Christoph A. Weber

Liquid-Liquid Phase Separation in Biology

Cells organize many of their biochemical reactions in non-membrane compartments. Recent evidence has shown that many of these compartments are liquids that form by phase separation from the cytoplasm. Here we discuss the basic physical concepts necessary to understand the consequences of liquid-like states for biological functions.

Polar patterns of driven filaments.

The emergence of collective motion exhibited by systems ranging from flocks of animals to self-propelled microorganisms to the cytoskeleton is a ubiquitous and fascinating self-organization phenomenon. Similarities between these systems, such as the inherent polarity of the constituents, a density-dependent transition to ordered phases or the existence of very large density fluctuations, suggest universal principles underlying pattern formation. This idea is followed by theoretical models at all levels of description: micro- or mesoscopic models directly map local forces and interactions using only a few, preferably simple, interaction rules, and more macroscopic approaches in the hydrodynamic limit rely on the systems’ generic symmetries. All these models characteristically have a broad parameter space with a manifold of possible patterns, most of which have not yet been experimentally verified. The complexity of interactions and the limited parameter control of existing experimental systems are major obstacles to our understanding of the underlying ordering principles. Here we demonstrate the emergence of collective motion in a high-density motility assay that consists of highly concentrated actin filaments propelled by immobilized molecular motors in a planar geometry. Above a critical density, the filaments self-organize to form coherently moving structures with persistent density modulations, such as clusters, swirls and interconnected bands. These polar nematic structures are long lived and can span length scales orders of magnitudes larger than their constituents. Our experimental approach, which offers control of all relevant system parameters, complemented by agent-based simulations, allows backtracking of the assembly and disassembly pathways to the underlying local interactions. We identify weak and local alignment interactions to be essential for the observed formation of patterns and their dynamics. The presented minimal polar-pattern-forming system may thus provide new insight into emerging order in the broad class of active fluids and self-propelled particles.

Proteomics strategy for quantitative protein interaction profiling in cell extracts

We report a proteomics strategy to both identify and quantify cellular target protein interactions with externally introduced ligands. We determined dissociation constants for target proteins interacting with the ligand of interest by combining quantitative mass spectrometry with a defined set of affinity purification experiments. We demonstrate the general utility of this methodology in interaction studies involving small-molecule kinase inhibitors, a tyrosine-phosphorylated peptide and an antibody as affinity ligands.

Chemotactic cell trapping in controlled alternating gradient fields

Directed cell migration toward spatio-temporally varying chemotactic stimuli requires rapid cytoskeletal reorganization. Numerous studies provide evidence that actin reorganization is controlled by intracellular redistribution of signaling molecules, such as the PI4,5P2/PI3,4,5P3 gradient. However, exploring underlying mechanisms is difficult and requires careful spatio-temporal control of external chemotactic stimuli. We designed a microfluidic setup to generate alternating chemotactic gradient fields for simultaneous multicell exposure, greatly facilitating statistical analysis. For a quantitative description of intracellular response dynamics, we apply alternating time sequences of spatially homogeneous concentration gradients across 300 μm, reorienting on timescales down to a few seconds. Dictyostelium discoideum amoebae respond to gradient switching rates below 0.02 Hz by readapting their migration direction. For faster switching, cellular repolarization ceases and is completely stalled at 0.1 Hz. In this “chemotactically trapped” cell state, external stimuli alternate faster than intracellular feedback is capable to respond by onset of directed migration. To investigate intracellular actin cortex rearrangement during gradient switching, we correlate migratory cell response with actin repolymerization dynamics, quantified by a fluorescence distribution moment of the GFP fusion protein LimEΔcc. We find two fundamentally different cell polarization types and we could reveal the role of PI3-Kinase for cellular repolarization. In the early aggregation phase, PI3-Kinase enhances the capability of D. discoideum cells to readjust their polarity in response to spatially alternating gradient fields, whereas in aggregation competent cells the effect of PI3-Kinase perturbation becomes less relevant.

Frozen steady states in active systems

Even simple active systems can show a plethora of intriguing phenomena and often we find complexity where we would have expected simplicity. One striking example is the occurrence of a quiescent or absorbing state with frozen fluctuations that at first sight seems to be impossible for active matter driven by the incessant input of energy. While such states were reported for externally driven systems through macroscopic shear or agitation, the investigation of frozen active states in inherently active systems like cytoskeletal suspensions or active gels is still at large. Using high-density motility assay experiments, we demonstrate that frozen steady states can arise in active systems if active transport is coupled to growth processes. The experiments are complemented by agent-based simulations which identify the coupling between self-organization, growth, and mechanical properties to be responsible for the pattern formation process.

Growth and division of active droplets provides a model for protocells

It has been proposed that during the early steps in the origin of life, small droplets could have formed via the segregation of molecules from complex mixtures by phase separation. These droplets could have provided chemical reaction centres. However, whether these droplets could divide and propagate is unclear. Here we examine the behaviour of droplets in systems that are maintained away from thermodynamic equilibrium by an external supply of energy. In these systems, droplets grow by the addition of droplet material generated by chemical reactions. Surprisingly, we find that chemically driven droplet growth can lead to shape instabilities that trigger the division of droplets into two smaller daughters. Therefore, chemically active droplets can exhibit cycles of growth and division that resemble the proliferation of living cells. Dividing active droplets could serve as a model for prebiotic protocells, where chemical reactions in the droplet play the role of a prebiotic metabolism. Droplets are an appealing picture for protocells in origin-of-life studies, but it’s unclear how they would have propagated by growth and division. Theory suggests that chemically active droplets spontaneously split into equal daughter droplets.

Long-Range Ordering of Vibrated Polar Disks

Vibrated polar disks have been used experimentally to investigate collective motion of driven particles, where fully ordered asymptotic regimes could not be reached. Here we present a model reproducing quantitatively the single, binary, and collective properties of this granular system. Using system sizes not accessible in the laboratory, we show in silico that true long-range order is possible in the experimental system. Exploring the models parameter space, we find a phase diagram qualitatively different from that of dilute or pointlike particle systems.

Binary Mixtures of Particles with Different Diffusivities Demix

The influence of size differences, shape, mass, and persistent motion on phase separation in binary mixtures has been intensively studied. Here we focus on the exclusive role of diffusivity differences in binary mixtures of equal-sized particles. We find an effective attraction between the less diffusive particles, which are essentially caged in the surrounding species with the higher diffusion constant. This effect leads to phase separation for systems above a critical size: A single close-packed cluster made up of the less diffusive species emerges. Experiments for testing our predictions are outlined.

Defect-Mediated Phase Transitions in Active Soft Matter

How do topological defects affect the degree of order in active matter? To answer this question we investigate an agent-based model of self-propelled particles, which accounts for polar alignment and short-ranged repulsive interactions. For strong alignment forces we find collectively moving polycrystalline states with fluctuating networks of grain boundaries. In the regime where repulsive forces dominate, the fluctuations generated by the active system give rise to quasi-long-range transitional order, but-unlike the thermal system-without creating topological defects.

Critical assessment of the Boltzmann approach to active systems.

Generic models of propelled particle systems posit that the emergence of polar order is driven by the competition between local alignment and noise. Although this notion has been confirmed employing the Boltzmann equation, the range of applicability of this equation remains elusive. We introduce a broad class of mesoscopic collision rules and analyze the prerequisites for the emergence of polar order in the framework of kinetic theory. Our findings suggest that a Boltzmann approach is appropriate for weakly aligning systems but is incompatible with experiments on cluster forming systems.