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Protein machines often exhibit long range interplay between different sites in order to achieve their biological tasks. We investigate and characterize the non--linear energy localization and the basic mechanisms of energy transfer in protein devices. By studying two different model protein machines, with different biological functions, we show that genuinely non--linear phenomena are responsible for energy transport between the different machine sites involved in the biological functions. The energy transfer turns out to be extremely efficient from an energetic point of view: by changing the energy initially provided to the model device, we identify a well defined range of energies where the time for the energy transport to occur is minimal and the amount of transferred energy is maximum. Furthermore, by introducing an implicit solvent, we show that the energy is localized on the internal residues of the protein structure, thus minimizing the dissipation.
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We propose a model for the formation of chromatin loops based on the diffusive sliding of a DNA-bound factor which can dimerise to form a molecular slip-link. Our slip-links mimic the behaviour of cohesin-like molecules, which, along with the CTCF protein, stabilize loops which organize the genome. By combining 3D Brownian dynamics simulations and 1D exactly solvable non-equilibrium models, we show that diffusive sliding is sufficient to account for the strong bias in favour of convergent CTCF-mediated chromosome loops observed experimentally. Importantly, our model does not require any underlying, and energetically costly, motor activity of cohesin. We also find that the diffusive motion of multiple slip-links along chromatin may be rectified by an intriguing ratchet effect that arises if slip-links bind to the chromatin at a preferred loading site. This emergent collective behaviour is driven by a 1D osmotic pressure which is set up near the loading point, and favours the extrusion of loops which are much larger than the ones formed by single slip-links.
Charge migration along DNA molecules has attracted scientific interest for over half a century. Reports on possible high rates of charge transfer between donor and acceptor through the DNA, obtained in the last decade from solution chemistry experiments on large numbers of molecules, triggered a series of direct electrical transport measurements through DNA single molecules, bundles and networks. These measurements are reviewed and presented here. From these experiments we conclude that electrical transport is feasible in short DNA molecules, in bundles and networks, but blocked in long single molecules that are attached to surfaces. The experimental background is complemented by an account of the theoretical/computational schemes that are applied to study the electronic and transport properties of DNA-based nanowires. Examples of selected applications are given, to show the capabilities and limits of current theoretical approaches to accurately describe the wires, interpret the transport measurements, and predict suitable strategies to enhance the conductivity of DNA nanostructures.
Semiflexible polymers characterized by the contour length $L$ and persistent length $ell_p$ confined in a spatial region $D$ have been described as a series of ``{em spherical blobs} and ``{em deflecting lines} by de Gennes and Odjik for $ell_p < D$ and $ell_p gg D$ respectively. Recently new intermediate regimes ({em extended de Gennes} and {em Gauss-de Gennes}) have been investigated by Tree {em et al.} [Phys. Rev. Lett. {bf 110}, 208103 (2013)]. In this letter we derive scaling relations to characterize these transitions in terms of universal scaled fluctuations in $d$-dimension as a function of $L,ell_p$, and $D$, and show that the Gauss-de Gennes regime is absent and extended de Gennes regime is vanishingly small for polymers confined in a 2D strip. We validate our claim by extensive Brownian dynamics (BD) simulation which also reveals that the prefactor $A$ used to describe the chain extension in the Odjik limit is independent of physical dimension $d$ and is the same as previously found by Yang {em et al.}[Y. Yang, T. W. Burkhardt, G. Gompper, Phys. Rev. E {bf 76}, 011804 (2007)]. Our studies are relevant for optical maps of DNA stretched inside a nano-strip.
An elastic rod model for semi-flexible polymers is presented. Theory for a continuum rod is reviewed, and it is shown that a popular discretised model used in numerical simulations gives the correct continuum limit. Correlation functions relating to both bending and twisting of the rod are derived for both continuous and discrete cases, and results are compared with numerical simulations. Finally, two possible implementations of the discretised model in the multi-purpose molecular dynamics software package LAMMPS are described.
Homologous gene shuffling between DNA promotes genetic diversity and is an important pathway for DNA repair. For this to occur, homologous genes need to find and recognize each other. However, despite its central role in homologous recombination, the mechanism of homology recognition is still an unsolved puzzle. While specific proteins are known to play a role at later stages of recombination, an initial coarse grained recognition step has been proposed. This relies on the sequence dependence of the DNA structural parameters, such as twist and rise, mediated by intermolecular interactions, in particular electrostatic ones. In this proposed mechanism, sequences having the same base pair text, or are homologous, have lower interaction energy than those sequences with uncorrelated base pair texts; the difference termed the recognition energy. Here, we probe how the recognition energy changes when one DNA fragment slides past another, and consider, for the first time, homologous sequences in antiparallel alignment. This dependence on sliding was termed the recognition well. We find that there is recognition well for anti-parallel, homologous DNA tracts, but only a very shallow one, so that their interaction will differ little from the interaction between two nonhomologous tracts. This fact may be utilized in single molecule experiments specially targeted to test the theory. As well as this, we test previous theoretical approximations in calculating the recognition well for parallel molecules against MC simulations, and consider more rigorously the optimization of the orientations of the fragments about their long axes. The more rigorous treatment affects the recognition energy a little, when the molecules are considered rigid. However when torsional flexibility of the DNA molecules is introduced, we find excellent agreement between analytical approximation and simulation.
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