Cell tree packings
Optimal packings of disconnected objects have been studied for centuries owing to their wide-ranging importance in physics, mathematics, materials science, and architecture. By contrast, the packing principles of linked objects, such as topologically complex polymers or cell-lineages, remain less well understood. In collaboration with the Shvartsman lab, we have investigated geometrically frustrated tree packing problems arising during the initial stages of animal development when interconnected cells assemble within a convex enclosure. Combining 3D imaging and mathematical modeling, we studied Drosophila egg chambers where 16 germline cells are connected by cytoplasmic bridges and form a branched tree. Our analysis relates the cell packings to tree packing problems on convex polyhedrons that generalize Platonic and Archimedean solids. The results of this study highlight the importance of topological and entropic constraints for tissue organization and dynamics.
Fundamental biological and biomimetic processes, from tissue morphogenesis to soft robotics, rely on the propagation of chemical and mechanical surface waves to signal and coordinate active force generation. The complex interplay between surface geometry and contraction wave dynamics is not yet well understood, but will be essential for the future design of chemically-driven soft robots and active materials. We study models that couple reaction-diffusion dynamics to non-Euclidean shell mechanics to identify generic features of chemo-mechanical wave propagation on active deformable surfaces. The theoretical framework is validated against recent data from contractile wave measurements on ascidian and starfish oocytes. The practical potential of chemo-mechanical coupling is demonstrated by simulating the spontaneous wave-induced locomotion of elastic shells.
Curved active turbulence
Recent experiments demonstrate the importance of substrate curvature for actively forced fluid dynamics. The covariant formulation and analysis of continuum models for non-equilibrium flows on curved surfaces poses interesting theoretical challenges. Our recent paper studies a generalized covariant Navier-Stokes model for fluid flows driven by active stresses in non-planar geometries. Direct numerical simulations reveal an anomalous turbulent phase that differs from externally forced classical 2D Kolmogorov turbulence. This new type of active turbulence is characterized by the self-assembly of finite-size vortices into linked chains of anti-ferromagnetic order, which percolate through the entire fluid domain, forming an active dynamic network.
Active matter logic
Chemically or optically powered active matter plays an increasingly important role in materials design, but its computational potential has yet to be explored systematically. The competition between energy consumption and dissipation imposes stringent physical constraints on the information transport in active flow networks. Combining insights from microbial experiments with concepts from lattice-field theory and non-equilibrium statistical mechanics, we demonstrated how the
inherent non-locality of incompressible active flow networks can be utilized to construct universal logical operations, Fredkin gates and memory storage in set-reset latches through the synchronized self-organization of many individual network components.
Mirror-symmetry breaking in active fluids
Turbulence provides an important mechanism for energy redistribution and mixing in interstellar gases, planetary atmospheres, and the oceans. Classical turbulence theory suggests for ordinary 3D fluids or gases, such as water or air, that larger vortices can transform into smaller ones but not vice versa, thus limiting energy transfer from smaller to larger scales. Our calculations predict that bacterial suspensions and other pattern-forming active fluids can deviate from this paradigm by creating turbulent flow structures that spontaneously break mirror symmetry and transport energy to larger scales. These results suggest that the collective dynamics of swimming microorganisms can enhance fluid mixing more strongly than previously thought.
Active flow networks
Active biological flow networks pervade nature and span a wide
range of scales, from arterial blood vessels and bronchial mucus
transport in humans to bacterial flow through porous media or
plasmodial shuttle streaming in slime molds. The self-organization principles that govern flow
statistics in such non-equilibrium systems remain incompletely understood. By merging concepts from lattice field theory, graph theory and physico-chemical reaction rate theory, our work aims to develop a generic foundational understanding of active flow networks.
Many bacterial species colonize surfaces and form dense 3D structures, known as biofilms, which are highly tolerant to antibiotics and constitute one of the major forms of bacterial biomass on Earth. Bacterial biofilms undergo remarkable structural changes during their development from initial attachment to maturity. In the past, biofilms have usually been studied at a coarse morphological level. Therefore, little has been known about the positional and orientational arrangements of individual cells in a biofilm. Our collaborators in the Drescher lab have developed an optical imaging technique that allows them to visualize every cell inside a large number of bacterial biofilms. This new method makes it possible to investigate architectural transitions during biofilm growth at single-cell resolution and to test mathematical models of biofilm formation in unprecedented detail.
Bacterial spin lattices
Despite their inherent non-equilibrium nature, living systems can self-organize in highly ordered collective states that share striking similarities with the thermodynamic equilibrium phases of conventional condensed matter and fluid systems. It is not clear when, or even whether, well-established theoretical concepts describing universal thermostatistics of equilibrium systems can capture and classify ordered states of living matter. Through microfluidic experiments and mathematical modelling, we demonstrate that lattices of hydrodynamically coupled bacterial vortices can spontaneously organize into distinct phases of ferro- and antiferromagnetic order. The preferred phase can be controlled by tuning the vortex coupling through changes of the inter-cavity gap widths. The emergence of opposing order regimes is tightly linked to the existence of geometry-induced edge currents, reminiscent of those in quantum systems.
Buckling and wrinkling are common symmetry-breaking phenomena that play important roles in a wide range of biological and physical systems. Examples range from embryogenesis and biological tissue differentiation to structure formation processes in heterogeneous thin films or on planetary surfaces. Yet, owing to the nonlinearity of the underlying stretching and bending forces, it has been difficult to predict the wrinkling patterns that occur when a curved multi-layered surface is subjected to mechanical stress. In collaboration with the Reis lab, we have developed a generalized Swift-Hohenberg theory that explains the transition between hexagonal and fingerprint-like structures, as observed in experimental studies of thin shells on curved soft substrates.
mRNA transport in Drosophila oocytes
Symmetry-breaking transitions play a crucial role in the embryonic development of higher organisms, resulting in complex body shapes characterized by front-back, left-right and top-bottom asymmetry. In the fruit fly Drosophila, the anterior-posterior axis is laid out during egg formation (oogenesis) through localization of bicoid and oskar mRNAs to the anterior and posterior poles of the oocyte, respectively. This mRNA localization is believed to be dominated by motor-driven transport on a weakly polarized microtubule cytoskeleton, but how the noncentrosomal microtubule cytoskeleton is organised in three dimensions, is not known. To understand better the effect of cytoskeletal architure on diffusive, hydrodynamic and motor-driven mRNA transport, we have developed a detailed theoretical model for stage 9 oocytes. Based on observed cortical microtubule nucleation densities, this experimentally constrained model provides a fully three-dimensional description of cytoskeleton, cytoplasmic flows and cargo transport that accurately reproduces mRNA localizations in wild-type oocytes and mutants. Our analysis suggests that the architecture of the microtubule cytoskeleton in Drosophila oocytes is more ordered than previously thought.
A major puzzle in biology is how mammalian sperm determine and maintain the correct swimming direction during the various phases of the sexual reproduction process. Whilst chemotaxis is assumed to dominate in the immediate vicinity of the ovum, it is unclear which biochemical or physical cues guide spermatozoa on their long journey towards the egg cell. Currently debated mechanisms range from peristaltic pumping to temperature sensing (thermotaxis) and direct response to fluid flow variations (rheotaxis), but little is known quantitatively about their relative importance. Using microfluidic devices, we investigated systematically the swimming behavior of human and bull sperm at physiologically relevant shear rates and viscosities. These measurements show that the interplay of fluid shear, steric surface interactions and flagellar beat dynamics leads to a stable upstream spiraling motion of sperm cells, thus providing a generic and robust rectification mechanism to support mammalian fertilization.
Surface interactions and control of microbial locomotion
Interactions between swimming cells and surfaces are essential to many microbiological processes, from the formation of biofilms to the fertilization of human egg cells. Until recently, however, relatively little was known about the physical mechanisms that govern the scattering of flagellated or ciliated microorganisms from solid surfaces. A better understanding of cell-surface interactions not only promises new biological insights but may also advance microfluidic techniques for controlling microbial locomotion, with potential applications in diagnostics, therapeutic protein synthesis and photosynthetic biofuel production. One of our recent papers shows that the surface scattering of mammalian spermatozoa and unicellular green algae is dominated by direct ciliary contact interactions. Building on this insight, we were able to construct optimal microfluidic ratchets that maximize rectification of initially uniform algae suspensions. Furthermore, our related work on confined bacterial suspensions demonstrates how curved boundaries can be used to control and stabilize the collective motion of microorganisms.
Self-propulsion and collective swimming of microorganisms
Bacteria and algae reach respectable swimming speeds of a few times their body length per second. Even more remarkably, ensembles of microorganisms exhibit complex collective behavior and can form coherent structures like turbulent vortices, spirals or bionematic jets. The characteristic length scales of these patterns may exceed the size of an individual organism by several orders in magnitude. Dynamical structure formation in bacterial systems
emerges due to a combination of environmental factors
(e.g., varying nutrient resources or oxygen gradients), biological competition,
chemical communication (deposition and detection of
messenger substances), and physical interactions. Part of our research focusses on identifying and understanding physical
processes that may
trigger collective dynamics in microbial suspensions.
We are interested in questions such as: How do individual bacteria and microalgae affect their fluid environment? Which generic or specific
mechanisms are responsible and/or necessary for the collective
behavior of these microorganisms? What role did hydrodynamic effects play in the evolution from unicellular to multicellular forms of life? How can collective motions be suppressed or enhanced by
Asexual reproduction and regeneration in multicellular organisms
Asexual reproduction by
fission or budding is a characteristic feature of bacteria
and single cell eukaryotes, such as yeast or amoeba. Higher multicellular
organisms usually reproduce sexually, because they lack the regenerative
capabilities required for asexual reproduction. Exceptions
are hydras and planarians (flatworms) which
can reproduce both sexually and asexually. Hydras are relatively primitive
organisms composed of only a very small number of cell
types. By contrast, planarians are bilaterally symmetric
animals, possess all three germ layers, a
complex central nervous system and many of
their genes can also be found in humans. Planarians exhibit
amazing regenerative abilities,
facilitated by stem cells that
are distributed throughout their bodies.
These stem cells not only enable the worms to heal
without scarring after wounding, but also allow for
asexual reproduction: In the course of a fission cycle, planarians can split in two or more pieces
and subsequently regenerate the missing body parts
within a few days. In collaboration with the Collins lab, we have studied internal and external factors that can affect the
fission and population dynamics in the asexual freshwater
planarian species Schmidtea mediterranea.
Thermostatistics and entropy
Over the past 60 years, a considerable number of theories and experiments have claimed the existence of negative absolute
temperature in spin systems and ultracold quantum gases. This has led to speculation that ultracold gases may be dark-energy
analogues and also suggests the feasibility of heat engines with efficiencies larger than one. Such negative temperature claims arise from the use of an entropy definition
that is inconsistent both mathematically and thermodynamically. These conceptual deficiencies can
be overcome if one adopts a microcanonical entropy functional originally derived by Gibbs. The resulting thermodynamic
framework is mathematically self-consistent and implies that absolute temperature remains positive even for systems with a bounded spectrum.
Relativistic diffusion and thermodynamics
Einstein's theory of relativity assumes
that particles cannot move faster than the speed of light.
Standard descriptions of diffusion and Brownian motion
processes are in conflict with this postulate. The latter fact
is rather unproblematic in most terrestrial applications,
but it may lead to inconsistencies in, for example, astrophysical
applications if one wants to describe the quasi-random
motion of particles in very hot plasmas. In recent years, we have studied different approaches towards formulating diffusion processes in a relativistically
consistent manner. A closely related problem concerns the relativistic generalization of thermodynamics. Einstein's theory predicts that observers who are in relative
motion measure different length and time intervals.
Historically, there has been some debate as to whether or
not this also applies to thermodynamics quantities. The
problem can be traced to the fact that thermodynamics
deals with extended systems which need to be handled
with care in relativity. Recently, we proposed a resolution of several conceptual difficulties
by introducing definitions of thermodynamic quantities
that are guided by photographic measurements.
Efficient Monte Carlo methods for financial risk measures
The recent crisis in the global financial markets demands a
critical review of current regulatory practice. Substantial
efforts are required to devise efficient quantitative
methods for a more reliable estimation of financial risks
in the future. Unlike the currently used industry standards for
risk evaluation, these tools must be able to detect extreme
loss scenarios that are unlikely to occur but whose
impact may be dramatic. In collaboration with Stefan Weber, we have developed
a new Monte-Carlo technique for the efficient estimation of improved risk measures that are sensitive to the tails of loss distributions.
Last modified: 03 October 2018