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Proteins often regulate their activities via allostery - or action at a distance - in which the binding of a ligand at one binding site influences the affinity for another ligand at a distal site. Although less studied than in proteins, allosteric effects have been observed in experiments with DNA as well. In these experiments two or more proteins bind at distinct DNA sites and interact indirectly with each other, via a mechanism mediated by the linker DNA molecule. We develop a mechanical model of DNA/protein interactions which predicts three distinct mechanisms of allostery. Two of these involve an enthalphy-mediated allostery, while a third mechanism is entropy driven. We analyze experiments of DNA allostery and highlight the distinctive signatures allowing one to identify which of the proposed mechanisms best fits the data.

DNA supercoiling is a key regulatory mechanism that orchestrates DNA readout, recombination, and genome maintenance. DNA-binding proteins often mediate these processes by bringing two distant DNA sites together, thereby inducing (transient) topological domains. In order to understand the dynamics and molecular architecture of protein induced topological domains in DNA, quantitative and time-resolved approaches are required. Here we present a methodology to determine the size and dynamics of topological domains in supercoiled DNA in real-time and at the single molecule level. Our approach is based on quantifying the extension fluctuations – in addition to the mean extension – of supercoiled DNA in magnetic tweezers. Using a combination of high-speed magnetic tweezers experiments, Monte Carlo simulations, and analytical theory, we map out the dependence of DNA extension fluctuations as a function of supercoiling density and external force. We find that in the plectonemic regime the extension variance increases linearly with increasing supercoiling density and show how this enables us to determine the formation and size of topological domains. In addition, we demonstrate how transient (partial) dissociation of DNA bridging proteins results in dynamic sampling of different topological states, which allows us to deduce the torsional stiffness of the plectonemic state and the kinetics of protein-plectoneme interactions. We expect our approach to enable quantification of the dynamics and reaction pathways of DNA processing enzymes and motor proteins, in the context of physiologically relevant forces and supercoiling densities.SignificanceIn the cell, long DNA molecules carry the genetic information and must be stored and maintained, yet remain accessible for read out and processing. DNA supercoiling facilitates compaction of DNA, modulates its accessibility, and spatially juxtaposes DNA sites distant in linear DNA sequence. By binding to two sites in supercoiled DNA, DNA bridging proteins can pinch off topological domains and alter DNA plectoneme dynamics. Here we show how DNA bridging and topological domain dynamics can be detected from changes in the extension fluctuations of supercoiled DNA molecules tethered in magnetic tweezers. Our work highlights how considering DNA extension fluctuations, in addition to the mean extension, provides additional information and enables the investigation of protein-DNA interactions that are otherwise invisible.

While analyzing the persistence length of DNA atomistic simulations Wu et al. [J. Chem. Phys. 142, 125103 (2015)] introduced an empirical formula to account for the observed length-dependence. In particular they found that the persistence length increases with the distance. Here, we derive the formula by Wu et al. using a non-local twistable wormlike chain which introduces couplings between distal sites. Finally, we show that the same formula can account for the length-scale dependence of the torsional persistence length and is, in fact, applicable to any kind of polymer model with non-local couplings., Comment: 3 pages, 1 Figure

We investigate the critical properties of a one dimensional stochastic lattice model with n (permutation symmetric) absorbing states. We analyze the cases with $n \leq 4$ by means of the non-hermitian density matrix renormalization group. For n=1 and n=2 we find that the model is respectively in the directed percolation and parity conserving universality class, consistent with previous studies. For n=3 and n=4, the model is in the active phase in the whole parameter space and the critical point is shifted to the limit of one infinite reaction rate. We show that in this limit the dynamics of the model can be mapped onto that of a zero temperature n-state Potts model. On the basis of our numerical and analytical results we conjecture that the model is in the same universality class for all $n \geq 3$ with exponents $z = \nu_\|/\nu_\perp = 2$, $\nu_\perp = 1$ and $\beta = 1$. These exponents coincide with those of the multispecies (bosonic) branching annihilating random walks. For n=3 we also show that, upon breaking the symmetry to a lower one ($Z_2$), one gets a transition either in the directed percolation, or in the parity conserving class, depending on the choice of parameters., Comment: 10 pages, RevTeX, and 10 PostScript figures included

The steady-state phase diagram of the one-dimensional reaction-diffusion model 2A -> 3A, 2A -> 0 is studied through the non-hermitian density matrix renormalization group. In the absence of single-particle diffusion the model reduces to the pair-contact process, which has a phase transition in the universality class of Directed Percolation (DP) and an infinite number of absorbing steady states. When single-particle diffusion is added, the number of absorbing steady states is reduced to two and the model does not show DP critical behaviour anymore. The exponents $\theta=\nu_{\|}/\nu_{\perp}$ and $\beta/\nu_{\perp}$ are calculated numerically. The value of $\beta/\nu_{\perp}$ is close to the value of the Parity Conserving universality class, in spite of the absence of local conservation laws., Comment: Substantially revised version, RevTeX, 10 Pages and 5 PostScript figures included

The steady-state phase diagram of the one-dimensional reaction-diffusion model 2A -> 3A, 2A -> 0 is studied through the non-hermitian density matrix renormalization group. In the absence of single-particle diffusion the model reduces to the pair-contact process, which has a phase transition in the universality class of Directed Percolation (DP) and an infinite number of absorbing steady states. When single-particle diffusion is added, the number of absorbing steady states is reduced to two and the model does not show DP critical behaviour anymore. The exponents $��=��_{\|}/��_{\perp}$ and $��/��_{\perp}$ are calculated numerically. The value of $��/��_{\perp}$ is close to the value of the Parity Conserving universality class, in spite of the absence of local conservation laws., Substantially revised version, RevTeX, 10 Pages and 5 PostScript figures included

The surface and bulk properties of the two-dimensional Q > 4 state Potts model in the vicinity of the first order bulk transition point have been studied by exact calculations and by density matrix renormalization group techniques. For the surface transition the complete analytical solution of the problem is presented in the $Q \to \infty$ limit, including the critical and tricritical exponents, magnetization profiles and scaling functions. According to the accurate numerical results the universality class of the surface transition is independent of the value of Q > 4. For the bulk transition we have numerically calculated the latent heat and the magnetization discontinuity and we have shown that the correlation lengths in the ordered and in the disordered phases are identical at the transition point., Comment: 11 pages, RevTeX, 6 PostScript figures included. Manuscript substantially extended, details on the analytical and numerical calculations added. To appear in Phys. Rev. B

The surface and bulk properties of the two-dimensional Q > 4 state Potts model in the vicinity of the first order bulk transition point have been studied by exact calculations and by density matrix renormalization group techniques. For the surface transition the complete analytical solution of the problem is presented in the $Q \to \infty$ limit, including the critical and tricritical exponents, magnetization profiles and scaling functions. According to the accurate numerical results the universality class of the surface transition is independent of the value of Q > 4. For the bulk transition we have numerically calculated the latent heat and the magnetization discontinuity and we have shown that the correlation lengths in the ordered and in the disordered phases are identical at the transition point., 11 pages, RevTeX, 6 PostScript figures included. Manuscript substantially extended, details on the analytical and numerical calculations added. To appear in Phys. Rev. B

Networks of steps, seen in STM observations of vicinal surfaces on Au and Pt (110), are analyzed. A simple model is introduced for the calculation of the free energy of the networks as function of the slope parameters, valid at low step densities. It predicts that the networks are unstable, or at least metastable, against faceting and gives an equilibrium crystal shape with sharp edges either between the (110) facet and rounded regions or between two rounded regions. Experimental observations of the equilibrium shapes of Au or Pt crystals at sufficiently low temperatures, i.e. below the deconstruction temperature of the (110) facet, could check the validity of these predictions., 14 pages, RevTex, uses epsf.sty, the file rotate.sty is included. To appear in the Proceedings of the Traverse City workshop on The Dynamics of Crystal Surfaces (August 1996); this work is an extension of Phys. Rev. Lett. {\bf 76}, 4191 (1996)

The phase diagram of the staggered six vertex, or body centered solid on solid model, is investigated by transfer matrix and finite size scaling techniques. The phase diagram contains a critical region, bounded by a Kosterlitz-Thouless line, and a second order line describing a deconstruction transition. In part of the phase diagram the deconstruction line and the Kosterlitz-Thouless line approach each other without merging, while the deconstruction changes its critical behaviour from Ising-like to a different universality class. Our model has the same type of symmetries as some other two-dimensional models, such as the fully frustrated XY model, and may be important for understanding their phase behaviour. The thermal behaviour for weak staggering is intricate. It may be relevant for the description of surfaces of ionic crystals of CsCl structure., Comment: 13 pages, RevTex, 1 Postscript file with all figures, to be published in Phys. Rev. B

The central focus of this thesis is the study of DNA, a biological molecule of paramount significance. It stores all genetic information in a series of base pairs, the four-letter biological equivalent of the alphabet, and is involved in a plethora of functions within the cell. We are interested in its physical properties, and particularly in three distinct aspects: micromechanics, capture by nanopore and hybridization. The first topic deals with the mechanical properties of a single molecule. Similar to cords from daily life, DNA can be stretched, bent and twisted. In fact, it is hardly ever free of mechanical stress within the cell, as it is constantly deformed by binding proteins. Unlike cords, however, DNA has a special feature: it twists upon bending and bends upon twisting. The first part of the thesis investigates how this twist-bend coupling influences the mechanics of DNA. The way DNA is forced to pass through a nanometer-sized hole is the focus of the second topic. Such a nanopore can be an open cylindrical protein, embedded in a cell membrane. Since DNA is negatively charged, it can be "squeezed" through the pore by applying a voltage difference between the two sides of the membrane. We study the capture from the one side of the membrane into the nanopore, and find that DNA first needs to overcome an entropic barrier. The third topic is devoted to DNA hybridization, the formation of the familiar double helix from two separate strands. The probability of this depends on how good the match is between the two sets of base pairs, which is exploited by several techniques to identify a sequence. A central problem is the detection of a low-abundance sequence (e.g. tumor DNA) in a sea of other sequences (e.g. healthy DNA), often differing by a single base pair. Here, we present a novel strategy that offers a greatly-enhanced detection sensitivity, with a direct diagnostic application. Throughout this work, we rely on theory (read: pen-and-paper calculations) and simulation (read: experiments on a computer) to make predictions about biophysical phenomena. In the end, we test their validity and relevance by comparing to experiments performed by collaborating groups. status: published