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The role of kernels is central to machine learning. Motivated by the importance of power-law distributions in statistical modeling, in this paper, we propose the notion of power-law kernels to investigate power-laws in learning problem. We…
DNA encoded libraries (DELs) are used for rapid large-scale screening of small molecules against a protein target. These combinatorial libraries are built through several cycles of chemistry and DNA ligation, producing large sets of…
A common developmental process, called branching morphogenesis, generates the epithelial trees in a variety of organs, including the lungs, kidneys, and glands. How branching morphogenesis can create epithelial architectures of very…
Large language models (LLMs) have shown promise in various natural language processing tasks, including their application to proteomics data to classify protein fragments. In this study, we curated a limited mass spectrometry dataset with…
Cellular uptake through the lipid membranes plays an important role in adsorbing nutrients and fighting infection and can be used for drug delivery and nanomedicine developments. Endocytosis is one of the known pathways of the cellular…
Mitochondria are complex organelles, and their proteomics analysis requires a combination of techniques. The emphasis in this chapter is made first on mitochondria preparation from cultured mammalian cells, then on the separation of the…
Nonlinear stiffening is a ubiquitous property of major types of biopolymers that make up the extracellular matrices (ECM) including collagen, fibrin and basement membrane. Within the ECM, many types of cells such as fibroblasts and cancer…
Biological cells in soft materials can be modeled as anisotropic force contraction dipoles. The corresponding elastic interaction potentials are long-ranged ($\sim 1/r^3$ with distance $r$) and depend sensitively on elastic constants,…
The electric double layer (EDL) has a pivotal role in screening charges on surfaces as in supercapacitor electrodes or colloidal and polymer solutions. Its structure is determined by correlations between the finite-sized ionic charge…
Contact inhibition plays a crucial role in the motility of cells, the process of wound healing, and the formation of tumors. By mimicking the mechanical motion of calls crawling on a substrate using a pseudopod, we constructed a minimal…
The biophysical interactions between the T cell receptor (TCR) and its ligands determine the specificity of the cellular immune response. However, the immense diversity of receptors and ligands has made it challenging to discover…
Living cells sense their environment through the binding of extra-cellular molecular ligands to cell surface receptors. Puzzlingly, vast numbers of signaling pathways exhibit a high degree of cross talk between different signals whereby…
A novel trait-structured Keller-Segel model that explores the dynamics of a migrating cell population guided by chemotaxis in response to an external ligand concentration is derived and analysed. Unlike traditional Keller-Segel models, this…
Coordinated rotational motion is an intriguing, yet still elusive mode of collective cell migration, which is relevant in pathological and morphogenetic processes. Most of the studies on this topic have been carried out on confined…
The adhesion zone of immune cells, the 'immunological synapse', exhibits characteristic domains of receptor-ligand complexes. The domain formation is likely caused by a length difference of the receptor-ligand complexes, and has been…
Clustering is a fundamental unsupervised learning approach. Many clustering algorithms -- such as $k$-means -- rely on the euclidean distance as a similarity measure, which is often not the most relevant metric for high dimensional data…
A chloroplast is a subcellular organelle of photosynthesis in plant and algal cells. A chloroplast genome encodes proteins of the photosynthetic electron transport chain and ribosomal proteins required to express them. Chloroplast-encoded…
Cancer cells can acquire a spectrum of stable hybrid epithelial/mesenchymal (E/M) states during epithelial-mesenchymal transition (EMT). Cells in these hybrid E/M phenotypes often combine epithelial and mesenchymal features and tend to…
The formation and dissociation of specific noncovalent interactions between a variety of macromolecules play a crucial role in the function of biological systems. During the last few years, three main lines of research led to a dramatic…
The endoplasmic reticulum (ER) is a network of sheet-like and tubular structures that spans much of a cell and contains molecules undergoing diffusive searches for targets, such as unfolded proteins searching for chaperones and…