Browsing by Author "Zwicker, David"

Abstract Droplets form a cornerstone of the spatiotemporal organization of biomolecules in cells. These droplets are controlled using physical processes like chemical reactions and imposed gradients, which are costly to simulate using traditional approaches, like solving the Cahn–Hilliard equation. To overcome this challenge, we here present an alternative, efficient method. The main idea is to focus on the relevant degrees of freedom, like droplet positions and sizes. We derive dynamical equations for these quantities using approximate analytical solutions obtained from a sharp interface limit and linearized equations in the bulk phases. We verify our method against fully-resolved simulations and show that it can describe interacting droplets under the influence of chemical reactions and external gradients using only a fraction of the computational costs of traditional methods. Our method can be extended to include other processes in the future and will thus serve as a relevant platform for understanding the dynamics of droplets in cells.

Phase separation has emerged as an essential concept for the spatial organization inside biological cells. However, despite the clear relevance to virtually all physiological functions, we understand surprisingly little about what phases form in a system of many interacting components, like in cells. Here we introduce a numerical method based on physical relaxation dynamics to study the coexisting phases in such systems. We use our approach to optimize interactions between components, similar to how evolution might have optimized the interactions of proteins. These evolved interactions robustly lead to a defined number of phases, despite substantial uncertainties in the initial composition, while random or designed interactions perform much worse. Moreover, the optimized interactions are robust to perturbations, and they allow fast adaption to new target phase counts. We thus show that genetically encoded interactions of proteins provide versatile control of phase behavior. The phases forming in our system are also a concrete example of a robust emergent property that does not rely on fine-tuning the parameters of individual constituents.

Droplets are essential for spatially controlling biomolecules in cells. To work properly, cells need to control the emergence and morphology of droplets. On the one hand, driven chemical reactions can affect droplets profoundly. For instance, reactions can control how droplets nucleate and how large they grow. On the other hand, droplets coexist with various organelles and other structures inside cells, which could affect their nucleation and morphology. To understand the interplay of these two aspects, we study a continuous field theory of active phase separation. Our numerical simulations reveal that reactions suppress nucleation while attractive walls enhance it. Intriguingly, these two effects are coupled, leading to shapes that deviate substantially from the spherical caps predicted for passive systems. These distortions result from anisotropic fluxes responding to the boundary conditions dictated by the Young–Dupré equation. Interestingly, an electrostatic analogy of chemical reactions confirms these effects. We thus demonstrate how driven chemical reactions affect the emergence and morphology of droplets, which could be crucial for understanding biological cells and improving technical applications, e.g., in chemical engineering.

Abstract Crossover interference is a phenomenon that affects the number and positioning of crossovers in meiosis and thus affects genetic diversity and chromosome segregation. Yet, the underlying mechanism is not fully understood, partly because quantification is difficult. To overcome this challenge, we introduce the interference length L int that quantifies changes in crossover patterning due to interference. We show that it faithfully captures known aspects of crossover interference and provides superior statistical power over previous measures such as the interference distance and the gamma shape parameter. We apply our analysis to empirical data and unveil a similar behavior of L int across species, which hints at a common mechanism. A recently proposed coarsening model generally captures these aspects, providing a unified view of crossover interference. Consequently, L int facilitates model refinements and general comparisons between alternative models of crossover interference.

Abstract Meiotic crossovers are limited in number and are prevented from occurring close to each other by crossover interference. In many species, crossover number is subject to sexual dimorphism, and a lower crossover number is associated with shorter chromosome axes lengths. How this patterning is imposed remains poorly understood. Here, we show that overexpression of the Arabidopsis pro-crossover protein HEI10 increases crossovers but maintains some interference and sexual dimorphism. Disrupting the synaptonemal complex by mutating ZYP1 also leads to an increase in crossovers but, in contrast, abolishes interference and disrupts the link between chromosome axis length and crossovers. Crucially, combining HEI10 overexpression and zyp1 mutation leads to a massive and unprecedented increase in crossovers. These observations support and can be predicted by, a recently proposed model in which HEI10 diffusion along the synaptonemal complex drives a coarsening process leading to well-spaced crossover-promoting foci, providing a mechanism for crossover patterning.

The continuous adaptation of networks like our vasculature ensures optimal network performance when challenged with changing loads. Here, we show that adaptation dynamics allow a network to memorize the position of an applied load within its network morphology. We identify that the irreversible dynamics of vanishing network links encode memory. Our analytical theory successfully predicts the role of all system parameters during memory formation, including parameter values which prevent memory formation. We thus provide analytical insight on the theory of memory formation in disordered systems.

Abstract Cell polarity networks are defined by quantitative features of their constituent feedback circuits, which must be tuned to enable robust and stable polarization, while also ensuring that networks remain responsive to dynamically changing cellular states and/or spatial cues during development. Using the PAR polarity network as a model, we demonstrate that these features are enabled by the dimerization of the polarity protein PAR-2 via its N-terminal RING domain. Combining theory and experiment, we show that dimer affinity is optimized to achieve dynamic, selective, and cooperative binding of PAR-2 to the plasma membrane during polarization. Reducing dimerization compromises positive feedback and robustness of polarization. Conversely, enhanced dimerization renders the network less responsive due to kinetic trapping of PAR-2 on internal membranes and reduced sensitivity of PAR-2 to the anterior polarity kinase, aPKC/PKC-3. Thus, our data reveal a key role for a dynamically oligomeric RING domain in optimizing interaction affinities to support a robust and responsive cell polarity network, and highlight how optimization of oligomerization kinetics can serve as a strategy for dynamic and cooperative intracellular targeting.

Turing’s mechanism is often invoked to explain periodic patterns in nature, although direct experimental support is scarce. Turing patterns form in reaction–diffusion systems when the activating species diffuse much slower than the inhibiting species, and the involved reactions are highly nonlinear. Such reactions can originate from cooperativity, whose physical interactions should also affect diffusion. We here take direct interactions into account and show that they strongly affect Turing patterns. We find that weak repulsion between the activator and inhibitor can substantially lower the required differential diffusivity and reaction nonlinearity. By contrast, strong interactions can induce phase separation, but the resulting length scale is still typically governed by the fundamental reaction–diffusion length scale. Taken together, our theory connects traditional Turing patterns with chemically active phase separation, thus describing a wider range of systems. Moreover, we demonstrate that even weak interactions affect patterns substantially, so they should be incorporated when modelling realistic systems.

Pancreatic ductal adenocarcinoma is a rare but lethal cancer. Recent evidence suggests that pancreatic intraepithelial neoplasia (PanIN), a microscopic precursor lesion that gives rise to pancreatic cancer, is larger and more prevalent than previously believed. Better understanding of the growth-law dynamics of PanINs may improve our ability to understand how a miniscule fraction makes the transition to invasive cancer. Here, using three-dimensional tissue mapping, we analyzed >1000 PanINs and found that lesion size is distributed according to a power law. Our data suggest that in bulk, PanIN size can be predicted by general growth behavior without consideration for the heterogeneity of the pancreatic microenvironment or an individual’s age, history, or lifestyle. Our models suggest that intraductal spread and fusing of lesions drive our observed size distribution. This analysis lays the groundwork for future mathematical modeling efforts integrating PanIN incidence, morphology, and molecular features to understand tumorigenesis and demonstrates the utility of combining experimental measurement with dynamic modeling in understanding tumorigenesis.

Pancreatic ductal adenocarcinoma is a rare but lethal cancer. Recent evidence reveals that pancreatic intraepithelial neoplasms (PanINs), the microscopic precursor lesions in the pancreatic ducts that can give rise to invasive pancreatic cancer, are significantly larger and more prevalent than previously believed. Better understanding of the growth law dynamics of PanINs may improve our ability to understand how a miniscule fraction of these lesions makes the transition to invasive cancer. Here, using artificial intelligence (AI)-based three-dimensional (3D) tissue mapping method, we measured the volumes of >1,000 PanIN and found that lesion size is distributed according to a power law with a fitted exponent of -1.7 over > 3 orders of magnitude. Our data also suggest that PanIN growth is not very sensitive to the pancreatic microenvironment or an individual's age, family history, and lifestyle, and is rather shaped by general growth behavior. We analyze several models of PanIN growth and fit the predicted size distributions to the observed data. The best fitting models suggest that both intraductal spread of PanIN lesions and fusing of multiple lesions into large, highly branched structures drive PanIN growth patterns. This work lays the groundwork for future mathematical modeling efforts integrating PanIN incidence, morphology, genomic, and transcriptomic features to understand pancreas tumorigenesis, and demonstrates the utility of combining experimental measurement of human tissues with dynamic modeling for understanding cancer tumorigenesis.

Meiotic crossovers, which are exchanges of genetic material between homologous chromosomes, are more evenly and distantly spaced along chromosomes than expected by chance. This is because the occurrence of one crossover reduces the likelihood of nearby crossover events — a conserved and intriguing phenomenon called crossover interference. Although crossover interference was first described over a century ago, the mechanism allowing coordination of the fate of potential crossover sites half a chromosome away remains elusive. In this review, we discuss the recently published evidence supporting a new model for crossover patterning, coined the coarsening model, and point out the missing pieces that are still needed to complete this fascinating puzzle.

We study the formation of vesicle condensates induced by the protein synapsin, as a cell-free model system mimicking vesicle pool formation in the synapse. The system can be considered as an example of liquid-liquid phase separation (LLPS) in biomolecular fluids, where one phase is a complex fluid itself consisting of vesicles and a protein network. We address the pertinent question why the LLPS is self-limiting and stops at a certain size, i.e., why macroscopic phase separation is prevented. Using fluorescence light microscopy, we observe different morphologies of the condensates (aggregates) depending on the protein-to-lipid ratio. Cryogenic electron microscopy then allows us to resolve individual vesicle positions and shapes in a condensate and notably the size and geometry of adhesion zones between vesicles. We hypothesize that the membrane tension induced by already formed adhesion zones then in turn limits the capability of vesicles to bind additional vesicles, resulting in a finite condensate size. In a simple numerical toy model we show that this effect can be accounted for by redistribution of effective binding particles on the vesicle surface, accounting for the synapsin-induced adhesion zone.