Dynamical Scaling and Phase Coexistence in Topologically Constrained DNA Melting

Abstract

There is a long-standing experimental observation that the melting of topologically constrained DNA, such as circular-closed plasmids, is less abrupt than that of linear molecules. This finding points to an intriguing role of topology in the physics of DNA denaturation, which is however poorly understood. Here, we shed light on this issue by combining large-scale Brownian Dynamics simulations with an analytically solvable phenomenological Landau mean field theory. We find that the competition between melting and supercoiling leads to phase coexistence of denatured and intact phases at the single molecule level. This coexistence occurs in a wide temperature range, thereby accounting for the broadening of the transition. Finally, our simulations show an intriguing topology-dependent scaling law governing the growth of denaturation bubbles in supercoiled plasmids, which can be understood within the proposed mean field theory.One of the most fascinating aspects of DNA is that its biological function is intimately linked to its local topology [1]. For instance, DNA looping [2,3] and supercoiling [1,4,5] are well-known regulators of gene expression, and a variety of proteins, such as Polymerases, Gyrases and Topoisomerases, can affect genomic function by acting on DNA topology [1,2].Fundamental biological processes such as DNA transcription and replication are associated with local opening of the double helix, a phenomenon that can be triggered in vitro by varying temperature, pH or salt concentration [6]. The melting transition of DNA from one double-stranded (ds) helix to two single-stranded (ss) coils has been intensively studied in the past by means of buoyant densities experiments [7], hyperchromicity spectra [8], AFM measurements [9], singlemolecule experiments [10] and fluorescence microscopy [11].In particular, experiments [6,7] and theories [12,13] have shown that the "helix-coil" transition in linear or nicked DNA molecules, which do not conserve the total linking number between the two strands, is abrupt and bears the signature of a first-order-like transition. On the other hand, the same transition is much smoother for DNA segments whose linking number is topologically preserved, such as circular, covalently-closed ones [7,14].Understanding the physical principles underlying DNA melting in topologically constrained (tc) DNA is important since this is the relevant scenario in vivo. For instance, bacterial DNA is circular, while in eukaryotes DNA wraps around histones [2], and specialised proteins are able to inhibit the diffusion of torsional stress [15].Intriguingly, and in stark contrast with the behaviour of linear, or topologically free (tf), DNA, the width of the melting transition of tcDNA is relatively insensitive to the precise nucleotide sequence [14] thereby suggesting that a universal physical mechanism, rather than biochemical details, may underlie the aforementioned broadening. While biophysical theories of tcDNA melting do exist, they do not reach a consensus as to whether the transition shoul...

Nonequilibrium Theory of Epigenomic Microphase Separation in the Cell Nucleus

“…Equilibrium Thermodynamics -We seek to thermodynamically characterise the theory in Eq. (1) first by finding an m minimising the free energy for a given n, and then by using the common tangent construction to assess whether the resulting uniform state is unstable to phase separation [39,40]. The optimal m * is m * = ± (χn(x, t) − a)/2b if n(x, t) > a/χ and 0 otherwise.…”

“…(1) we obtain the minimised f * = f (m * , n), which we need to further minimise with respect to n, subject to the constraint that V n(x) dx/V = n 0 . This can be done via the common tangent construction [28,39,40], by finding points in phase space where pressure P = f − n∂f /∂n and chemical potential µ = ∂f /∂n of the two phases are equal, while having a 1)). The three equilibrium phases are: (UD) uniform (n = n0) and epigenetically disordered (m 2 = 0); (UO) uniform (n = n0) and epigenetically ordered (m 2 > 0) and (DO) demixed and epigenetically ordered (n = n+, m 2 > 0 and n = n−,m 2 = 0).…”

Integrating transposable elements in the 3D genome

“…Specifically, we consider a stretch of 1.6kbp long DNA with persistence length l p = 150bp = 50nm and regularly interspersed with soft sites that display a lower bending rigidity l f . This lower local DNA rigidity may be due to, for instance, to denaturation bubbles [104], R-loops [105] or replication stress [106]. In these conditions -which may be reproduced in vitro by considering DNA with a sequence of bases that modulates its local flexibility [84] -we ask what is the integration pattern displayed by an invading DNA element by counting the number of integration events in each segment of the polymer over many (1000) independent simulations.…”

Nonequilibrium Theory of Epigenomic Microphase Separation in the Cell Nucleus

“…Equilibrium Thermodynamics -We seek to thermodynamically characterise the theory in Eq. (1) first by finding an m minimising the free energy for a given n, and then by using the common tangent construction to assess whether the resulting uniform state is unstable to phase separation [40,41]. The optimal m * is m * = ± (χn(x, t) − a)/2b if n(x, t) > a/χ and 0 otherwise.…”

“…(1) we obtain the minimised f * = f (m * , n), which we need to further minimise with respect to n, subject to the constraint that V n(x) dx/V = n 0 . This can be done via the common tangent construction [28,40,41], by finding points in phase space where pressure P = f − n∂f /∂n and chemical potential µ = ∂f /∂n of the two phases are equal, while having a lower free energy than the mixed/uniform phase. Graphically, these conditions can be solved by finding the points (n − , f * (n − )) and (n + , f * (n + )) at which the tangents to f have the same slope µ and the same intercept P [42].…”