Kalender

The assembly of molecular building blocks into functional complexes is central to biology and materials science. We investigate the generative and predictive capabilities of a geometric model, the morphometric approach to solvation free energy, in a simulation setting. We show that biologically relevant structural motifs appear for generic building blocks under geometric optimization. Applying the same method to the self-assembly of protein subunits, we show that geometric fit alone predicts the native nucleation states of various systems. To overcome limitations in efficiency of the geometric model caused by its short-range nature, we introduce a novel energetic bias based on persistent homology. By combining these shape-based potentials we obtain an efficient simulation strategy increasing success rates by an order of magnitude, or enabling assembly in the first place, when compared to the geometric model alone. Integrating topological descriptions into energy functions offers a general strategy for overcoming kinetic barriers in molecular simulations, with potential applications in drug design, material development, and the study of complex self-assembly processes.

The FNT is a novel algorithm for multivariate polynomial interpolation with a runtime of nearly Nlog(N), where N scales only sub-exponentially with spatial dimension, surpassing the runtime of the tensorial Fast Fourier Transform (FFT). We have proven and demonstrated the optimal geometric approximation rates for a class of analytic functions—termed Bos–Levenberg–Trefethen functions—to be reached by the FNT and to be maintained for the derivatives of the interpolants. This establishes the FNT as a new standard in spectral methods, particularly suitable for high-dimensional, non-periodic PDE problems, interpolation tasks, arising as the computational bottleneck in solving, e.g. 6D Boltzmann, Fokker-Planck, or Vlasov equations, multi-body Hamiltonian systems, and the inference of governing equations in complex self-organizing systems.

Fluorescence microscopy has been the workhorse of biological microscopy in the last half a century, also leading to super-resolution microscopy. In the first part of this presentation, I will discuss the application of cryogenic fluorescence microscopy for improving the photophysics of fluorophores, thus, allowing us to reach three-dimensional angstrom resolution in resolving several sites of a single protein or protein complex. While fluorescence labeling remains a powerful tool, it poses fundamental limitations, which have motivated many groups to develop fluorescence-free measurement methods. Among various contrast mechanisms, scattering offers unique opportunities. About two decades ago, we showed that single gold nanoparticles as small as 5 nm could be detected via interferometric detection of their scattering, coined iSCAT. Since then, it has been shown that unlabeled nano-objects such as proteins and viruses as small as 10 kDa can be detected, counted and tracked. We will discuss the application of this method in characterizing extracellular vesicles and cellular secretomes. Furthermore, I will present our most recent results on three-dimensional label-free imaging of cellular events such as the endoplasmic reticulum and microtubule dynamics as well as virus diffusion via confocal iSCAT microscopy. In addition to our iSCAT work, I plan to present an efficient method for delivery of nanoparticles and small molecules to well-defined positions on a cell.

All animals develop from a single-celled zygote and undergo complex morphogenetic processes to form multicellular organisms. These processes are regulated by intrinsic and extrinsic factors that drive key developmental events, such as symmetry breaking, cell division, and differentiation. Despite the remarkable conservation of these pathways across species, the evolutionary origins of these morphogenetic mechanisms remain unclear. A major challenge in addressing this question is the limited availability of microscopy and cell biological data from key protists that occupy pivotal phylogenetic positions in the eukaryotic tree, including those identified as the closest unicellular relatives of animals. In this talk, I will show how close animal relatives such as Ichthyosporeans display strikingly diverse developmental strategies, from coenocytic growth with cellularization to cleavage-based colony formation. These systems provide unique opportunities to probe how cells coordinate in space, establish polarity, and differentiate, posing critical questions about the evolutionary transition to multicellularity. Finally, I will outline how we aim to move beyond animal origins by implementing, optimizing, and developing Expansion Microscopy (ExM) to study a broader diversity of microbial eukaryotes. This approach allows us to uncover the diversity of cellular forms, cytoskeletal architectures, and life cycles across lineages, providing new perspectives on how distinct multicellular developmental programs emerge. Our long-term goal is to establish an Expansion Microscopy Atlas of Microbial Eukaryotes, creating a framework to identify general principles of multicellular transitions across eukaryotic life.

Using periodic surfaces as a scaffold is a convenient route to making periodic entanglements, which are interesting in the context of physics, biomaterials and chemical frameworks. I will present a systematic way of enumerating and characterising new tangled periodic structures, using low-dimensional topology and combinatorics. As a second part, the morphometric approach to solvation free energy is a geometry-based theory that incorporates a weighted combination of geometric measures over the solvent accessible surface for solute configurations in a solvent. I will demonstrate that employing this geometric technique in simulating the self assembly of sphere clusters, viruses and short flexible tubes results in an assortment of interesting geometric structures. This gives insight into the role of shape in the physical process of self assembly.