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Both symmetry and organized breaking of symmetry have a pivotal r\^ole in our understanding of structure and pattern formation in physical systems, including the origin of mass in the Universe and the chiral structure of biological…
A stochastic model of autoregulated bursty gene expression by Kumar et al. [Phys. Rev. Lett. 113, 268105 (2014)] has been exactly solved in steady-state conditions under the implicit assumption that protein numbers are sufficiently large…
Coregulation of the expression of groups of genes has been extensively demonstrated empirically in bacterial and eukaryotic systems. Such coregulation can arise through the use of shared regulatory motifs, which allow the coordinated…
An input-output approach to stability analysis is explored for networked systems with uncertain link dynamics. The main result consists of a collection of integral quadratic constraints, which together imply robust stability of the…
Only about 1,000 qualitatively different protein folds are believed to exist in nature. Here, we review theoretical studies which suggest that some folds are intrinsically more designable than others, {\it i.e.} are lowest energy states of…
Stochastic block models (SBMs) are often used to find assortative community structures in networks, such that the probability of connections within communities is higher than in between communities. However, classic SBMs are not limited to…
The past decade has witnessed the development and success of coarse-grained network models of proteins for predicting many equilibrium properties related to collective modes of motion. Curiously, the results are usually robust towards the…
Evolution-based protein structure prediction models have achieved breakthrough success in recent years. However, they struggle to generalize beyond evolutionary priors and on sequences lacking rich homologous data. Here we present a novel,…
Large-scale online platforms and marketplace systems often evaluate new policies through experiments that randomize treatment across operational units (e.g., geographies, regions, or clusters) over many time periods. In these settings,…
The adsorption or adhesion of large particles (proteins, colloids, cells, >...) at the liquid-solid interface plays an important role in many diverse applications. Despite the apparent complexity of the process, two features are…
Proteins are an important class of biomolecules that serve as essential building blocks of the cells. Their three-dimensional structures are responsible for their functions. In this thesis we have investigated the protein structures using a…
Simple nonlinear dynamical systems with multiple stable stationary states are often taken as models for switchlike biological systems. This paper considers the interaction of multiple such simple multistable systems when they are embedded…
Random fiber networks form the structural foundation of numerous biological tissues and engineered materials. From a mechanics perspective, understanding the structure-function relationships of random fiber networks is particularly…
The time evolution of the formation probability of native bonds has been studied for designed sequences which fold fast into the native conformation. From this analysis a clear hierarchy of bonds emerge a) local, fast forming highly stable…
This paper studies the structural controllability of a class of uncertain switched linear systems, where the parameters of subsystems state matrices are either unknown or zero. The structural controllability is a generalization of the…
While on the one hand, chaotic dynamical systems can be predicted for all time given exact knowledge of an initial state, they are also in many cases rapidly mixing, meaning that smooth probabilistic information (quantified by measures) on…
We consider two types of Go models of a protein (crambin) and study their kinetics through molecular dynamics simulations. In the first model, the residue -- residue contact interactions are selected based on a cutoff distance, $R_c$,…
Structure determination is key to understanding protein function at a molecular level. Whilst significant advances have been made in predicting structure and function from amino acid sequence, researchers must still rely on expensive,…
A framework is presented for understanding the common character of proteins. Proteins are linear chain molecules. However, the simple model of a polymer viewed as spheres tethered together does not account for many of the observed…
We point out that in the first order time-dependent perturbation theory, the transition probability may behave nonsmoothly in time and have kinks periodically. Moreover, the detailed temporal evolution can be sensitive to the exact…