Scientific

Cytoplasmic streaming is the persistent circulation of the fluid contents of large eukaryotic cells, driven by the action of molecular motors moving along cytoskeletal filaments, entraining fluid. Discovered in 1774 by Bonaventura Corti, it is now recognized as a common phenomenon in a very broad range of model organisms, from plants to flies and worms. This talk will discuss physical approaches to understanding this phenomenon through a combination of experiments (on aquatic plants, Drosophila, and other active matter systems), theory, and computation. A particular focus will be on streaming in the Drosophilaoocyte, for which I will describe a recently discovered "swirling instability" of the microtubule cytoskeleton.

The swimming sperm of many external fertilizing marine organisms face complex fluid flows during their search for egg cells. Aided by chemotaxis, relatively weak flows and marine turbulence enhance spermegg fertilization rates through hydrodynamic guidance and mixing. However, strong flows can mechanically inhibit flagellar motility through elastohydrodynamic interactions - a phenomenon that remains poorly understood. We explore the effects of flow on the buckling dynamics of sperm flagella in an extensional flow through detailed numerical simulations, which are informed by microfluidic experiments and high-speed imaging. Compressional fluid forces lead to rich buckling dynamics of the sperm flagellum beyond a critical dimensionless sperm number, Sp, which represents the ratio of viscous force to elastic force. For non-motile sperm, the maximum buckling curvature and the number of buckling locations, or buckling mode, increase with increasing sperm number. In contrast, motile sperm exhibit an intrinsic flagellar curvature due to the propagation of bending waves along the flagellum. In compressional flow, this preexisting curvature acts as a precursor for buckling, which enhances local curvature without creating new buckling modes and leads to asymmetric beating. However, in extensional flow, flagellar beating remains symmetric with a smaller head yawing amplitude due to tensile forces. We also explore sperm motility in different shear flows. In the presence of Poiseuille flow, the sperm moves downstream or upstream depending on the flow strength along with net movement toward the centerline.

The reaction coordinate describing a transition between reactant and product is a fundamental concept in the theory of chemical reactions. Within transition-path theory, a quantitative definition of the reaction coordinate is found in the committor, which is the probability that a trajectory initiated from a given microstate first reaches the product before the reactant. Here we demonstrate an information-theoretic origin for the committor, show how it naturally arises from selecting out the transition-path ensemble from the equilibrium ensemble, and prove that the resulting entropy production is fully determined by committor dynamics. Our results provide parallel stochastic-thermodynamic and information-theoretic measures of the relevance of any system coordinate to the reaction, each of which are maximized by the committor, providing further support for its status as the ‘true’ reaction coordinate.

The prevalence of intrinsically disordered polypeptides (IDPs) and protein regions in structural biology has prompted the recent development of molecular dynamics (MD) force fields for the more realistic representations of such systems. Using experimental NMR backbone scalar 3J-coupling constants of the intrinsically disordered proteins alpha-synuclein and amyloid-beta in their native aqueous environment as a metric, we compare the performance of four recent MD force fields, namely AMBER ff14SB, CHARMM C36m, AMBER ff99SB-disp, and AMBER ff99SBnmr2, by partitioning the polypeptides into an overlapping series of heptapeptides for which a cumulative total of 276 us MD simulations are performed. The results show substantial differences between the different force fields at the individual residue level. Except for ff99SBnmr2, the force fields systematically underestimate the scalar 3J(HN,Ha) couplings, due to an underrepresentation of beta-conformations and an overrepresentation of either alpha- or PPII conformations. The study demonstrates that the incorporation of coil library information in modern molecular dynamics force fields, as shown here for ff99SBnmr2, provides substantially improved performance and more realistic sampling of local backbone phi,psi dihedral angles of IDPs as reflected in good accuracy of computed scalar 3J(HN,Ha)-couplings with < 0.5 Hz error. Such force fields will enable a better understanding how structural dynamics and thermodynamics influence IDP function. Although the methodology based on heptapeptides used here does not allow the assessment of potential intramolecular long-range interactions, its computational affordability permits well-converged simulations that can be easily parallelized. This should make the quantitative validation of intrinsic disorder observed in MD simulations of polypeptides with experimental scalar J-couplings widely applicable.

We discuss deformation theory of rational curves and Mori’s famous Bend and Break techniques as well as their applications to Geometric Manin’s Conjecture. The lecture series contain introductory components as well as problem sessions and they aim for graduate students and postdocs.