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Central to the functioning of a living cell is its ability to control the readout or expression of information encoded in the genome. In many cases, a single transcription factor protein activates or represses the expression of many genes.…
Most microorganisms regulate their cell size. We review here some of the mathematical formulations of the problem of cell size regulation. We focus on coarse-grained stochastic models and the statistics they generate. We review the…
Proteins contain a large fraction of regular, repeating conformations, called secondary structure. A simple, generic definition of secondary structure is presented which consists of measuring local correlations along the protein chain.…
Directed cycles form the fundamental motifs in natural, social and artificial networks, yet their distinct computational roles remain under-explored, particularly in the context of higher-order structure and function. In this work, we…
Auto-regulatory feedback loops are one of the most common network motifs. A wide variety of stochastic models have been constructed to understand how the fluctuations in protein numbers in these loops are influenced by the kinetic…
Composed of amino acid chains that influence how they fold and thus dictating their function and features, proteins are a class of macromolecules that play a central role in major biological processes and are required for the structure,…
Biological systems excel at building spatial structures on scales ranging from nanometers to kilometers and exhibit temporal patterning from milliseconds to years. One approach that nature has taken to accomplish this relies on the…
Living systems are capable of locomotion, reconfiguration, and replication. To perform these tasks, cells spatiotemporally coordinate the interactions of force-generating, "active" molecules that create and manipulate non-equilibrium…
The mechanisms by which a protein's 3D structure can be determined based on its amino acid sequence have long been one of the key mysteries of biophysics. Often simplistic models, such as those derived from geometric constraints, capture…
Circadian clocks play a pivotal role in orchestrating numerous physiological and developmental events. Waveform shapes of the oscillations of protein abundances can be informative about the underlying biochemical processes of circadian…
Deep learning approaches have produced substantial breakthroughs in fields such as image classification and natural language processing and are making rapid inroads in the area of protein design. Many generative models of proteins have been…
Complexes of physically interacting proteins constitute fundamental functional units responsible for driving biological processes within cells. A faithful reconstruction of the entire set of complexes is therefore essential to understand…
Proteins carry out biological functions through the coordinated action of groups of residues organized into structural arrangements. These arrangements, which we refer to as protein units, exist at an intermediate scale, being larger than…
Proteins are macromolecules that perform essential functions in all living organisms. Designing novel proteins with specific structures and desired functions has been a long-standing challenge in the field of bioengineering. Existing…
Many aspects of the study of protein folding and dynamics have been affected by the recent advances in machine learning. Methods for the prediction of protein structures from their sequences are now heavily based on machine learning tools.…
Gene Regulatory Networks are networks of interactions in biological organisms responsible for determining the production levels of proteins and peptides. Proteins are workers of a cell factory, and their production defines the goal of a…
Much evolutionary information is stored in the fluctuations of protein length distributions. The genome size and non-coding DNA content can be calculated based only on the protein length distributions. So there is intrinsic relationship…
Proteins play a central role in biology from immune recognition to brain activity. While major advances in machine learning have improved our ability to predict protein structure from sequence, determining protein function from structure…
Mathematical models play an increasingly important role in the interpretation of biological experiments. Studies often present a model that generates the observations, connecting hypothesized process to an observed pattern. Such generative…
Protein structure prediction is pivotal for understanding the structure-function relationship of proteins, advancing biological research, and facilitating pharmaceutical development and experimental design. While deep learning methods and…