2017 
Dolgushev, M., Wittmer, J. P., Johner, A., Benzerara, O., Meyer, H., & Baschnagel, J. (2017). Marginally compact hyperbranched polymer trees. Soft Matter, 13(13), 2499–2512.
Abstract: Assuming Gaussian chain statistics along the chain contour, we generate by means of a proper fractal generator hyperbranched polymer trees which are marginally compact. Static and dynamical properties, such as the radial intrachain pair density distribution rho(pair)(r) or the shearstress relaxation modulus G(t), are investigated theoretically and by means of computer simulations. We emphasize that albeit the selfcontact density rho(c) = rho(pair)(r approximate to 0) similar to log(N/S)/root S diverges logarithmically with the total mass N, this effect becomes rapidly irrelevant with increasing spacer length S. In addition to this it is seen that the standard Rouse analysis must necessarily become inappropriate for compact objects for which the relaxation time tau p of mode p must scale as tau(p) similar to (N/p)(5/3) rather than the usual square power law for linear chains.


Lee, N. K., Diddens, D., Meyer, H., & Johner, A. (2017). Local Chain Segregation and Entanglements in a Confined Polymer Melt. Phys. Rev. Lett., 118(6), 5 pp.
Abstract: The reptation mechanism, introduced by de Gennes and Edwards, where a polymer diffuses along a fluffy tube, defined by the constraints imposed by its surroundings, convincingly describes the relaxation of long polymers in concentrated solutions and melts. We propose that the scale for the tube diameter is set by local chain segregation, which we study analytically. We show that the concept of local segregation is especially operational for confined geometries, where segregation extends overmesoscopic domains, drastically reducing binary contacts, and provide an estimate of the entanglement length. Our predictions are quantitatively supported by extensive molecular dynamics simulations on systems consisting of long, entangled chains.


2016 
Baschnagel, J., Meyer, H., Wittmer, J., Kulic, I., Mohrbach, H., Ziebert, F., et al. (2016). Semiflexible Chains at Surfaces: WormLike Chains and beyond. Polymers, 8(8), 35 pp.
Abstract: We give an extended review of recent numerical and analytical studies on semiflexible chains near surfaces undertaken at Institut Charles Sadron (sometimes in collaboration) with a focus on static properties. The statistical physics of thin confined layers, strict twodimensional (2D) layers and adsorption layers (both at equilibrium with the dilute bath and from irreversible chemisorption) are discussed for the wellknown wormlikechain (WLC) model. There is mounting evidence that biofilaments (except stable dDNA) are not fully described by the WLC model. A number of augmented models, like the (super) helical WLC model, the polymorphic model of microtubules (MT) and a model with (strongly) nonlinear flexural elasticity are presented, and some aspects of their surface behavior are analyzed. In many cases, we use approaches different from those in our previous work, give additional results and try to adopt a more general point of view with the hope to shed some light on this complex field.
Keywords: semiflexible polymers; polymers at interfaces; biopolymers


Diddens, D., Lee, N. K., Obukhov, S., Baschnagel, J., & Johner, A. (2016). Disentanglement of Two Single Polymer Chains: Contacts and Knots. ACS Macro Lett., 5(6), 740–744.
Abstract: Understanding the consequences of the non crossing constraint is one of the remaining challenges in the physics of walks and polymers. To address this problem, we performed molecular simulations for the separation of only two initially connected, overlapping polymer chains with interactions tuned such that they are nearly random walks. The separation time for a configuration strongly correlates with the number of monomer contacts between both chains. We obtain a broad distribution of separation times with a slowly decaying tail. Knots only play a role for those configurations that contribute to the tail of the distribution. In contrast, when starting from the same initial configuration but allowing for chain crossings, separation is qualitatively faster and the time distribution narrow. The simulation results are rationalized by analytical theory. A theory of contacts based on polymer fractality and criticality is presented, along with the expected effects of knots.


Fierling, J., Johner, A., Kulic, I. M., Mohrbach, H., & Muller, M. M. (2016). How biofilaments twist membranes. Soft Matter, 12(26), 5747–5757.
Abstract: We study the deformations of a fluid membrane imposed by adhering stiff biofilaments due to the torques they apply. In the limit of small deformations, we derive a general expression for the energy and the deformation field of the membrane. This expression is specialised to different important cases including closed and helical biofilaments. In particular, we analyse interfacemediated interactions and membrane wrapping when the filaments apply a local torque distribution on a tubular membrane.


Kwon, A. Y., Nam, G. M., Johner, A., Kim, S., Hong, S. C., & Lee, N. K. (2016). Competition between BZ and BL transitions in a single DNA molecule: Computational studies. Phys. Rev. E, 93(2), 12 pp.
Abstract: Under negative torsion, DNA adopts lefthanded helical forms, such as ZDNA and LDNA. Using the random copolymer model developed for a wormlike chain, we represent a single DNA molecule with structural heterogeneity as a helical chain consisting of monomers which can be characterized by different helical senses and pitches. By Monte Carlo simulation, where we take into account bending and twist fluctuations explicitly, we study sequence dependence of BZ transitions under torsional stress and tension focusing on the interaction with BL transitions. We consider core sequences, (GC)(n) repeats or (TG)(n) repeats, which can interconvert between the righthanded B form and the lefthanded Z form, imbedded in a random sequence, which can convert to lefthanded L form with different (tension dependent) helical pitch. We show that ZDNA formation from the (GC)(n) sequence is always supported by unwinding torsional stress but ZDNA formation from the (TG)(n) sequence, which are more costly to convert but numerous, can be strongly influenced by the quenched disorder in the surrounding random sequence.


Lee, N.  K., & Johner, A. (2016). Defects on semiflexible filaments: Kinks and twist kinks. Journal of the Korean Physical Society, 68(7), 923–928.
Abstract: Due to local interactions with ligands or to global constraints, semiflexible filaments can exhibit localized defects. We focus on filaments laying flat on a surface. The two lowest order singularities are addressed: discontinuities of the orientation, which are called kink, and discontinuities of the curvature. The latter are called twist kinks in flattened helical filaments where they can form spontaneously. We calculate the partition functions for a given defect fugacity and discuss some often measured quantities like the correlation of the orientation along the filament.


2015 
Kwon, A.  Y., Lee, N.  K., Hong, S.  C., Fierling, J., & Johner, A. (2015). Annealed Random Copolymer Model of the BZ Transition in DNA: Torsional Responses. Biophysical Journal, 108(10), 2562–2572.
Abstract: Both in vivo and in vitro, specific sequences in doublestranded DNA can adopt the lefthanded Zform when underwound. Recently, the BZ transition of DNA has been studied in detail in magnetic tweezers experiments by several groups. We present a theoretical description of this transition, based on an annealed random copolymer model. The transition of a switchable sequence is discussed as a function of energetic and geometric parameters of the B and Zforms, of the applied boundary conditions, and of the characteristics of the BZ interface. We address a possible torsional softening upon the BZ transition. The model can be also applied to other biofilaments with annealed torsional/flexural degrees of freedom.


Lee, N.  K., Jung, Y., & Johner, A. (2015). Irreversible Adsorption of WormLike Chains. Macromolecules, 48(20), 7681–7688.
Abstract: We present a theory for the irreversible adsorption of semiflexible polymers, described as wormlike chains (WLC) of persistence length 1 and contour length S, from dilute solution, with a focus on chemisorption (reaction limited adsorption). Early stages are dominated by single chain adsorption. For stiff to moderately flexible chains, shorter than S* similar to l(5/3)/b(2/3) with b the monomer size, adsorption proceeds out of the first binding point with minimal, flat, adsorption loops of size s(0) similar to l(1/3) b(2/3) by simple zipping in S/s(0) steps. For more flexible chains obeying S > S*, adsorption proceeds by multiple zipping from several nucleation points distant along the chain. At a certain typical surface concentration, larger than the 2d overlap concentration, steric hindrance between incoming polymers and those lying already flat on the surface becomes relevant. The interfacial profile built by stiff loops dangling in the solution comprises an inner layer and an outer layer, where the concentration decreases with the distance z to the surface as similar to 1/z and similar to 1/z(2), respectively. This is in contrast to the similar to 1/z(4/3) profile predicted for reversible WLC adsorption. The last distant adsorption spots are filled by end grafted chains. We also provide typical adsorption times and a short discussion of physisorption.


Weysser, F., Benzerara, O., Johner, A., & Kulic, I. M. (2015). Topological energy storage of work generated by nanomotors. Soft Matter, 11(4), 732–740.
Abstract: Most macroscopic machines rely on wheels and gears. Yet, rigid gears are entirely impractical on the nanoscale. Here we propose a more useful method to couple any rotary engine to any other mechanical elements on the nanoand microscale. We argue that a rotary molecular motor attached to an entangled polymer energy storage unit, which together form what we call the “tanglotron” device, is a viable concept that can be experimentally implemented. We derive the torqueentanglement relationship for a tanglotron (its “equation of state”) and show that it can be understood by simple statistical mechanics arguments. We find that a typical entanglement at low packing density costs around 6kT. In the high entanglement regime, the free energy diverges logarithmically close to a maximal geometric packing density. We outline several promising applications of the tanglotron idea and conclude that the transmission, storage and backconversion of topological entanglement energy are not only physically feasible but also practical for a number of reasons.


2014 
Fierling, J., Mohrbach, H., Kulic, I., Lee, N.  K., & Johner, A. (2014). Biofilaments as annealed semiflexible copolymers. Epl, 106(5).
Abstract: In many in vivo or in vitro situations, biofilaments manifest some annealed heterogeneity and should be considered as annealed random copolymers. The building blocks of the filaments differ from each other, for example, by the internal structure of the monomer, by the presence of some adsorbed species or by the curvature. Based on the copolymer concept, we embed the description of these systems in a common formalism. We demonstrate how the annealed heterogeneous nature of the filament is reflected by statistical correlations like the tangenttangent correlation function or the cyclization probability. Our results show that annealed filaments adapt cooperatively to external constraints. This could contribute to explain anomalous elasticity manifested by biofilaments. Copyright (C) EPLA, 2014


Fierling, J., Mueller, M. M., Mohrbach, H., Johner, A., & Kulic, I. M. (2014). Crunching biofilament rings. Epl, 107(6).
Abstract: We discuss a curious example for the collective mechanical behavior of coupled nonlinear monomer units entrapped in a circular filament. Within a simple model we elucidate how multistability of monomer units and exponentially large degeneracy of the filament's ground state emerge as a collective feature of the closed filament. Surprisingly, increasing the monomer frustration, i.e., the bending prestrain within the circular filament, leads to a conformational softening of the system. The phenomenon, that we term polymorphic crunching, is discussed and applied to a possible scenario for membrane tube deformation by switchable dynamin or FtsZ filaments. We find an important role of cooperative interunit interaction for efficient ringinduced membrane fission. Copyright (C) EPLA, 2014


Herrmann, L., Johner, A., & Kekicheff, P. (2014). Interactions between Charged Lamellae in Aqueous Solution. Physical Review Letters, 113(26).
Abstract: Interactions between charged surfaces in aqueous solutions, widespread in soft matter and biology, are very complex and, despite many efforts, their full explanation remains challenging. We support the idea that, in contrast to extremely small separations (d


Johner, A., Thalmann, F., Baschnagel, J., Meyer, H., Obukhov, S., & Wittmer, J. P. (2014). Twodimensional polymeric liquids and polymer stars: learning from conflicting theories. Journal of Statistical MechanicsTheory and Experiment, 2014.
Abstract: We discuss systems for which two carefully derived, yet conflicting, theories coexisted. Dense polymers in two dimensions and starshaped polymers in the thetaregime are considered. In both cases the two proposed theories are in a sense exact, but turn out to satisfy different crossing rules (for the 2d polymer) or to correspond to different orders of limits. Finally, both theories prove very useful, albeit for different subclasses of physical systems.


Lorchat, P., Konko, I., Combet, J., Jestin, J., Johner, A., Laschewski, A., et al. (2014). New regime in polyelectrolyte solutions. Epl, 106(2).
Abstract: Usually polyelectrolyte solutions present a peak in the polyion/polyion structure factor for some value q* of the momentum transfer (scattering vector). We describe a new regime in dense polymer solutions, typically above similar to 1mol/L, where q* is proportional to the concentration c of the solution. It is however not observed for all polyelectrolytes but only for those of intermediate stiffness, usually together with an ultimate regime where q* is proportional to root c and local orientational order prevails. This regime is robust against sample preparation and stable over time. We can understand it as jammed with randomly oriented persistent segments. This may explain why fully developed nematic order is so difficult to observe in synthetic polyelectrolytes. Copyright (C) EPLA, 2014


Obukhov, S., Johner, A., Baschnagel, J., Meyer, H., & Wittmer, J. P. (2014). Melt of polymer rings: The decorated loop model. Epl, 105(4).
Abstract: Melts of unconcatenated and unknotted polymer rings are a paradigm for soft matter ruled by topological interactions. We propose a description of a system of rings of length N as a collection of smaller polydisperse Gaussian loops, ranging from the entanglement length to the skeleton ring length similar to N2/3, assembled in random trees. Individual rings in the melt are predicted to be marginally compact with a mean square radius of gyration Rg(2) similar to N2/3 (1const center dot N1/3). As a rule, simple power laws for asymptotically long rings come with sluggish crossovers. Experiments and computer simulations merely deal with crossover regimes typically extending to N similar to 10(34). The estimated crossover functions allow for a satisfactory fit of simulation data. Copyright (C) EPLA, 2014


Son, A., Kwon, A.  Y., Johner, A., Hong, S.  C., & Lee, N.  K. (2014). Underwound DNA under tension: LDNA vs. plectoneme. Epl, 105(4).
Abstract: In many biological processes DNA experiences force in the pN range and torque that underwinds it. Magnetic tweezers experiments show that the superhelicity(sigma)extension curve, the socalled bell curve, is asymmetric with respect to the inversion of sigma. We study the case of underwound DNA which was not addressed theoretically before. While the case of overwound DNA is fully explained by the formation of supercoil, the extension of underwound DNA reveals nontrivial tension dependence. We show that plectonemic coils form at moderate tension, whereas lefthanded DNA, socalled “LDNA”, prevails at high tension (above approximate to 0.5 pN). In a narrow but physiologically relevant crossover range of tension, that is between 0.4 pN and 0.7 pN, extra unwinding turns are statistically distributed to either plectoneme or LDNA. In this regime the states of a torsionally stressed DNA should be most sensitive to external mechanical stimuli. Copyright (C) EPLA, 2014


2013 
Balko, S. M., Kreer, T., Costanzo, P. J., Patten, T. E., Johner, A., Kuhl, T. L., et al. (2013). Polymer Brushes under High Load. Plos One, 8(3).
Abstract: Polymer coatings are frequently used to provide repulsive forces between surfaces in solution. After 25 years of design and study, a quantitative model to explain and predict repulsion under strong compression is still lacking. Here, we combine experiments, simulations, and theory to study polymer coatings under high loads and demonstrate a validated model for the repulsive forces, proposing that this universal behavior can be predicted from the polymer solution properties.


Lee, N.  K., Johner, A., Lee, I.  B., & Hong, S.  C. (2013). DNA triplex folding: Moderate versus high salt conditions. European Physical Journal E, 36(6).
Abstract: Some specific sequences in duplex DNA can give rise to local formation of a triple helical DNA called triplex together with a separate strand. Recent singlemolecule FRET experiments, performed on DNA strands designed to fold into a triplex, allow us to measure the folding and unfolding time distributions under neutral pH conditions. The average times of both processes are of the order of 1 s. The folding time is moderately sensitive to salt concentration. The average unfolding time is found to be nearly constant. Interestingly, the distributions of the unfolding time revealed heterogeneous kinetics at moderate salt concentration (similar to 10 mM), but not at high salt (similar to 100 mM). We relate this salt dependence to different folding paths and folded states, which are governed by the (saltdependent) stiffness of the third singlestranded donor sequence. Finally we comment on the formation of intramolecular triplex named HDNA in a torsionally constrained duplex under physiological salt conditions, which mimics the in vivo situation of triplex folding.


Schulmann, N., Meyer, H., Kreer, T., Cavallo, A., Johner, A., Baschnagel, J., et al. (2013). Strictly TwoDimensional SelfAvoiding Walks: Density Crossover Scaling. Polymer Science Series C, 55(1), 181–211.
Abstract: The density crossover scaling of thermodynamic and conformational properties of solutions and melts of selfavoiding and highly flexible polymer chains without chain intersections confined to strictly two dimensions (d = 2) is investigated by means of molecular dynamics and Monte Carlo simulations of a standard coarse grained beadspring model. We focus on properties related to the contact exponent theta(2) set by the intrachain subchain size distribution. With R – Nnu being the size of chains of length N and rho the monomer density, the interaction energy e(int) between monomers from different chains and the corresponding number n(int) of interchain contacts per monomer are found to scale as e(int) similar to n(int) similar to 1/Nnu theta 2 with nu = 3/4 and theta(2) = 19/12 for dilute solutions and nu = 1/d and theta(2) = 3/4 for N >> g(rho) approximate to 1/rho(2). Irrespective of rho, long chains thus become compact packings of blobs of contour length L similar to Nn(int) similar to Rdp with d(p) = d – theta(2) = 5/4 being the fractal line dimension. Due to the generalized Porod scattering of the compact chains, the Kratky representation of the intramolecular form factor F(q) reveals a nonmonotonous behavior approaching with increasing chain length and density a powerlaw slope F(q)q(d)/rho approximate to 1/(qR)(theta 2) in the intermediate regime of the wavevector. The specific intermolecular contact probability is argued to imply an enhanced compatibility for polymer blends confined to ultrathin films. We comment briefly on finite persistence length effects.

