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In eukaryotic cell nuclei, a variety of DNA interactions with nuclear elements occur, which, in combination with intra- and inter- chromosomal cross-talks, shape a functional 3D architecture. In some cases they are organized by active, i.e.…
We theoretically address minimal search strategies of active, self-propelled particles towards hidden targets in three-dimensional space. The particles can sense if a target is close, e.g., by detecting signaling molecules released by a…
Protein fitness optimization involves finding a protein sequence that maximizes desired quantitative properties in a combinatorially large design space of possible sequences. Recent advances in steering protein generative models (e.g.,…
Efficient search acts as a strong selective force in biological systems ranging from cellular populations to predator-prey systems. The search processes commonly involve finding a stationary or mobile target within a heterogeneously…
Generating protein sequences that fold into a intended 3D structure is a fundamental step in de novo protein design. De facto methods utilize autoregressive generation, but this eschews higher order interactions that could be exploited to…
We investigate the dynamics of DNA translocation through a nanopore driven by an external force using Langevin dynamics simulations in two dimensions (2D) to study how the translocation dynamics depend on the details of the DNA sequences.…
For a substance diffusing on a curved surface, we obtain an explicit relation valid for very small values of the time, between the local concentration, the diffusion coefficient, the intrinsic spatial curvature and the time. We recover the…
The function of biomolecules such as proteins depends on their ability to interconvert between a wide range of structures or "conformations." Researchers have endeavored for decades to develop computational methods to predict the…
A theory is presented of the longitudinal dispersion of DNA under equilibrium confined in a nanochannel. Orientational fluctuations of the DNA chain build up to give rise to substantial fluctuations of the coil in the longitudinal direction…
Proteins are complex biomolecules that perform a variety of crucial functions within living organisms. Designing and generating novel proteins can pave the way for many future synthetic biology applications, including drug discovery.…
Diffusion coefficient measurements are important for many biological and material investigations, such as particle dynamics, kinetics, and size determinations. Amongst current measurement methods, single particle tracking (SPT) offers the…
Biological learning achieves temporal credit assignment despite sparse and imprecise feedback, often relying on neuromodulatory signals acting over space and time. Here, we introduce a learning mechanism in which error information diffuses…
Protein design with desirable properties has been a significant challenge for many decades. Generative artificial intelligence is a promising approach and has achieved great success in various protein generation tasks. Notably, diffusion…
Previous theoretical studies have shown that measuring the transverse current across DNA strands while they translocate through a nanopore or channel may provide a statistically distinguishable signature of the DNA bases, and may thus allow…
To model discrete sequences such as DNA, proteins, and language using diffusion, practitioners must choose between three major methods: diffusion in discrete space, Gaussian diffusion in Euclidean space, or diffusion on the simplex. Despite…
Gene expression and regulation rely on an apparently finely tuned set of reactions between some proteins and DNA. Such DNA-binding proteins have to find specific sequences on very long DNA molecules and they mostly do so in absence of any…
Discrete diffusion models have demonstrated great promise in modeling various sequence data, ranging from human language to biological sequences. Inspired by the success of RL in language models, there is growing interest in further…
In population genetics, diffusions on the unit interval are often used to model the frequency path of an allele. In this setting we derive approximations for fixation probabilities, expected hitting times and the expected…
Several organelles in eukaryotic cells, including mitochondria and the endoplasmic reticulum, form interconnected tubule networks extending throughout the cell. These tubular networks host many biochemical pathways that rely on proteins…
Methods of transfer learning try to combine knowledge from several related tasks (or domains) to improve performance on a test task. Inspired by causal methodology, we relax the usual covariate shift assumption and assume that it holds true…