for inter-module communication while optimizing the parameters. After convergence to an optimal parameter set---but not during earlier iterations---the intermodule communication as well as the individual modules\' state dynamics agree with the dynamics of the nonmodularized network. Our modular parameter identification approach allows for easy parallelization; it can reduce the computational complexity for larger networks and decrease the probability to converge to suboptimal local minima. We demonstrate the algorithm\'s performance in parameter estimation for two biomolecular networks, a synthetic genetic oscillator and a mammalian signaling pathway.
AU - Lang, Moritz
AU - Stelling, Jörg
ID - 1170
IS - 6
JF - SIAM Journal on Scientific Computing
TI - Modular parameter identification of biomolecular networks
VL - 38
ER -
TY - CONF
AB - In recent years, several biomolecular systems have been shown to be scale-invariant (SI), i.e. to show the same output dynamics when exposed to geometrically scaled input signals (u → pu, p > 0) after pre-adaptation to accordingly scaled constant inputs. In this article, we show that SI systems-as well as systems invariant with respect to other input transformations-can realize nonlinear differential operators: when excited by inputs obeying functional forms characteristic for a given class of invariant systems, the systems' outputs converge to constant values directly quantifying the speed of the input.
AU - Lang, Moritz
AU - Sontag, Eduardo
ID - 1320
TI - Scale-invariant systems realize nonlinear differential operators
VL - 2016-July
ER -