DNA confined in a two-dimensional strip geometry

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.Comment: 6 pages, 4 figure

Conformations and Dynamics of Semi-Flexible Polymers

In this dissertation, we investigate the conformations, transverse fluctuations and dynamics of two-dimensional (2D) semi-flexible polymers both in the bulk and under channel confinement. We present unified scaling relations in regard to various quantities of interest for a broad range of combinations of chain length and chain stiffness using Langevin dynamics simulation. We also present a three-dimensional (3D) heterogeneous semi-flexible chain model for a double stranded DNA (dsDNA). Our model not only confirms the established findings for homogeneous dsDNA, but also predicts new physical phenomenon for heterogeneous dsDNA. The problems studied in this dissertation are relevant to analysis of the conformations and dynamics of biopolymers (such as DNA) in living organisms, and also offer insights for developing devices which operate on the single-molecule level. In particular, we present a unified description for the dynamics of building-blocks (monomers) of a semi-flexible chain. We consider the full range of flexibility from the case where the chain is fully flexible (no stiffness at all) to the case where the chain behaves like a rod (infinite stiffness). Our theory predicts qualitatively different sub-diffusive regimes for the monomer dynamics originating from the chain stiffness by studying the mean square displacement (MSD) of the monomers before the chain dynamics become purely diffusive. For the conformations in the bulk, we present results confirmed and agreed by two completely different models of semi-flexible polymers, with one of which is the bead-spring model (studied by Langevin dynamics) in the continuum space, the other (studied by Monte Carlo) is a self-avoiding walk chain on the square lattice, where only discrete bond angles are possible. We point out the universal features of chain conformations and fluctuations which are independent of the models. For the conformations under channel confinement, we discover qualitatively different conformations and dynamics of the chain as a function of the channel width and chain stiffness, and show how globule like shapes ( de Gennes blobs ) for more flexible chains continuously go over to shapes in the form of deflections from the wall ( Odijk limit ) for more stiff chains. We provide theoretical arguments how these regimes occur and interpolate among each other as one varies different parameters of the model. We also demonstrate the effect of physical dimensions (either 2D or 3D) on these regimes and argue that since in 2D the excluded volume (EV) effect is more severe compared to 3D, certain regimes do not exist in 2D. Finally, we study a model of a dsDNA , where both base-pairing and base-stacking interactions are accounted for albeit at a low computational cost compared to the other existing models. Our model correctly recovers the stiffness for dsDNA and ssDNA at different temperatures. Under most conditions of interest, a dsDNA can locally denature and form bubbles due to thermal fluctuations. At a critical temperature, a dsDNA undergoes a phase transition, in which the two strands of dsDNA completely melt to two single strands (two ssDNA). By considering EV interactions and calculating the bubble size distribution, recent studies have shown that this denaturation process is a first order transition. We show that for a homogeneous dsDNA made of only AT or GC pairs, our simulation results agree with the previous conclusion of first order transition, however, for sequences of periodic AT and GC regions, when the periodic size is relatively large compared to the sequence length, we show that the bubble size distribution exhibits peaks expressing the sequence pattern, and more importantly, the denaturation is no longer a first order transition. All these studies reported in the dissertation are relevant to the physics of living systems

Universal monomer dynamics of a two dimensional semi-flexible chain

We present a unified scaling theory for the dynamics of monomers for dilute solutions of semiflexible polymers under good solvent conditions in the free draining limit. Our theory encompasses the well-known regimes of mean square displacements (MSDs) of stiff chains growing like t^{3/4} with time due to bending motions, and the Rouse-like regime t^{2 \nu / (1+ 2\nu)} where \nu is the Flory exponent describing the radius R of a swollen flexible coil. We identify how the prefactors of these laws scale with the persistence length l_p, and show that a crossover from stiff to flexible behavior occurs at a MSD of order l^2_p (at a time proportional to l^3_p). A second crossover (to diffusive motion) occurs when the MSD is of order R^2. Large scale Molecular Dynamics simulations of a bead-spring model with a bond bending potential (allowing to vary l_p from 1 to 200 Lennard-Jones units) provide compelling evidence for the theory, in D=2 dimensions where \nu=3/4. Our results should be valuable for understanding the dynamics of DNA (and other semiflexible biopolymers) adsorbed on substrates.Comment: 4-page paper with 5 figures. 3-page supplemental information with 3 figure

Conformations, Transverse Fluctuations and Crossover Dynamics of a Semi-Flexible Chain in Two Dimensions

We present a unified scaling description for the dynamics of monomers of a semiflexible chain under good solvent condition in the free draining limit. We consider both the cases where the contour length $L$ is comparable to the persistence length $\ell_p$ and the case $L\gg \ell_p$. Our theory captures the early time monomer dynamics of a stiff chain characterized by $t^{3/4}$ dependence for the mean square displacement(MSD) of the monomers, but predicts a first crossover to the Rouse regime of $t^{2\nu/{1+2\nu}}$ for $\tau_1 \sim \ell_p^3$, and a second crossover to the purely diffusive dynamics for the entire chain at $\tau_2 \sim L^{5/2}$. We confirm the predictions of this scaling description by studying monomer dynamics of dilute solution of semi-flexible chains under good solvent conditions obtained from our Brownian dynamics (BD) simulation studies for a large choice of chain lengths with number of monomers per chain N = 16 - 2048 and persistence length $\ell_p = 1 - 500$ Lennard-Jones (LJ) units. These BD simulation results further confirm the absence of Gaussian regime for a 2d swollen chain from the slope of the plot of $\langle R_N^2 \rangle/2L \ell_p \sim L/\ell_p$ which around $L/\ell_p \sim 1$ changes suddenly from $\left(L/\ell_p \right) \rightarrow \left(L/\ell_p \right)^{0.5}$, also manifested in the power law decay for the bond autocorrelation function disproving the validity of the WLC in 2d. We further observe that the normalized transverse fluctuations of the semiflexible chains for different stiffness $\sqrt{\langle l_{\bot}^2\rangle}/L$ as a function of renormalized contour length $L/\ell_p$ collapse on the same master plot and exhibits power law scaling $\sqrt{\langle l_{\bot}^2\rangle}/L \sim (L/\ell_p)^\eta$ at extreme limits, where $\eta = 0.5$ for extremely stiff chains ($L/\ell_p \gg 1$), and $\eta = -0.25$ for fully flexible chains.Comment: 14 pages, 18 figure

Pharmacological changes in cellular Ca2+ homeostasis parallel initiation of atrial arrhythmogenesis in murine langendorff-perfused hearts

Intracellular Ca2+ overload has been associated with established atrial arrhythmogenesis. The present experiments went on to correlate acute initiation of atrial arrhythmogenesis in Langendorff-perfused mouse hearts with changes in Ca2+ homeostasis in isolated atrial myocytes following pharmacological procedures that modified the storage or release of sarcoplasmic reticular (SR) Ca2+ or inhibited entry of extracellular Ca2+.Caffeine (1mmol/L) elicited diastolic Ca2+ waves in regularly stimulated atrial myocytes immediately following addition. This was followed by a decline in the amplitude of the evoked transients and the disappearance of such diastolic events, suggesting partial SR Ca2+ depletion.Cyclopiazonic acid (CPA; 0.15µmol/L) produced more gradual reductions in evoked Ca2+ transients and abolished diastolic Ca2+ events produced by the further addition of caffeine.Nifedipine (0.5µmol/L) produced immediate reductions in evoked Ca2+ transients. Further addition of caffeine produced an immediate increase followed by a decline in the amplitude of the evoked Ca2+ transients, without eliciting diastolic Ca2+ events.These findings correlated with changes in spontaneous and provoked atrial arrhythmogenecity in mouse isolated Langendorf-perfused hearts. Thus, caffeine was pro-arrhythmogenic immediately following but not >5min after application and both CPA and nifedipine pretreatment inhibited such arrhythmogenesis.Together, these findings relate acute atrial arrhythmogenesis in intact hearts to diastolic Ca2+ events in atrial myocytes that, in turn, depend upon a finite SR Ca2+ store and diastolic Ca2+ release following Ca2+-induced Ca2+ release initiated by the entry of extracellular Ca2+

The RyR2-P2328S mutation downregulates Nav1.5 producing arrhythmic substrate in murine ventricles.

Catecholaminergic polymorphic ventricular tachycardia (CPVT) predisposes to ventricular arrhythmia due to altered Ca(2+) homeostasis and can arise from ryanodine receptor (RyR2) mutations including RyR2-P2328S. Previous reports established that homozygotic murine RyR2-P2328S (RyR2 (S/S)) hearts show an atrial arrhythmic phenotype associated with reduced action potential (AP) conduction velocity and sodium channel (Nav1.5) expression. We now relate ventricular arrhythmogenicity and slowed AP conduction in RyR2 (S/S) hearts to connexin-43 (Cx43) and Nav1.5 expression and Na(+) current (I Na). Stimulation protocols applying extrasystolic S2 stimulation following 8 Hz S1 pacing at progressively decremented S1S2 intervals confirmed an arrhythmic tendency despite unchanged ventricular effective refractory periods (VERPs) in Langendorff-perfused RyR2 (S/S) hearts. Dynamic pacing imposing S1 stimuli then demonstrated that progressive reductions of basic cycle lengths (BCLs) produced greater reductions in conduction velocity at equivalent BCLs and diastolic intervals in RyR2 (S/S) than WT, but comparable changes in AP durations (APD90) and their alternans. Western blot analyses demonstrated that Cx43 protein expression in whole ventricles was similar, but Nav1.5 expression in both whole tissue and membrane fractions were significantly reduced in RyR2 (S/S) compared to wild-type (WT). Loose patch-clamp studies similarly demonstrated reduced I Na in RyR2 (S/S) ventricles. We thus attribute arrhythmogenesis in RyR2 (S/S) ventricles resulting from arrhythmic substrate produced by reduced conduction velocity to downregulated Nav1.5 reducing I Na, despite normal determinants of repolarization and passive conduction. The measured changes were quantitatively compatible with earlier predictions of linear relationships between conduction velocity and the peak I Na of the AP but nonlinear relationships between peak I Na and maximum Na(+) permeability.This work was supported by Royal Society / National Science Foundation of China International Joint Project Grant (JP100994/ No.81211130599) (JAF and AM), Issac Newton Trust/ Wellcome Trust ISSF/ University of Cambridge Joint Research Grants Scheme (JAF) and by the Wellcome Trust and Medical Research Council (CLH).This is the final version of the article. It was first available from Springer via http://dx.doi.org/10.1007/s00424-015-1750-

Dna Confined In A Two-Dimensional Strip Geometry

Semiflexible polymers characterized by the contour length L and persistent length confined in a spatial region D have been described as a series of spherical blobs and deflecting lines by de Gennes and Odjik for and , respectively. Recently new intermediate regimes (extended de Gennes and Gauss-de Gennes) have been investigated by Tree et al. (Phys. Rev. Lett., 110 (2013) 208103). In this letter we derive scaling relations to characterize these transitions in terms of universal scaled fluctuations in d-dimension as a function of , and D, and show that the Gauss-de Gennes regime is absent and the extended de Gennes regime is vanishingly small for polymers confined in a 2D strip. We validate our claim by an 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 the physical dimension d and is the same as previously found by Yang et al. (Phys. Rev. E, 76 (2007) 011804). Our studies are relevant for optical maps of DNA stretched inside a nanostrip. © Copyright 2014 EPLA

Dynamics Of Dna Squeezed Inside A Nanochannel Via A Sliding Gasket

We use Brownian dynamics (BD) simulation of a coarse-grained (CG) bead-spring model of DNA to study the nonequilibrim dynamics of a single DNA molecule confined inside a rectangular nanochannel being squeezed with a sliding gasket piston or nanodozer . From our simulations we extract the nonequilibrim density profile c(x, t) of the squeezed molecule along the channel axis (x-coordinate) and then analyze the non-equilibrium profile using a recently introduced phenomenological Nonlinear Partial Differential Equation (NPDE) model. Since the NPDE approach also fits the experimental results well and is numerically efficient to implement, the combined BD + NPDE methods can be a powerful approach to analyze details of the confined molecular dynamics. In particular, the overall excellent agreement between the two complementary sets of data provides a strategy for carrying out large scale simulation on semi-flexible biopolymers in confinement at biologically relevant length scales

Evolution Of Nested Folding States In Compression Of A Strongly Confined Semiflexible Chain

We use Brownian dynamics (BD) simulations to probe the physics of nonequilibrium polymer compression in extreme nanoconfinement. In our system, modeled on the nanodozer assay , a gasket translating at a fixed sliding speed impinges on a nanochannel extended chain. In square channels with diameter much smaller than the chain persistence length, we find that chain compression proceeds through a unique folding kinetics driven by repeated double-fold nucleation events and growth of nested folds. We show that the folding kinetics can be understood by coupling a theory for deterministic contour spooling across the folds with a dynamically varying energy landscape for fold nucleation. These findings are critical for understanding compression of nanochannel confined DNA in the sub-persistence length (Odijk) regime