Metric space magnitude, an active field of research in algebraic topology, is a scalar quantity that summarizes the effective number of distinct points that live in a general metric space. The weighting vector is a closely-related concept that captures, in a nontrivial way, much of the underlying geometry of the original metric space. Recent work has demonstrated that when the metric space is Euclidean, the weighting vector serves as an effective tool for boundary detection. We recast this result and show the weighting vector may be viewed as a solution to a kernelized SVM. As one consequence, we apply this new insight to the task of outlier detection, and we demonstrate performance that is competitive or exceeds performance of state-of-the-art techniques on benchmark data sets. Under mild assumptions, we show the weighting vector, which has computational cost of matrix inversion, can be efficiently approximated in linear time. We show how nearest neighbor methods can approximate solutions to the minimization problems defined by SVMs.Preprint. Under review.

Therapeutic modalities targeting pathogenic proteins are the gold standard of treatment for multiple disease indications. Unfortunately, a significant portion of these proteins are considered "undruggable" by standard small molecule-based approaches, largely due to their disordered nature and instability. Designing functional peptides to undruggable targets, either as standalone binders or fusions to effector domains, thus presents a unique opportunity for therapeutic intervention. In this work, we adapt recent models for contrastive language-image pre-training (CLIP) to devise a unified, sequence-based framework to design target-specific peptides. Furthermore, by leveraging known experimental binding proteins as scaffolds, we create a streamlined inference pipeline, termed Cut&CLIP, that efficiently selects peptides for downstream screening. Finally, we experimentally fuse candidate peptides to E3 ubiquitin ligase domains and demonstrate robust intracellular degradation of pathogenic protein targets in human cells, motivating further development of our technology for future clinical translation.

Germ cells are the vehicle of human reproduction, arising early in embryonic development and developing throughout adult life until menopause onset in women. Primordial germ cells are the common precursors of germline cells in both sexes, undergoing sexual specification into oogonia or gonocytes which further develop into oocytes or spermatocytes during development. Methods for recapitulation of primordial germ cell and oogonia formation have been developed extensively in recent decades, but fundamental technical limitations in their methodologies, throughput, and yield limit their utilization. Recently, transcription factor (TF)-based methods for human primordial germ cell-like cell (hPGCLC) formation, mouse meiotic entry, and mouse oocyte maturation have demonstrated the feasibility of gene overexpression screening in identifying potent regulators of germ cell development. Here we screened 47 folliculogenesis-regulating TFs for their role in hPGCLC and oogonia formation, identifying DLX5, HHEX, and FIGLA whose individual overexpression enhances hPGCLC formation from hiPSCs. Additionally, we identify a set of three TFs, ZNF281, LHX8, and SOHLH1 whose combinatorial overexpression drives direct oogonia-like formation from hiPSCs in a four-day, feeder-free monolayer culture condition with additional feeder-free culture capabilities post-isolation. We characterize these TF-based germ cells via gene and protein expression analyses, and demonstrate their broad similarity to in vivo germ cells. Together, these results identify novel regulators of human germ cell development and establish new TF-based tools for human in vitro oogenesis research.