The goal of of B5 is to understand the physical mechanism behind the maintenance of the epigenetic state of chromatin through multiple cell generations. This is achieved by combining experiments and the-ory to study a well-defined setup which includes chromatin stretching, polymer-assisted conden-sation and enzymatic reactions.

During the duplication of chromosomes, epigenetic information which resided in posttranslational modifications on histone proteins is equally distributed between the two daughter chromosomes. We proposed recently that the missing epigenetic tags can be reconstructed with the help of condensates that are formed from proteins such as HP1. Polymer-assisted condensates are formed around stretches of heterochromatin and serve as liquid reaction containers where enzymes (such as SUV39H1 methylase) add missing tags. The Schiessel group has used their expertise in computer simulations on small model chromosomes to demonstrate that polymer-assisted condensates are capable of maintaining the epigenetic state through 40 generations, thus reaching the Hayflick limit. The Brugués group uses their expertise in single molecule approaches and cell free extracts to test these ideas by using optical tweezers where a full chromosome and single DNA strands can be held in place and stretched in the cytoplasm from Xenopus egg extracts, a system in which replication can be induced. We will quantify the dynamics of the epigenetic state and test whether it can be maintained in the presence of HP1 and SUV39H1 through multiple cell generations. Simulations and theory will study how increasing tension breaks up HP1 droplets, transforming chromosomes into strings of micelles.

1. Can we visualize experimentally HP1 condensates forming along stretched chromosomes?
2. What happens to the number and sizes of HP1 droplets as one increases the tension and how does it depend on the epigenetic sequence written along the string of nucleosomes?
3. Can we demonstrate that condensate formation is maintained through several duplications in the presence of enzymatic reactions but suppressed otherwise? Does the disruption of an epigenetic condensate (for example by force) lead to the loss of epigenetic memory?

• Topic 1 (Schiessel): Geometry and function of co-polymer-assisted micelles (Theory)
• Topic 2 (Brugués): Emergent properties of chromatin (Experimental)

The PhD students in the theory part of the project will be trained in mathematical-analytical methods, various simulation methods and numerical concepts. The PhD students in the experimental part will be trained in quantitative microscopy, optical tweezers, condensate quantification and manipulation, DNA biophysics.

• Candidates have a Masters degree in physics or related fields.
• Candidates should have a sound basis in biophysics, computational biology, or closely related fields.
• Experience in computer simulations is expected in Topic 1.
• Experience with in vitro reconstitution systems is a plus in Topic 2.

The goal of of B1 is to characterize the molecular interaction landscape of immobile and mobile (translationally silenced and competent) nature of RNA molecules inside RNP granules to provide a mechanistic understanding of regulation in condensates and disease phenotypes

RNP granules, such as neuronal transport granules (NTGs) or stress-induced RNP granules (SGs), are condensates that play key roles in translation regulation. Their aberrant state is as-sociated with neurodegeneration and cancer. RNP granule assembly and the underlying regula-tory mechanisms are not understood. Our preliminary data show that the RNA-binding protein Ras GTPase-activating protein-binding protein 1 (G3BP1) interacts with unfolded RNA molecules to assemble RNP granules. RNA accumulation in granules leads to RNA-RNA interactions, inhibiting RNA mobility and translatability. The DEAD-box RNA helicase (DDX3X) localizes to RNP granules to attenuate RNA-RNA interactions, rendering the condensates dynamic and ena-bling mRNA translation. DDX3X disease variants cannot resolve RNA-RNA interactions causing RNA granule persistence. We suggest that RNP granules mediate inhibitory RNA-RNA interactions, which must be modulated by RNA helicases to regulate RNA availability and translatability.

1. How do RNP granules regulate RNA availability and translatability in physiology and disease?
2. How do RNA helicases regulate RNA structure, dynamics, and organization within RNP granules?

Topic 1: RNA structures and dynamics in multi-component biomolecular condensates (Schlierf)
Topic 2: Revealing the functional role of RNA-protein condensates in regulating RNA availability (Alberti)

The PhD students will be trained in smFRET and FCS and analysis, advanced imaging and analysis, protein biochemistry and RNP-like granule reconstitution.

• Candidates have a Masters degree in physics, biology or related fields
• Candidates should have a sound basis in biochemistry, biophysics, enzymology, quantitative biology, or closely related fields.
• Experience in microscopy, in vitro reconstitution, and protein isolation methods are expected

The goal of of A5 is to understand how condensates respond to mechanical forces and how condensate-mediated capillary forces influence the shape and organization of biopolymers.

Biomolecular condensates are mostly considered as special biochemical environments. However, due to their tendency to minimize their interfacial area, condensates generate relevant capillary forces that can bundle and bend soft cellular structures. Recently, the Grill lab has explored the mechanical effects of condensates on various biopolymers such as nucleic acids and cytoskeletal filaments. In collaboration with the Hyman and Jülicher groups, the Grill group has discovered the prewetting and co-condensation of transcription factors on DNA and that condensates can bundle DNA. Furthermore, the Grill group has discovered a condensate dynamic instability that is crucial to establishing the actin cell cortex during early nematode development. Finally, preliminary data from the Grill lab demonstrate shape changes of cortical condensates are likely driven by condensate surface tension and identify a mechanical role of DNA-binding proteins during the assembly of the nuclear periphery (Collaboration with von Appen group at MPI-CBG). Despite this progress, the rich interplay between condensate interfacial energies, condensate-polymer interaction energies, and biopolymer bending energies has not been systematically studied and remains poorly understood.

1) How do condensates respond to mechanical forces and exert capillary forces on various cellular structures?

2) Can we predict the mechanical condensate-polymer behavior?

3) How to measure the interfacial properties and interaction energies of condensates and their substrates?

Regulatory RNA folding in and around condensates

The PhD students will be trained in in soft matter physics concepts, single-molecule experiments, protein and nucleic acid molecular biology methods, data and image analysis methods and state-of-the-art instrumentation such as optical tweezers and light-sheet microscopy.

• Candidates have a Masters degree in physics, biology or related fields
• Candidates should have a sound basis in (theoretical) biophysics, polymer science, quantitative biology, or closely related fields.
• Experience in microscopy and protein isolation methods are expected

The goal of of A3 is to understand how local interactions of solvent and biomolecules drive phase separation and regulate condensate biochemistry

Solvation water is fundamental to the structure and function of proteins and integral in coordinating biochemical reactions. Phase separation of intrinsically disordered proteins into two coexisting liquid phases is entropically unfavorable and creates compartments with a distinct solvent environment. The Adams group has developed spectroscopic methods to study the solvation of proteins and have shown that the global solvation is sensitive to molecular level changes in the protein sequence. Application of this technique to biomolecular condensates has provided insight into their solvent environment and the local water-protein interactions. Desolvation of specific molecular groups entropically drives phase transitions, while water inside of condensates is tightly bound to the proteins and has fewer degrees of freedom, resulting an environment with a stiff hydrogen bonding network.

How does physical chemistry of the solvent influence local interactions in condensates? How are molecular properties of condensates linked to their macroscopic properties? How do local mutations of proteins impact the condensate environment? What are the molecular properties of cytoplasm and how do solvent properties of the cytoplasm regulate spatiotemporal organization of condensates?

Local Hydration of Post Translationally Modified Condensate Proteins.

The PhD students will be trained in various spectroscopic methods, microscopy, and physical chemistry concepts.

• Candidates have a Masters degree in chemistry, physics or related fields
• Candidates should have a sound basis in physical chemistry, physics, biochemistry, or closely related fields.
• Experience in spectroscopy is expected

The goal of of A2 is to understand how molecular architecture regulates existence, composition, and properties of multi-component condensates.

Cellular condensates contain many components and their precise composition dictates functionality. A key means to regulate condensate composition and properties is through changes in the abundance of other “regulator” molecules that interact with core condensate components through multiple folded or disordered domains. Harmon has studied compositional regulation the-oretically and developed robust and scalable coarse-grained simulations for the phase separation of multi-domain biopolymers containing folded as well as disordered domains. Compositional regulation has been explored in some minimal model systems. However, the general principles by which molecular architecture dictates regulatory possibilities in multi-component condensates remains unknown.

What are the basic principles that determine how regulatory proteins control multi-component condensates? How does the design of the scaffold proteins relate to their response to differently designed regulators? To what extent can basic principles of condensate regulation be extended to the higher complexity case of proteins containing folded as well as disordered domains?

Regulation of condensates driven by multi-domain proteins

The PhD students will be trained in different methodologies for coarse grained simulations, and in analytical and numerical tech-niques, in particular solving Cahn-Hilliard equations and kinetic models for interface dynamics. Using simulations, a library of multi-domain proteins will be studied.

• Candidates have a Masters degree in physics or related fields
• Candidates should have a sound basis in statistical physics, soft matter theory or closely related fields.
• Experience in computer simulations and numerical methods are expected

The goal of of A4 is to understand formation, dissolution and functions of multi-component polymer assisted condensates using generic concepts of polymer physics.

Large biopolymers such as DNA and RNA,play a pivotal role in the formation of condensates, owing to their low mixing entropy and vast number of conformational degrees of freedom. In particular, they can locally trigger condensate formation.
The Sommer group has pioneered analytical and simulation-based approaches to study polymers in multi-component solutions, predicting unusual phase transitions such as co-nonsolvency and polymer-assisted condensation (PAC). In collaboration with the Schiessel group, the PAC concept has been applied to explain the formation of heterochromatin and mechanisms of epigenetic inheritance.
Currently, we are investigating more complex scenarios, including wetting behavior and compartmentalization in multi-component condensates. Computer simulations play a key role in exploring and analyzing these complex phase behaviors.

1. How can multi-phase coexistence be incorporated into the polymer-assisted condensation (PAC) model?
2. How can coarse-grained simulations be refined to model specific condensate problems such as DNA target search, DNA repair, polymerization/depolymerization processes (PAR), or post-translational modifications?
3. How can field-theoretic methods be applied to explore the phase space of complex protein/polynucleotide solutions? How can these concepts be extended to understand the dynamics of condensates?

The PhD students will be trained in mathematical-analytical methods, polymer physics and statistical thermodynamics of phase transitions, various simulation methods and numerical concepts.

• Candidates have a Masters degree in physics or related fields
• Candidates should have a sound basis in statistical physics, soft matter theory or closely related fields.
• Experience in computer simulations and numerical methods are expected

The goal of A1 is to understand how surface condensation of scaffold proteins at biological membranes can control the patterning and the mechanics of an acto-myosin cell cortex.

The formation of epithelial tissue requires precise spatiotemporal control of cell surface properties such as formation of adhesion complexes that are linked to the cell cortex at the level of the cell membrane^1,2. The Honigmann group has discovered that surface condensation of ZO scaffold proteins at the membrane is a mechanism that cells exploit to pattern adhesion complexes and the actin cortex³. In vitro reconstitutions have shown that ZO surface condensates can nucleate and bundle actin fibers, which can drive the formation of a variety of cortical patterns^4-6. How ZO surface condensation and actin polymerization are linked and what mechanical properties emerge from this is not understood.

How does surface condensation of ZO proteins induce actin recruitment and polymerization? and What are the mechanical properties of a condensed ZO1-actin cortex on the membrane?

Linking surface condensation of scaffold proteins to the assembly of cell junctions

The PhD students will be trained in protein and membrane biochemistry methods including membrane reconstitutions, biophysical methods such as fluorescence fluctuation spectroscopy, in addition to super-resolution microscopy and image analysis methods.

• Candidates have a Masters degree in biophysics or related fields
• Candidates are expected to have a solid basis in physics, biology, or related fields.
• Experience in fluorescence microscopy is plus