The problem of counting graph homomorphisms is considered. We show that the counting problem corresponding to a given graph is #P-complete unless every connected component of the graph is an isolated vertex without a loop, a complete graph with all loops present, or a complete unlooped bipartite graph.

DNA looping plays a fundamental role in a wide variety of biological processes, providing the backbone for long range interactions on DNA. Here we develop the first model for DNA looping by an arbitrarily large number of proteins and solve it analytically in the case of identical binding. We uncover a switchlike transition between looped and unlooped phases and identify the key parameters that ...

Loops are ubiquitous topological elements formed when proteins simultaneously bind to two noncontiguous DNA sites. While a loop-mediating protein may regulate initiation at a promoter, the presence of the protein at the other site may be an obstacle for RNA polymerases (RNAP) transcribing a different gene. To test whether a DNA loop alters the extent to which a protein blocks transcription, the...

The lysogenic state of the λ switch is exceptionally stable, still, it is capable of responding to DNA-damage and rapidly enter the lytic state. We invented an assay where PNA mediated tethering of a plasmid allowed for single molecule investigations of the effect of supercoiling on the efficiency of the epigenetic λ switch. Compared with non-supercoiled DNA, the presence of supercoils enhances...

Tethered particle motion (TPM) has become an important tool for single-molecule studies of biomolecules; however, concerns remain that the method may alter the dynamics of the biophysical process under study. We investigate the effect of the attached microsphere on an illustrative biological example: the formation and breakdown of protein-mediated DNA loops in the lac repressor system. By compa...

Chromatin fibers composed of DNA and proteins fold into consecutive loops to form rod-shaped chromosome in mitosis. Although the loop growth dynamics is investigated several studies, its detailed processes are unclear. Here, we describe time evolution length for thermal-driven as an iterative map by calculating physical quantities involved processes. We quantify energy during chromatin formatio...

Gene expression regulation is a fundamental biological process which deploys specific sets of genomic information depending on physiological or environmental conditions. Several transcription factors (including lac repressor, LacI) are present in the cell at very low copy number and increase their local concentration by binding to multiple sites on DNA and looping the intervening sequence. In t...

The heart develops from a linear tubular precursor, which loops to the right and undergoes terminal differentiation to form the multichambered heart. Heart looping is the earliest manifestation of left-right asymmetry and determines the eventual heart situs. The signalling processes that impart laterality to the unlooped heart tube and thus allow the developing organ to interpret the left-right...

DNA looping plays a key role in many fundamental biological processes, including gene regulation, recombination, and chromosomal organization. The looping of DNA is often mediated by proteins whose structural features and physical interactions can alter the length scale at which the looping occurs. Looping and unlooping processes are controlled by thermodynamic contributions associated with mec...