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Motivation: RNA design aims to find RNA sequences that fold into a given target secondary structure, a problem also known as RNA inverse folding. However, not all target structures are designable. Recent advances in RNA designability have…
Stochastic computational models in the form of pure jump processes occur frequently in the description of chemical reactive processes, of ion channel dynamics, and of the spread of infections in populations. For spatially extended models,…
The problem of RNA secondary structure design (also called inverse folding) is the following: given a target secondary structure, one aims to create a sequence that folds into, or is compatible with, a given structure. In several practical…
Nucleic acids have been regarded as stiff polymers with long-range flexibility and generally modeled using elastic rod models of polymer physics. Notwithstanding, investigations carried out over the past few years on single fragments of…
We describe a dynamic programming algorithm for predicting optimal RNA secondary structure, including pseudoknots. The algorithm has a worst case complexity of ${\cal O}(N^6)$ in time and ${\cal O}(N^4)$ in storage. The description of the…
Resonant inelastic x-ray scattering (RIXS) is a well-established tool for studying electronic, nuclear and collective dynamics of excited atoms, molecules and solids. An extension of this powerful method to a time-resolved probe technique…
Understanding the dynamic nature of biological systems is fundamental to deciphering cellular behavior, developmental processes, and disease progression. Single-cell RNA sequencing (scRNA-seq) has provided static snapshots of gene…
In biology, predicting RNA secondary structures plays a vital role in determining its physical and chemical properties. Although we have powerful energy models to predict them as well as parametric analysis to understand the models…
Single molecule force spectroscopy methods can be used to generate folding trajectories of biopolymers from arbitrary regions of the folding landscape. We illustrate the complexity of the folding kinetics and generic aspects of the collapse…
Secondary structure formation of nucleic acids strongly depends on salt concentration and temperature. We develop a theory for RNA folding that correctly accounts for sequence effects, the entropic contributions associated with loop…
Solutions to the stochastic wave equation on the unit sphere are approximated by spectral methods. Strong, weak, and almost sure convergence rates for the proposed numerical schemes are provided and shown to depend only on the smoothness of…
This contribution focuses on the fascinating RNA molecule, its sequence-dependent folding driven by base-pairing interactions, the interplay between these interactions and natural evolution, and its multiple regulatory roles. The four of us…
In the current AFM experiments the distribution of unfolding times, P(t), is measured by applying a constant stretching force f_s from which the apparent unfolding rate is obtained. To describe the complexity of the underlying energy…
Ribonucleic acid (RNA) is involved in many regulatory and catalytic processes in the cell. The function of any RNA molecule is intimately related with its structure. In-line probing experiments provide valuable structural datasets for a…
We study numerically the behavior of RNA secondary structures under influence of a varying external force. This allows to measure the work $W$ during the resulting fast unfolding and refolding processes. Here, we investigate a medium-size…
Using a Brownian dynamics simulation, we numerically studied the interaction of DNA with histone and proposed an octamer-rotation model to describe the process of nucleosome formation. Nucleosome disruption under stretching was also…
We demonstrate how direct simulation of stochastic, individual-based models can be combined with continuum numerical analysis techniques to study the dynamics of evolving diseases. % Sidestepping the necessity of obtaining explicit…
The deformations of flagella are important in the motility of single- and multi-flagellated bacteria. Existing numerical methods have treated flagella as extensible filaments with a large extensional modulus, resulting in a stiff numerical…
In a general stochastic multistate promoter model of dynamic mRNA/protein interactions, we identify the stationary joint distribution of the promoter state, mRNA, and protein levels through an explicit `stick-breaking' construction of…
A theory of the unzipping of double-stranded (ds) DNA is presented, and is compared to recent micromanipulation experiments. It is shown that the interactions which stabilize the double helix and the elastic rigidity of single strands (ss)…