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Recognition and binding of specific sites on DNA by proteins is central for many cellular functions such as transcription, replication, and recombination. In the process of recognition, a protein rapidly searches for its specific site on a…

Gene regulation is one of the most important fundamental biological processes in living cells. It involves multiple protein molecules that locate specific sites on DNA and assemble gene initiation or gene repression multi-molecular…

Protein-DNA interactions are critical for the successful functioning of all natural systems. The key role in these interactions is played by processes of protein search for specific sites on DNA. Although it has been studied for many years,…

Some proteins can find their targets on DNA faster than by pure diffusion in the three-dimensional cytoplasm, through the process of facilitated diffusion: They can loosely bind to DNA and temporarily slide along it, thus being guided by…

We study a protein-DNA target search model with explicit DNA dynamics applicable to in vitro experiments. We show that the DNA dynamics plays a crucial role for the effectiveness of protein "jumps" between sites distant along the DNA…

We study the target searching on the DNA for proteins in the presence of non-constant drift and non-Gaussian $\alpha$-stable L\'evy fluctuations. The target searching is realized by the facilitated diffusion process. The existing works are…

The model of facilitated diffusion describes how DNA-binding proteins, such as transcription factors (TFs), find their chromosomal targets by combining 3D diffusion through the cytoplasm and 1D sliding along nonspecific DNA sequences. The…

We study a model for a protein searching for a target, using facilitated diffusion, on a DNA molecule confined in a finite volume. The model includes three distinct pathways for facilitated diffusion: (a) sliding - in which the protein…

Protein-DNA interactions are crucial for all biological processes. One of the most important fundamental aspects of these interactions is the process of protein searching and recognizing specific binding sites on DNA. A large number of…

In living cells, proteins combine 3D bulk diffusion and 1D sliding along the DNA to reach a target faster. This process is known as facilitated diffusion, and we investigate its dynamics in the physiologically relevant case of confined DNA.…

The most common gene regulation mechanism is when a protein binds to a regulatory sequence to change RNA transcription. However, these sequences are short relative to the genome length, so finding them poses a challenging search problem.…

The mechanism allowing a protein to search of a target sequence on DNA is currently described as an intermittent process composed of 3D diffusion in bulk and 1D diffusion along the DNA molecule. Due to the relevant charge of protein and…

Proteins can locate their specific targets on DNA up to two orders of magnitude faster than the Smoluchowski three-dimensional diffusion rate. This happens due to non-specific adsorption of proteins to DNA and subsequent one-dimensional…

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…

Several processes in the cell, such as gene regulation, start when key proteins recognise and bind to short DNA sequences. However, as these sequences can be hundreds of million times shorter than the genome, they are hard to find by simple…

In gene expression, various kinds of proteins need to bind to specific locus of DNA. It is still not clear how these proteins find their target locus. In this study, the mean first-passage time (FPT) of protein binding to its target locus…

For most of the important processes in DNA metabolism, a protein has to reach a specific binding site on the DNA. The specific binding site may consist of just a few base pairs while the DNA is usually several millions of base pairs long.…

Strong experimental and theoretical evidence shows that transcription factors and other specific DNA-binding proteins find their sites using a two-mode search: alternating between 3D diffusion through the cell and 1D sliding along the DNA.…

It is known since the early days of molecular biology that proteins locate their specific targets on DNA up to two orders of magnitude faster than the Smoluchowski 3D diffusion rate. It was the idea due to Delbruck that they are…

We consider a problem of finding a target located in a finite $d$-dimensional domain, using $N$ independent random walkers, when partial information on the target location is given as a probability distribution. When $N$ is large, the…