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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…

In this short note, a correction is made to the recently proposed solution [1] to a 1D biased diffusion model for linear DNA translocation and a new analysis will be given to the data in [1]. It was pointed out [2] by us recently that this…

Despite having been studied for decades, first passage processes remain an active area of research. In this contribution we examine a particle diffusing in an annulus with an inner absorbing boundary and an outer reflective boundary. We…

Diffusion of transported particles in the intracellular medium is described by means of a generalized diffusion equation containing forces due to the cytoskeleton network and to the protein motors. We find that the enhanced diffusion…

Migration of immune cells within the human body allows them to fulfill their main function of detecting pathogens. Adopting an optimal navigation and search strategy by these cells is of crucial importance to achieve an efficient immune…

A popular approach to protein design is to combine a generative model with a discriminative model for conditional sampling. The generative model samples plausible sequences while the discriminative model guides a search for sequences with…

This tutorial provides an in-depth guide on inference-time guidance and alignment methods for optimizing downstream reward functions in diffusion models. While diffusion models are renowned for their generative modeling capabilities,…

Diffusion models are state-of-the-art methods in generative modeling when samples from a target probability distribution are available, and can be efficiently sampled, using score matching to estimate score vectors guiding a Langevin…

Transfer learning of diffusion models to smaller target domains is challenging, as naively fine-tuning the model often results in poor generalization. Test-time guidance methods help mitigate this by offering controllable improvements in…

Membrane targeting domains play crucial roles in the association of signalling molecules to the plasma membrane. For most peripheral proteins, the protein-to-membrane interaction is transient. After proteins dissociate from the membrane…

We describe an explicitly discrete model of the process of DNA branch migration. The model matches the existing data well, but we find that branch migration along long strands of DNA ($N \simge 40$~bp) is also well modeled by continuum…

Predicting the binding structure of a small molecule ligand to a protein -- a task known as molecular docking -- is critical to drug design. Recent deep learning methods that treat docking as a regression problem have decreased runtime…

Cellular networks are often composed of thin tubules connecting much larger node compartments. These structures serve for active or diffusion transport of proteins. Examples are glial networks in the brain, the endoplasmic reticulum in…

Using analytical calculations and computer simulations we consider both the lateral diffusion of a membrane protein and the fluctuation spectrum of the membrane in which the protein is embedded. The membrane protein interacts with the…

Intracellular transport processes are essential to the healthy development of many organisms as well as more generally to healthy cellular function. The complex dynamics and interactions between protein molecules and filaments on different…

Adapting a pretrained diffusion model to new objectives at inference time remains an open problem in generative modeling. Existing steering methods suffer from inaccurate value estimation, especially at high noise levels, which biases…

To fully leverage the capabilities of diffusion models, we are often interested in optimizing downstream reward functions during inference. While numerous algorithms for reward-guided generation have been recently proposed due to their…

Diffusion models, a family of generative models based on deep learning, have become increasingly prominent in cutting-edge machine learning research. With a distinguished performance in generating samples that resemble the observed data,…

Causal inference across multiple data sources offers a promising avenue to enhance the generalizability and replicability of scientific findings. However, data integration methods for time-to-event outcomes, common in biomedical research,…

It is widely recognized that the cleaving rate of a restriction enzyme on target DNA sequences is several orders of magnitude faster than the maximal one calculated from the diffusion--limited theory. It was therefore commonly assumed that…